___ ____ ____ ____ ____ ® /__ / ____/ / ____/ Stata 19.0 ___/ / /___/ / /___/ SE—Standard Edition Statistics and Data Science Copyright 1985-2025 StataCorp LLC StataCorp 4905 Lakeway Drive College Station, Texas 77845 USA 800-782-8272 https://www.stata.com 979-696-4600 service@stata.com Stata license: Single-user perpetual Serial number: 401906342834 Licensed to: CarlosMendez Nagoya University Notes: 1. Stata is running in batch mode. 2. Unicode is supported; see help unicode_advice. 3. Maximum number of variables is set to 5,000 but can be increased; see help set_maxvar. . do content/post/stata_sdid/analysis.do . *============================================================================ > === . * analysis.do . * Synthetic Difference-in-Differences (SDID): California's Proposition 99 . * Companion script for the Stata tutorial post `stata_sdid`. . * . * Run (batch): . * "/Applications/Stata/StataSE.app/Contents/MacOS/stata-se" -b do analysis. > do . * . * Requires (all from SSC): sdid, synth, synth2 . * . ssc install sdid . * . ssc install synth2 . * . ssc install synth . * . * Data: prop99_example.dta (Arkhangelsky et al. 2021 / Abadie et al. 2010). . * 39 US states, 1970-2000, outcome = cigarette packs per capita. . * California is the single treated unit; Proposition 99 takes effect 19 > 89. . * The panel is OUTCOME-ONLY (no covariates), so synthetic control and S > DID . * see exactly the same information set -- an apples-to-apples compariso > n. . * Estimand: ATT -- the effect of Proposition 99 on California, 1989-200 > 0. . *============================================================================ > === . . clear all . set more off . set scheme s2color . set linesize 100 . . cd "/Users/carlos/GitHub/starter-academic-v501/content/post/stata_sdid" // students: set this to > your local copy of this post folder /Users/carlos/GitHub/starter-academic-v501/content/post/stata_sdid . capture mkdir web_app . capture mkdir web_app/data . . * Site colour palette (RGB strings for Stata graphs) . global TREAT "217 119 87" // #d97757 warm orange -> California / observed . global CTRL "106 155 204" // #6a9bcc steel blue -> control / synthetic . global TEAL "0 212 200" // #00d4c8 teal -> SDID . global INK "20 20 19" // #141413 . . *------------------------------------------------------------------------------- . * 1. DATA . *------------------------------------------------------------------------------- . capture confirm file prop99_example.dta . if _rc { . webuse set www.damianclarke.net/stata/ . webuse prop99_example.dta, clear . save prop99_example.dta, replace . } . use prop99_example.dta, clear . describe Contains data from prop99_example.dta Observations: 1,209 Variables: 4 4 Apr 2022 08:37 ---------------------------------------------------------------------------------------------------- Variable Storage Display Value name type format label Variable label ---------------------------------------------------------------------------------------------------- state str14 %14s State year int %8.0g Year packspercapita float %9.0g PacksPerCapita treated byte %8.0g ---------------------------------------------------------------------------------------------------- Sorted by: . tab treated treated | Freq. Percent Cum. ------------+----------------------------------- 0 | 1,197 99.01 99.01 1 | 12 0.99 100.00 ------------+----------------------------------- Total | 1,209 100.00 . summarize packspercapita Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- packsperca~a | 1,209 118.8932 32.7674 40.7 296.2 . . encode state, gen(id) . xtset id year Panel variable: id (strongly balanced) Time variable: year, 1970 to 2000 Delta: 1 unit . summ id if state=="California", meanonly . local ca = r(mean) . scalar ca_id = `ca' . di as result "California id = `ca'" California id = 3 . . *------------------------------------------------------------------------------- . * 2. EDA: California vs. the simple average of the 38 control states . *------------------------------------------------------------------------------- . preserve . gen byte iscal = state=="California" . collapse (mean) packs=packspercapita, by(iscal year) . reshape wide packs, i(year) j(iscal) (j = 0 1) Data Long -> Wide ----------------------------------------------------------------------------- Number of observations 62 -> 31 Number of variables 3 -> 3 j variable (2 values) iscal -> (dropped) xij variables: packs -> packs0 packs1 ----------------------------------------------------------------------------- . label var packs1 "California" . label var packs0 "Average of 38 controls" . twoway (line packs1 year, lcolor("$TREAT") lwidth(thick)) /// > (line packs0 year, lcolor("$CTRL") lwidth(medthick) lpattern(dash)), /// > xline(1989, lcolor(gs10) lpattern(solid)) /// > ytitle("Cigarette packs per capita") xtitle("") /// > xlabel(1970(5)2000) /// > legend(order(1 "California" 2 "Average of 38 controls") pos(1) ring(0) cols(1) size(sma > ll)) /// > title("California vs. the raw control average", size(medium)) /// > note("Vertical line: Proposition 99 takes effect (1989).") . graph export "stata_sdid_raw_trends.png", replace width(2000) file stata_sdid_raw_trends.png written in PNG format . restore . . *------------------------------------------------------------------------------- . * 3. The original difference-in-differences: a raw 2x2 . *------------------------------------------------------------------------------- . gen byte cal = state=="California" . gen byte post = year>=1989 . quietly summ packspercapita if cal==1 & post==0 . scalar m_ca_pre = r(mean) . quietly summ packspercapita if cal==1 & post==1 . scalar m_ca_post = r(mean) . quietly summ packspercapita if cal==0 & post==0 . scalar m_co_pre = r(mean) . quietly summ packspercapita if cal==0 & post==1 . scalar m_co_post = r(mean) . scalar did2x2 = (m_ca_post - m_ca_pre) - (m_co_post - m_co_pre) . di as result "2x2 DiD = " did2x2 2x2 DiD = -27.349111 . * identical to the interaction in a saturated regression: . reg packspercapita i.cal##i.post Source | SS df MS Number of obs = 1,209 -------------+---------------------------------- F(3, 1205) = 105.07 Model | 268939.059 3 89646.3529 Prob > F = 0.0000 Residual | 1028093.89 1,205 853.189952 R-squared = 0.2073 -------------+---------------------------------- Adj R-squared = 0.2054 Total | 1297032.95 1,208 1073.70277 Root MSE = 29.209 ------------------------------------------------------------------------------ packsperca~a | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- 1.cal | -14.359 6.788699 -2.12 0.035 -27.67799 -1.040019 1.post | -28.51142 1.747208 -16.32 0.000 -31.93932 -25.08351 | cal#post | 1 1 | -27.34911 10.91131 -2.51 0.012 -48.75638 -5.941839 | _cons | 130.5695 1.087062 120.11 0.000 128.4368 132.7023 ------------------------------------------------------------------------------ . drop cal post . . *------------------------------------------------------------------------------- . * 4. The original synthetic control (Abadie et al. 2010) via synth2 . * Match on the full pre-period outcome PATH (each pre-year a separate . * predictor) -- the fair analogue to SDID's unit weights. . *------------------------------------------------------------------------------- . local preds "" . forvalues y = 1970/1988 { 2. local preds "`preds' packspercapita(`y')" 3. } . . synth2 packspercapita `preds', trunit(`ca') trperiod(1989) frame(sc2) symbol(2) nofigure Fitting results in the pretreatment periods: -------------------------------------------------------------------------------- Treated Unit : California Treatment Time : 1989 -------------------------------------------------------------------------------- Number of Control Units = 38 Root Mean Squared Error = 1.65640 Number of Covariates = 19 R-squared = 0.97699 -------------------------------------------------------------------------------- Covariate balance in the pretreatment periods: --------------------------------------------------------------------------------------- Covariate | V.weight Treated