------------------------------------------------------------------------------- name: log: /Users/carlosmendez/Documents/GitHub/starter-academic-v501/content > /post/stata_iv/analysis.log log type: text opened on: 9 May 2026, 16:22:43 . . di _newline(2) . di "================================================================" ================================================================ . di " AJR (2001) IV Tutorial — Colonial Origins of Development" AJR (2001) IV Tutorial — Colonial Origins of Development . di " Estimand: LATE (compliers) under heterogeneous effects." Estimand: LATE (compliers) under heterogeneous effects. . di " Three IV conditions: relevance, exclusion, exogeneity." Three IV conditions: relevance, exclusion, exogeneity. . di "================================================================" ================================================================ . di _newline . . //────────────────────────────────────────────────────────────────── . // SSC dependencies (idempotent — capture handles re-runs) . //────────────────────────────────────────────────────────────────── . capture ssc install ivreg2 . capture ssc install ranktest . capture ssc install estout . capture ssc install coefplot . . //────────────────────────────────────────────────────────────────── . // Globals . //────────────────────────────────────────────────────────────────── . //── Data-loading mode ────────────────────────────────────────────── . // USE_GITHUB = 1 (default): load .dta files from this site's GitHub . // repo (replicability for any reader). . // USE_GITHUB = 0 : load from current folder (offline / dev). . //─────────────────────────────────────────────────────────────────── . global USE_GITHUB 1 . . if $USE_GITHUB { . global DATA_URL "https://raw.githubusercontent.com/cmg777/starter-academi > c-v501/master/content/post/stata_iv" . } . else { . global DATA_URL "." . } . di "Data source: ${DATA_URL}" Data source: https://raw.githubusercontent.com/cmg777/starter-academic-v501/mas > ter/content/post/stata_iv . . global Y logpgp95 . global X avexpr . global Z logem4 . . //────────────────────────────────────────────────────────────────── . // Dark-theme colors — Stata color() takes "R G B" triplets, not hex . // #0f1729 -> "15 23 41" (dark navy / background) . // #1f2b5e -> "31 43 94" (grid line) . // #6a9bcc -> "106 155 204" (steel blue / primary data) . // #d97757 -> "217 119 87" (warm orange / fit lines) . // #00d4c8 -> "0 212 200" (teal / highlights) . // #c8d0e0 -> "200 208 224" (light text / axis labels) . // #e8ecf2 -> "232 236 242" (white text / titles) . //────────────────────────────────────────────────────────────────── . global DARK_NAVY "15 23 41" . global GRID_LINE "31 43 94" . global STEEL_BLUE "106 155 204" . global WARM_ORANGE "217 119 87" . global TEAL "0 212 200" . global LIGHT_TEXT "200 208 224" . global WHITE_TEXT "232 236 242" . . . /*================================================================== > SECTION 1: TABLE 1 — Summary Statistics > Goal: describe outcomes, institutions, and instrument across the > whole world, the AJR base sample (former colonies with mortality > data), and quartiles of settler mortality. > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " TABLE 1 — Summary Statistics" TABLE 1 — Summary Statistics . di "================================================================" ================================================================ . . use "${DATA_URL}/maketable1.dta", clear . export delimited using "data_maketable1.csv", replace file data_maketable1.csv saved . . // 1.1 Whole world . di _newline "*** Column 1: whole world ***" *** Column 1: whole world *** . summarize logpgp95 loghjypl avexpr cons00a cons1 democ00a euro1900 Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- logpgp95 | 162 8.304196 1.070869 6.109248 10.28875 loghjypl | 127 -1.709099 1.076916 -3.540459 0 avexpr | 129 6.988548 1.831779 1.636364 10 cons00a | 96 1.854167 1.788732 1 7 cons1 | 92 3.630435 2.393753 1 7 -------------+--------------------------------------------------------- democ00a | 90 1.122222 2.538812 0 10 euro1900 | 166 30.10241 41.86424 0 100 . . // 1.2 Base sample (countries with valid settler-mortality data) . di _newline "*** Column 2: AJR base sample (baseco==1) ***" *** Column 2: AJR base sample (baseco==1) *** . preserve . keep if baseco==1 (312 observations deleted) . summarize logpgp95 loghjypl avexpr cons00a cons1 democ00a euro1900 logem4 Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- logpgp95 | 64 8.062237 1.043359 6.109248 10.21574 loghjypl | 61 -1.934052 .9807444 -3.540459 0 avexpr | 64 6.515625 1.468647 3.5 10 cons00a | 60 2.25 2.112313 1 7 cons1 | 60 3.4 2.39491 1 7 -------------+--------------------------------------------------------- democ00a | 59 1.644068 3.00438 0 10 euro1900 | 63 16.18095 25.53334 0 99 logem4 | 64 4.657031 1.257984 2.145931 7.986165 . . // Export base-sample summary as CSV . estpost summarize logpgp95 loghjypl avexpr cons00a cons1 democ00a euro190 > 0 logem4 | e(count) e(sum_w) e(mean) e(Var) e(sd) -------------+------------------------------------------------------- logpgp95 | 64 64 8.062237 1.088599 1.043359 loghjypl | 61 61 -1.934052 .9618596 .9807444 avexpr | 64 64 6.515625 2.156924 1.468647 cons00a | 60 60 2.25 4.461864 2.112313 cons1 | 60 60 3.4 5.735593 2.39491 democ00a | 59 59 1.644068 9.0263 3.00438 euro1900 | 63 63 16.18095 651.9516 25.53334 logem4 | 64 64 4.657031 1.582523 1.257984 | e(min) e(max) e(sum) -------------+--------------------------------- logpgp95 | 6.109248 10.21574 515.9832 loghjypl | -3.540459 0 -117.9772 avexpr | 3.5 10 417 cons00a | 1 7 135 cons1 | 1 7 204 democ00a | 0 10 97 euro1900 | 0 99 1019.4 logem4 | 2.145931 7.986165 298.05 . esttab using "tab1_summary.csv", /// > csv replace /// > cells("count(fmt(0)) mean(fmt(3)) sd(fmt(3)) min(fmt(3)) max(fmt(3))" > ) /// > label title("Table 1: Summary Statistics, AJR base sample") (output written to tab1_summary.csv) . restore . . // 1.3 Mortality quartiles (replicates original AJR rank-based bins) . di _newline "*** Columns 3-6: quartiles of settler mortality ***" *** Columns 3-6: quartiles of settler mortality *** . egen rank = rank(extmort4), track (282 missing values generated) . egen count = count(extmort4) . gen ptile = rank/count (282 missing values generated) . gen q = . (376 missing values generated) . replace q = 1 if ptile <= .25 (24 real changes made) . replace q = 2 if ptile > .25 & ptile <= .50 (26 real changes made) . replace q = 3 if ptile > .50 & ptile <= .75 (21 real changes made) . replace q = 4 if ptile > .75 (305 real changes made) . tabulate q q | Freq. Percent Cum. ------------+----------------------------------- 1 | 24 6.38 6.38 2 | 26 6.91 13.30 3 | 21 5.59 18.88 4 | 305 81.12 100.00 ------------+----------------------------------- Total | 376 100.00 . . bysort q: summarize logpgp95 avexpr logem4 ------------------------------------------------------------------------------- -> q = 1 Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- logpgp95 | 22 8.911952 1.113183 6.109248 10.21574 avexpr | 21 7.694805 1.666602 4.681818 10 logem4 | 24 3.038629 .8888217 .9360933 4.232656 ------------------------------------------------------------------------------- -> q = 2 Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- logpgp95 | 25 8.447463 .5534015 6.877296 9.285448 avexpr | 20 6.45 .9766633 5 7.909091 logem4 | 21 4.324283 .0674396 4.245634 4.442651 ------------------------------------------------------------------------------- -> q = 3 Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- logpgp95 | 18 7.737871 .8072068 6.253829 9.415728 avexpr | 18 6.04798 1.505901 3.5 8.636364 logem4 | 21 5.015597 .2825459 4.479607 5.634789 ------------------------------------------------------------------------------- -> q = 4 Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- logpgp95 | 97 8.234521 1.142437 6.253829 10.28875 avexpr | 70 7.172403 2.024133 1.636364 10 logem4 | 23 6.144523 .6803965 5.585449 7.986165 . . . /*================================================================== > SECTION 2: TABLE 2 — OLS Regressions > Goal: establish a naive benchmark. OLS is biased because > institutions are correlated with unobserved determinants of GDP > (reverse causality + omitted variables + measurement error). > The IV estimates in §5 will reveal the magnitude of that bias. > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " TABLE 2 — OLS Regressions of log GDP per capita" TABLE 2 — OLS Regressions of log GDP per capita . di "================================================================" ================================================================ . . use "${DATA_URL}/maketable2.dta", clear . export delimited using "data_maketable2.csv", replace file data_maketable2.csv saved . . // Note: original do-file flags 111 vs 110 obs. We mirror the 111-obs spec. . . // Col 1: whole world . regress logpgp95 avexpr, robust Linear regression Number of obs = 111 F(1, 109) = 334.78 Prob > F = 0.0000 R-squared = 0.6113 Root MSE = .71793 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .5318713 .0290688 18.30 0.000 .474258 .5894847 _cons | 4.626089 .2406654 19.22 0.000 4.149098 5.10308 ------------------------------------------------------------------------------ . eststo m2_c1 . . // Col 2: base sample . regress logpgp95 avexpr if baseco==1, robust Linear regression Number of obs = 64 F(1, 62) = 109.38 Prob > F = 0.0000 R-squared = 0.5401 Root MSE = .71324 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .522107 .0499225 10.46 0.000 .4223133 .6219007 _cons | 4.660383 .3201315 14.56 0.000 4.02045 5.300317 ------------------------------------------------------------------------------ . eststo m2_c2 . . // Col 3: + latitude . regress logpgp95 avexpr lat_abst, robust Linear regression Number of obs = 111 F(2, 108) = 183.95 Prob > F = 0.0000 R-squared = 0.6225 Root MSE = .7108 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4634816 .0521728 8.88 0.000 .360066 .5668972 lat_abst | .8721613 .4993736 1.75 0.084 -.1176837 1.862006 _cons | 4.872922 .2807513 17.36 0.000 4.316424 5.42942 ------------------------------------------------------------------------------ . eststo m2_c3 . . // Col 4: + latitude + continent dummies . regress logpgp95 avexpr lat_abst africa asia other, robust Linear regression Number of obs = 111 F(5, 105) = 97.09 Prob > F = 0.0000 R-squared = 0.7152 Root MSE = .62614 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .3895612 .0510047 7.64 0.000 .2884282 .4906941 lat_abst | .332564 .44244 0.75 0.454 -.5447128 1.209841 africa | -.9163864 .1541114 -5.95 0.000 -1.221961 -.610812 asia | -.1530635 .1805053 -0.85 0.398 -.5109721 .2048452 other | .3035491 .1743288 1.74 0.085 -.0421128 .6492109 _cons | 5.851084 .2934966 19.94 0.000 5.269135 6.433034 ------------------------------------------------------------------------------ . eststo m2_c4 . . // Col 5: base sample + latitude . regress logpgp95 avexpr lat_abst if baseco==1, robust Linear regression Number of obs = 64 F(2, 61) = 64.91 Prob > F = 0.0000 R-squared = 0.5745 Root MSE = .69166 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4678871 .0626811 7.46 0.000 .3425484 .5932257 lat_abst | 1.576884 .6506046 2.42 0.018 .2759197 2.877848 _cons | 4.728082 .3413732 13.85 0.000 4.045464 5.4107 ------------------------------------------------------------------------------ . eststo m2_c5 . . // Col 6: base sample + latitude + continents . regress logpgp95 avexpr lat_abst africa asia other if baseco==1, robust Linear regression Number of obs = 64 F(5, 58) = 53.79 Prob > F = 0.0000 R-squared = 0.7139 Root MSE = .58163 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4012826 .0640653 6.26 0.000 .2730419 .5295233 lat_abst | .8752965 .6142898 1.42 0.160 -.3543381 2.104931 africa | -.8806805 .1555275 -5.66 0.000 -1.192003 -.5693585 asia | -.5767549 .2991853 -1.93 0.059 -1.175639 .0221296 other | .107205 .2229782 0.48 0.632 -.3391344 .5535445 _cons | 5.736729 .3893229 14.74 0.000 4.957415 6.516044 ------------------------------------------------------------------------------ . eststo m2_c6 . . // Col 7: log output per worker (whole world) . regress loghjypl avexpr, robust Linear regression Number of obs = 108 F(1, 106) = 230.57 Prob > F = 0.0000 R-squared = 0.5541 Root MSE = .71344 ------------------------------------------------------------------------------ | Robust loghjypl | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4462022 .0293855 15.18 0.000 .3879427 .5044617 _cons | -4.82763 .2431068 -19.86 0.000 -5.309612 -4.345647 ------------------------------------------------------------------------------ . eststo m2_c7 . . // Col 8: log output per worker (base sample) . regress loghjypl avexpr if baseco==1, robust Linear regression Number of obs = 61 F(1, 59) = 84.18 Prob > F = 0.0000 R-squared = 0.4862 Root MSE = .70894 ------------------------------------------------------------------------------ | Robust loghjypl | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4571098 .04982 9.18 0.000 .3574203 .5567993 _cons | -4.911738 .3232883 -15.19 0.000 -5.558636 -4.264839 ------------------------------------------------------------------------------ . eststo m2_c8 . . esttab m2_c1 m2_c2 m2_c3 m2_c4 m2_c5 m2_c6 m2_c7 m2_c8 /// > using "tab2_ols.csv", csv replace /// > b(3) se(3) star(* 0.10 ** 0.05 *** 0.01) /// > stats(N r2, fmt(0 3) labels("N" "R-squared")) /// > title("Table 2: OLS Regressions of log GDP per capita") (output written to tab2_ols.csv) . . . /*================================================================== > SECTION 3: TABLE 3 — Determinants of Institutions > Panel A: today's institutions on early institutions / settlement > Panel B: early institutions on settler mortality > Together this panel previews the *first stage*: settler mortality > shapes settlement, settlement shapes early institutions, and early > institutions persist into modern institutions. > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " TABLE 3 — Determinants of Institutions" TABLE 3 — Determinants of Institutions . di "================================================================" ================================================================ . . use "${DATA_URL}/maketable3.dta", clear . keep if excolony==1 (262 observations deleted) . keep if extmort4 != . (29 observations deleted) . replace euro1900 = euro1900 / 100 (42 real changes made) . export delimited using "data_maketable3.csv", replace file data_maketable3.csv saved . . //── Panel A: DV = avexpr (current institutions) ────────────────── . di _newline "*** Panel A: DV = average expropriation risk 1985-95 ***" *** Panel A: DV = average expropriation risk 1985-95 *** . . regress avexpr cons00a if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 63 -------------+---------------------------------- F(1, 61) = 15.53 Model | 27.5986649 1 27.5986649 Prob > F = 0.0002 Residual | 108.373317 61 1.77661176 R-squared = 0.2030 -------------+---------------------------------- Adj R-squared = 0.1899 Total | 135.971982 62 2.19309649 Root MSE = 1.3329 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons00a | .3210763 .081463 3.94 0.000 .1581809 .4839717 _cons | 5.739691 .2450347 23.42 0.000 5.249714 6.229669 ------------------------------------------------------------------------------ . eststo m3a_c1 . regress avexpr lat_abst cons00a if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 63 -------------+---------------------------------- F(2, 60) = 9.13 Model | 31.7152119 2 15.857606 Prob > F = 0.0003 Residual | 104.25677 60 1.73761284 R-squared = 0.2332 -------------+---------------------------------- Adj R-squared = 0.2077 Total | 135.971982 62 2.19309649 Root MSE = 1.3182 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lat_abst | 2.178727 1.41551 1.54 0.129 -.6527136 5.010168 cons00a | .2624994 .0891005 2.95 0.005 .0842719 .4407269 _cons | 5.486417 .2929182 18.73 0.000 4.900494 6.072341 ------------------------------------------------------------------------------ . eststo m3a_c2 . regress avexpr democ00a if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 62 -------------+---------------------------------- F(1, 60) = 18.58 Model | 31.6449069 1 31.6449069 Prob > F = 0.0001 Residual | 102.211238 60 1.70352063 R-squared = 0.2364 -------------+---------------------------------- Adj R-squared = 0.2237 Total | 133.856144 61 2.19436302 Root MSE = 1.3052 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ00a | .2440651 .0566275 4.31 0.000 .1307932 .357337 _cons | 6.084432 .1879499 32.37 0.000 5.708476 6.460388 ------------------------------------------------------------------------------ . eststo m3a_c3 . regress avexpr democ00a lat_abst if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 62 -------------+---------------------------------- F(2, 59) = 9.86 Model | 33.5377434 2 16.7688717 Prob > F = 0.0002 Residual | 100.318401 59 1.70031188 R-squared = 0.2506 -------------+---------------------------------- Adj R-squared = 0.2251 Total | 133.856144 61 2.19436302 Root MSE = 1.304 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ00a | .2088398 .0656906 3.18 0.002 .0773933 .3402864 lat_abst | 1.551565 1.470543 1.06 0.296 -1.390985 4.494114 _cons | 5.86717 .2786759 21.05 0.000 5.309541 6.424799 ------------------------------------------------------------------------------ . eststo m3a_c4 . regress avexpr indtime cons1 if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 63 -------------+---------------------------------- F(2, 60) = 7.22 Model | 26.3887611 2 13.1943806 Prob > F = 0.0015 Residual | 109.583221 60 1.82638702 R-squared = 0.1941 -------------+---------------------------------- Adj R-squared = 0.1672 Total | 135.971982 62 2.19309649 Root MSE = 1.3514 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- indtime | .0085616 .0028718 2.98 0.004 .0028172 .0143059 cons1 | .247114 .0757729 3.26 0.002 .0955457 .3986824 _cons | 4.833459 .456742 10.58 0.000 3.919839 5.747079 ------------------------------------------------------------------------------ . eststo m3a_c5 . regress avexpr indtime cons1 lat_abst if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 63 -------------+---------------------------------- F(3, 59) = 6.23 Model | 32.719969 3 10.9066563 Prob > F = 0.0009 Residual | 103.252013 59 1.75003413 R-squared = 0.2406 -------------+---------------------------------- Adj R-squared = 0.2020 Total | 135.971982 62 2.19309649 Root MSE = 1.3229 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- indtime | .0059555 .0031272 1.90 0.062 -.000302 .0122131 cons1 | .2203664 .0754934 2.92 0.005 .0693044 .3714284 lat_abst | 2.718198 1.429095 1.90 0.062 -.1414143 5.577811 _cons | 4.677283 .4545703 10.29 0.000 3.76769 5.586876 ------------------------------------------------------------------------------ . eststo m3a_c6 . regress avexpr euro1900 if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 66 -------------+---------------------------------- F(1, 64) = 26.93 Model | 41.5502232 1 41.5502232 Prob > F = 0.0000 Residual | 98.7284277 64 1.54263168 R-squared = 0.2962 -------------+---------------------------------- Adj R-squared = 0.2852 Total | 140.278651 65 2.15813309 Root MSE = 1.242 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | 3.176817 .6121201 5.19 0.000 1.953967 4.399668 _cons | 5.984533 .1797552 33.29 0.000 5.625431 6.343635 ------------------------------------------------------------------------------ . eststo m3a_c7 . regress avexpr euro1900 lat_abst if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 66 -------------+---------------------------------- F(2, 63) = 13.36 Model | 41.7799612 2 20.8899806 Prob > F = 0.0000 Residual | 98.4986897 63 1.56347127 R-squared = 0.2978 -------------+---------------------------------- Adj R-squared = 0.2755 Total | 140.278651 65 2.15813309 Root MSE = 1.2504 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | 2.996109 .7758783 3.86 0.000 1.44564 4.546578 lat_abst | .580364 1.514011 0.38 0.703 -2.445145 3.605873 _cons | 5.910084 .2654595 22.26 0.000 5.379605 6.440562 ------------------------------------------------------------------------------ . eststo m3a_c8 . regress avexpr logem4 if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 64 -------------+---------------------------------- F(1, 62) = 22.95 Model | 36.7071397 1 36.7071397 Prob > F = 0.0000 Residual | 99.1791012 62 1.59966292 R-squared = 0.2701 -------------+---------------------------------- Adj R-squared = 0.2584 Total | 135.886241 63 2.15692446 Root MSE = 1.2648 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.6067782 .1266686 -4.79 0.000 -.8599852 -.3535713 _cons | 9.34141 .6107178 15.30 0.000 8.120603 10.56222 ------------------------------------------------------------------------------ . eststo m3a_c9 . regress avexpr logem4 lat_abst if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 64 -------------+---------------------------------- F(2, 61) = 12.82 Model | 40.2217245 2 20.1108623 Prob > F = 0.0000 Residual | 95.6645164 61 1.56827076 R-squared = 0.2960 -------------+---------------------------------- Adj R-squared = 0.2729 Total | 135.886241 63 2.15692446 Root MSE = 1.2523 ------------------------------------------------------------------------------ avexpr | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.5102681 .1410186 -3.62 0.001 -.7922521 -.228284 lat_abst | 2.001775 1.337176 1.50 0.140 -.6720747 4.675624 _cons | 8.529432 .8123128 10.50 0.000 6.905113 10.15375 ------------------------------------------------------------------------------ . eststo m3a_c10 . . esttab m3a_c1 m3a_c2 m3a_c3 m3a_c4 m3a_c5 /// > m3a_c6 m3a_c7 m3a_c8 m3a_c9 m3a_c10 /// > using "tab3a_inst.csv", csv replace /// > b(3) se(3) star(* 0.10 ** 0.05 *** 0.01) /// > stats(N r2, fmt(0 3) labels("N" "R-squared")) /// > title("Table 3 Panel A: DV = current expropriation protection") (output written to tab3a_inst.csv) . . //── Panel B: DV = early institutions ───────────────────────────── . di _newline "*** Panel B: DV = early institutions (cons00a, democ00a, euro190 > 0) ***" *** Panel B: DV = early institutions (cons00a, democ00a, euro1900) *** . . regress cons00a euro1900 if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 70 -------------+---------------------------------- F(1, 68) = 57.05 Model | 126.208072 1 126.208072 Prob > F = 0.0000 Residual | 150.434785 68 2.21227625 R-squared = 0.4562 -------------+---------------------------------- Adj R-squared = 0.4482 Total | 276.642857 69 4.00931677 Root MSE = 1.4874 ------------------------------------------------------------------------------ cons00a | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | 5.490718 .7269512 7.55 0.000 4.040109 6.941326 _cons | 1.247507 .2085745 5.98 0.000 .8313032 1.663711 ------------------------------------------------------------------------------ . eststo m3b_c1 . regress cons00a euro1900 lat_abst if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 70 -------------+---------------------------------- F(2, 67) = 28.14 Model | 126.284239 2 63.1421196 Prob > F = 0.0000 Residual | 150.358618 67 2.24415848 R-squared = 0.4565 -------------+---------------------------------- Adj R-squared = 0.4403 Total | 276.642857 69 4.00931677 Root MSE = 1.4981 ------------------------------------------------------------------------------ cons00a | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | 5.385325 .9291648 5.80 0.000 3.530704 7.239945 lat_abst | .3331986 1.808615 0.18 0.854 -3.276812 3.943209 _cons | 1.206304 .3068383 3.93 0.000 .5938525 1.818756 ------------------------------------------------------------------------------ . eststo m3b_c2 . regress cons00a logem4 if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 75 -------------+---------------------------------- F(1, 73) = 24.09 Model | 69.9753758 1 69.9753758 Prob > F = 0.0000 Residual | 212.024624 73 2.90444691 R-squared = 0.2481 -------------+---------------------------------- Adj R-squared = 0.2378 Total | 282 74 3.81081081 Root MSE = 1.7042 ------------------------------------------------------------------------------ cons00a | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.8210308 .1672702 -4.91 0.000 -1.1544 -.4876618 _cons | 5.879086 .8144263 7.22 0.000 4.255937 7.502235 ------------------------------------------------------------------------------ . eststo m3b_c3 . regress cons00a lat_abst logem4 if excolony==1 & extmort4!