Synthetic Control Average Control | Value Bias Value Bias ----------------------+---------------------------------------------------------------- packspercapita(1970) | 0.0575 123.0000 117.3614 -4.58% 120.0842 -2.37% packspercapita(1971) | 0.0630 121.0000 119.7564 -1.03% 123.8632 2.37% packspercapita(1972) | 0.0775 123.5000 124.5763 0.87% 129.1789 4.60% packspercapita(1973) | 0.0762 124.4000 124.3053 -0.08% 131.5395 5.74% packspercapita(1974) | 0.0718 126.7000 126.4153 -0.22% 134.6684 6.29% packspercapita(1975) | 0.0725 127.1000 126.7159 -0.30% 136.9316 7.74% packspercapita(1976) | 0.0802 128.0000 128.4025 0.31% 141.2605 10.36% packspercapita(1977) | 0.0696 126.4000 126.6217 0.18% 141.0895 11.62% packspercapita(1978) | 0.0589 126.1000 126.0853 -0.01% 140.4737 11.40% packspercapita(1979) | 0.0514 121.9000 122.8776 0.80% 138.0868 13.28% packspercapita(1980) | 0.0466 120.2000 120.1817 -0.02% 138.0895 14.88% packspercapita(1981) | 0.0431 118.6000 119.6467 0.88% 137.9868 16.35% packspercapita(1982) | 0.0432 115.4000 116.4915 0.95% 136.2947 18.11% packspercapita(1983) | 0.0391 110.8000 110.9973 0.18% 131.2500 18.46% packspercapita(1984) | 0.0311 104.8000 103.4059 -1.33% 124.9026 19.18% packspercapita(1985) | 0.0288 102.8000 103.1442 0.33% 123.1158 19.76% packspercapita(1986) | 0.0289 99.7000 99.5867 -0.11% 120.5947 20.96% packspercapita(1987) | 0.0288 97.5000 100.4232 3.00% 117.5868 20.60% packspercapita(1988) | 0.0317 90.1000 91.9269 2.03% 113.8237 26.33% --------------------------------------------------------------------------------------- Note: "V.weight" is the optimal covariate weight in the diagonal of V matrix. "Synthetic Control" is the weighted average of donor units with optimal weights. "Average Control" is the simple average of all control units with equal weights. Optimal Unit Weights: --------------------------- Unit | U.weight --------------+------------ Utah | 0.3940 Montana | 0.2320 Nevada | 0.2050 Connecticut | 0.1090 NewHampshire | 0.0450 Colorado | 0.0150 --------------------------- Note: The unit Alabama Arkansas Delaware Georgia Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Minnesota Mississippi Missouri Nebraska NewMexico NorthCarolina NorthDakota Ohio Oklahoma Pennsylvania RhodeIsland SouthCarolina SouthDakota Tennessee Texas Vermont Virginia WestVirginia Wisconsin Wyoming in the donor pool get a weight of 0. Prediction results in the posttreatment periods: ----------------------------------------------------------- Time | Actual Outcome Synthetic Outcome Treatment Effect ------+---------------------------------------------------- 1989 | 82.4000 90.8038 -8.4038 1990 | 77.8000 86.9790 -9.1790 1991 | 68.7000 81.3086 -12.6086 1992 | 67.5000 81.2037 -13.7037 1993 | 63.4000 80.9067 -17.5067 1994 | 58.6000 80.6205 -22.0205 1995 | 56.4000 79.2257 -22.8257 1996 | 54.5000 78.4651 -23.9651 1997 | 53.8000 80.0214 -26.2214 1998 | 52.3000 75.5979 -23.2979 1999 | 47.2000 74.6804 -27.4804 2000 | 41.6000 68.1639 -26.5639 ------+---------------------------------------------------- Mean | 60.3500 79.8314 -19.4814 ----------------------------------------------------------- Note: The average treatment effect over the posttreatment period is -19.4814. Finished. . scalar sc_att = e(att) . scalar sc_rmse = e(rmse) . matrix scU = e(U_wt) . matrix list scU scU[6,1] Weight Utah .394 Montana .232 Nevada .205 Connecticut .109 NewHampshire .045 Colorado .015 . . * export synth2 donor weights (rownames carry the donor names) . local rn : rownames scU . file open fh using "web_app/data/sc_omega.csv", write replace . file write fh "state,weight" _n . local i = 0 . foreach s of local rn { 2. local ++i 3. local w = scU[`i',1] 4. file write fh "`s',`w'" _n 5. } . file close fh . . * pull California's synthetic path + gap out of the synth2 frame (by var label) . tempfile scser . frame change sc2 . keep if id==`ca' (1,178 observations deleted) . foreach v of varlist _all { 2. local lbl : variable label `v' 3. if strpos("`lbl'","prediction") rename `v' sc_synth 4. if