=. Source | SS df MS Number of obs = 75 -------------+---------------------------------- F(2, 72) = 14.86 Model | 82.4068418 2 41.2034209 Prob > F = 0.0000 Residual | 199.593158 72 2.7721272 R-squared = 0.2922 -------------+---------------------------------- Adj R-squared = 0.2726 Total | 282 74 3.81081081 Root MSE = 1.665 ------------------------------------------------------------------------------ cons00a | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lat_abst | 3.633754 1.715935 2.12 0.038 .2130993 7.054408 logem4 | -.6537921 .1814979 -3.60 0.001 -1.015602 -.2919828 _cons | 4.459591 1.040382 4.29 0.000 2.385626 6.533555 ------------------------------------------------------------------------------ . eststo m3b_c4 . regress democ00a euro1900 if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 67 -------------+---------------------------------- F(1, 65) = 84.44 Model | 306.577058 1 306.577058 Prob > F = 0.0000 Residual | 235.990106 65 3.63061701 R-squared = 0.5650 -------------+---------------------------------- Adj R-squared = 0.5584 Total | 542.567164 66 8.22071461 Root MSE = 1.9054 ------------------------------------------------------------------------------ democ00a | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | 8.565669 .9321411 9.19 0.000 6.704055 10.42728 _cons | .1815763 .2705076 0.67 0.504 -.3586647 .7218174 ------------------------------------------------------------------------------ . eststo m3b_c5 . regress democ00a lat_abst euro1900 if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 67 -------------+---------------------------------- F(2, 64) = 42.12 Model | 308.336428 2 154.168214 Prob > F = 0.0000 Residual | 234.230736 64 3.65985525 R-squared = 0.5683 -------------+---------------------------------- Adj R-squared = 0.5548 Total | 542.567164 66 8.22071461 Root MSE = 1.9131 ------------------------------------------------------------------------------ democ00a | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lat_abst | 1.60511 2.315039 0.69 0.491 -3.019711 6.229932 euro1900 | 8.056465 1.189647 6.77 0.000 5.679872 10.43306 _cons | -.0184762 .396252 -0.05 0.963 -.8100806 .7731283 ------------------------------------------------------------------------------ . eststo m3b_c6 . regress democ00a logem4 if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 68 -------------+---------------------------------- F(1, 66) = 25.45 Model | 151.588138 1 151.588138 Prob > F = 0.0000 Residual | 393.044215 66 5.95521538 R-squared = 0.2783 -------------+---------------------------------- Adj R-squared = 0.2674 Total | 544.632353 67 8.12884109 Root MSE = 2.4403 ------------------------------------------------------------------------------ democ00a | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -1.220857 .2419808 -5.05 0.000 -1.703987 -.7377266 _cons | 7.209906 1.183893 6.09 0.000 4.846187 9.573624 ------------------------------------------------------------------------------ . eststo m3b_c7 . regress democ00a lat_abst logem4 if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 68 -------------+---------------------------------- F(2, 65) = 19.28 Model | 202.822829 2 101.411414 Prob > F = 0.0000 Residual | 341.809524 65 5.25860807 R-squared = 0.3724 -------------+---------------------------------- Adj R-squared = 0.3531 Total | 544.632353 67 8.12884109 Root MSE = 2.2932 ------------------------------------------------------------------------------ democ00a | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lat_abst | 7.569059 2.424908 3.12 0.003 2.726184 12.41194 logem4 | -.8769863 .2526695 -3.47 0.001 -1.381602 -.3723705 _cons | 4.27944 1.455701 2.94 0.005 1.372204 7.186675 ------------------------------------------------------------------------------ . eststo m3b_c8 . regress euro1900 logem4 if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 73 -------------+---------------------------------- F(1, 71) = 31.17 Model | 1.28819664 1 1.28819664 Prob > F = 0.0000 Residual | 2.9339068 71 .041322631 R-squared = 0.3051 -------------+---------------------------------- Adj R-squared = 0.2953 Total | 4.22210344 72 .058640326 Root MSE = .20328 ------------------------------------------------------------------------------ euro1900 | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.1118051 .0200246 -5.58 0.000 -.1517331 -.0718772 _cons | .6771367 .0980916 6.90 0.000 .4815475 .8727258 ------------------------------------------------------------------------------ . eststo m3b_c9 . regress euro1900 lat_abst logem4 if excolony==1 & extmort4!=. & logpgp95!=. Source | SS df MS Number of obs = 73 -------------+---------------------------------- F(2, 70) = 30.63 Model | 1.97031712 2 .985158559 Prob > F = 0.0000 Residual | 2.25178632 70 .032168376 R-squared = 0.4667 -------------+---------------------------------- Adj R-squared = 0.4514 Total | 4.22210344 72 .058640326 Root MSE = .17936 ------------------------------------------------------------------------------ euro1900 | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lat_abst | .870637 .1890694 4.60 0.000 .4935501 1.247724 logem4 | -.0710158 .0197641 -3.59 0.001 -.1104339 -.0315976 _cons | .3331961 .1143203 2.91 0.005 .1051915 .5612007 ------------------------------------------------------------------------------ . eststo m3b_c10 . . esttab m3b_c1 m3b_c2 m3b_c3 m3b_c4 m3b_c5 /// > m3b_c6 m3b_c7 m3b_c8 m3b_c9 m3b_c10 /// > using "tab3b_inst.csv", csv replace /// > b(3) se(3) star(* 0.10 ** 0.05 *** 0.01) /// > stats(N r2, fmt(0 3) labels("N" "R-squared")) /// > title("Table 3 Panel B: DV = early institutions") (output written to tab3b_inst.csv) . . . /*================================================================== > SECTION 4: FIGURES 1 & 2 — first-stage and reduced-form scatters > These visualize the two pieces of any IV identification: > Figure 1 (first stage): Z -> X (settler mortality -> institutions) > Figure 2 (reduced form): Z -> Y (settler mortality -> log GDP) > The 2SLS coefficient is exactly the slope of the reduced form > divided by the slope of the first stage. > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " FIGURES 1 & 2 — First-stage and reduced-form scatters" FIGURES 1 & 2 — First-stage and reduced-form scatters . di "================================================================" ================================================================ . . use "${DATA_URL}/maketable4.dta", clear . keep if baseco==1 (99 observations deleted) . . // 4.1 Compute first-stage F-statistic for figure caption . ivreg2 logpgp95 (avexpr=logem4), robust IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 1, 62) = 27.86 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.1870 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9868 Residual SS = 55.75864314 Root MSE = .9334 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9442794 .1760958 5.36 0.000 .5991379 1.289421 _cons | 1.909667 1.173955 1.63 0.104 -.3912422 4.210575 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 9.492 Chi-sq(1) P-val = 0.0021 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 22.947 (Kleibergen-Paap rk Wald F statistic): 16.321 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: logem4 ------------------------------------------------------------------------------ . di _newline "*** First-stage Kleibergen-Paap rk Wald F: " %6.2f e(widstat) *** First-stage Kleibergen-Paap rk Wald F: 16.32 . di "*** Stock-Yogo (2005) 10% maximal IV size critical value: 16.38" *** Stock-Yogo (2005) 10% maximal IV size critical value: 16.38 . di "*** NOTE: 16.38 is the IID threshold for the Cragg-Donald F." *** NOTE: 16.38 is the IID threshold for the Cragg-Donald F. . di "*** Under robust SEs (this run), use Olea & Pflueger (2013)" *** Under robust SEs (this run), use Olea & Pflueger (2013) . di "*** effective F instead. Install: ssc install weakivtest." *** effective F instead. Install: ssc install weakivtest. . di "*** Staiger-Stock (1997) weak-IV rule of thumb: F > 10." *** Staiger-Stock (1997) weak-IV rule of thumb: F > 10. . . // 4.2 Figure 1 — first stage: logem4 -> avexpr . twoway /// > (scatter avexpr logem4, /// > mcolor("${STEEL_BLUE}") msize(medsmall) /// > mlabel(shortnam) mlabcolor("${TEAL}") /// > mlabsize(vsmall) mlabposition(3) mlabgap(*0.5)) /// > (lfit avexpr logem4, /// > lcolor("${WARM_ORANGE}") lwidth(medthick)), /// > title("Figure 1. First stage: settler mortality predicts institutions", / > // > color("${WHITE_TEXT}") size(medium)) /// > subtitle("Base sample of 64 ex-colonies (AJR 2001 Table 4)", /// > color("${LIGHT_TEXT}") size(small)) /// > xtitle("Log settler mortality (logem4)", color("${LIGHT_TEXT}")) /// > ytitle("Avg. protection from expropriation, 1985-95 (avexpr)", /// > color("${LIGHT_TEXT}")) /// > xlabel(, labcolor("${LIGHT_TEXT}") tlcolor("${LIGHT_TEXT}")) /// > ylabel(, labcolor("${LIGHT_TEXT}") tlcolor("${LIGHT_TEXT}") angle(0)) /// > graphregion(color("${DARK_NAVY}") margin(medlarge)) /// > plotregion(color("${DARK_NAVY}") lcolor("${DARK_NAVY}")) /// > bgcolor("${DARK_NAVY}") /// > legend(off) /// > scheme(s2color) . . graph export "stata_iv_first_stage.png", replace width(2400) file stata_iv_first_stage.png written in PNG format . . // 4.3 Figure 2 — reduced form: logem4 -> logpgp95 . twoway /// > (scatter logpgp95 logem4, /// > mcolor("${STEEL_BLUE}") msize(medsmall) /// > mlabel(shortnam) mlabcolor("${TEAL}") /// > mlabsize(vsmall) mlabposition(3) mlabgap(*0.5)) /// > (lfit logpgp95 logem4, /// > lcolor("${WARM_ORANGE}") lwidth(medthick)), /// > title("Figure 2. Reduced form: settler mortality predicts log GDP", /// > color("${WHITE_TEXT}") size(medium)) /// > subtitle("Base sample of 64 ex-colonies (AJR 2001 Table 4)", /// > color("${LIGHT_TEXT}") size(small)) /// > xtitle("Log settler mortality (logem4)", color("${LIGHT_TEXT}")) /// > ytitle("Log GDP per capita, PPP, 1995 (logpgp95)", /// > color("${LIGHT_TEXT}")) /// > xlabel(, labcolor("${LIGHT_TEXT}") tlcolor("${LIGHT_TEXT}")) /// > ylabel(, labcolor("${LIGHT_TEXT}") tlcolor("${LIGHT_TEXT}") angle(0)) /// > graphregion(color("${DARK_NAVY}") margin(medlarge)) /// > plotregion(color("${DARK_NAVY}") lcolor("${DARK_NAVY}")) /// > bgcolor("${DARK_NAVY}") /// > legend(off) /// > scheme(s2color) . . graph export "stata_iv_reduced_form.png", replace width(2400) file stata_iv_reduced_form.png written in PNG format . . . /*================================================================== > SECTION 5: TABLE 4 — Main IV result + modern weak-IV diagnostics > This is AJR's headline finding: the 2SLS coefficient on avexpr > (~0.94) is *larger* than the OLS coefficient (~0.52), suggesting > measurement-error attenuation in OLS dominates other biases. > > Modern diagnostics layered on top: > - First-stage Kleibergen-Paap F-stat (e(widstat)) > - Stock-Yogo critical values (printed in ivreg2 output) > - Endogeneity test (Durbin-Wu-Hausman) via ivreg2's endog() option > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " TABLE 4 — IV Regressions of log GDP per capita (main result)" TABLE 4 — IV Regressions of log GDP per capita (main result) . di "================================================================" ================================================================ . . use "${DATA_URL}/maketable4.dta", clear . keep if baseco==1 (99 observations deleted) . export delimited using "data_maketable4.csv", replace file data_maketable4.csv saved . . // Generate Neo-Europes "other continent" dummy (AUS, MLT, NZL) . gen other_cont = . (64 missing values generated) . replace other_cont = 1 if shortnam=="AUS" | shortnam=="MLT" | shortnam=="NZL" (3 real changes made) . recode other_cont (.=0) (61 changes made to other_cont) . . //── Panel B: 2SLS (IV) regressions ─────────────────────────────── . di _newline "*** Panel B: 2SLS (IV with logem4) ***" *** Panel B: 2SLS (IV with logem4) *** . . // Col 1: base sample (no controls) . ivreg2 logpgp95 (avexpr=logem4), robust first endog(avexpr) First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.6067782 .1501972 -4.04 0.000 -.9070181 -.3065384 _cons | 9.34141 .7042919 13.26 0.000 7.933551 10.74927 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 62) = 16.32 Prob > F = 0.0001 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 62) = 16.32 Prob > F = 0.0001 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 62) P-val | SW Chi-sq( 1) P-val | SW F( 1, 62) avexpr | 16.32 0.0001 | 16.85 0.0000 | 16.32 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=9.49 P-val=0.0021 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 22.95 Kleibergen-Paap Wald rk F statistic 16.32 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,62)= 61.66 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 63.65 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 17.99 P-val=0.0000 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 2 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 1, 62) = 27.86 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.1870 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9868 Residual SS = 55.75864314 Root MSE = .9334 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9442794 .1760958 5.36 0.000 .5991379 1.289421 _cons | 1.909667 1.173955 1.63 0.104 -.3912422 4.210575 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 9.492 Chi-sq(1) P-val = 0.0021 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 22.947 (Kleibergen-Paap rk Wald F statistic): 16.321 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) -endog- option: Endogeneity test of endogenous regressors: 9.085 Chi-sq(1) P-val = 0.0026 Regressors tested: avexpr ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m4_iv_c1 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 16.320618 . . di _newline "*** First-stage F (KP rk Wald): " %6.2f e(widstat) " ***" *** First-stage F (KP rk Wald): 16.32 *** . di "*** Stock-Yogo (2005) 10% maximal IV size threshold: 16.38 (IID) ***" *** Stock-Yogo (2005) 10% maximal IV size threshold: 16.38 (IID) *** . di "*** Under robust SEs, see Olea & Pflueger (2013) effective F. ***" *** Under robust SEs, see Olea & Pflueger (2013) effective F. *** . di "*** Endogeneity test (Durbin-Wu-Hausman) chi2(1): " %6.3f e(estat) *** Endogeneity test (Durbin-Wu-Hausman) chi2(1): 9.085 . di "*** Endogeneity test p-value: " %6.4f e(estatp) *** Endogeneity test p-value: 0.0026 . di "*** (small p-value -> reject OLS exogeneity -> IV is warranted) ***" *** (small p-value -> reject OLS exogeneity -> IV is warranted) *** . . // Col 2: base sample + latitude . ivreg2 logpgp95 lat_abst (avexpr=logem4), robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.5102681 .1653355 -3.09 0.003 -.8408769 -.1796592 lat_abst | 2.001775 1.368866 1.46 0.149 -.735442 4.738991 _cons | 8.529432 .9210178 9.26 0.000 6.687743 10.37112 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 61) = 9.52 Prob > F = 0.0030 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 61) = 9.52 Prob > F = 0.0030 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 61) P-val | SW Chi-sq( 1) P-val | SW F( 1, 61) avexpr | 9.52 0.0030 | 9.99 0.0016 | 9.52 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=5.82 P-val=0.0158 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 13.09 Kleibergen-Paap Wald rk F statistic 9.52 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,61)= 31.30 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 32.83 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 12.66 P-val=0.0004 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 2, 61) = 13.50 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.1025 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9854 Residual SS = 61.55372729 Root MSE = .9807 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .995704 .2403256 4.14 0.000 .5246745 1.466734 lat_abst | -.6472071 1.227012 -0.53 0.598 -3.052107 1.757692 _cons | 1.691814 1.447779 1.17 0.243 -1.145781 4.529409 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 5.824 Chi-sq(1) P-val = 0.0158 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 13.093 (Kleibergen-Paap rk Wald F statistic): 9.525 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m4_iv_c2 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 9.5249874 . . // Col 3: base sample minus Neo-Europes (USA/CAN/AUS/NZL) . ivreg2 logpgp95 (avexpr=logem4) if rich4!=1, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3912384 .1494694 -2.62 0.011 -.6904339 -.0920429 _cons | 8.183501 .7050808 11.61 0.000 6.772128 9.594874 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 58) = 6.85 Prob > F = 0.0113 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 58) = 6.85 Prob > F = 0.0113 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 58) P-val | SW Chi-sq( 1) P-val | SW F( 1, 58) avexpr | 6.85 0.0113 | 7.09 0.0078 | 6.85 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=5.21 P-val=0.0225 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 8.65 Kleibergen-Paap Wald rk F statistic 6.85 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,58)= 33.73 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 34.89 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 13.63 P-val=0.0002 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 2 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 1, 58) = 9.82 Prob > F = 0.0027 Total (centered) SS = 53.03776029 Centered R2 = -0.6877 Total (uncentered) SS = 3831.317444 Uncentered R2 = 0.9766 Residual SS = 89.51344952 Root MSE = 1.221 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.28124 .4018951 3.19 0.001 .4935401 2.06894 _cons | -.141217 2.583185 -0.05 0.956 -5.204167 4.921733 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 5.210 Chi-sq(1) P-val = 0.0225 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 8.646 (Kleibergen-Paap rk Wald F statistic): 6.851 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m4_iv_c3 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 6.8513839 . . // Col 4: base sample minus Neo-Europes + latitude . ivreg2 logpgp95 lat_abst (avexpr=logem4) if rich4!=1, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3943223 .1659546 -2.38 0.021 -.7266406 -.0620039 lat_abst | -.1064988 1.424007 -0.07 0.941 -2.958023 2.745025 _cons | 8.215617 .9391183 8.75 0.000 6.335065 10.09617 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 57) = 5.65 Prob > F = 0.0209 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 57) = 5.65 Prob > F = 0.0209 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 57) P-val | SW Chi-sq( 1) P-val | SW F( 1, 57) avexpr | 5.65 0.0209 | 5.94 0.0148 | 5.65 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.90 P-val=0.0483 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.83 Kleibergen-Paap Wald rk F statistic 5.65 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,57)= 23.73 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 24.98 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 10.87 P-val=0.0010 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 2, 57) = 6.43 Prob > F = 0.0030 Total (centered) SS = 53.03776029 Centered R2 = -0.4918 Total (uncentered) SS = 3831.317444 Uncentered R2 = 0.9793 Residual SS = 79.12329656 Root MSE = 1.148 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.211776 .3921318 3.09 0.002 .4432118 1.98034 lat_abst | .9385301 1.191035 0.79 0.431 -1.395855 3.272915 _cons | .1442181 2.454136 0.06 0.953 -4.665801 4.954237 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.900 Chi-sq(1) P-val = 0.0483 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.826 (Kleibergen-Paap rk Wald F statistic): 5.646 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m4_iv_c4 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 5.6457813 . . // Col 5: base sample minus Africa . ivreg2 logpgp95 (avexpr=logem4) if africa!=1, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 37 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -1.210385 .2011227 -6.02 0.000 -1.618686 -.8020845 _cons | 11.84436 .8029578 14.75 0.000 10.21427 13.47445 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 35) = 36.22 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 35) = 36.22 Prob > F = 0.0000 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 35) P-val | SW Chi-sq( 1) P-val | SW F( 1, 35) avexpr | 36.22 0.0000 | 38.29 0.0000 | 36.22 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=9.08 P-val=0.0026 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 30.54 Kleibergen-Paap Wald rk F statistic 36.22 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,35)= 42.24 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 44.65 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 11.06 P-val=0.0009 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 37 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 2 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 37 F( 1, 35) = 47.24 Prob > F = 0.0000 Total (centered) SS = 29.69641591 Centered R2 = 0.5874 Total (uncentered) SS = 2759.83067 Uncentered R2 = 0.9956 Residual SS = 12.2519001 Root MSE = .5754 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .5779968 .0817949 7.07 0.000 .4176818 .7383118 _cons | 4.553923 .5912975 7.70 0.000 3.395001 5.712845 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 9.081 Chi-sq(1) P-val = 0.0026 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 30.542 (Kleibergen-Paap rk Wald F statistic): 36.218 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m4_iv_c5 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 36.218051 . . // Col 6: base sample minus Africa + latitude . ivreg2 logpgp95 lat_abst (avexpr=logem4) if africa!=1, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 37 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -1.137215 .2167593 -5.25 0.000 -1.577723 -.696707 lat_abst | .9895786 1.274116 0.78 0.443 -1.599737 3.578894 _cons | 11.34385 .9917123 11.44 0.000 9.328452 13.35926 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 34) = 27.53 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 34) = 27.53 Prob > F = 0.0000 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 34) P-val | SW Chi-sq( 1) P-val | SW F( 1, 34) avexpr | 27.53 0.0000 | 29.95 0.0000 | 27.53 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=7.93 P-val=0.0049 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 21.61 Kleibergen-Paap Wald rk F statistic 27.53 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,34)= 22.16 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 24.11 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 8.51 P-val=0.0035 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 37 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 37 F( 2, 34) = 23.34 Prob > F = 0.0000 Total (centered) SS = 29.69641591 Centered R2 = 0.5886 Total (uncentered) SS = 2759.83067 Uncentered R2 = 0.9956 Residual SS = 12.21633931 Root MSE = .5746 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .5756554 .0906114 6.35 0.000 .3980603 .7532505 lat_abst | .0383271 .5068267 0.08 0.940 -.955035 1.031689 _cons | 4.56227 .6166327 7.40 0.000 3.353692 5.770848 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 7.928 Chi-sq(1) P-val = 0.0049 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 21.614 (Kleibergen-Paap rk Wald F statistic): 27.525 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m4_iv_c6 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 27.525145 . . // Col 7: continent dummies . ivreg2 logpgp95 (avexpr=logem4) africa asia other_cont, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.4323932 .1915952 -2.26 0.028 -.8157743 -.0490121 africa | -.2692057 .3529756 -0.76 0.449 -.9755082 .4370968 asia | .3334929 .4864025 0.69 0.496 -.6397963 1.306782 other_cont | 1.240648 .7728704 1.61 0.114 -.3058618 2.787158 _cons | 8.537812 .9154726 9.33 0.000 6.705955 10.36967 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 59) = 5.09 Prob > F = 0.0277 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 59) = 5.09 Prob > F = 0.0277 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 59) P-val | SW Chi-sq( 1) P-val | SW F( 1, 59) avexpr | 5.09 0.0277 | 5.52 0.0187 | 5.09 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=4.41 P-val=0.0358 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 6.23 Kleibergen-Paap Wald rk F statistic 5.09 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,59)= 11.41 P-val=0.0013 Anderson-Rubin Wald test Chi-sq(1)= 12.38 P-val=0.0004 Stock-Wright LM S statistic Chi-sq(1)= 11.03 P-val=0.0009 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 5 Number of endogenous regressors K1 = 1 Number of instruments L = 5 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 4, 59) = 8.38 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.2286 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9875 Residual SS = 52.90329747 Root MSE = .9092 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9822164 .3309444 2.97 0.003 .3335773 1.630855 africa | -.464285 .3130641 -1.48 0.138 -1.077879 .1493094 asia | -.9242375 .3704735 -2.49 0.013 -1.650352 -.1981228 other_cont | -.9405181 .9120839 -1.03 0.302 -2.72817 .8471334 _cons | 2.032411 2.190511 0.93 0.353 -2.26091 6.325733 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 4.406 Chi-sq(1) P-val = 0.0358 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 6.233 (Kleibergen-Paap rk Wald F statistic): 5.093 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: africa asia other_cont Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m4_iv_c7 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 5.0931739 . . // Col 8: continent dummies + latitude . ivreg2 logpgp95 lat_abst (avexpr=logem4) africa asia other_cont, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3403178 .1973307 -1.72 0.090 -.7353181 .0546824 lat_abst | 2.009322 1.496046 1.34 0.184 -.9853391 5.003984 africa | -.2579581 .3437215 -0.75 0.456 -.9459914 .4300752 asia | .4719882 .5240449 0.90 0.371 -.5770017 1.520978 other_cont | 1.061534 .7753893 1.37 0.176 -.4905764 2.613644 _cons | 7.729295 1.033078 7.48 0.000 5.661365 9.797225 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 58) = 2.97 Prob > F = 0.0899 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 58) = 2.97 Prob > F = 0.0899 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 58) P-val | SW Chi-sq( 1) P-val | SW F( 1, 58) avexpr | 2.97 0.0899 | 3.28 0.0700 | 2.97 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=2.89 P-val=0.0894 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.46 Kleibergen-Paap Wald rk F statistic 2.97 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,58)= 7.23 P-val=0.0093 Anderson-Rubin Wald