strpos("`lbl'","treatment effect") rename `v' sc_effect 5. } . keep year sc_synth sc_effect . save `scser', replace (file /var/folders/f_/4_1h2nwn2w91_4qmnp8p1snm0000gn/T//St11275.000002 not found) file /var/folders/f_/4_1h2nwn2w91_4qmnp8p1snm0000gn/T//St11275.000002 saved as .dta format . frame change default . . * SC inference: in-space placebo (RMSPE-ratio) test -> p-value (optional) . capture noisily synth2 packspercapita `preds', trunit(`ca') trperiod(1989) placebo(unit) nofigure Fitting results in the pretreatment periods: -------------------------------------------------------------------------------- Treated Unit : California Treatment Time : 1989 -------------------------------------------------------------------------------- Number of Control Units = 38 Root Mean Squared Error = 1.65640 Number of Covariates = 19 R-squared = 0.97699 -------------------------------------------------------------------------------- Covariate balance in the pretreatment periods: --------------------------------------------------------------------------------------- Covariate | V.weight Treated Synthetic Control Average Control | Value Bias Value Bias ----------------------+---------------------------------------------------------------- packspercapita(1970) | 0.0575 123.0000 117.3614 -4.58% 120.0842 -2.37% packspercapita(1971) | 0.0630 121.0000 119.7564 -1.03% 123.8632 2.37% packspercapita(1972) | 0.0775 123.5000 124.5763 0.87% 129.1789 4.60% packspercapita(1973) | 0.0762 124.4000 124.3053 -0.08% 131.5395 5.74% packspercapita(1974) | 0.0718 126.7000 126.4153 -0.22% 134.6684 6.29% packspercapita(1975) | 0.0725 127.1000 126.7159 -0.30% 136.9316 7.74% packspercapita(1976) | 0.0802 128.0000 128.4025 0.31% 141.2605 10.36% packspercapita(1977) | 0.0696 126.4000 126.6217 0.18% 141.0895 11.62% packspercapita(1978) | 0.0589 126.1000 126.0853 -0.01% 140.4737 11.40% packspercapita(1979) | 0.0514 121.9000 122.8776 0.80% 138.0868 13.28% packspercapita(1980) | 0.0466 120.2000 120.1817 -0.02% 138.0895 14.88% packspercapita(1981) | 0.0431 118.6000 119.6467 0.88% 137.9868 16.35% packspercapita(1982) | 0.0432 115.4000 116.4915 0.95% 136.2947 18.11% packspercapita(1983) | 0.0391 110.8000 110.9973 0.18% 131.2500 18.46% packspercapita(1984) | 0.0311 104.8000 103.4059 -1.33% 124.9026 19.18% packspercapita(1985) | 0.0288 102.8000 103.1442 0.33% 123.1158 19.76% packspercapita(1986) | 0.0289 99.7000 99.5867 -0.11% 120.5947 20.96% packspercapita(1987) | 0.0288 97.5000 100.4232 3.00% 117.5868 20.60% packspercapita(1988) | 0.0317 90.1000 91.9269 2.03% 113.8237 26.33% --------------------------------------------------------------------------------------- Note: "V.weight" is the optimal covariate weight in the diagonal of V matrix. "Synthetic Control" is the weighted average of donor units with optimal weights. "Average Control" is the simple average of all control units with equal weights. Optimal Unit Weights: --------------------------- Unit | U.weight --------------+------------ Utah | 0.3940 Montana | 0.2320 Nevada | 0.2050 Connecticut | 0.1090 NewHampshire | 0.0450 Colorado | 0.0150 --------------------------- Note: The unit Alabama Arkansas Delaware Georgia Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Minnesota Mississippi Missouri Nebraska NewMexico NorthCarolina NorthDakota Ohio Oklahoma Pennsylvania RhodeIsland SouthCarolina SouthDakota Tennessee Texas Vermont Virginia WestVirginia Wisconsin Wyoming in the donor pool get a weight of 0. Prediction results in the posttreatment periods: ----------------------------------------------------------- Time | Actual Outcome Synthetic Outcome Treatment Effect ------+---------------------------------------------------- 1989 | 82.4000 90.8038 -8.4038 1990 | 77.8000 86.9790 -9.1790 1991 | 68.7000 81.3086 -12.6086 1992 | 67.5000 81.2037 -13.7037 1993 | 63.4000 80.9067 -17.5067 1994 | 58.6000 80.6205 -22.0205 1995 | 56.4000 79.2257 -22.8257 1996 | 54.5000 78.4651 -23.9651 1997 | 53.8000 80.0214 -26.2214 1998 | 52.3000 75.5979 -23.2979 1999 | 47.2000 74.6804 -27.4804 2000 | 41.6000 68.1639 -26.5639 ------+---------------------------------------------------- Mean | 60.3500 79.8314 -19.4814 ----------------------------------------------------------- Note: The average treatment effect over the posttreatment period is -19.4814. Implementing placebo test using fake treatment unit Alabama...Arkansas...Colorado...Connecticut...De > laware...Georgia...Idaho...Illinois...Indiana...Iowa...Kansas...Kentucky...Louisiana...Maine...Min > nesota...Mississippi...Missouri...Montana...Nebraska...Nevada...NewHampshire...NewMexico...NorthCa > rolina...NorthDakota...Ohio...Oklahoma...Pennsylvania...RhodeIsland...SouthCarolina...SouthDakota. > ..Tennessee...Texas...Utah...Vermont...Virginia...WestVirginia...Wisconsin...Wyoming... In-space placebo test results using fake treatment units: ------------------------------------------------------------------------------- Unit | Pre MSPE Post MSPE Post/Pre MSPE Pre MSPE of Fake Unit/ | Pre MSPE of Treated Unit ---------------+--------------------------------------------------------------- California | 2.7437 423.2949 154.2810 1.0000 Alabama | 3.3144 13.3988 4.0426 1.2080 Arkansas | 4.1998 17.7623 4.2293 1.5307 Colorado | 8.3848 50.7846 6.0567 3.0561 Connecticut | 8.6870 217.9797 25.0928 3.1662 Delaware | 11.7272 180.9220 15.4275 4.2743 Georgia | 1.1926 96.3529 80.7891 0.4347 Idaho | 4.6477 39.4554 8.4892 1.6940 Illinois | 2.0817 24.6882 11.8594 0.7587 Indiana | 12.8941 218.1950 16.9221 4.6996 Iowa | 6.0498 25.7266 4.2525 2.2050 Kansas | 6.2763 6.9810 1.1123 2.2876 Kentucky | 284.7957 1599.5168 5.6164 103.8013 Louisiana | 0.9814 30.2430 30.8150 0.3577 Maine | 5.1346 77.2638 15.0478 1.8714 Minnesota | 11.0624 21.2777 1.9234 4.0320 Mississippi | 3.0156 35.6779 11.8313 1.0991 Missouri | 0.1917 109.1983 569.7330 0.0699 Montana | 4.0778 181.5533 44.5219 1.4863 Nebraska | 0.7114 72.2221 101.5254 0.2593 Nevada | 40.3226 82.8161 2.0538 14.6966 NewHampshire | 3436.5953 134.9018 0.0393 1252.5580 NewMexico | 1.9224 7.5067 3.9049 0.7007 NorthCarolina | 81.3897 57.3684 0.7049 29.6646 NorthDakota | 7.3737 80.1903 10.8752 2.6875 Ohio | 1.6982 6.8088 4.0095 0.6189 Oklahoma | 3.8470 252.3751 65.6026 1.4022 Pennsylvania | 1.0329 8.4220 8.1541 0.3765 RhodeIsland | 14.3919 706.9300 49.1201 5.2455 SouthCarolina | 1.4021 38.4495 27.4235 0.5110 SouthDakota | 1.2707 65.0543 51.1954 0.4631 Tennessee | 5.1794 111.2945 21.4880 1.8878 Texas | 3.6756 243.4357 66.2301 1.3397 Utah | 593.7642 223.2758 0.3760 216.4131 Vermont | 6.6784 247.3277 37.0341 2.4341 Virginia | 0.6655 262.0003 393.6671 0.2426 WestVirginia | 6.3383 291.9732 46.0646 2.3102 Wisconsin | 1.7052 62.1844 36.4680 0.6215 Wyoming | 29.3926 30.5095 1.0380 10.7129 ------------------------------------------------------------------------------- Note: The probability of obtaining a post/pretreatment MSPE ratio as large as California's is 0.0769. In-space placebo test results using fake treatment units (continued): ---------------------------------------------------------------- Time | Treatment Effect p-value of Treatment Effect | Two-sided Right-sided Left-sided ------+--------------------------------------------------------- 1989 | -8.4038 0.1538 0.9487 0.0769 1990 | -9.1790 0.2308 0.8462 0.1795 1991 | -12.6086 0.1538 0.8974 0.1282 1992 | -13.7037 0.1282 0.9231 0.1026 1993 | -17.5067 0.1026 0.9487 0.0769 1994 | -22.0205 0.0769 0.9744 0.0513 1995 | -22.8257 0.0769 0.9744 0.0513 1996 | -23.9651 0.0769 0.9744 0.0513 1997 | -26.2214 0.1026 0.9487 0.0769 1998 | -23.2979 0.1026 0.9487 0.0769 1999 | -27.4804 0.0769 0.9744 0.0513 2000 | -26.5639 0.0769 1.0000 0.0256 ---------------------------------------------------------------- Note: (1) The two-sided p-value of the treatment effect for a particular period is defined as the frequency that the absolute values of the placebo effects are greater than or equal to the absolute value of treatment effect. (2) The right-sided (left-sided) p-value of the treatment effect for a particular period is defined as the frequency