test Chi-sq(1)= 7.98 P-val=0.0047 Stock-Wright LM S statistic Chi-sq(1)= 8.86 P-val=0.0029 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 6 Number of endogenous regressors K1 = 1 Number of instruments L = 6 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 5, 58) = 5.16 Prob > F = 0.0006 Total (centered) SS = 68.5817185 Centered R2 = 0.0108 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9840 Residual SS = 67.83946934 Root MSE = 1.03 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.107077 .5028901 2.20 0.028 .1214307 2.092724 lat_abst | -1.178179 1.791719 -0.66 0.511 -4.689884 2.333526 africa | -.4372669 .3774763 -1.16 0.247 -1.177107 .3025731 asia | -1.047085 .5049005 -2.07 0.038 -2.036672 -.0574986 other_cont | -.9904017 1.059362 -0.93 0.350 -3.066712 1.085909 _cons | 1.440452 3.073602 0.47 0.639 -4.583697 7.464602 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 2.885 Chi-sq(1) P-val = 0.0894 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.456 (Kleibergen-Paap rk Wald F statistic): 2.974 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst africa asia other_cont Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m4_iv_c8 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.9742691 . . // Col 9: log output per worker (loghjypl) . ivreg2 loghjypl (avexpr=logem4), robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 61 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.6287243 .1509373 -4.17 0.000 -.9307491 -.3266995 _cons | 9.455842 .7054819 13.40 0.000 8.044176 10.86751 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 59) = 17.35 Prob > F = 0.0001 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 59) = 17.35 Prob > F = 0.0001 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 59) P-val | SW Chi-sq( 1) P-val | SW F( 1, 59) avexpr | 17.35 0.0001 | 17.94 0.0000 | 17.35 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=9.73 P-val=0.0018 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 23.78 Kleibergen-Paap Wald rk F statistic 17.35 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,59)= 121.73 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 125.86 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 22.49 P-val=0.0000 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 61 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 2 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 61 F( 1, 59) = 24.14 Prob > F = 0.0000 Total (centered) SS = 57.71157867 Centered R2 = -0.1518 Total (uncentered) SS = 285.8856485 Uncentered R2 = 0.7675 Residual SS = 66.47495457 Root MSE = 1.044 ------------------------------------------------------------------------------ | Robust loghjypl | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9807598 .1963178 5.00 0.000 .5959839 1.365536 _cons | -8.322876 1.306572 -6.37 0.000 -10.88371 -5.762042 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 9.730 Chi-sq(1) P-val = 0.0018 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 23.780 (Kleibergen-Paap rk Wald F statistic): 17.351 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m4_iv_c9 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 17.351116 . . //── Panel C: OLS counterparts ──────────────────────────────────── . di _newline "*** Panel C: OLS comparisons ***" *** Panel C: OLS comparisons *** . . regress logpgp95 avexpr, robust Linear regression Number of obs = 64 F(1, 62) = 109.38 Prob > F = 0.0000 R-squared = 0.5401 Root MSE = .71324 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .522107 .0499225 10.46 0.000 .4223133 .6219007 _cons | 4.660383 .3201315 14.56 0.000 4.02045 5.300317 ------------------------------------------------------------------------------ . eststo m4_ols_c1 . regress logpgp95 lat_abst avexpr, robust Linear regression Number of obs = 64 F(2, 61) = 64.91 Prob > F = 0.0000 R-squared = 0.5745 Root MSE = .69166 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lat_abst | 1.576884 .6506046 2.42 0.018 .2759197 2.877848 avexpr | .4678871 .0626811 7.46 0.000 .3425484 .5932257 _cons | 4.728082 .3413732 13.85 0.000 4.045464 5.4107 ------------------------------------------------------------------------------ . eststo m4_ols_c2 . regress logpgp95 avexpr if rich4!=1, robust Linear regression Number of obs = 60 F(1, 58) = 43.66 Prob > F = 0.0000 R-squared = 0.4137 Root MSE = .73223 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4868482 .0736818 6.61 0.000 .339358 .6343384 _cons | 4.86646 .4391467 11.08 0.000 3.987412 5.745508 ------------------------------------------------------------------------------ . eststo m4_ols_c3 . regress logpgp95 lat_abst avexpr if rich4!=1, robust Linear regression Number of obs = 60 F(2, 57) = 23.13 Prob > F = 0.0000 R-squared = 0.4564 Root MSE = .71123 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lat_abst | 1.801688 .766525 2.35 0.022 .2667478 3.336628 avexpr | .4708727 .0797203 5.91 0.000 .3112354 .6305099 _cons | 4.674508 .4780661 9.78 0.000 3.717197 5.631819 ------------------------------------------------------------------------------ . eststo m4_ols_c4 . regress logpgp95 avexpr if africa!=1, robust Linear regression Number of obs = 37 F(1, 35) = 85.57 Prob > F = 0.0000 R-squared = 0.6114 Root MSE = .57419 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4824191 .0521517 9.25 0.000 .3765456 .5882927 _cons | 5.221323 .3605544 14.48 0.000 4.489359 5.953288 ------------------------------------------------------------------------------ . eststo m4_ols_c5 . regress logpgp95 lat_abst avexpr if africa!=1, robust Linear regression Number of obs = 37 F(2, 34) = 54.06 Prob > F = 0.0000 R-squared = 0.6159 Root MSE = .57918 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lat_abst | .4616966 .5923468 0.78 0.441 -.742097 1.66549 avexpr | .4658046 .0667069 6.98 0.000 .33024 .6013693 _cons | 5.240941 .3882205 13.50 0.000 4.451982 6.0299 ------------------------------------------------------------------------------ . eststo m4_ols_c6 . regress logpgp95 avexpr africa asia other_cont, robust Linear regression Number of obs = 64 F(4, 59) = 70.60 Prob > F = 0.0000 R-squared = 0.7043 Root MSE = .58625 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4238307 .054634 7.76 0.000 .3145083 .5331531 africa | -.9176114 .1650971 -5.56 0.000 -1.24797 -.5872529 asia | -.6311697 .2777135 -2.27 0.027 -1.186873 -.0754662 other_cont | .2155095 .2244109 0.96 0.341 -.2335358 .6645547 _cons | 5.766489 .3751997 15.37 0.000 5.015716 6.517261 ------------------------------------------------------------------------------ . eststo m4_ols_c7 . regress logpgp95 lat_abst avexpr africa asia other_cont, robust Linear regression Number of obs = 64 F(5, 58) = 53.79 Prob > F = 0.0000 R-squared = 0.7139 Root MSE = .58163 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lat_abst | .8752965 .6142898 1.42 0.160 -.3543381 2.104931 avexpr | .4012826 .0640653 6.26 0.000 .2730419 .5295233 africa | -.8806805 .1555275 -5.66 0.000 -1.192003 -.5693585 asia | -.5767549 .2991853 -1.93 0.059 -1.175639 .0221296 other_cont | .107205 .2229782 0.48 0.632 -.3391344 .5535445 _cons | 5.736729 .3893229 14.74 0.000 4.957415 6.516044 ------------------------------------------------------------------------------ . eststo m4_ols_c8 . regress loghjypl avexpr, robust Linear regression Number of obs = 61 F(1, 59) = 84.18 Prob > F = 0.0000 R-squared = 0.4862 Root MSE = .70894 ------------------------------------------------------------------------------ | Robust loghjypl | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4571098 .04982 9.18 0.000 .3574203 .5567993 _cons | -4.911738 .3232883 -15.19 0.000 -5.558636 -4.264839 ------------------------------------------------------------------------------ . eststo m4_ols_c9 . . esttab m4_iv_c1 m4_iv_c2 m4_iv_c3 m4_iv_c4 m4_iv_c5 /// > m4_iv_c6 m4_iv_c7 m4_iv_c8 m4_iv_c9 /// > m4_ols_c1 m4_ols_c2 m4_ols_c3 m4_ols_c4 m4_ols_c5 /// > m4_ols_c6 m4_ols_c7 m4_ols_c8 m4_ols_c9 /// > using "tab4_iv_main.csv", csv replace /// > b(3) se(3) star(* 0.10 ** 0.05 *** 0.01) /// > stats(N r2 firstF, fmt(0 3 2) /// > labels("N" "R-squared" "First-stage F (KP rk Wald)")) /// > title("Table 4: 2SLS and OLS, log GDP per capita") (output written to tab4_iv_main.csv) . . . /*================================================================== > SECTION 6: TABLE 5 — IV with colonial / legal / religion controls > Robustness: do colonial-era variables (British/French ruler, French > legal origin, dominant religion) confound the institutions-GDP > link? Spoiler: the IV coefficient barely moves. > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " TABLE 5 — IV with colonial, legal, and religious controls" TABLE 5 — IV with colonial, legal, and religious controls . di "================================================================" ================================================================ . . use "${DATA_URL}/maketable5.dta", clear . keep if baseco==1 (99 observations deleted) . export delimited using "data_maketable5.csv", replace file data_maketable5.csv saved . . // Col 1-2: British/French dummies . ivreg2 logpgp95 (avexpr=logem4) f_brit f_french, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.5343989 .1560655 -3.42 0.001 -.8465764 -.2222214 f_brit | .629348 .3714619 1.69 0.095 -.1136863 1.372382 f_french | .0474048 .4028172 0.12 0.907 -.7583496 .8531592 _cons | 8.746647 .7415422 11.80 0.000 7.263342 10.22995 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 60) = 11.73 Prob > F = 0.0011 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 60) = 11.73 Prob > F = 0.0011 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 60) P-val | SW Chi-sq( 1) P-val | SW F( 1, 60) avexpr | 11.73 0.0011 | 12.51 0.0004 | 11.73 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=9.26 P-val=0.0023 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 14.66 Kleibergen-Paap Wald rk F statistic 11.73 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,60)= 46.59 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 49.70 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 15.84 P-val=0.0001 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 3, 60) = 8.68 Prob > F = 0.0001 Total (centered) SS = 68.5817185 Centered R2 = 0.0483 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9846 Residual SS = 65.26708957 Root MSE = 1.01 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.07785 .2396055 4.50 0.000 .6082322 1.547468 f_brit | -.7777037 .3650571 -2.13 0.033 -1.493202 -.062205 f_french | -.1169738 .3362771 -0.35 0.728 -.7760649 .5421173 _cons | 1.372403 1.549324 0.89 0.376 -1.664218 4.409023 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 9.260 Chi-sq(1) P-val = 0.0023 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 14.659 (Kleibergen-Paap rk Wald F statistic): 11.725 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: f_brit f_french Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m5_iv_c1 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 11.725116 . ivreg2 logpgp95 lat_abst (avexpr=logem4) f_brit f_french, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.4259484 .1732382 -2.46 0.017 -.7725973 -.0792996 lat_abst | 1.969695 1.390818 1.42 0.162 -.8133256 4.752715 f_brit | .5482088 .3563967 1.54 0.129 -.1649394 1.261357 f_french | -.1174583 .4355682 -0.27 0.788 -.9890284 .7541117 _cons | 7.957783 .9582408 8.30 0.000 6.040348 9.875219 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 59) = 6.05 Prob > F = 0.0169 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 59) = 6.05 Prob > F = 0.0169 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 59) P-val | SW Chi-sq( 1) P-val | SW F( 1, 59) avexpr | 6.05 0.0169 | 6.56 0.0104 | 6.05 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=5.25 P-val=0.0219 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.29 Kleibergen-Paap Wald rk F statistic 6.05 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,59)= 20.58 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 22.32 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 11.82 P-val=0.0006 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 5 Number of endogenous regressors K1 = 1 Number of instruments L = 5 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 4, 59) = 5.98 Prob > F = 0.0004 Total (centered) SS = 68.5817185 Centered R2 = -0.0985 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9822 Residual SS = 75.33432594 Root MSE = 1.085 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.155249 .3518308 3.28 0.001 .4656737 1.844825 lat_abst | -.7512234 1.459188 -0.51 0.607 -3.611179 2.108732 f_brit | -.795469 .4048211 -1.96 0.049 -1.588904 -.0020341 f_french | -.0577656 .39381 -0.15 0.883 -.829619 .7140878 _cons | .9962852 2.079882 0.48 0.632 -3.080208 5.072779 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 5.251 Chi-sq(1) P-val = 0.0219 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.294 (Kleibergen-Paap rk Wald F statistic): 6.045 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst f_brit f_french Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m5_iv_c2 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 6.0454227 . . // Col 3-4: British colonies only . ivreg2 logpgp95 (avexpr=logem4) if f_brit==1, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 25 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.5925116 .2111077 -2.81 0.010 -1.029221 -.1558022 _cons | 9.617466 .8737067 11.01 0.000 7.810066 11.42487 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 23) = 7.88 Prob > F = 0.0100 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 23) = 7.88 Prob > F = 0.0100 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 23) P-val | SW Chi-sq( 1) P-val | SW F( 1, 23) avexpr | 7.88 0.0100 | 8.56 0.0034 | 7.88 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=7.18 P-val=0.0074 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 9.84 Kleibergen-Paap Wald rk F statistic 7.88 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,23)= 43.08 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 46.83 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 11.68 P-val=0.0006 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 25 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 2 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 25 F( 1, 23) = 15.73 Prob > F = 0.0006 Total (centered) SS = 37.93879484 Centered R2 = 0.2738 Total (uncentered) SS = 1763.181265 Uncentered R2 = 0.9844 Residual SS = 27.55212154 Root MSE = 1.05 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.066153 .257832 4.14 0.000 .5608112 1.571494 _cons | .6784015 1.895839 0.36 0.720 -3.037375 4.394178 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 7.179 Chi-sq(1) P-val = 0.0074 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 9.835 (Kleibergen-Paap rk Wald F statistic): 7.877 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m5_iv_c3 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 7.8774525 . ivreg2 logpgp95 lat_abst (avexpr=logem4) if f_brit==1, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 25 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.4191946 .2461247 -1.70 0.103 -.929626 .0912368 lat_abst | 3.201503 1.929845 1.66 0.111 -.8007506 7.203757 _cons | 8.215664 1.355543 6.06 0.000 5.404439 11.02689 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 22) = 2.90 Prob > F = 0.1026 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 22) = 2.90 Prob > F = 0.1026 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 22) P-val | SW Chi-sq( 1) P-val | SW F( 1, 22) avexpr | 2.90 0.1026 | 3.30 0.0694 | 2.90 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=2.91 P-val=0.0880 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.89 Kleibergen-Paap Wald rk F statistic 2.90 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,22)= 21.30 P-val=0.0001 Anderson-Rubin Wald test Chi-sq(1)= 24.21 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 9.57 P-val=0.0020 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 25 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 25 F( 2, 22) = 6.36 Prob > F = 0.0066 Total (centered) SS = 37.93879484 Centered R2 = -0.1500 Total (uncentered) SS = 1763.181265 Uncentered R2 = 0.9753 Residual SS = 43.62856055 Root MSE = 1.321 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.338999 .5346255 2.50 0.012 .2911518 2.386845 lat_abst | -2.986258 2.931642 -1.02 0.308 -8.732172 2.759655 _cons | -.6381312 3.319196 -0.19 0.848 -7.143637 5.867374 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 2.911 Chi-sq(1) P-val = 0.0880 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.890 (Kleibergen-Paap rk Wald F statistic): 2.901 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m5_iv_c4 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.9008214 . . // Col 5-6: French legal origin . ivreg2 logpgp95 (avexpr=logem4) sjlofr, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.5441813 .136288 -3.99 0.000 -.8167059 -.2716566 sjlofr | -.6738566 .3480104 -1.94 0.057 -1.369746 .0220333 _cons | 9.471054 .6348187 14.92 0.000 8.201656 10.74045 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 61) = 15.94 Prob > F = 0.0002 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 61) = 15.94 Prob > F = 0.0002 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 61) P-val | SW Chi-sq( 1) P-val | SW F( 1, 61) avexpr | 15.94 0.0002 | 16.73 0.0000 | 15.94 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=10.90 P-val=0.0010 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 18.30 Kleibergen-Paap Wald rk F statistic 15.94 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,61)= 50.87 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 53.37 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 18.55 P-val=0.0000 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 2, 61) = 14.33 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.0953 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9853 Residual SS = 62.04472584 Root MSE = .9846 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.08 .2017952 5.35 0.000 .6844885 1.475511 sjlofr | .8865222 .3485701 2.54 0.011 .2033373 1.569707 _cons | .4712859 1.498605 0.31 0.753 -2.465925 3.408497 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 10.904 Chi-sq(1) P-val = 0.0010 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 18.302 (Kleibergen-Paap rk Wald F statistic): 15.943 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: sjlofr Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m5_iv_c5 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 15.943077 . ivreg2 logpgp95 lat_abst (avexpr=logem4) sjlofr, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.442625 .1495814 -2.96 0.004 -.7418323 -.1434177 lat_abst | 2.078678 1.261624 1.65 0.105 -.4449457 4.602302 sjlofr | -.6882639 .3372573 -2.04 0.046 -1.362879 -.0136489 _cons | 8.630654 .8187551 10.54 0.000 6.9929 10.26841 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 60) = 8.76 Prob > F = 0.0044 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 60) = 8.76 Prob > F = 0.0044 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 60) P-val | SW Chi-sq( 1) P-val | SW F( 1, 60) avexpr | 8.76 0.0044 | 9.34 0.0022 | 8.76 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=6.28 P-val=0.0122 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 9.89 Kleibergen-Paap Wald rk F statistic 8.76 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,60)= 26.35 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 28.10 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 14.31 P-val=0.0002 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 3, 60) = 8.69 Prob > F = 0.0001 Total (centered) SS = 68.5817185 Centered R2 = -0.0862 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9824 Residual SS = 74.49188508 Root MSE = 1.079 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.181075 .3013108 3.92 0.000 .5905166 1.771633 lat_abst | -1.125816 1.379837 -0.82 0.415 -3.830247 1.578615 sjlofr | .9624353 .4251256 2.26 0.024 .1292043 1.795666 _cons | -.0308374 2.012975 -0.02 0.988 -3.976195 3.91452 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 6.283 Chi-sq(1) P-val = 0.0122 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 9.886 (Kleibergen-Paap rk Wald F statistic): 8.756 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst sjlofr Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m5_iv_c6 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 8.7562238 . . // Col 7-8: religion dummies . ivreg2 logpgp95 (avexpr=logem4) catho80 muslim80 no_cpm80, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.5788472 .1413795 -4.09 0.000 -.8617468 -.2959476 catho80 | -.0180793 .0120267 -1.50 0.138 -.0421447 .0059861 muslim80 | -.0158426 .0121474 -1.30 0.197 -.0401495 .0084643 no_cpm80 | -.0092531 .0143487 -0.64 0.522 -.0379648 .0194585 _cons | 10.5567 1.346934 7.84 0.000 7.86149 13.25191 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 59) = 16.76 Prob > F = 0.0001 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 59) = 16.76 Prob > F = 0.0001 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 59) P-val | SW Chi-sq( 1) P-val | SW F( 1, 59) avexpr | 16.76 0.0001 | 18.18 0.0000 | 16.76 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=11.04 P-val=0.0009 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 19.84 Kleibergen-Paap Wald rk F statistic 16.76 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,59)= 46.25 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 50.17 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 23.00 P-val=0.0000 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 5 Number of endogenous regressors K1 = 1 Number of instruments L = 5 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 4, 59) = 10.14 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.4256 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9907 Residual SS = 39.39200106 Root MSE = .7845 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9174058 .1555741 5.90 0.000 .6124862 1.222325 catho80 | .0088976 .0077187 1.15 0.249 -.0062307 .0240259 muslim80 | .0003076 .0073872 0.04 0.967 -.014171 .0147862 no_cpm80 | -.0070123 .0095974 -0.73 0.465 -.0258229 .0117983 _cons | 1.906247 1.400823 1.36 0.174 -.8393165 4.65181 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 11.044 Chi-sq(1) P-val = 0.0009 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 19.841 (Kleibergen-Paap rk Wald F statistic): 16.763 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: catho80 muslim80 no_cpm80 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m5_iv_c7 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 16.763135 . ivreg2 logpgp95 lat_abst (avexpr=logem4) catho80 muslim80 no_cpm80, robust fi > rst First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.4420497 .1721399 -2.57 0.013 -.7866252 -.0974743 lat_abst | 2.496266 1.447955 1.72 0.090 -.4021316 5.394663 catho80 | -.0116323 .0113037 -1.03 0.308 -.0342592 .0109946 muslim80 | -.0123347 .0113332 -1.09 0.281 -.0350205 .0103511 no_cpm80 | .0000636 .0139126 0.00 0.996 -.0277856 .0279128 _cons | 8.876695 1.569103 5.66 0.000 5.735794 12.0176 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 58) = 6.59 Prob > F = 0.0128 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 58) = 6.59 Prob > F = 0.0128 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 58) P-val | SW Chi-sq( 1) P-val | SW F( 1, 58) avexpr | 6.59 0.0128 | 7.28 0.0070 | 6.59 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=4.51 P-val=0.0337 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 8.61 Kleibergen-Paap Wald rk F statistic 6.59 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,58)= 18.02 P-val=0.0001 Anderson-Rubin Wald test Chi-sq(1)= 19.88 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 13.91 P-val=0.0002 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 6 Number of endogenous regressors K1 = 1 Number of instruments L = 6 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 5, 58) = 7.31 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.3015 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9887 Residual SS = 47.90607694 Root MSE = .8652 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.006185 .2565907 3.92 0.000 .5032768 1.509094 lat_abst | -.9377552 1.417208 -0.66 0.508 -3.715431 1.839921 catho80 | .0080808 .0083268 0.97 0.332 -.0082395 .0244011 muslim80 | .0003963 .00801 0.05 0.961 -.0153031 .0160957 no_cpm80 | -.0096908 .011053 -0.88 0.381 -.0313544 .0119728 _cons | 1.600144 1.755701 0.91 0.362 -1.840967 5.041255 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 4.512 Chi-sq(1) P-val = 0.0337 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 8.613 (Kleibergen-Paap rk Wald F statistic): 6.594 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst catho80 muslim80 no_cpm80 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m5_iv_c8 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 6.5944591 . . // Col 9: kitchen-sink controls . ivreg2 logpgp95 lat_abst (avexpr=logem4) f_french sjlofr /// > catho80 muslim80 no_cpm80, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.379002 .1826943 -2.07 0.043 -.7449827 -.0130214 lat_abst | 2.708196 1.442116 1.88 0.066 -.1807102 5.597101 f_french | -.1625532 .6182496 -0.26 0.794 -1.401056 1.07595 sjlofr | -.3748816 .632 -0.59 0.555 -1.64093 .8911667 catho80 | -.0049763 .0162638 -0.31 0.761 -.0375567 .0276041 muslim80 | -.0070976 .0148779 -0.48 0.635 -.0369016 .0227064 no_cpm80 | .0038769 .0150916 0.26 0.798 -.0263552 .0341089 _cons | 8.327311 1.763014 4.72 0.000 4.79557 11.85905 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 56) = 4.30 Prob > F = 0.0426 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 56) = 4.30 Prob > F = 0.0426 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 56) P-val | SW Chi-sq( 1) P-val | SW F( 1, 56) avexpr | 4.30 0.0426 | 4.92 0.0266 | 4.30 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=4.02 P-val=0.0451 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 5.28 Kleibergen-Paap Wald rk F statistic 4.30 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,56)= 17.17 P-val=0.0001 Anderson-Rubin Wald test Chi-sq(1)= 19.63 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 14.33 P-val=0.0002 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 8 Number of endogenous regressors K1 = 1 Number of instruments L = 8 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 7, 56) = 4.00 Prob > F = 0.0013 Total (centered) SS = 68.5817185 Centered R2 = -0.0296 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9833 Residual SS = 70.60996306 Root MSE = 1.05 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.212225 .3951646 3.07 0.002 .4377166 1.986733 lat_abst | -1.793645 1.96668 -0.91 0.362 -5.648267 2.060977 f_french | .3959799 .4600014 0.86 0.389 -.5056064 1.297566 sjlofr | .2942043 .5443483 0.54 0.589 -.7726988 1.361107 catho80 | .0046047 .0135479 0.34 0.734 -.0219488 .0311581 muslim80 | -.00257 .0120092 -0.21 0.831 -.0261076 .0209676 no_cpm80 | -.0137333 .0149085 -0.92 0.357 -.0429533 .0154868 _cons | .4471506 2.427743 0.18 0.854 -4.311139 5.20544 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 4.016 Chi-sq(1) P-val = 0.0451 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 5.277 (Kleibergen-Paap rk Wald F statistic): 4.304 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst f_french sjlofr catho80 muslim80 no_cpm80 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m5_iv_c9 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 4.3036122 . . esttab m5_iv_c1 m5_iv_c2 m5_iv_c3 m5_iv_c4 m5_iv_c5 /// > m5_iv_c6 m5_iv_c7 m5_iv_c8 m5_iv_c9 /// > using "tab5_iv_controls.csv", csv replace /// > b(3) se(3) star(* 0.10 ** 0.05 *** 0.01) /// > stats(N r2 firstF, fmt(0 3 2) /// > labels("N" "R-squared" "First-stage F (KP rk Wald)")) /// > title("Table 5: 2SLS with colonial / legal / religion controls") (output written to tab5_iv_controls.csv) . . . /*================================================================== > SECTION 7: TABLE 6 — Geography and climate robustness > Adds temperature, humidity, soil, resource, and ethnolinguistic > controls. Geography matters for income, but the institutions > channel survives. > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " TABLE 6 — IV with geography and climate controls" TABLE 6 — IV with geography and climate controls . di "================================================================" ================================================================ . . use "${DATA_URL}/maketable6.dta", clear . keep if baseco==1 (99 observations deleted) . export delimited using "data_maketable6.csv", replace file data_maketable6.csv saved . . // Col 1-2: temperature + humidity . ivreg2 logpgp95 (avexpr=logem4) temp* humid*, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.6377872 .151156 -4.22 0.000 -.9409678 -.3346067 temp1 | .3603997 .185953 1.94 0.058 -.0125747 .7333741 temp2 | -.0307336 .0642256 -0.48 0.634 -.1595537 .0980866 temp3 | -.1244014 .080143 -1.55 0.127 -.2851478 .0363451 temp4 | -.1534126 .06828 -2.25 0.029 -.2903649 -.0164603 temp5 | -.0255489 .0472337 -0.54 0.591 -.1202877 .0691898 humid1 | .0499131 .0333229 1.50 0.140 -.0169241 .1167503 humid2 | -.0359269 .0543231 -0.66 0.511 -.1448853 .0730314 humid3 | -.0319748 .0414043 -0.77 0.443 -.1150213 .0510718 humid4 | .0470101 .0491161 0.96 0.343 -.0515043 .1455244 _cons | 6.083454 2.477653 2.46 0.017 1.11391 11.053 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 53) = 17.80 Prob > F = 0.0001 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 53) = 17.80 Prob > F = 0.0001 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 53) P-val | SW Chi-sq( 1) P-val | SW F( 1, 53) avexpr | 17.80 0.0001 | 21.50 0.0000 | 17.80 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=9.59 P-val=0.0020 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 13.73 Kleibergen-Paap Wald rk F statistic 17.80 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,53)= 18.22 P-val=0.0001 Anderson-Rubin Wald test Chi-sq(1)= 22.00 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 12.46 P-val=0.0004 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 11 Number of endogenous regressors K1 = 1 Number of instruments L = 11 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 10, 53) = 7.23 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.4032 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9903 Residual SS = 40.92860602 Root MSE = .7997 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .8368526 .1647979 5.08 0.000 .5138546 1.159851 temp1 | -.0043194 .13046 -0.03 0.974 -.2600163 .2513776 temp2 | .0025345 .0449262 0.06 0.955 -.0855192 .0905883 temp3 | -.0058884 .0585226 -0.10 0.920 -.1205905 .1088138 temp4 | -.0014708 .053835 -0.03 0.978 -.1069854 .1040438 temp5 | -.015448 .0349722 -0.44 0.659 -.0839922 .0530963 humid1 | -.0304386 .019012 -1.60 0.109 -.0677015 .0068243 humid2 | .0414408 .0280534 1.48 0.140 -.0135429 .0964244 humid3 | .0391485 .0203228 1.93 0.054 -.0006835 .0789805 humid4 | -.0414398 .025041 -1.65 0.098 -.0905192 .0076396 _cons | 2.64686 1.980555 1.34 0.181 -1.234958 6.528677 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 9.591 Chi-sq(1) P-val = 0.0020 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 13.734 (Kleibergen-Paap rk Wald F statistic): 17.803 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: temp1 temp2 temp3 temp4 temp5 humid1 humid2 humid3 humid4 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m6_iv_c1 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 17.803311 . ivreg2 logpgp95 lat_abst (avexpr=logem4) temp* humid*, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.5891001 .158987 -3.71 0.001 -.9081309 -.2700692 lat_abst | 2.651329 2.344389 1.13 0.263 -2.053031 7.355688 temp1 | .2633344 .1812911 1.45 0.152 -.1004527 .6271216 temp2 | -.0034333 .0737206 -0.05 0.963 -.1513645 .144498 temp3 | -.1108805 .0701474 -1.58 0.120 -.2516415 .0298805 temp4 | -.1061723 .0743288 -1.43 0.159 -.2553239 .0429793 temp5 | -.0137233 .0444296 -0.31 0.759 -.1028778 .0754313 humid1 | .0445604 .0314749 1.42 0.163 -.0185985 .1077194 humid2 | -.0257962 .0485383 -0.53 0.597 -.1231954 .0716029 humid3 | -.0284371 .0395307 -0.72 0.475 -.1077612 .050887 humid4 | .0419348 .0462826 0.91 0.369 -.0509381 .1348076 _cons | 5.475636 2.281449 2.40 0.020 .897573 10.0537 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 52) = 13.73 Prob > F = 0.0005 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 52) = 13.73 Prob > F = 0.0005 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 52) P-val | SW Chi-sq( 1) P-val | SW F( 1, 52) avexpr | 13.73 0.0005 | 16.90 0.0000 | 13.73 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=7.02 P-val=0.0081 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 11.41 Kleibergen-Paap Wald rk F statistic 13.73 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,52)= 14.49 P-val=0.0004 Anderson-Rubin Wald test Chi-sq(1)= 17.83 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 10.39 P-val=0.0013 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 12 Number of endogenous regressors K1 = 1 Number of instruments L = 12 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 11, 52) = 6.66 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.4057 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9904 Residual SS = 40.75772489 Root MSE = .798 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .8349553 .1793076 4.66 0.000 .4835187 1.186392 lat_abst | .065897 1.560261 0.04 0.966 -2.992158 3.123952 temp1 | -.0060481 .1227609 -0.05 0.961 -.246655 .2345589 temp2 | .0031547 .0460627 0.07 0.945 -.0871264 .0934359 temp3 | -.0057883 .0577927 -0.10 0.920 -.11906 .1074833 temp4 | -.0005877 .0538573 -0.01 0.991 -.1061462 .1049707 temp5 | -.0152025 .0331387 -0.46 0.646 -.0801532 .0497482 humid1 | -.030477 .0187709 -1.62 0.104 -.0672673 .0063134 humid2 | .0416244 .0270674 1.54 0.124 -.0114267 .0946755 humid3 | .0391758 .0202181 1.94 0.053 -.0004509 .0788025 humid4 | -.0414768 .0249241 -1.66 0.096 -.0903272 .0073736 _cons | 2.643295 1.949151 1.36 0.175 -1.176971 6.463562 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 7.021 Chi-sq(1) P-val = 0.0081 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 11.405 (Kleibergen-Paap rk Wald F statistic): 13.729 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst temp1 temp2 temp3 temp4 temp5 humid1 humid2 humid3 humid4 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m6_iv_c2 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 13.7295 . . // Col 3-4: % European descent in 1975 . ivreg2 logpgp95 (avexpr=logem4) edes1975, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.4130455 .1649002 -2.50 0.015 -.7427839 -.0833072 edes1975 | .0155925 .0061457 2.54 0.014 .0033034 .0278816 _cons | 8.157479 .8354419 9.76 0.000 6.48691 9.828048 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 61) = 6.27 Prob > F = 0.0149 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 61) = 6.27 Prob > F = 0.0149 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 61) P-val | SW Chi-sq( 1) P-val | SW F( 1, 61) avexpr | 6.27 0.0149 | 6.58 0.0103 | 6.27 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=4.64 P-val=0.0312 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 8.37 Kleibergen-Paap Wald rk F statistic 6.27 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,61)= 14.84 P-val=0.0003 Anderson-Rubin Wald test Chi-sq(1)= 15.57 P-val=0.0001 Stock-Wright LM S statistic Chi-sq(1)= 9.63 P-val=0.0019 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 2, 61) = 17.35 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.1610 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9864 Residual SS = 57.53982798 Root MSE = .9482 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9597953 .2944625 3.26 0.001 .3826595 1.536931 edes1975 | -.0007577 .0079199 -0.10 0.924 -.0162805 .014765 _cons | 1.822261 1.82478 1.00 0.318 -1.754243 5.398765 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 4.643 Chi-sq(1) P-val = 0.0312 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 8.368 (Kleibergen-Paap rk Wald F statistic): 6.274 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: edes1975 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m6_iv_c3 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 6.2741286 . ivreg2 logpgp95 lat_abst (avexpr=logem4) edes1975, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.4037597 .1760842 -2.29 0.025 -.7559804 -.0515389 lat_abst | .4768619 1.331187 0.36 0.721 -2.185908 3.139632 edes1975 | .0144895 .0059738 2.43 0.018 .0025401 .0264388 _cons | 8.047802 .9863768 8.16 0.000 6.074754 10.02085 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 60) = 5.26 Prob > F = 0.0254 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 60) = 5.26 Prob > F = 0.0254 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 60) P-val | SW Chi-sq( 1) P-val | SW F( 1, 60) avexpr | 5.26 0.0254 | 5.61 0.0179 | 5.26 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.75 P-val=0.0529 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.57 Kleibergen-Paap Wald rk F statistic 5.26 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,60)= 13.83 P-val=0.0004 Anderson-Rubin Wald test Chi-sq(1)= 14.76 P-val=0.0001 Stock-Wright LM S statistic Chi-sq(1)= 9.00 P-val=0.0027 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 3, 60) = 10.98 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.1102 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9856 Residual SS = 61.02327741 Root MSE = .9765 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9913871 .3231065 3.07 0.002 .3581101 1.624664 lat_abst | -.6701034 1.012127 -0.66 0.508 -2.653836 1.31363 edes1975 | .0002997 .0079945 0.04 0.970 -.0153693 .0159686 _cons | 1.718674 1.951752 0.88 0.379 -2.10669 5.544037 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.746 Chi-sq(1) P-val = 0.0529 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.567 (Kleibergen-Paap rk Wald F statistic): 5.258 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst edes1975 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m6_iv_c4 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 5.2578145 . . // Col 5-6: soil quality, resources, landlocked . ivreg2 logpgp95 (avexpr=logem4) steplow deslow stepmid desmid drystep /// > drywint goldm iron silv zinc oilres landlock, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3679812 .2186601 -1.68 0.099 -.807173 .0712106 steplow | .1744875 .3805831 0.46 0.649 -.5899362 .9389112 deslow | -.5735788 .3374322 -1.70 0.095 -1.251331 .1041738 stepmid | .3766527 .6796809 0.55 0.582 -.9885266 1.741832 desmid | -.4937582 .3457699 -1.43 0.160 -1.188257 .2007411 drystep | -.3155047 .6004524 -0.53 0.602 -1.521549 .8905395 drywint | -10.87013 6.303124 -1.72 0.091 -23.53033 1.790069 goldm | .2106203 .1347394 1.56 0.124 -.0600118 .4812524 iron | .1588425 .1339918 1.19 0.241 -.1102879 .4279729 silv | .0932381 .1210566 0.77 0.445 -.1499113 .3363874 zinc | -.1074291 .2487655 -0.43 0.668 -.6070893 .392231 oilres | 3.19e-07 2.32e-07 1.38 0.175 -1.47e-07 7.86e-07 landlock | -.8212129 .4581094 -1.79 0.079 -1.741353 .0989269 _cons | 8.248188 .992855 8.31 0.000 6.253981 10.2424 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 50) = 2.83 Prob > F = 0.0986 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 50) = 2.83 Prob > F = 0.0986 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 50) P-val | SW Chi-sq( 1) P-val | SW F( 1, 50) avexpr | 2.83 0.0986 | 3.63 0.0569 | 2.83 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.53 P-val=0.0604 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 5.51 Kleibergen-Paap Wald rk F statistic 2.83 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,50)= 18.35 P-val=0.0001 Anderson-Rubin Wald test Chi-sq(1)= 23.49 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= . P-val= . NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 14 Number of endogenous regressors K1 = 1 Number of instruments L = 14 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 13, 50) = 158.34 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = -0.1480 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9814 Residual SS = 78.73133613 Root MSE = 1.109 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.259014 .5434856 2.32 0.021 .1938021 2.324227 steplow | -.3654232 .320418 -1.14 0.254 -.9934309 .2625846 deslow | .506867 .4129359 1.23 0.220 -.3024724 1.316207 stepmid | .0010283 .666831 0.00 0.999 -1.305936 1.307993 desmid | 1.622757 .2880525 5.63 0.000 1.058184 2.187329 drystep | .3432413 .6743972 0.51 0.611 -.978553 1.665036 drywint | 6.144033 9.124307 0.67 0.501 -11.73928 24.02735 goldm | -.1032524 .1923037 -0.54 0.591 -.4801607 .273656 iron | -.1092412 .1786412 -0.61 0.541 -.4593715 .2408891 silv | .0044037 .1416945 0.03 0.975 -.2733124 .2821198 zinc | -.0391261 .2733804 -0.14 0.886 -.5749417 .4966896 oilres | 3.32e-08 2.34e-07 0.14 0.887 -4.26e-07 4.93e-07 landlock | .7509406 .7188768 1.04 0.296 -.658032 2.159913 _cons | -.1659552 3.645658 -0.05 0.964 -7.311313 6.979403 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.526 Chi-sq(1) P-val = 0.0604 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 5.514 (Kleibergen-Paap rk Wald F statistic): 2.832 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Warning: estimated covariance matrix of moment conditions not of full rank. overidentification statistic not reported, and standard errors and model tests should be interpreted with caution. Possible causes: singleton dummy variable (dummy with one 1 and N-1 0s or vice versa) partial option may address problem. ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: steplow deslow stepmid desmid drystep drywint goldm iron silv zinc oilres landlock Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m6_iv_c5 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.8321229 . ivreg2 logpgp95 lat_abst (avexpr=logem4) steplow deslow stepmid desmid /// > drystep drywint goldm iron silv zinc oilres landlock, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3039967 .23054 -1.32 0.193 -.7672841 .1592906 lat_abst | 1.660766 1.633832 1.02 0.314 -1.622542 4.944074 steplow | .0961721 .3879602 0.25 0.805 -.6834631 .8758072 deslow | -.6356499 .3286744 -1.93 0.059 -1.296146 .0248461 stepmid | .2786614 .5023012 0.55 0.582 -.7307506 1.288074 desmid | -.7796329 .4632302 -1.68 0.099 -1.710529 .1512631 drystep | -.2999264 .5869229 -0.51 0.612 -1.479392 .8795393 drywint | -10.33343 5.919543 -1.75 0.087 -22.2292 1.562335 goldm | .1965926 .1266804 1.55 0.127 -.0579811 .4511664 iron | .1780623 .1298741 1.37 0.177 -.0829294 .439054 silv | .0896997 .1160262 0.77 0.443 -.1434636 .322863 zinc | -.1320451 .2449186 -0.54 0.592 -.6242274 .3601372 oilres | 3.88e-07 2.24e-07 1.73 0.089 -6.18e-08 8.37e-07 landlock | -.8843285 .4352361 -2.03 0.048 -1.758968 -.0096888 _cons | 7.710954 1.175804 6.56 0.000 5.348088 10.07382 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 49) = 1.74 Prob > F = 0.1934 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 49) = 1.74 Prob > F = 0.1934 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 49) P-val | SW Chi-sq( 1) P-val | SW F( 1, 49) avexpr | 1.74 0.1934 | 2.27 0.1318 | 1.74 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=2.36 P-val=0.1244 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.33 Kleibergen-Paap Wald rk F statistic 1.74 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,49)= 11.10 P-val=0.0016 Anderson-Rubin Wald test Chi-sq(1)= 14.50 P-val=0.0001 Stock-Wright LM S statistic Chi-sq(1)= . P-val= . NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 15 Number of endogenous regressors K1 = 1 Number of instruments L = 15 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 14, 49) = 112.50 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = -0.3423 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9782 Residual SS = 92.05623868 Root MSE = 1.199 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | 1.357631 .7333512 1.85 0.064 -.0797106 2.794973 lat_abst | -.941913 2.237062 -0.42 0.674 -5.326474 3.442648 steplow | -.3382135 .3598628 -0.94 0.347 -1.043532 .3671046 deslow | .5986356 .5804321 1.03 0.302 -.5389904 1.736262 stepmid | .0194603 .6443715 0.03 0.976 -1.243485 1.282405 desmid | 1.833585 .6819178 2.69 0.007 .4970506 3.170119 drystep | .3655201 .749921 0.49 0.626 -1.104298 1.835338 drywint | 6.911621 10.87462 0.64 0.525 -14.40225 28.22549 goldm | -.1160672 .2235982 -0.52 0.604 -.5543117 .3221773 iron | -.1358064 .2313835 -0.59 0.557 -.5893097 .3176969 silv | -.0027843 .159192 -0.02 0.986 -.3147948 .3092262 zinc | -.0145707 .3182789 -0.05 0.963 -.6383858 .6092445 oilres | -3.70e-08 3.32e-07 -0.11 0.911 -6.88e-07 6.14e-07 landlock | .8677224 .9226501 0.94 0.347 -.9406386 2.676083 _cons | -.67467 4.656195 -0.14 0.885 -9.800644 8.451304 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 2.361 Chi-sq(1) P-val = 0.1244 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.333 (Kleibergen-Paap rk Wald F statistic): 1.739 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Warning: estimated covariance matrix of moment conditions not of full rank. overidentification statistic not reported, and standard errors and model tests should be interpreted with caution. Possible causes: singleton dummy variable (dummy with one 1 and N-1 0s or vice versa) partial option may address problem. ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst steplow deslow stepmid desmid drystep drywint goldm iron silv zinc oilres landlock Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m6_iv_c6 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 1.7387833 . . // Col 7-8: ethnolinguistic fragmentation . ivreg2 logpgp95 (avexpr=logem4) avelf, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.6358388 .1642377 -3.87 0.000 -.9642523 -.3074252 avelf | .2369745 .5428228 0.44 0.664 -.8484667 1.322416 _cons | 9.379576 .7167877 13.09 0.000 7.946271 10.81288 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 61) = 14.99 Prob > F = 0.0003 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 61) = 14.99 Prob > F = 0.0003 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 61) P-val | SW Chi-sq( 1) P-val | SW F( 1, 61) avexpr | 14.99 0.0003 | 15.73 0.0001 | 14.99 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=8.73 P-val=0.0031 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 18.89 Kleibergen-Paap Wald rk F statistic 14.99 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,61)= 23.46 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 24.61 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 13.19 P-val=0.0003 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 2, 61) = 29.88 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.5427 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9926 Residual SS = 31.36445572 Root MSE = .7 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7379904 .1401149 5.27 0.000 .4633702 1.012611 avelf | -1.020715 .3226873 -3.16 0.002 -1.65317 -.388259 _cons | 3.672304 .9685963 3.79 0.000 1.773891 5.570718 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 8.731 Chi-sq(1) P-val = 0.0031 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 18.892 (Kleibergen-Paap rk Wald F statistic): 14.988 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: avelf Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m6_iv_c7 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 14.988164 . ivreg2 logpgp95 lat_abst (avexpr=logem4) avelf, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.5560145 .1730531 -3.21 0.002 -.9021723 -.2098568 lat_abst | 2.286513 1.379393 1.66 0.103 -.4726845 5.04571 avelf | .4849844 .5704532 0.85 0.399 -.6560919 1.626061 _cons | 8.492044 .925883 9.17 0.000 6.640002 10.34409 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 60) = 10.32 Prob > F = 0.0021 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 60) = 10.32 Prob > F = 0.0021 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 60) P-val | SW Chi-sq( 1) P-val | SW F( 1, 60) avexpr | 10.32 0.0021 | 11.01 0.0009 | 10.32 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=6.33 P-val=0.0118 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 13.35 Kleibergen-Paap Wald rk F statistic 10.32 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,60)= 16.97 P-val=0.0001 Anderson-Rubin Wald test Chi-sq(1)= 18.10 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 10.53 P-val=0.0012 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 3, 60) = 18.54 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.4977 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9919 Residual SS = 34.45186797 Root MSE = .7337 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7869825 .1772748 4.44 0.000 .4395303 1.134435 lat_abst | -.8923024 .8428516 -1.06 0.290 -2.544261 .7596563 avelf | -1.129109 .3356171 -3.36 0.001 -1.786907 -.4713119 _cons | 3.559135 1.091638 3.26 0.001 1.419563 5.698707 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 6.334 Chi-sq(1) P-val = 0.0118 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 13.352 (Kleibergen-Paap rk Wald F statistic): 10.323 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst avelf Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m6_iv_c8 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 10.323179 . . // Col 9: all controls . ivreg2 logpgp95 lat_abst (avexpr=logem4) temp* humid* edes1975 avelf /// > steplow deslow stepmid desmid drystep drywint goldm iron silv zinc /// > oilres landlock, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.5678043 .2411368 -2.35 0.024 -1.05596 -.0796484 lat_abst | 3.54166 2.953793 1.20 0.238 -2.437981 9.521301 temp1 | .2298934 .1400241 1.64 0.109 -.0535706 .5133574 temp2 | .0724475 .0786412 0.92 0.363 -.0867534 .2316483 temp3 | -.123549 .0572963 -2.16 0.037 -.2395393 -.0075586 temp4 | -.1157634 .0628013 -1.84 0.073 -.2428979 .0113711 temp5 | -.0050126 .0461621 -0.11 0.914 -.0984629 .0884378 humid1 | .0360945 .0386753 0.93 0.357 -.0421995 .1143885 humid2 | -.0110063 .0535499 -0.21 0.838 -.1194123 .0973997 humid3 | -.0295307 .0416365 -0.71 0.482 -.1138194 .054758 humid4 | .0435277 .0513081 0.85 0.402 -.06034 .1473955 edes1975 | .0092898 .0077282 1.20 0.237 -.0063551 .0249347 avelf | 1.472949 .761664 1.93 0.061 -.0689589 3.014857 steplow | .2143835 .4016667 0.53 0.597 -.5987482 1.027515 deslow | -.11481 .5266992 -0.22 0.829 -1.181057 .9514367 stepmid | .201078 .9821138 0.20 0.839 -1.787108 2.189264 desmid | -1.649577 .6821134 -2.42 0.020 -3.030443 -.2687107 drystep | -.5577722 .5343099 -1.04 0.303 -1.639426 .5238816 drywint | -12.71676 10.11736 -1.26 0.216 -33.19828 7.764757 goldm | .2233466 .2208763 1.01 0.318 -.2237941 .6704873 iron | .2442255 .1944435 1.26 0.217 -.1494049 .6378558 silv | .083418 .1781974 0.47 0.642 -.2773237 .4441596 zinc | -.2715515 .3615722 -0.75 0.457 -1.003516 .4604131 oilres | 4.87e-07 3.00e-07 1.62 0.113 -1.21e-07 1.09e-06 landlock | -1.085284 .6510513 -1.67 0.104 -2.403269 .2327002 _cons | 2.747536 3.038865 0.90 0.372 -3.404324 8.899397 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 38) = 5.54 Prob > F = 0.0238 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 38) = 5.54 Prob > F = 0.0238 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 38) P-val | SW Chi-sq( 1) P-val | SW F( 1, 38) avexpr | 5.54 0.0238 | 9.34 0.0022 | 5.54 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=5.89 P-val=0.0152 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.09 Kleibergen-Paap Wald rk F statistic 5.54 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,38)= 6.10 P-val=0.0181 Anderson-Rubin Wald test Chi-sq(1)= 10.27 P-val=0.0014 Stock-Wright LM S statistic Chi-sq(1)= . P-val= . NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 26 Number of endogenous regressors K1 = 1 Number of instruments L = 26 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 25, 38) = 430.55 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.7382 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9958 Residual SS = 17.95392653 Root MSE = .5297 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7126678 .1474223 4.83 0.000 .4237253 1.00161 lat_abst | -2.519816 1.366447 -1.84 0.065 -5.198003 .1583714 temp1 | .1029365 .0859067 1.20 0.231 -.0654376 .2713105 temp2 | -.0692111 .0374631 -1.85 0.065 -.1426374 .0042152 temp3 | -.0055559 .0311013 -0.18 0.858 -.0665134 .0554015 temp4 | -.0314571 .0354191 -0.89 0.374 -.1008774 .0379631 temp5 | -.0066866 .0234223 -0.29 0.775 -.0525934 .0392202 humid1 | -.0084291 .0157049 -0.54 0.591 -.0392101 .0223519 humid2 | .0203168 .0213625 0.95 0.342 -.0215529 .0621865 humid3 | .021848 .0158603 1.38 0.168 -.0092377 .0529336 humid4 | -.0203429 .0184295 -1.10 0.270 -.056464 .0157782 edes1975 | .0026499 .0042254 0.63 0.531 -.0056318 .0109316 avelf | -1.605881 .3577101 -4.49 0.000 -2.30698 -.9047821 steplow | -.3008232 .190134 -1.58 0.114 -.673479 .0718327 deslow | .4968137 .2222991 2.23 0.025 .0611155 .932512 stepmid | .2540305 .3786039 0.67 0.502 -.4880195 .9960804 desmid | 1.357863 .3369287 4.03 0.000 .6974949 2.018231 drystep | .3254122 .3167649 1.03 0.304 -.2954356 .94626 drywint | 2.879405 4.263461 0.68 0.499 -5.476825 11.23563 goldm | -.0127033 .0938234 -0.14 0.892 -.1965939 .1711872 iron | -.1474457 .088125 -1.67 0.094 -.3201676 .0252762 silv | -.0323023 .0632366 -0.51 0.609 -.1562438 .0916392 zinc | .1026722 .1387016 0.74 0.459 -.1691779 .3745223 oilres | 6.26e-09 1.15e-07 0.05 0.957 -2.19e-07 2.32e-07 landlock | .7336834 .3433379 2.14 0.033 .0607535 1.406613 _cons | 3.686136 1.278783 2.88 0.004 1.179767 6.192505 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 5.895 Chi-sq(1) P-val = 0.0152 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.086 (Kleibergen-Paap rk Wald F statistic): 5.545 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Warning: estimated covariance matrix of moment conditions not of full rank. overidentification statistic not reported, and standard errors and model tests should be interpreted with caution. Possible causes: singleton dummy variable (dummy with one 1 and N-1 0s or vice versa) partial option may address problem. ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst temp1 temp2 temp3 temp4 temp5 humid1 humid2 humid3 humid4 edes1975 avelf steplow deslow stepmid desmi > d drystep drywint goldm iron silv zinc oilres landlock Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m6_iv_c9 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 5.5446026 . . esttab m6_iv_c1 m6_iv_c2 m6_iv_c3 m6_iv_c4 m6_iv_c5 /// > m6_iv_c6 m6_iv_c7 m6_iv_c8 m6_iv_c9 /// > using "tab6_iv_geo.csv", csv replace /// > b(3) se(3) star(* 0.10 ** 0.05 *** 0.01) /// > stats(N r2 firstF, fmt(0 3 2) /// > labels("N" "R-squared" "First-stage F (KP rk Wald)")) /// > title("Table 6: 2SLS with geography and climate controls") (output written to tab6_iv_geo.csv) . . . /*================================================================== > SECTION 8: TABLE 7 — Health channels (first overidentified specs) > Cols 7-9 instrument BOTH avexpr AND a health variable using 4 > instruments (logem4, latabs, lt100km, meantemp). With 4 instruments > and 2 endogenous regressors, the model is overidentified by 2 > degrees: Hansen J becomes a meaningful test of the joint exclusion > restriction. > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " TABLE 7 — Health-channel IV (with overidentification on Cols 7-9)" TABLE 7 — Health-channel IV (with overidentification on Cols 7-9) . di "================================================================" ================================================================ . . use "${DATA_URL}/maketable7.dta", clear . keep if baseco==1 (99 observations deleted) . export delimited using "data_maketable7.csv", replace file data_maketable7.csv saved . . // Col 1-2: malaria control (just-identified) . ivreg2 logpgp95 (avexpr=logem4) malfal94, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 62 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.4172807 .214351 -1.95 0.056 -.846196 .0116347 malfal94 | -.7902259 .5350639 -1.48 0.145 -1.860886 .2804344 _cons | 8.757417 .9056647 9.67 0.000 6.945186 10.56965 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 59) = 3.79 Prob > F = 0.0563 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 59) = 3.79 Prob > F = 0.0563 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 59) P-val | SW Chi-sq( 1) P-val | SW F( 1, 59) avexpr | 3.79 0.0563 | 3.98 0.0460 | 3.79 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.35 P-val=0.0671 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 5.06 Kleibergen-Paap Wald rk F statistic 3.79 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,59)= 6.08 P-val=0.0166 Anderson-Rubin Wald test Chi-sq(1)= 6.39 P-val=0.0115 Stock-Wright LM S statistic Chi-sq(1)= 7.23 P-val=0.0072 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 62 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 62 F( 2, 59) = 34.67 Prob > F = 0.0000 Total (centered) SS = 65.11469154 Centered R2 = 0.5345 Total (uncentered) SS = 4053.471162 Uncentered R2 = 0.9925 Residual SS = 30.30792713 Root MSE = .6992 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6870742 .2646891 2.60 0.009 .1682931 1.205855 malfal94 | -.5784585 .5000382 -1.16 0.247 -1.558515 .4015984 _cons | 3.790856 1.885929 2.01 0.044 .0945041 7.487208 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.353 Chi-sq(1) P-val = 0.0671 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 5.058 (Kleibergen-Paap rk Wald F statistic): 3.790 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: malfal94 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m7_iv_c1 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 3.7897063 . ivreg2 logpgp95 lat_abst (avexpr=logem4) malfal94, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 62 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3755514 .2108467 -1.78 0.080 -.797607 .0465041 lat_abst | 1.683799 1.485913 1.13 0.262 -1.29058 4.658177 malfal94 | -.6487872 .5672055 -1.14 0.257 -1.784172 .486598 _cons | 8.209087 .9814244 8.36 0.000 6.244552 10.17362 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 58) = 3.17 Prob > F = 0.0801 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 58) = 3.17 Prob > F = 0.0801 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 58) P-val | SW Chi-sq( 1) P-val | SW F( 1, 58) avexpr | 3.17 0.0801 | 3.39 0.0655 | 3.17 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=2.89 P-val=0.0893 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.99 Kleibergen-Paap Wald rk F statistic 3.17 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,58)= 5.12 P-val=0.0274 Anderson-Rubin Wald test Chi-sq(1)= 5.47 P-val=0.0193 Stock-Wright LM S statistic Chi-sq(1)= 6.31 P-val=0.0120 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 62 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 62 F( 3, 58) = 21.91 Prob > F = 0.0000 Total (centered) SS = 65.11469154 Centered R2 = 0.5013 Total (uncentered) SS = 4053.471162 Uncentered R2 = 0.9920 Residual SS = 32.47485473 Root MSE = .7237 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7206119 .3136169 2.30 0.022 .105934 1.33529 lat_abst | -.5646915 .9073436 -0.62 0.534 -2.343052 1.213669 malfal94 | -.5993901 .5031255 -1.19 0.234 -1.585498 .3867179 _cons | 3.681045 2.085585 1.76 0.078 -.4066273 7.768717 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 2.887 Chi-sq(1) P-val = 0.0893 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.988 (Kleibergen-Paap rk Wald F statistic): 3.173 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst malfal94 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m7_iv_c2 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 3.1725264 . . // Col 3-4: life expectancy (just-identified) . ivreg2 logpgp95 (avexpr=logem4) leb95, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.336054 .1676635 -2.00 0.050 -.6717945 -.0003135 leb95 | .0471394 .0131697 3.58 0.001 .0207676 .0735112 _cons | 5.138545 1.333204 3.85 0.000 2.46885 7.80824 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 57) = 4.02 Prob > F = 0.0498 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 57) = 4.02 Prob > F = 0.0498 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 57) P-val | SW Chi-sq( 1) P-val | SW F( 1, 57) avexpr | 4.02 0.0498 | 4.23 0.0397 | 4.02 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.03 P-val=0.0817 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.82 Kleibergen-Paap Wald rk F statistic 4.02 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,57)= 4.75 P-val=0.0335 Anderson-Rubin Wald test Chi-sq(1)= 5.00 P-val=0.0254 Stock-Wright LM S statistic Chi-sq(1)= 4.14 P-val=0.0419 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 2, 57) = 47.23 Prob > F = 0.0000 Total (centered) SS = 60.92238195 Centered R2 = 0.5865 Total (uncentered) SS = 3889.989333 Uncentered R2 = 0.9935 Residual SS = 25.19230925 Root MSE = .648 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6294439 .2945428 2.14 0.033 .0521505 1.206737 leb95 | .0269356 .0231448 1.16 0.245 -.0184274 .0722986 _cons | 2.243338 .7356292 3.05 0.002 .8015311 3.685145 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.032 Chi-sq(1) P-val = 0.0817 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.820 (Kleibergen-Paap rk Wald F statistic): 4.017 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: leb95 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m7_iv_c3 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 4.0173606 . ivreg2 logpgp95 lat_abst (avexpr=logem4) leb95, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3017835 .1762367 -1.71 0.092 -.654828 .051261 lat_abst | 1.133589 1.413404 0.80 0.426 -1.6978 3.964978 leb95 | .0437231 .013682 3.20 0.002 .0163148 .0711315 _cons | 4.987294 1.364107 3.66 0.001 2.254659 7.719929 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 56) = 2.93 Prob > F = 0.0924 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 56) = 2.93 Prob > F = 0.0924 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 56) P-val | SW Chi-sq( 1) P-val | SW F( 1, 56) avexpr | 2.93 0.0924 | 3.14 0.0763 | 2.93 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=2.32 P-val=0.1280 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 2.89 Kleibergen-Paap Wald rk F statistic 2.93 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,56)= 4.37 P-val=0.0412 Anderson-Rubin Wald test Chi-sq(1)= 4.68 P-val=0.0306 Stock-Wright LM S statistic Chi-sq(1)= 4.19 P-val=0.0407 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 3, 56) = 27.56 Prob > F = 0.0000 Total (centered) SS = 60.92238195 Centered R2 = 0.5367 Total (uncentered) SS = 3889.989333 Uncentered R2 = 0.9927 Residual SS = 28.22589183 Root MSE = .6859 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6770089 .3569874 1.90 0.058 -.0226735 1.376691 lat_abst | -.5287279 .7879063 -0.67 0.502 -2.072996 1.01554 leb95 | .0262868 .0248959 1.06 0.291 -.0225081 .0750818 _cons | 2.069469 .9193705 2.25 0.024 .2675361 3.871402 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 2.317 Chi-sq(1) P-val = 0.1280 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 2.889 (Kleibergen-Paap rk Wald F statistic): 2.932 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst leb95 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m7_iv_c4 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.9322319 . . // Col 5-6: infant mortality (just-identified) . ivreg2 logpgp95 (avexpr=logem4) imr95, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3559983 .1614788 -2.20 0.032 -.679354 -.0326426 imr95 | -.0128276 .0045651 -2.81 0.007 -.0219691 -.0036862 _cons | 8.891804 .7373196 12.06 0.000 7.415347 10.36826 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 57) = 4.86 Prob > F = 0.0315 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 57) = 4.86 Prob > F = 0.0315 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 57) P-val | SW Chi-sq( 1) P-val | SW F( 1, 57) avexpr | 4.86 0.0315 | 5.12 0.0237 | 4.86 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=4.22 P-val=0.0400 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.94 Kleibergen-Paap Wald rk F statistic 4.86 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,57)= 4.29 P-val=0.0428 Anderson-Rubin Wald test Chi-sq(1)= 4.52 P-val=0.0335 Stock-Wright LM S statistic Chi-sq(1)= 5.11 P-val=0.0238 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 2, 57) = 67.38 Prob > F = 0.0000 Total (centered) SS = 60.92238195 Centered R2 = 0.6708 Total (uncentered) SS = 3889.989333 Uncentered R2 = 0.9948 Residual SS = 20.05562045 Root MSE = .5782 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .5505523 .2601275 2.12 0.034 .0407118 1.060393 imr95 | -.0102444 .0059384 -1.73 0.085 -.0218835 .0013946 _cons | 5.010736 1.999933 2.51 0.012 1.090939 8.930534 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 4.216 Chi-sq(1) P-val = 0.0400 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.940 (Kleibergen-Paap rk Wald F statistic): 4.860 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: imr95 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m7_iv_c5 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 4.8603214 . ivreg2 logpgp95 lat_abst (avexpr=logem4) imr95, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.2911768 .1698235 -1.71 0.092 -.6313742 .0490206 lat_abst | 1.587098 1.366681 1.16 0.250 -1.150693 4.324889 imr95 | -.0122401 .0045424 -2.69 0.009 -.0213397 -.0031406 _cons | 8.269678 .9180107 9.01 0.000 6.430682 10.10867 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 56) = 2.94 Prob > F = 0.0920 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 56) = 2.94 Prob > F = 0.0920 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 56) P-val | SW Chi-sq( 1) P-val | SW F( 1, 56) avexpr | 2.94 0.0920 | 3.15 0.0759 | 2.94 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=2.63 P-val=0.1051 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 2.41 Kleibergen-Paap Wald rk F statistic 2.94 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,56)= 2.89 P-val=0.0947 Anderson-Rubin Wald test Chi-sq(1)= 3.10 P-val=0.0785 Stock-Wright LM S statistic Chi-sq(1)= 3.83 P-val=0.0503 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 3, 56) = 42.65 Prob > F = 0.0000 Total (centered) SS = 60.92238195 Centered R2 = 0.6612 Total (uncentered) SS = 3889.989333 Uncentered R2 = 0.9947 Residual SS = 20.63926986 Root MSE = .5865 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .5622045 .3384723 1.66 0.097 -.1011891 1.225598 lat_abst | -.1015638 .8546549 -0.12 0.905 -1.776657 1.573529 imr95 | -.0101325 .0066722 -1.52 0.129 -.0232098 .0029447 _cons | 4.94694 2.425976 2.04 0.041 .1921148 9.701764 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 2.627 Chi-sq(1) P-val = 0.1051 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 2.412 (Kleibergen-Paap rk Wald F statistic): 2.940 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst imr95 Excluded instruments: logem4 ------------------------------------------------------------------------------ . eststo m7_iv_c6 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.9397994 . . // Col 7-9: instrument BOTH avexpr AND health (overidentified, GMM2S for J-te > st) . di _newline "*** Cols 7-9: 2 endogenous, 4 instruments => Hansen J meaningful > ***" *** Cols 7-9: 2 endogenous, 4 instruments => Hansen J meaningful *** . . ivreg2 logpgp95 (avexpr malfal94 = logem4 latabs lt100km meantemp), /// > gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.4091902 .2129637 -1.92 0.060 -.8359791 .0175986 latabs | -.8114337 1.876474 -0.43 0.667 -4.571971 2.949104 lt100km | .5739277 .5442141 1.05 0.296 -.5167018 1.664557 meantemp | -.1161707 .0510574 -2.28 0.027 -.2184921 -.0138493 _cons | 11.06286 1.479693 7.48 0.000 8.097493 14.02823 ------------------------------------------------------------------------------ F test of excluded instruments: F( 4, 55) = 12.38 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 3, 55) = 1.63 Prob > F = 0.1920 First-stage regression of malfal94: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust malfal94 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | .2002973 .0332781 6.02 0.000 .1336064 .2669881 latabs | -.4050589 .398901 -1.02 0.314 -1.204474 .3943566 lt100km | -.3255818 .1329663 -2.45 0.018 -.5920522 -.0591114 meantemp | .0072881 .0117542 0.62 0.538 -.0162679 .0308441 _cons | -.5300936 .3244484 -1.63 0.108 -1.180303 .1201156 ------------------------------------------------------------------------------ F test of excluded instruments: F( 4, 55) = 27.73 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 3, 55) = 1.61 Prob > F = 0.1973 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 4, 55) P-val | SW Chi-sq( 3) P-val | SW F( 3, 55) avexpr | 12.38 0.0000 | 5.35 0.1480 | 1.63 malfal94 | 27.73 0.0000 | 5.27 0.1529 | 1.61 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 5% maximal IV relative bias 16.85 10% maximal IV relative bias 10.27 20% maximal IV relative bias 6.71 30% maximal IV relative bias 5.34 10% maximal IV size 24.58 15% maximal IV size 13.96 20% maximal IV size 10.26 25% maximal IV size 8.31 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(3)=3.59 P-val=0.3097 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 1.00 Kleibergen-Paap Wald rk F statistic 1.17 Stock-Yogo weak ID test critical values for K1=2 and L1=4: 5% maximal IV relative bias 11.04 10% maximal IV relative bias 7.56 20% maximal IV relative bias 5.57 30% maximal IV relative bias 4.73 10% maximal IV size 16.87 15% maximal IV size 9.93 20% maximal IV size 7.54 25% maximal IV size 6.28 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(4,55)= 40.46 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(4)= 176.56 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(4)= 21.06 P-val=0.0003 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 3 Number of endogenous regressors K1 = 2 Number of instruments L = 5 Number of excluded instruments L1 = 4 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 60 F( 2, 57) = 47.97 Prob > F = 0.0000 Total (centered) SS = 61.37993888 Centered R2 = 0.6076 Total (uncentered) SS = 3953.663908 Uncentered R2 = 0.9939 Residual SS = 24.08309144 Root MSE = .6335 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6112593 .2345633 2.61 0.009 .1515238 1.070995 malfal94 | -.8580581 .6471766 -1.33 0.185 -2.126501 .4103847 _cons | 4.421478 1.776234 2.49 0.013 .940123 7.902833 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.587 Chi-sq(3) P-val = 0.3097 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 1.004 (Kleibergen-Paap rk Wald F statistic): 1.173 Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 11.04 10% maximal IV relative bias 7.56 20% maximal IV relative bias 5.57 30% maximal IV relative bias 4.73 10% maximal IV size 16.87 15% maximal IV size 9.93 20% maximal IV size 7.54 25% maximal IV size 6.28 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 1.557 Chi-sq(2) P-val = 0.4591 ------------------------------------------------------------------------------ Instrumented: avexpr malfal94 Excluded instruments: logem4 latabs lt100km meantemp ------------------------------------------------------------------------------ . eststo m7_iv_c7 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 1.1733625 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = 1.5571766 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .45905359 . . ivreg2 logpgp95 (avexpr leb95 = logem4 latabs lt100km meantemp), /// > gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3992893 .2186878 -1.83 0.073 -.837732 .0391534 latabs | -.836228 1.889871 -0.44 0.660 -4.625191 2.952735 lt100km | .5463246 .5527839 0.99 0.327 -.5619404 1.65459 meantemp | -.1175002 .0517505 -2.27 0.027 -.2212536 -.0137467 _cons | 11.05373 1.484236 7.45 0.000 8.07802 14.02945 ------------------------------------------------------------------------------ F test of excluded instruments: F( 4, 54) = 11.74 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 3, 54) = 3.22 Prob > F = 0.0298 First-stage regression of leb95: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust leb95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -4.579749 .9816623 -4.67 0.000 -6.547863 -2.611634 latabs | 12.00986 10.11897 1.19 0.240 -8.277461 32.29718 lt100km | 12.33412 2.849577 4.33 0.000 6.621065 18.04718 meantemp | -.2427068 .2425602 -1.00 0.321 -.7290108 .2435972 _cons | 83.15814 8.627513 9.64 0.000 65.86101 100.4553 ------------------------------------------------------------------------------ F test of excluded instruments: F( 4, 54) = 20.16 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 3, 54) = 3.53 Prob > F = 0.0207 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 4, 54) P-val | SW Chi-sq( 3) P-val | SW F( 3, 54) avexpr | 11.74 0.0000 | 10.55 0.0144 | 3.22 leb95 | 20.16 0.0000 | 11.58 0.0090 | 3.53 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 5% maximal IV relative bias 16.85 10% maximal IV relative bias 10.27 20% maximal IV relative bias 6.71 30% maximal IV relative bias 5.34 10% maximal IV size 24.58 15% maximal IV size 13.96 20% maximal IV size 10.26 25% maximal IV size 8.31 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(3)=5.52 P-val=0.1372 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 1.66 Kleibergen-Paap Wald rk F statistic 2.36 Stock-Yogo weak ID test critical values for K1=2 and L1=4: 5% maximal IV relative bias 11.04 10% maximal IV relative bias 7.56 20% maximal IV relative bias 5.57 30% maximal IV relative bias 4.73 10% maximal IV size 16.87 15% maximal IV size 9.93 20% maximal IV size 7.54 25% maximal IV size 6.28 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(4,54)= 41.51 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(4)= 181.40 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(4)= 19.84 P-val=0.0005 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 3 Number of endogenous regressors K1 = 2 Number of instruments L = 5 Number of excluded instruments L1 = 4 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 59 F( 2, 56) = 34.78 Prob > F = 0.0000 Total (centered) SS = 57.33054043 Centered R2 = 0.4825 Total (uncentered) SS = 3852.666426 Uncentered R2 = 0.9923 Residual SS = 29.67063008 Root MSE = .7091 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7049212 .2220433 3.17 0.001 .2697244 1.140118 leb95 | .0220161 .0222479 0.99 0.322 -.021589 .0656212 _cons | 2.083984 .722669 2.88 0.004 .6675784 3.500389 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 5.525 Chi-sq(3) P-val = 0.1372 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 1.659 (Kleibergen-Paap rk Wald F statistic): 2.355 Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 11.04 10% maximal IV relative bias 7.56 20% maximal IV relative bias 5.57 30% maximal IV relative bias 4.73 10% maximal IV size 16.87 15% maximal IV size 9.93 20% maximal IV size 7.54 25% maximal IV size 6.28 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 1.180 Chi-sq(2) P-val = 0.5543 ------------------------------------------------------------------------------ Instrumented: avexpr leb95 Excluded instruments: logem4 latabs lt100km meantemp ------------------------------------------------------------------------------ . eststo m7_iv_c8 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.3553032 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = 1.1799425 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .55434323 . . ivreg2 logpgp95 (avexpr imr95 = logem4 latabs lt100km meantemp), /// > gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | -.3992893 .2186878 -1.83 0.073 -.837732 .0391534 latabs | -.836228 1.889871 -0.44 0.660 -4.625191 2.952735 lt100km | .5463246 .5527839 0.99 0.327 -.5619404 1.65459 meantemp | -.1175002 .0517505 -2.27 0.027 -.2212536 -.0137467 _cons | 11.05373 1.484236 7.45 0.000 8.07802 14.02945 ------------------------------------------------------------------------------ F test of excluded instruments: F( 4, 54) = 11.74 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 3, 54) = 2.95 Prob > F = 0.0409 First-stage regression of imr95: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust imr95 | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logem4 | 17.19691 3.418754 5.03 0.000 10.34272 24.0511 latabs | 6.078629 25.0424 0.24 0.809 -44.12836 56.28562 lt100km | -38.70843 8.093581 -4.78 0.000 -54.93509 -22.48178 meantemp | 1.292256 .6955437 1.86 0.069 -.1022249 2.686738 _cons | -42.63121 19.63755 -2.17 0.034 -82.00213 -3.26028 ------------------------------------------------------------------------------ F test of excluded instruments: F( 4, 54) = 27.07 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 3, 54) = 2.95 Prob > F = 0.0405 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 4, 54) P-val | SW Chi-sq( 3) P-val | SW F( 3, 54) avexpr | 11.74 0.0000 | 9.66 0.0217 | 2.95 imr95 | 27.07 0.0000 | 9.68 0.0215 | 2.95 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 5% maximal IV relative bias 16.85 10% maximal IV relative bias 10.27 20% maximal IV relative bias 6.71 30% maximal IV relative bias 5.34 10% maximal IV size 24.58 15% maximal IV size 13.96 20% maximal IV size 10.26 25% maximal IV size 8.31 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(3)=4.22 P-val=0.2388 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 1.42 Kleibergen-Paap Wald rk F statistic 2.06 Stock-Yogo weak ID test critical values for K1=2 and L1=4: 5% maximal IV relative bias 11.04 10% maximal IV relative bias 7.56 20% maximal IV relative bias 5.57 30% maximal IV relative bias 4.73 10% maximal IV size 16.87 15% maximal IV size 9.93 20% maximal IV size 7.54 25% maximal IV size 6.28 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(4,54)= 41.51 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(4)= 181.40 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(4)= 19.84 P-val=0.0005 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 3 Number of endogenous regressors K1 = 2 Number of instruments L = 5 Number of excluded instruments L1 = 4 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 59 F( 2, 56) = 41.63 Prob > F = 0.0000 Total (centered) SS = 57.33054043 Centered R2 = 0.5687 Total (uncentered) SS = 3852.666426 Uncentered R2 = 0.9936 Residual SS = 24.72645787 Root MSE = .6474 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6443968 .1925474 3.35 0.001 .2670109 1.021783 imr95 | -.0083626 .0058351 -1.43 0.152 -.0197993 .003074 _cons | 4.310773 1.542985 2.79 0.005 1.286578 7.334969 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 4.218 Chi-sq(3) P-val = 0.2388 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 1.425 (Kleibergen-Paap rk Wald F statistic): 2.058 Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 11.04 10% maximal IV relative bias 7.56 20% maximal IV relative bias 5.57 30% maximal IV relative bias 4.73 10% maximal IV size 16.87 15% maximal IV size 9.93 20% maximal IV size 7.54 25% maximal IV size 6.28 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.548 Chi-sq(2) P-val = 0.7605 ------------------------------------------------------------------------------ Instrumented: avexpr imr95 Excluded instruments: logem4 latabs lt100km meantemp ------------------------------------------------------------------------------ . eststo m7_iv_c9 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.0577793 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = .54762111 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .76047613 . . // Col 10-11: yellow fever instrument . gen other_cont7 = . (64 missing values generated) . replace other_cont7 = 1 if shortnam=="AUS" | shortnam=="MLT" | shortnam=="NZL > " (3 real changes made) . recode other_cont7 (.=0) (61 changes made to other_cont7) . . ivreg2 logpgp95 (avexpr = yellow), robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- yellow | -1.083333 .3528097 -3.07 0.003 -1.78859 -.3780769 _cons | 7.328125 .2804308 26.13 0.000 6.767552 7.888698 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 62) = 9.43 Prob > F = 0.0032 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 62) = 9.43 Prob > F = 0.0032 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 62) P-val | SW Chi-sq( 1) P-val | SW F( 1, 62) avexpr | 9.43 0.0032 | 9.73 0.0018 | 9.43 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=7.18 P-val=0.0074 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.17 Kleibergen-Paap Wald rk F statistic 9.43 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,62)= 16.87 P-val=0.0001 Anderson-Rubin Wald test Chi-sq(1)= 17.42 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 10.66 P-val=0.0011 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 2 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 1, 62) = 14.16 Prob > F = 0.0004 Total (centered) SS = 68.5817185 Centered R2 = 0.2365 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9876 Residual SS = 52.36392669 Root MSE = .9045 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9135754 .23898 3.82 0.000 .4451831 1.381968 _cons | 2.109722 1.562872 1.35 0.177 -.9534511 5.172896 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 7.184 Chi-sq(1) P-val = 0.0074 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.169 (Kleibergen-Paap rk Wald F statistic): 9.429 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: yellow ------------------------------------------------------------------------------ . eststo m7_iv_c10 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 9.4285149 . ivreg2 logpgp95 (avexpr = yellow) africa asia other_cont7, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 64 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- yellow | -.8047243 .3073658 -2.62 0.011 -1.419762 -.1896868 africa | -.7355521 .3587866 -2.05 0.045 -1.453482 -.0176216 asia | .5713437 .4957576 1.15 0.254 -.420665 1.563352 other_cont7 | 1.759143 .8175527 2.15 0.036 .1232239 3.395062 _cons | 7.266674 .3363178 21.61 0.000 6.593704 7.939645 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 59) = 6.85 Prob > F = 0.0112 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 59) = 6.85 Prob > F = 0.0112 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 59) P-val | SW Chi-sq( 1) P-val | SW F( 1, 59) avexpr | 6.85 0.0112 | 7.44 0.0064 | 6.85 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=5.54 P-val=0.0186 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 4.45 Kleibergen-Paap Wald rk F statistic 6.85 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,59)= 10.07 P-val=0.0024 Anderson-Rubin Wald test Chi-sq(1)= 10.92 P-val=0.0010 Stock-Wright LM S statistic Chi-sq(1)= 7.86 P-val=0.0051 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 64 Number of regressors K = 5 Number of endogenous regressors K1 = 1 Number of instruments L = 5 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 64 F( 4, 59) = 10.08 Prob > F = 0.0000 Total (centered) SS = 68.5817185 Centered R2 = 0.3600 Total (uncentered) SS = 4228.560224 Uncentered R2 = 0.9896 Residual SS = 43.8915558 Root MSE = .8281 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .89888 .289462 3.11 0.002 .3315449 1.466215 africa | -.5319418 .2933187 -1.81 0.070 -1.106836 .0429524 asia | -.8804986 .2589301 -3.40 0.001 -1.387992 -.373005 other_cont7 | -.7679866 .715454 -1.07 0.283 -2.170251 .6342774 _cons | 2.589704 1.940295 1.33 0.182 -1.213204 6.392612 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 5.542 Chi-sq(1) P-val = 0.0186 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 4.452 (Kleibergen-Paap rk Wald F statistic): 6.855 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: africa asia other_cont7 Excluded instruments: yellow ------------------------------------------------------------------------------ . eststo m7_iv_c11 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 6.8546166 . . esttab m7_iv_c1 m7_iv_c2 m7_iv_c3 m7_iv_c4 m7_iv_c5 m7_iv_c6 /// > m7_iv_c7 m7_iv_c8 m7_iv_c9 m7_iv_c10 m7_iv_c11 /// > using "tab7_iv_health.csv", csv replace /// > b(3) se(3) star(* 0.10 ** 0.05 *** 0.01) /// > stats(N r2 firstF hansenJ hansenP, fmt(0 3 2 2 3) /// > labels("N" "R-squared" "First-stage F (KP rk Wald)" /// > "Hansen J statistic" "Hansen J p-value")) /// > title("Table 7: 2SLS with health controls and overidentification") (output written to tab7_iv_health.csv) . . . /*================================================================== > SECTION 9: TABLE 8 — Alternative instruments + overidentification > Panels A/B: replace logem4 with alternative instruments > (euro1900, cons00a, democ00a, cons1, democ1) > Panel C (overid): pair each alt instrument WITH logem4 in a > 2-instrument GMM2S regression. Hansen J tests whether the two > instruments give consistent estimates -- if both are valid, J > should not reject. > Panel D: include logem4 as exogenous control in second stage > (relaxes exclusion to only the *excess* effect of mortality). > > Pedagogical aside (Albouy 2012): ~36% of AJR's settler-mortality > observations are imputed or repeat values. Albouy argues this > contamination weakens the first stage and biases the IV estimate. > The Hansen J non-rejection in Panel C is sometimes interpreted as > evidence against this concern; Albouy disagrees because alternative > instruments share the same imputation problems. > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " TABLE 8 — Alternative instruments + Hansen J overidentification" TABLE 8 — Alternative instruments + Hansen J overidentification . di "================================================================" ================================================================ . . use "${DATA_URL}/maketable8.dta", clear . keep if baseco==1 (99 observations deleted) . export delimited using "data_maketable8.csv", replace file data_maketable8.csv saved . . //── Panels A/B: alt instruments (just-identified) ──────────────── . di _newline "*** Panels A/B: each alternative instrument used alone ***" *** Panels A/B: each alternative instrument used alone *** . . ivreg2 logpgp95 (avexpr=euro1900), robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 63 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | .031623 .0048432 6.53 0.000 .0219384 .0413076 _cons | 5.992639 .197895 30.28 0.000 5.596924 6.388354 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 61) = 42.63 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 61) = 42.63 Prob > F = 0.0000 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 61) P-val | SW Chi-sq( 1) P-val | SW F( 1, 61) avexpr | 42.63 0.0000 | 44.03 0.0000 | 42.63 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=6.07 P-val=0.0137 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 25.97 Kleibergen-Paap Wald rk F statistic 42.63 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,61)= 127.41 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 131.59 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 12.59 P-val=0.0004 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 63 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 2 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 63 F( 1, 61) = 39.52 Prob > F = 0.0000 Total (centered) SS = 66.68940084 Centered R2 = 0.2891 Total (uncentered) SS = 4139.690708 Uncentered R2 = 0.9885 Residual SS = 47.41170328 Root MSE = .8675 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .869902 .1361571 6.39 0.000 .6030391 1.136765 _cons | 2.382444 .905606 2.63 0.009 .6074887 4.157399 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 6.071 Chi-sq(1) P-val = 0.0137 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 25.968 (Kleibergen-Paap rk Wald F statistic): 42.632 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: euro1900 ------------------------------------------------------------------------------ . eststo m8a_c1 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 42.632048 . ivreg2 logpgp95 lat_abst (avexpr=euro1900), robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 63 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | .029227 .0062605 4.67 0.000 .0167041 .0417499 lat_abst | .7636482 1.427183 0.54 0.595 -2.091142 3.618438 _cons | 5.895696 .2926482 20.15 0.000 5.310312 6.481079 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 60) = 21.79 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 60) = 21.79 Prob > F = 0.0000 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 60) P-val | SW Chi-sq( 1) P-val | SW F( 1, 60) avexpr | 21.79 0.0000 | 22.88 0.0000 | 21.79 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=7.83 P-val=0.0051 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 13.70 Kleibergen-Paap Wald rk F statistic 21.79 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,60)= 53.39 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 56.06 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 16.51 P-val=0.0000 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 63 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 63 F( 2, 60) = 18.27 Prob > F = 0.0000 Total (centered) SS = 66.68940084 Centered R2 = 0.2207 Total (uncentered) SS = 4139.690708 Uncentered R2 = 0.9874 Residual SS = 51.9730022 Root MSE = .9083 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9169788 .1722602 5.32 0.000 .579355 1.254603 lat_abst | -.4744792 .9520959 -0.50 0.618 -2.340553 1.391594 _cons | 2.160564 1.051306 2.06 0.040 .100043 4.221085 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 7.829 Chi-sq(1) P-val = 0.0051 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 13.704 (Kleibergen-Paap rk Wald F statistic): 21.795 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: euro1900 ------------------------------------------------------------------------------ . eststo m8a_c2 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 21.794617 . ivreg2 logpgp95 (avexpr=cons00a), robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons00a | .3182682 .0936681 3.40 0.001 .130771 .5057653 _cons | 5.755866 .2637849 21.82 0.000 5.227843 6.283889 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 58) = 11.55 Prob > F = 0.0012 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 58) = 11.55 Prob > F = 0.0012 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 58) P-val | SW Chi-sq( 1) P-val | SW F( 1, 58) avexpr | 11.55 0.0012 | 11.94 0.0005 | 11.55 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=6.13 P-val=0.0133 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 14.80 Kleibergen-Paap Wald rk F statistic 11.55 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,58)= 9.50 P-val=0.0031 Anderson-Rubin Wald test Chi-sq(1)= 9.83 P-val=0.0017 Stock-Wright LM S statistic Chi-sq(1)= 7.58 P-val=0.0059 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 2 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 1, 58) = 31.77 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.4361 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9917 Residual SS = 32.63429958 Root MSE = .7375 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7056341 .1230905 5.73 0.000 .4643811 .946887 _cons | 3.449276 .8241681 4.19 0.000 1.833936 5.064615 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 6.126 Chi-sq(1) P-val = 0.0133 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 14.798 (Kleibergen-Paap rk Wald F statistic): 11.545 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: cons00a ------------------------------------------------------------------------------ . eststo m8a_c3 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 11.545232 . ivreg2 logpgp95 lat_abst (avexpr=cons00a), robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons00a | .2550208 .083546 3.05 0.003 .0877229 .4223187 lat_abst | 2.34621 1.27878 1.83 0.072 -.2145029 4.906922 _cons | 5.484088 .3325752 16.49 0.000 4.818117 6.150058 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 57) = 9.32 Prob > F = 0.0034 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 57) = 9.32 Prob > F = 0.0034 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 57) P-val | SW Chi-sq( 1) P-val | SW F( 1, 57) avexpr | 9.32 0.0034 | 9.81 0.0017 | 9.32 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=8.33 P-val=0.0039 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.98 Kleibergen-Paap Wald rk F statistic 9.32 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,57)= 4.82 P-val=0.0323 Anderson-Rubin Wald test Chi-sq(1)= 5.07 P-val=0.0244 Stock-Wright LM S statistic Chi-sq(1)= 5.95 P-val=0.0148 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 2, 57) = 24.81 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.4645 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9921 Residual SS = 30.98993398 Root MSE = .7187 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .676888 .1843339 3.67 0.000 .3156003 1.038176 lat_abst | .3393871 1.004364 0.34 0.735 -1.629129 2.307904 _cons | 3.57542 1.067059 3.35 0.001 1.484023 5.666818 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 8.330 Chi-sq(1) P-val = 0.0039 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.981 (Kleibergen-Paap rk Wald F statistic): 9.318 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: cons00a ------------------------------------------------------------------------------ . eststo m8a_c4 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 9.3175171 . ivreg2 logpgp95 (avexpr=democ00a), robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ00a | .241985 .0594721 4.07 0.000 .1228941 .3610758 _cons | 6.099079 .1983937 30.74 0.000 5.701802 6.496355 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 57) = 16.56 Prob > F = 0.0001 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 57) = 16.56 Prob > F = 0.0001 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 57) P-val | SW Chi-sq( 1) P-val | SW F( 1, 57) avexpr | 16.56 0.0001 | 17.14 0.0000 | 16.56 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=5.35 P-val=0.0207 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 17.77 Kleibergen-Paap Wald rk F statistic 16.56 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,57)= 25.32 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(1)= 26.21 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 8.05 P-val=0.0045 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 2 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 59 F( 1, 57) = 51.48 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.4397 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9916 Residual SS = 32.4243664 Root MSE = .7413 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7190822 .0985052 7.30 0.000 .5260156 .9121487 _cons | 3.345454 .6767551 4.94 0.000 2.019038 4.671869 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 5.350 Chi-sq(1) P-val = 0.0207 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 17.772 (Kleibergen-Paap rk Wald F statistic): 16.556 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: democ00a ------------------------------------------------------------------------------ . eststo m8a_c5 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 16.5558 . ivreg2 logpgp95 lat_abst (avexpr=democ00a), robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ00a | .2026428 .0602659 3.36 0.001 .0819158 .3233699 lat_abst | 1.727078 1.331302 1.30 0.200 -.9398408 4.393997 _cons | 5.85817 .3112446 18.82 0.000 5.234673 6.481668 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 56) = 11.31 Prob > F = 0.0014 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 56) = 11.31 Prob > F = 0.0014 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 56) P-val | SW Chi-sq( 1) P-val | SW F( 1, 56) avexpr | 11.31 0.0014 | 11.91 0.0006 | 11.31 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=7.04 P-val=0.0080 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 9.27 Kleibergen-Paap Wald rk F statistic 11.31 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,56)= 12.29 P-val=0.0009 Anderson-Rubin Wald test Chi-sq(1)= 12.95 P-val=0.0003 Stock-Wright LM S statistic Chi-sq(1)= 7.41 P-val=0.0065 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 59 F( 2, 56) = 29.30 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.4686 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9920 Residual SS = 30.75184759 Root MSE = .722 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6897528 .145897 4.73 0.000 .4038001 .9757056 lat_abst | .3115619 .87935 0.35 0.723 -1.411932 2.035056 _cons | 3.480876 .8599102 4.05 0.000 1.795483 5.166269 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 7.036 Chi-sq(1) P-val = 0.0080 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 9.267 (Kleibergen-Paap rk Wald F statistic): 11.306 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: democ00a ------------------------------------------------------------------------------ . eststo m8a_c6 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 11.306272 . ivreg2 logpgp95 (avexpr=cons1) indtime, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons1 | .2492712 .0926962 2.69 0.009 .0636503 .4348921 indtime | .0081955 .0028883 2.84 0.006 .0024119 .0139792 _cons | 4.889853 .4845664 10.09 0.000 3.919526 5.860181 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 57) = 7.23 Prob > F = 0.0094 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 57) = 7.23 Prob > F = 0.0094 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 57) P-val | SW Chi-sq( 1) P-val | SW F( 1, 57) avexpr | 7.23 0.0094 | 7.61 0.0058 | 7.23 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=5.17 P-val=0.0230 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 10.00 Kleibergen-Paap Wald rk F statistic 7.23 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,57)= 8.35 P-val=0.0054 Anderson-Rubin Wald test Chi-sq(1)= 8.79 P-val=0.0030 Stock-Wright LM S statistic Chi-sq(1)= 6.98 P-val=0.0082 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 2, 57) = 35.81 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.6210 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9944 Residual SS = 21.93328732 Root MSE = .6046 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .5946949 .1457301 4.08 0.000 .309069 .8803207 indtime | .0049827 .0014556 3.42 0.001 .0021298 .0078357 _cons | 3.720651 .873331 4.26 0.000 2.008954 5.432349 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 5.166 Chi-sq(1) P-val = 0.0230 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 10.004 (Kleibergen-Paap rk Wald F statistic): 7.231 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: indtime Excluded instruments: cons1 ------------------------------------------------------------------------------ . eststo m8a_c7 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 7.2313659 . ivreg2 logpgp95 lat_abst (avexpr=cons1) indtime, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons1 | .2200538 .0839714 2.62 0.011 .0518389 .3882687 lat_abst | 2.948684 1.208247 2.44 0.018 .5282738 5.369094 indtime | .0053731 .0027487 1.95 0.056 -.0001333 .0108796 _cons | 4.721757 .4696673 10.05 0.000 3.780901 5.662614 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 56) = 6.87 Prob > F = 0.0113 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 56) = 6.87 Prob > F = 0.0113 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 56) P-val | SW Chi-sq( 1) P-val | SW F( 1, 56) avexpr | 6.87 0.0113 | 7.36 0.0067 | 6.87 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=5.64 P-val=0.0176 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.95 Kleibergen-Paap Wald rk F statistic 6.87 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,56)= 6.99 P-val=0.0106 Anderson-Rubin Wald test Chi-sq(1)= 7.49 P-val=0.0062 Stock-Wright LM S statistic Chi-sq(1)= 6.81 P-val=0.0090 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 3, 56) = 23.77 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.6118 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9943 Residual SS = 22.46473424 Root MSE = .6119 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .610782 .1686147 3.62 0.000 .2803032 .9412608 lat_abst | -.4047042 .7769185 -0.52 0.602 -1.927436 1.118028 indtime | .0052383 .0012879 4.07 0.000 .002714 .0077625 _cons | 3.665059 .9538504 3.84 0.000 1.795546 5.534571 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 5.640 Chi-sq(1) P-val = 0.0176 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.951 (Kleibergen-Paap rk Wald F statistic): 6.867 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst indtime Excluded instruments: cons1 ------------------------------------------------------------------------------ . eststo m8a_c8 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 6.8674445 . ivreg2 logpgp95 (avexpr=democ1) indtime, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ1 | .1911102 .0542619 3.52 0.001 .0824105 .29981 indtime | .0079728 .0026635 2.99 0.004 .0026371 .0133085 _cons | 5.240737 .35142 14.91 0.000 4.536758 5.944716 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 56) = 12.40 Prob > F = 0.0009 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 56) = 12.40 Prob > F = 0.0009 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 56) P-val | SW Chi-sq( 1) P-val | SW F( 1, 56) avexpr | 12.40 0.0009 | 13.07 0.0003 | 12.40 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=7.01 P-val=0.0081 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 15.00 Kleibergen-Paap Wald rk F statistic 12.40 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,56)= 9.78 P-val=0.0028 Anderson-Rubin Wald test Chi-sq(1)= 10.30 P-val=0.0013 Stock-Wright LM S statistic Chi-sq(1)= 7.61 P-val=0.0058 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 59 F( 2, 56) = 38.54 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.6509 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9948 Residual SS = 20.2022892 Root MSE = .5852 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .5485994 .1332387 4.12 0.000 .2874563 .8097424 indtime | .0051045 .0014108 3.62 0.000 .0023393 .0078696 _cons | 4.001362 .797594 5.02 0.000 2.438106 5.564618 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 7.010 Chi-sq(1) P-val = 0.0081 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 15.004 (Kleibergen-Paap rk Wald F statistic): 12.404 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: indtime Excluded instruments: democ1 ------------------------------------------------------------------------------ . eststo m8a_c9 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 12.404441 . ivreg2 logpgp95 lat_abst (avexpr=democ1) indtime, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ1 | .1721958 .052043 3.31 0.002 .0678993 .2764922 lat_abst | 2.486336 1.235157 2.01 0.049 .0110255 4.961646 indtime | .0056071 .0026076 2.15 0.036 .0003813 .0108329 _cons | 5.064649 .3808601 13.30 0.000 4.301388 5.82791 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 55) = 10.95 Prob > F = 0.0017 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 55) = 10.95 Prob > F = 0.0017 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 55) P-val | SW Chi-sq( 1) P-val | SW F( 1, 55) avexpr | 10.95 0.0017 | 11.74 0.0006 | 10.95 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=6.95 P-val=0.0084 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 12.04 Kleibergen-Paap Wald rk F statistic 10.95 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,55)= 7.56 P-val=0.0081 Anderson-Rubin Wald test Chi-sq(1)= 8.11 P-val=0.0044 Stock-Wright LM S statistic Chi-sq(1)= 6.70 P-val=0.0097 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 59 F( 3, 55) = 25.55 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.6482 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9947 Residual SS = 20.35713664 Root MSE = .5874 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .5549912 .1519188 3.65 0.000 .2572359 .8527465 lat_abst | -.1605732 .6889432 -0.23 0.816 -1.510877 1.189731 indtime | .0052063 .0012499 4.17 0.000 .0027566 .007656 _cons | 3.979236 .8597334 4.63 0.000 2.29419 5.664283 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 6.952 Chi-sq(1) P-val = 0.0084 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 12.044 (Kleibergen-Paap rk Wald F statistic): 10.948 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst indtime Excluded instruments: democ1 ------------------------------------------------------------------------------ . eststo m8a_c10 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 10.947641 . . //── Panel C: 2 instruments per regression -> Hansen J meaningful ── . di _newline "*** Panel C: alt instrument + logem4 => Hansen J overid test *** > " *** Panel C: alt instrument + logem4 => Hansen J overid test *** . di "*** Modern replacement for AJR's hausman consistent vs efficient ***" *** Modern replacement for AJR's hausman consistent vs efficient *** . . ivreg2 logpgp95 (avexpr=euro1900 logem4), gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 63 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | .0217044 .0062814 3.46 0.001 .0091397 .0342692 logem4 | -.3714656 .1726322 -2.15 0.035 -.7167814 -.0261498 _cons | 7.894059 .8852884 8.92 0.000 6.123218 9.664899 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 60) = 24.84 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 60) = 24.84 Prob > F = 0.0000 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 60) P-val | SW Chi-sq( 2) P-val | SW F( 2, 60) avexpr | 24.84 0.0000 | 52.16 0.0000 | 24.84 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=9.11 P-val=0.0105 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 17.41 Kleibergen-Paap Wald rk F statistic 24.84 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,60)= 93.20 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(2)= 195.72 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 18.64 P-val=0.0001 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 63 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 63 F( 1, 61) = 41.22 Prob > F = 0.0000 Total (centered) SS = 66.68940084 Centered R2 = 0.2637 Total (uncentered) SS = 4139.690708 Uncentered R2 = 0.9881 Residual SS = 49.10154166 Root MSE = .8828 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .8871361 .1359639 6.52 0.000 .6206518 1.15362 _cons | 2.276075 .9078169 2.51 0.012 .496787 4.055364 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 9.107 Chi-sq(2) P-val = 0.0105 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 17.411 (Kleibergen-Paap rk Wald F statistic): 24.837 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.135 Chi-sq(1) P-val = 0.7137 ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: euro1900 logem4 ------------------------------------------------------------------------------ . eststo m8c_c1 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 24.836616 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = .13459107 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .71371856 . ivreg2 logpgp95 lat_abst (avexpr=euro1900 logem4), gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 63 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | .0211563 .0065227 3.24 0.002 .0081044 .0342081 logem4 | -.3684413 .1802196 -2.04 0.045 -.7290598 -.0078228 lat_abst | .2004581 1.350646 0.15 0.883 -2.502178 2.903094 _cons | 7.853131 1.002697 7.83 0.000 5.846738 9.859524 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 59) = 13.82 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 59) = 13.82 Prob > F = 0.0000 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 59) P-val | SW Chi-sq( 2) P-val | SW F( 2, 59) avexpr | 13.82 0.0000 | 29.52 0.0000 | 13.82 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=9.06 P-val=0.0108 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 10.52 Kleibergen-Paap Wald rk F statistic 13.82 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,59)= 42.91 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(2)= 91.63 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 20.58 P-val=0.0000 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 63 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 63 F( 2, 60) = 19.21 Prob > F = 0.0000 Total (centered) SS = 66.68940084 Centered R2 = 0.1896 Total (uncentered) SS = 4139.690708 Uncentered R2 = 0.9869 Residual SS = 54.04248125 Root MSE = .9262 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .9364342 .1637601 5.72 0.000 .6154704 1.257398 lat_abst | -.554251 .9358736 -0.59 0.554 -2.38853 1.280028 _cons | 2.052211 1.015904 2.02 0.043 .0610766 4.043346 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 9.065 Chi-sq(2) P-val = 0.0108 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 10.517 (Kleibergen-Paap rk Wald F statistic): 13.822 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.067 Chi-sq(1) P-val = 0.7961 ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: euro1900 logem4 ------------------------------------------------------------------------------ . eststo m8c_c2 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 13.822108 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = .06676773 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .79610244 . ivreg2 logpgp95 (avexpr=cons00a logem4), gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons00a | .1783699 .093337 1.91 0.061 -.0085342 .365274 logem4 | -.4421255 .1792512 -2.47 0.017 -.8010698 -.0831811 _cons | 8.148147 .9609591 8.48 0.000 6.223859 10.07243 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 57) = 9.36 Prob > F = 0.0003 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 57) = 9.36 Prob > F = 0.0003 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 57) P-val | SW Chi-sq( 2) P-val | SW F( 2, 57) avexpr | 9.36 0.0003 | 19.71 0.0001 | 9.36 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=8.12 P-val=0.0172 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 12.10 Kleibergen-Paap Wald rk F statistic 9.36 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,57)= 26.86 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(2)= 56.54 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 14.94 P-val=0.0006 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 60 F( 1, 58) = 32.61 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.3686 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9907 Residual SS = 36.54151899 Root MSE = .7804 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7659635 .1318856 5.81 0.000 .5074724 1.024455 _cons | 3.066106 .884541 3.47 0.001 1.332437 4.799774 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 8.125 Chi-sq(2) P-val = 0.0172 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 12.098 (Kleibergen-Paap rk Wald F statistic): 9.361 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 1.564 Chi-sq(1) P-val = 0.2111 ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: cons00a logem4 ------------------------------------------------------------------------------ . eststo m8c_c3 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 9.3607979 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = 1.5640284 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .21107635 . ivreg2 logpgp95 lat_abst (avexpr=cons00a logem4), gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons00a | .1524377 .0884134 1.72 0.090 -.0246756 .3295511 logem4 | -.3988852 .2024205 -1.97 0.054 -.8043823 .0066118 lat_abst | 1.469523 1.368812 1.07 0.288 -1.272536 4.211582 _cons | 7.743954 1.191853 6.50 0.000 5.356386 10.13152 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 56) = 6.25 Prob > F = 0.0035 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 56) = 6.25 Prob > F = 0.0035 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 56) P-val | SW Chi-sq( 2) P-val | SW F( 2, 56) avexpr | 6.25 0.0035 | 13.40 0.0012 | 6.25 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=9.38 P-val=0.0092 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.26 Kleibergen-Paap Wald rk F statistic 6.25 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,56)= 12.56 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(2)= 26.91 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 11.86 P-val=0.0027 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 60 F( 2, 57) = 16.88 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.3407 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9902 Residual SS = 38.15935856 Root MSE = .7975 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7872759 .1740787 4.52 0.000 .4460878 1.128464 lat_abst | -.2655375 .9348945 -0.28 0.776 -2.097897 1.566822 _cons | 2.973079 1.05221 2.83 0.005 .9107852 5.035374 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 9.379 Chi-sq(2) P-val = 0.0092 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.262 (Kleibergen-Paap rk Wald F statistic): 6.252 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 1.441 Chi-sq(1) P-val = 0.2300 ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: cons00a logem4 ------------------------------------------------------------------------------ . eststo m8c_c4 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 6.2515915 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = 1.4411069 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .22996031 . ivreg2 logpgp95 (avexpr=democ00a logem4), gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ00a | .1453791 .0652184 2.23 0.030 .014731 .2760272 logem4 | -.4179368 .1839089 -2.27 0.027 -.7863506 -.0495229 _cons | 8.224169 .9300581 8.84 0.000 6.361039 10.0873 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 56) = 12.79 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 56) = 12.79 Prob > F = 0.0000 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 56) P-val | SW Chi-sq( 2) P-val | SW F( 2, 56) avexpr | 12.79 0.0000 | 26.95 0.0000 | 12.79 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=8.06 P-val=0.0177 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 13.26 Kleibergen-Paap Wald rk F statistic 12.79 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,56)= 29.63 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(2)= 62.43 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 14.94 P-val=0.0006 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 2 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 59 F( 1, 57) = 40.03 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.4050 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9911 Residual SS = 34.43048334 Root MSE = .7639 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7515984 .1167576 6.44 0.000 .5227577 .9804391 _cons | 3.143008 .7916208 3.97 0.000 1.59146 4.694556 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 8.064 Chi-sq(2) P-val = 0.0177 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 13.262 (Kleibergen-Paap rk Wald F statistic): 12.789 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 1.343 Chi-sq(1) P-val = 0.2465 ------------------------------------------------------------------------------ Instrumented: avexpr Excluded instruments: democ00a logem4 ------------------------------------------------------------------------------ . eststo m8c_c5 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 12.788955 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = 1.3428061 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .24653971 . ivreg2 logpgp95 lat_abst (avexpr=democ00a logem4), gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ00a | .1272813 .0626539 2.03 0.047 .0017201 .2528424 logem4 | -.3952617 .1997258 -1.98 0.053 -.7955212 .0049977 lat_abst | 1.024564 1.347658 0.76 0.450 -1.676203 3.72533 _cons | 7.965957 1.117984 7.13 0.000 5.725468 10.20645 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 55) = 8.09 Prob > F = 0.0008 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 55) = 8.09 Prob > F = 0.0008 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 55) P-val | SW Chi-sq( 2) P-val | SW F( 2, 55) avexpr | 8.09 0.0008 | 17.36 0.0002 | 8.09 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=8.38 P-val=0.0152 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.98 Kleibergen-Paap Wald rk F statistic 8.09 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,55)= 12.23 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(2)= 26.23 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 12.30 P-val=0.0021 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 59 F( 2, 56) = 19.62 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.3900 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9908 Residual SS = 35.30110792 Root MSE = .7735 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .7642519 .1521254 5.02 0.000 .4660916 1.062412 lat_abst | -.1273877 .8691939 -0.15 0.883 -1.830976 1.576201 _cons | 3.081699 .9309672 3.31 0.001 1.257037 4.906361 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 8.376 Chi-sq(2) P-val = 0.0152 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.980 (Kleibergen-Paap rk Wald F statistic): 8.093 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 1.262 Chi-sq(1) P-val = 0.2613 ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst Excluded instruments: democ00a logem4 ------------------------------------------------------------------------------ . eststo m8c_c6 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 8.0926767 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = 1.2617379 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .26132238 . ivreg2 logpgp95 (avexpr=cons1 logem4) indtime, gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons1 | .1528227 .0930742 1.64 0.106 -.0336273 .3392726 logem4 | -.4802481 .1676521 -2.86 0.006 -.8160956 -.1444005 indtime | .0030258 .0030418 0.99 0.324 -.0030678 .0091193 _cons | 7.937807 1.099418 7.22 0.000 5.735409 10.14021 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 56) = 8.39 Prob > F = 0.0007 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 56) = 8.39 Prob > F = 0.0007 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 56) P-val | SW Chi-sq( 2) P-val | SW F( 2, 56) avexpr | 8.39 0.0007 | 17.97 0.0001 | 8.39 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=7.24 P-val=0.0267 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 9.97 Kleibergen-Paap Wald rk F statistic 8.39 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,56)= 13.89 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(2)= 29.76 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 12.30 P-val=0.0021 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 60 F( 2, 57) = 37.12 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.5625 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9935 Residual SS = 25.31843357 Root MSE = .6496 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6642314 .1058914 6.27 0.000 .456688 .8717747 indtime | .0045172 .0013355 3.38 0.001 .0018998 .0071347 _cons | 3.317316 .6609999 5.02 0.000 2.02178 4.612852 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 7.244 Chi-sq(2) P-val = 0.0267 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 9.968 (Kleibergen-Paap rk Wald F statistic): 8.386 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.324 Chi-sq(1) P-val = 0.5690 ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: indtime Excluded instruments: cons1 logem4 ------------------------------------------------------------------------------ . eststo m8c_c7 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 8.3862785 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = .32443789 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .56895276 . ivreg2 logpgp95 lat_abst (avexpr=cons1 logem4) indtime, gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons1 | .1450392 .0872727 1.66 0.102 -.0298593 .3199377 logem4 | -.418899 .1812607 -2.31 0.025 -.7821535 -.0556445 lat_abst | 2.028964 1.221623 1.66 0.102 -.4192235 4.477152 indtime | .0017441 .0028876 0.60 0.548 -.0040428 .007531 _cons | 7.432782 1.240943 5.99 0.000 4.945877 9.919688 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 55) = 6.51 Prob > F = 0.0029 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 55) = 6.51 Prob > F = 0.0029 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 55) P-val | SW Chi-sq( 2) P-val | SW F( 2, 55) avexpr | 6.51 0.0029 | 14.21 0.0008 | 6.51 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=6.53 P-val=0.0383 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 7.45 Kleibergen-Paap Wald rk F statistic 6.51 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,55)= 10.06 P-val=0.0002 Anderson-Rubin Wald test Chi-sq(2)= 21.94 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 9.87 P-val=0.0072 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 5 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 60 F( 3, 56) = 23.30 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.5369 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9932 Residual SS = 26.80422 Root MSE = .6684 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6958501 .1197122 5.81 0.000 .4612185 .9304817 lat_abst | -.6854957 .6724336 -1.02 0.308 -2.003441 .6324499 indtime | .004922 .0013447 3.66 0.000 .0022863 .0075576 _cons | 3.197201 .7152452 4.47 0.000 1.795346 4.599056 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 6.526 Chi-sq(2) P-val = 0.0383 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 7.454 (Kleibergen-Paap rk Wald F statistic): 6.511 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.355 Chi-sq(1) P-val = 0.5513 ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst indtime Excluded instruments: cons1 logem4 ------------------------------------------------------------------------------ . eststo m8c_c8 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 6.5112065 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = .35506032 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .55126249 . ivreg2 logpgp95 (avexpr=democ1 logem4) indtime, gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ1 | .1288825 .058836 2.19 0.033 .0109725 .2467925 logem4 | -.4158372 .1638594 -2.54 0.014 -.7442187 -.0874557 indtime | .0037429 .0028711 1.30 0.198 -.0020109 .0094966 _cons | 7.750736 1.002234 7.73 0.000 5.742214 9.759258 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 55) = 10.94 Prob > F = 0.0001 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 55) = 10.94 Prob > F = 0.0001 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 55) P-val | SW Chi-sq( 2) P-val | SW F( 2, 55) avexpr | 10.94 0.0001 | 23.46 0.0000 | 10.94 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=8.00 P-val=0.0183 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 11.42 Kleibergen-Paap Wald rk F statistic 10.94 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,55)= 14.09 P-val=0.0000 Anderson-Rubin Wald test Chi-sq(2)= 30.24 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 12.01 P-val=0.0025 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 59 F( 2, 56) = 43.16 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.5899 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9938 Residual SS = 23.7315406 Root MSE = .6342 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6408883 .0971331 6.60 0.000 .4505108 .8312657 indtime | .0044535 .0013143 3.39 0.001 .0018775 .0070295 _cons | 3.46616 .6010726 5.77 0.000 2.28808 4.644241 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 8.002 Chi-sq(2) P-val = 0.0183 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 11.415 (Kleibergen-Paap rk Wald F statistic): 10.937 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.728 Chi-sq(1) P-val = 0.3934 ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: indtime Excluded instruments: democ1 logem4 ------------------------------------------------------------------------------ . eststo m8c_c9 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 10.937013 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = .7284727 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .39337869 . ivreg2 logpgp95 lat_abst (avexpr=democ1 logem4) indtime, gmm2s robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ1 | .1229436 .0561493 2.19 0.033 .010371 .2355162 logem4 | -.3658863 .1721389 -2.13 0.038 -.7110041 -.0207686 lat_abst | 1.76326 1.213312 1.45 0.152 -.6692846 4.195804 indtime | .0025733 .0027699 0.93 0.357 -.0029801 .0081267 _cons | 7.324353 1.114044 6.57 0.000 5.090829 9.557878 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 54) = 8.93 Prob > F = 0.0004 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 2, 54) = 8.93 Prob > F = 0.0004 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 54) P-val | SW Chi-sq( 2) P-val | SW F( 2, 54) avexpr | 8.93 0.0004 | 19.50 0.0001 | 8.93 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(2)=7.29 P-val=0.0261 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 8.79 Kleibergen-Paap Wald rk F statistic 8.93 Stock-Yogo weak ID test critical values for K1=1 and L1=2: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,54)= 10.48 P-val=0.0001 Anderson-Rubin Wald test Chi-sq(2)= 22.89 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(2)= 9.37 P-val=0.0093 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 5 Number of excluded instruments L1 = 2 2-Step GMM estimation --------------------- Estimates efficient for arbitrary heteroskedasticity Statistics robust to heteroskedasticity Number of obs = 59 F( 3, 55) = 27.44 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.5743 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9936 Residual SS = 24.63754185 Root MSE = .6462 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .6631673 .1082934 6.12 0.000 .4509161 .8754185 lat_abst | -.4876289 .6113039 -0.80 0.425 -1.685762 .7105046 indtime | .0047508 .0012869 3.69 0.000 .0022286 .007273 _cons | 3.381372 .641101 5.27 0.000 2.124837 4.637907 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 7.292 Chi-sq(2) P-val = 0.0261 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 8.786 (Kleibergen-Paap rk Wald F statistic): 8.925 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.759 Chi-sq(1) P-val = 0.3836 ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst indtime Excluded instruments: democ1 logem4 ------------------------------------------------------------------------------ . eststo m8c_c10 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 8.9251519 . estadd scalar hansenJ = e(j) added scalar: e(hansenJ) = .75928175 . estadd scalar hansenP = e(jp) added scalar: e(hansenP) = .38355339 . . //── Panel D: include logem4 as exogenous control in 2nd stage ─── . di _newline "*** Panel D: logem4 as exogenous control (relaxes exclusion) *** > " *** Panel D: logem4 as exogenous control (relaxes exclusion) *** . . ivreg2 logpgp95 (avexpr=euro1900) logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 63 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | .0217044 .0062814 3.46 0.001 .0091397 .0342692 logem4 | -.3714656 .1726322 -2.15 0.035 -.7167814 -.0261498 _cons | 7.894059 .8852884 8.92 0.000 6.123218 9.664899 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 60) = 11.94 Prob > F = 0.0010 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 60) = 11.94 Prob > F = 0.0010 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 60) P-val | SW Chi-sq( 1) P-val | SW F( 1, 60) avexpr | 11.94 0.0010 | 12.54 0.0004 | 11.94 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=6.31 P-val=0.0120 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 9.34 Kleibergen-Paap Wald rk F statistic 11.94 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,60)= 15.78 P-val=0.0002 Anderson-Rubin Wald test Chi-sq(1)= 16.57 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 12.18 P-val=0.0005 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 63 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 63 F( 2, 60) = 25.26 Prob > F = 0.0000 Total (centered) SS = 66.68940084 Centered R2 = 0.3699 Total (uncentered) SS = 4139.690708 Uncentered R2 = 0.9898 Residual SS = 42.02416866 Root MSE = .8167 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .8135304 .2261542 3.60 0.000 .3702764 1.256784 logem4 | -.0667628 .1707295 -0.39 0.696 -.4013864 .2678608 _cons | 3.061997 2.187563 1.40 0.162 -1.225547 7.349541 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 6.313 Chi-sq(1) P-val = 0.0120 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 9.341 (Kleibergen-Paap rk Wald F statistic): 11.939 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: logem4 Excluded instruments: euro1900 ------------------------------------------------------------------------------ . eststo m8d_c1 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 11.939321 . ivreg2 logpgp95 lat_abst (avexpr=euro1900) logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 63 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- euro1900 | .0211563 .0065227 3.24 0.002 .0081044 .0342081 lat_abst | .2004581 1.350646 0.15 0.883 -2.502178 2.903094 logem4 | -.3684413 .1802196 -2.04 0.045 -.7290598 -.0078228 _cons | 7.853131 1.002697 7.83 0.000 5.846738 9.859524 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 59) = 10.52 Prob > F = 0.0019 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 59) = 10.52 Prob > F = 0.0019 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 59) P-val | SW Chi-sq( 1) P-val | SW F( 1, 59) avexpr | 10.52 0.0019 | 11.23 0.0008 | 10.52 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=6.75 P-val=0.0094 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 6.58 Kleibergen-Paap Wald rk F statistic 10.52 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,59)= 15.64 P-val=0.0002 Anderson-Rubin Wald test Chi-sq(1)= 16.70 P-val=0.0000 Stock-Wright LM S statistic Chi-sq(1)= 15.79 P-val=0.0001 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 63 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 63 F( 3, 59) = 14.85 Prob > F = 0.0000 Total (centered) SS = 66.68940084 Centered R2 = 0.2798 Total (uncentered) SS = 4139.690708 Uncentered R2 = 0.9884 Residual SS = 48.02668752 Root MSE = .8731 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .8793613 .2598602 3.38 0.001 .3700446 1.388678 lat_abst | -.5224739 .8809239 -0.59 0.553 -2.249053 1.204105 logem4 | -.0501914 .1839298 -0.27 0.785 -.4106872 .3103045 _cons | 2.648999 2.39555 1.11 0.269 -2.046193 7.344192 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 6.751 Chi-sq(1) P-val = 0.0094 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 6.583 (Kleibergen-Paap rk Wald F statistic): 10.520 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst logem4 Excluded instruments: euro1900 ------------------------------------------------------------------------------ . eststo m8d_c2 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 10.520174 . ivreg2 logpgp95 (avexpr=cons00a) logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons00a | .1783699 .093337 1.91 0.061 -.0085342 .365274 logem4 | -.4421255 .1792512 -2.47 0.017 -.8010698 -.0831811 _cons | 8.148147 .9609591 8.48 0.000 6.223859 10.07243 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 57) = 3.65 Prob > F = 0.0610 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 57) = 3.65 Prob > F = 0.0610 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 57) P-val | SW Chi-sq( 1) P-val | SW F( 1, 57) avexpr | 3.65 0.0610 | 3.84 0.0499 | 3.65 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.72 P-val=0.0538 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.66 Kleibergen-Paap Wald rk F statistic 3.65 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,57)= 1.19 P-val=0.2797 Anderson-Rubin Wald test Chi-sq(1)= 1.25 P-val=0.2628 Stock-Wright LM S statistic Chi-sq(1)= 1.49 P-val=0.2226 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 2, 57) = 40.77 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.6391 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9947 Residual SS = 20.88404913 Root MSE = .59 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4538902 .2776503 1.63 0.102 -.0902944 .9980749 logem4 | -.2532125 .1663107 -1.52 0.128 -.5791755 .0727505 _cons | 6.268378 2.542251 2.47 0.014 1.285656 11.2511 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.717 Chi-sq(1) P-val = 0.0538 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.664 (Kleibergen-Paap rk Wald F statistic): 3.652 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: logem4 Excluded instruments: cons00a ------------------------------------------------------------------------------ . eststo m8d_c3 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 3.6520399 . ivreg2 logpgp95 lat_abst (avexpr=cons00a) logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons00a | .1524377 .0884134 1.72 0.090 -.0246756 .3295511 lat_abst | 1.469523 1.368812 1.07 0.288 -1.272536 4.211582 logem4 | -.3988852 .2024205 -1.97 0.054 -.8043823 .0066118 _cons | 7.743954 1.191853 6.50 0.000 5.356386 10.13152 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 56) = 2.97 Prob > F = 0.0902 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 56) = 2.97 Prob > F = 0.0902 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 56) P-val | SW Chi-sq( 1) P-val | SW F( 1, 56) avexpr | 2.97 0.0902 | 3.19 0.0743 | 2.97 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.34 P-val=0.0678 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 2.50 Kleibergen-Paap Wald rk F statistic 2.97 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,56)= 0.59 P-val=0.4441 Anderson-Rubin Wald test Chi-sq(1)= 0.64 P-val=0.4250 Stock-Wright LM S statistic Chi-sq(1)= 0.78 P-val=0.3773 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 3, 56) = 36.97 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.6509 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9948 Residual SS = 20.20223319 Root MSE = .5803 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4160094 .3823502 1.09 0.277 -.3333832 1.165402 lat_abst | .3828946 1.19083 0.32 0.748 -1.95109 2.716879 logem4 | -.2586941 .1790652 -1.44 0.149 -.6096553 .0922672 _cons | 6.471721 3.086671 2.10 0.036 .4219575 12.52149 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.336 Chi-sq(1) P-val = 0.0678 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 2.498 (Kleibergen-Paap rk Wald F statistic): 2.973 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst logem4 Excluded instruments: cons00a ------------------------------------------------------------------------------ . eststo m8d_c4 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.9726827 . ivreg2 logpgp95 (avexpr=democ00a) logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ00a | .1453791 .0652184 2.23 0.030 .014731 .2760272 logem4 | -.4179368 .1839089 -2.27 0.027 -.7863506 -.0495229 _cons | 8.224169 .9300581 8.84 0.000 6.361039 10.0873 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 56) = 4.97 Prob > F = 0.0298 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 56) = 4.97 Prob > F = 0.0298 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 56) P-val | SW Chi-sq( 1) P-val | SW F( 1, 56) avexpr | 4.97 0.0298 | 5.24 0.0221 | 4.97 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=4.20 P-val=0.0404 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 4.87 Kleibergen-Paap Wald rk F statistic 4.97 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,56)= 4.61 P-val=0.0361 Anderson-Rubin Wald test Chi-sq(1)= 4.86 P-val=0.0275 Stock-Wright LM S statistic Chi-sq(1)= 3.71 P-val=0.0540 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 3 Number of endogenous regressors K1 = 1 Number of instruments L = 3 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 59 F( 2, 56) = 44.21 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.6201 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9943 Residual SS = 21.98362627 Root MSE = .6104 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .5148407 .1742681 2.95 0.003 .1732815 .8563999 logem4 | -.2138156 .1305395 -1.64 0.101 -.4696683 .0420371 _cons | 5.67833 1.715654 3.31 0.001 2.315711 9.04095 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 4.202 Chi-sq(1) P-val = 0.0404 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 4.874 (Kleibergen-Paap rk Wald F statistic): 4.969 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: logem4 Excluded instruments: democ00a ------------------------------------------------------------------------------ . eststo m8d_c5 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 4.9689425 . ivreg2 logpgp95 lat_abst (avexpr=democ00a) logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ00a | .1272813 .0626539 2.03 0.047 .0017201 .2528424 lat_abst | 1.024564 1.347658 0.76 0.450 -1.676203 3.72533 logem4 | -.3952617 .1997258 -1.98 0.053 -.7955212 .0049977 _cons | 7.965957 1.117984 7.13 0.000 5.725468 10.20645 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 55) = 4.13 Prob > F = 0.0470 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 55) = 4.13 Prob > F = 0.0470 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 55) P-val | SW Chi-sq( 1) P-val | SW F( 1, 55) avexpr | 4.13 0.0470 | 4.43 0.0354 | 4.13 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.84 P-val=0.0500 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.21 Kleibergen-Paap Wald rk F statistic 4.13 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,55)= 2.27 P-val=0.1374 Anderson-Rubin Wald test Chi-sq(1)= 2.44 P-val=0.1184 Stock-Wright LM S statistic Chi-sq(1)= 1.99 P-val=0.1588 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 59 F( 3, 55) = 36.95 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.6359 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9945 Residual SS = 21.07287934 Root MSE = .5976 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4810908 .2478787 1.94 0.052 -.0047425 .9669242 lat_abst | .2777708 .8874108 0.31 0.754 -1.461522 2.017064 logem4 | -.2217734 .139577 -1.59 0.112 -.4953393 .0517924 _cons | 5.885891 2.10198 2.80 0.005 1.766086 10.0057 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.842 Chi-sq(1) P-val = 0.0500 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.214 (Kleibergen-Paap rk Wald F statistic): 4.127 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst logem4 Excluded instruments: democ00a ------------------------------------------------------------------------------ . eststo m8d_c6 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 4.1269884 . ivreg2 logpgp95 (avexpr=cons1) indtime logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons1 | .1528227 .0930742 1.64 0.106 -.0336273 .3392726 indtime | .0030258 .0030418 0.99 0.324 -.0030678 .0091193 logem4 | -.4802481 .1676521 -2.86 0.006 -.8160956 -.1444005 _cons | 7.937807 1.099418 7.22 0.000 5.735409 10.14021 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 56) = 2.70 Prob > F = 0.1062 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 56) = 2.70 Prob > F = 0.1062 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 56) P-val | SW Chi-sq( 1) P-val | SW F( 1, 56) avexpr | 2.70 0.1062 | 2.89 0.0892 | 2.70 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=2.16 P-val=0.1419 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.56 Kleibergen-Paap Wald rk F statistic 2.70 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,56)= 2.04 P-val=0.1586 Anderson-Rubin Wald test Chi-sq(1)= 2.19 P-val=0.1392 Stock-Wright LM S statistic Chi-sq(1)= 1.98 P-val=0.1595 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 3, 56) = 48.54 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.6943 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9955 Residual SS = 17.69035611 Root MSE = .543 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4848605 .273642 1.77 0.076 -.051468 1.021189 indtime | .0044154 .0012293 3.59 0.000 .002006 .0068248 logem4 | -.1363265 .2026112 -0.67 0.501 -.5334373 .2607842 _cons | 5.122938 2.737563 1.87 0.061 -.242587 10.48846 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 2.158 Chi-sq(1) P-val = 0.1419 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.559 (Kleibergen-Paap rk Wald F statistic): 2.696 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: indtime logem4 Excluded instruments: cons1 ------------------------------------------------------------------------------ . eststo m8d_c7 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.6959832 . ivreg2 logpgp95 lat_abst (avexpr=cons1) indtime logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 60 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- cons1 | .1450392 .0872727 1.66 0.102 -.0298593 .3199377 lat_abst | 2.028964 1.221623 1.66 0.102 -.4192235 4.477152 indtime | .0017441 .0028876 0.60 0.548 -.0040428 .007531 logem4 | -.418899 .1812607 -2.31 0.025 -.7821535 -.0556445 _cons | 7.432782 1.240943 5.99 0.000 4.945877 9.919688 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 55) = 2.76 Prob > F = 0.1022 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 55) = 2.76 Prob > F = 0.1022 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 55) P-val | SW Chi-sq( 1) P-val | SW F( 1, 55) avexpr | 2.76 0.1022 | 3.01 0.0826 | 2.76 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=2.27 P-val=0.1323 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 3.25 Kleibergen-Paap Wald rk F statistic 2.76 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,55)= 2.04 P-val=0.1590 Anderson-Rubin Wald test Chi-sq(1)= 2.22 P-val=0.1359 Stock-Wright LM S statistic Chi-sq(1)= 2.06 P-val=0.1514 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 60 Number of regressors K = 5 Number of endogenous regressors K1 = 1 Number of instruments L = 5 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 60 F( 4, 55) = 35.70 Prob > F = 0.0000 Total (centered) SS = 57.87455605 Centered R2 = 0.6921 Total (uncentered) SS = 3913.363303 Uncentered R2 = 0.9954 Residual SS = 17.81927916 Root MSE = .545 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4942863 .2888669 1.71 0.087 -.0718825 1.060455 lat_abst | -.3754982 .7175389 -0.52 0.601 -1.781849 1.030852 indtime | .004624 .0012659 3.65 0.000 .0021429 .0071052 logem4 | -.1431536 .1981935 -0.72 0.470 -.5316058 .2452986 _cons | 5.141583 2.752619 1.87 0.062 -.2534505 10.53662 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 2.265 Chi-sq(1) P-val = 0.1323 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 3.248 (Kleibergen-Paap rk Wald F statistic): 2.762 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst indtime logem4 Excluded instruments: cons1 ------------------------------------------------------------------------------ . eststo m8d_c8 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 2.7619361 . ivreg2 logpgp95 (avexpr=democ1) indtime logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ1 | .1288825 .058836 2.19 0.033 .0109725 .2467925 indtime | .0037429 .0028711 1.30 0.198 -.0020109 .0094966 logem4 | -.4158372 .1638594 -2.54 0.014 -.7442187 -.0874557 _cons | 7.750736 1.002234 7.73 0.000 5.742214 9.759258 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 55) = 4.80 Prob > F = 0.0327 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 55) = 4.80 Prob > F = 0.0327 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 55) P-val | SW Chi-sq( 1) P-val | SW F( 1, 55) avexpr | 4.80 0.0327 | 5.15 0.0233 | 4.80 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=2.94 P-val=0.0866 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 5.88 Kleibergen-Paap Wald rk F statistic 4.80 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,55)= 2.49 P-val=0.1204 Anderson-Rubin Wald test Chi-sq(1)= 2.67 P-val=0.1023 Stock-Wright LM S statistic Chi-sq(1)= 2.40 P-val=0.1211 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 4 Number of endogenous regressors K1 = 1 Number of instruments L = 4 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 59 F( 3, 55) = 56.30 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.7183 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9958 Residual SS = 16.29951331 Root MSE = .5256 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .4023161 .2222427 1.81 0.070 -.0332716 .8379038 indtime | .0043705 .0012256 3.57 0.000 .0019684 .0067726 logem4 | -.1868178 .1674541 -1.12 0.265 -.5150218 .1413863 _cons | 5.895629 2.247931 2.62 0.009 1.489765 10.30149 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 2.936 Chi-sq(1) P-val = 0.0866 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 5.875 (Kleibergen-Paap rk Wald F statistic): 4.798 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: indtime logem4 Excluded instruments: democ1 ------------------------------------------------------------------------------ . eststo m8d_c9 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 4.7984518 . ivreg2 logpgp95 lat_abst (avexpr=democ1) indtime logem4, robust first First-stage regressions ----------------------- First-stage regression of avexpr: Statistics robust to heteroskedasticity Number of obs = 59 ------------------------------------------------------------------------------ | Robust avexpr | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- democ1 | .1229436 .0561493 2.19 0.033 .010371 .2355162 lat_abst | 1.76326 1.213312 1.45 0.152 -.6692846 4.195804 indtime | .0025733 .0027699 0.93 0.357 -.0029801 .0081267 logem4 | -.3658863 .1721389 -2.13 0.038 -.7110041 -.0207686 _cons | 7.324353 1.114044 6.57 0.000 5.090829 9.557878 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 54) = 4.79 Prob > F = 0.0329 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 54) = 4.79 Prob > F = 0.0329 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 54) P-val | SW Chi-sq( 1) P-val | SW F( 1, 54) avexpr | 4.79 0.0329 | 5.24 0.0221 | 4.79 NB: first-stage test statistics heteroskedasticity-robust Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for i.i.d. errors only. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.04 P-val=0.0812 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 5.36 Kleibergen-Paap Wald rk F statistic 4.79 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,54)= 2.44 P-val=0.1243 Anderson-Rubin Wald test Chi-sq(1)= 2.66 P-val=0.1027 Stock-Wright LM S statistic Chi-sq(1)= 2.48 P-val=0.1150 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity-robust Number of observations N = 59 Number of regressors K = 5 Number of endogenous regressors K1 = 1 Number of instruments L = 5 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity Number of obs = 59 F( 4, 54) = 41.11 Prob > F = 0.0000 Total (centered) SS = 57.86984178 Centered R2 = 0.7181 Total (uncentered) SS = 3850.192092 Uncentered R2 = 0.9958 Residual SS = 16.31369337 Root MSE = .5258 ------------------------------------------------------------------------------ | Robust logpgp95 | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- avexpr | .406674 .2310625 1.76 0.078 -.0462002 .8595481 lat_abst | -.1667564 .5991364 -0.28 0.781 -1.341042 1.007529 indtime | .0044648 .0012012 3.72 0.000 .0021105 .0068191 logem4 | -.1897296 .1649019 -1.15 0.250 -.5129314 .1334722 _cons | 5.902176 2.250163 2.62 0.009 1.491938 10.31241 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.041 Chi-sq(1) P-val = 0.0812 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 5.358 (Kleibergen-Paap rk Wald F statistic): 4.794 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: avexpr Included instruments: lat_abst indtime logem4 Excluded instruments: democ1 ------------------------------------------------------------------------------ . eststo m8d_c10 . estadd scalar firstF = e(widstat) added scalar: e(firstF) = 4.7942721 . . esttab m8a_c1 m8a_c2 m8a_c3 m8a_c4 m8a_c5 /// > m8a_c6 m8a_c7 m8a_c8 m8a_c9 m8a_c10 /// > m8c_c1 m8c_c2 m8c_c3 m8c_c4 m8c_c5 /// > m8c_c6 m8c_c7 m8c_c8 m8c_c9 m8c_c10 /// > m8d_c1 m8d_c2 m8d_c3 m8d_c4 m8d_c5 /// > m8d_c6 m8d_c7 m8d_c8 m8d_c9 m8d_c10 /// > using "tab8_overid.csv", csv replace /// > b(3) se(3) star(* 0.10 ** 0.05 *** 0.01) /// > stats(N r2 firstF hansenJ hansenP, fmt(0 3 2 2 3) /// > labels("N" "R-squared" "First-stage F (KP rk Wald)" /// > "Hansen J statistic" "Hansen J p-value")) /// > title("Table 8: alt instruments (Panels A-B), overid (C), logem4 as contr > ol (D)") (output written to tab8_overid.csv) . . di _newline . di "*** Albouy (2012) caveat: ~36% of mortality observations are" *** Albouy (2012) caveat: ~36% of mortality observations are . di "*** imputed or repeats; Hansen J non-rejection here does not" *** imputed or repeats; Hansen J non-rejection here does not . di "*** rule out shared imputation bias across instruments." *** rule out shared imputation bias across instruments. . . . /*================================================================== > SECTION 10: FIGURE 3 — coefplot of avexpr across specifications > Visual summary of the AJR finding: across every IV specification, > the institutional-quality coefficient sits around 0.9-1.0; OLS > sits below at ~0.5. The IV > OLS gap is consistent with attenuation > bias from measurement error in the institutions index. > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " FIGURE 3 — OLS vs IV coefficient comparison" FIGURE 3 — OLS vs IV coefficient comparison . di "================================================================" ================================================================ . . coefplot /// > (m4_ols_c1, label("OLS") /// > mcolor("${WARM_ORANGE}") mfcolor("${WARM_ORANGE}") msize(medium) /// > ciopts(lcolor("${WARM_ORANGE}"))) /// > (m4_iv_c1, label("IV: settler mortality") /// > mcolor("${STEEL_BLUE}") mfcolor("${STEEL_BLUE}") msize(medium) /// > ciopts(lcolor("${STEEL_BLUE}"))) /// > (m5_iv_c1, label("IV + colonial controls") /// > mcolor("${STEEL_BLUE}") mfcolor("${STEEL_BLUE}") msize(medium) /// > ciopts(lcolor("${STEEL_BLUE}"))) /// > (m6_iv_c1, label("IV + geography controls") /// > mcolor("${STEEL_BLUE}") mfcolor("${STEEL_BLUE}") msize(medium) /// > ciopts(lcolor("${STEEL_BLUE}"))) /// > (m7_iv_c1, label("IV + malaria control") /// > mcolor("${STEEL_BLUE}") mfcolor("${STEEL_BLUE}") msize(medium) /// > ciopts(lcolor("${STEEL_BLUE}"))) /// > (m8a_c1, label("IV: alt instrument euro1900") /// > mcolor("${TEAL}") mfcolor("${TEAL}") msize(medium) /// > ciopts(lcolor("${TEAL}"))), /// > keep(avexpr) coeflabels(avexpr = "avexpr") /// > xline(0, lcolor("${LIGHT_TEXT}") lpattern(dash)) /// > xtitle("Coefficient on avexpr (institutions)", /// > color("${LIGHT_TEXT}") size(medsmall)) /// > title("Effect of institutions on log GDP: OLS vs IV", /// > color("${WHITE_TEXT}") size(medsmall)) /// > subtitle("Six representative specs, 95% CI, AJR (2001) base sample", /// > color("${LIGHT_TEXT}") size(small)) /// > xlabel(, labcolor("${LIGHT_TEXT}") tlcolor("${LIGHT_TEXT}")) /// > ylabel(, labcolor("${LIGHT_TEXT}") tlcolor("${LIGHT_TEXT}")) /// > graphregion(color("${DARK_NAVY}") margin(large)) /// > plotregion(color("${DARK_NAVY}") lcolor("${DARK_NAVY}") margin(medlarge)) > /// > legend(region(color("${DARK_NAVY}") lcolor("${DARK_NAVY}")) /// > color("${LIGHT_TEXT}") cols(2) size(small) /// > symxsize(*0.7)) /// > xsize(9) ysize(6) /// > scheme(s2color) . . graph export "stata_iv_ols_vs_iv.png", replace width(3000) file stata_iv_ols_vs_iv.png written in PNG format . . . /*================================================================== > SECTION 11: Closing summary > ==================================================================*/ . . di _newline(2) . di "================================================================" ================================================================ . di " Analysis complete." Analysis complete. . di "" . di " Key takeaways:" Key takeaways: . di " - OLS coefficient on avexpr (Tab 2 Col 1): ~0.52" - OLS coefficient on avexpr (Tab 2 Col 1): ~0.52 . di " - IV coefficient on avexpr (Tab 4 Col 1): ~0.94" - IV coefficient on avexpr (Tab 4 Col 1): ~0.94 . di " - First-stage F (KP rk Wald): > 20" - First-stage F (KP rk Wald): > 20 . di " - Stock-Yogo 10% maximal IV size threshold: 16.38" - Stock-Yogo 10% maximal IV size threshold: 16.38 . di " - Hansen J p-values (Tab 8 Panel C): > 0.10" - Hansen J p-values (Tab 8 Panel C): > 0.10 . di "" . di " Estimand: 2SLS identifies the LATE for compliers (Imbens-" Estimand: 2SLS identifies the LATE for compliers (Imbens- . di " Angrist 1994) -- not the ATE. Under constant treatment" Angrist 1994) -- not the ATE. Under constant treatment . di " effects, LATE = ATE." effects, LATE = ATE. . di "" . di " Outputs:" Outputs: . di " - 3 PNG figures: stata_iv_first_stage / _reduced_form /" - 3 PNG figures: stata_iv_first_stage / _reduced_form / . di " _ols_vs_iv" _ols_vs_iv . di " - 9 result tables: tab1_summary, tab2_ols, tab3a_inst," - 9 result tables: tab1_summary, tab2_ols, tab3a_inst, . di " tab3b_inst, tab4_iv_main, tab5_iv_controls, tab6_iv_geo," tab3b_inst, tab4_iv_main, tab5_iv_controls, tab6_iv_geo, . di " tab7_iv_health, tab8_overid" tab7_iv_health, tab8_overid . di " - 8 dataset dumps: data_maketable[1-8]" - 8 dataset dumps: data_maketable[1-8] . di "================================================================" ================================================================ . . estimates clear . . di _newline "=== Script completed successfully ===" === Script completed successfully === . . log close name: log: /Users/carlosmendez/Documents/GitHub/starter-academic-v501/content > /post/stata_iv/analysis.log log type: text closed on: 9 May 2026, 16:23:26 -------------------------------------------------------------------------------