that the placebo effects are greater (smaller) than or equal to the treatment effect. (3) If the estimated treatment effect is positive, then the right-sided p-value is recommended; whereas the left-sided p-value is recommended if the estimated treatment effect is negative. Finished. . if _rc==0 { . matrix scPV = e(pval) . di as result "--- synth2 in-space placebo p-values e(pval) ---" --- synth2 in-space placebo p-values e(pval) --- . matrix list scPV scPV[12,4] p-value: p-value: p-value: Tr.Eff. two-sided right-sided left-sided 1989 -8.4037933 .15384615 .94871795 .07692308 1990 -9.1790009 .23076923 .84615385 .17948718 1991 -12.608604 .15384615 .8974359 .12820513 1992 -13.703697 .12820513 .92307692 .1025641 1993 -17.506699 .1025641 .94871795 .07692308 1994 -22.0205 .07692308 .97435897 .05128205 1995 -22.825699 .07692308 .97435897 .05128205 1996 -23.965103 .07692308 .97435897 .05128205 1997 -26.221401 .1025641 .94871795 .07692308 1998 -23.297901 .1025641 .94871795 .07692308 1999 -27.480396 .07692308 .97435897 .05128205 2000 -26.563904 .07692308 1 .02564103 . } . . *------------------------------------------------------------------------------- . * 5. Synthetic difference-in-differences (Arkhangelsky et al. 2021) via sdid . * Run A: point estimate + canonical figure + returned unit/time weights . *------------------------------------------------------------------------------- . use prop99_example.dta, clear . encode state, gen(id) . . sdid packspercapita state year treated, method(sdid) vce(noinference) graph g1on /// > returnweights mattitles /// > g1_opt(ylabel(-110(20)50) xtitle("")) /// > g2_opt(ylabel(0(25)150) ytitle("Packs per capita")) Synthetic Difference-in-Differences Estimator ----------------------------------------------------------------------------- packsperca~a | ATT Std. Err. t P>|t| [95% Conf. Interval] -------------+--------------------------------------------------------------- treated | -15.60383 . . . . . ----------------------------------------------------------------------------- 95% CIs and p-values are based on large-sample approximations. Refer to Arkhangelsky et al., (2021) for theoretical derivations. . graph export "stata_sdid_sdid_main.png", replace width(2000) file stata_sdid_sdid_main.png written in PNG format . scalar sdid_att = e(ATT) . di as result "SDID ATT = " sdid_att SDID ATT = -15.60383 . . * capture the treated + SDID synthetic outcome trajectories . matrix S = e(series) . tempfile sdidser . preserve . clear . svmat S, names(col) number of observations will be reset to 31 Press any key to continue, or Break to abort Number of observations (_N) was 0, now 31. . rename (Yco1989 Ytr1989) (sdid_synth ca_actual) . keep year sdid_synth ca_actual . save `sdidser', replace (file /var/folders/f_/4_1h2nwn2w91_4qmnp8p1snm0000gn/T//St11275.000003 not found) file /var/folders/f_/4_1h2nwn2w91_4qmnp8p1snm0000gn/T//St11275.000003 saved as .dta format . restore . . * export SDID unit weights (omega) and time weights (lambda) . preserve . keep state omega1989 . duplicates drop Duplicates in terms of all variables (1,170 observations deleted) . rename omega1989 omega . gsort -omega . export delimited using "web_app/data/sdid_omega.csv", replace file web_app/data/sdid_omega.csv saved . restore . tempfile lamf . preserve . keep year lambda1989 . duplicates drop Duplicates in terms of all variables (1,178 observations deleted) . rename lambda1989 lambda . export delimited using "web_app/data/sdid_lambda.csv", replace file web_app/data/sdid_lambda.csv saved . save `lamf', replace (file /var/folders/f_/4_1h2nwn2w91_4qmnp8p1snm0000gn/T//St11275.000006 not found) file /var/folders/f_/4_1h2nwn2w91_4qmnp8p1snm0000gn/T//St11275.000006 saved as .dta format . restore . capture drop omega1989 lambda1989 . . * Run B: placebo inference (the valid choice with ONE treated unit) . sdid packspercapita state year treated, vce(placebo) seed(1213) Placebo replications (50). This may take some time. ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 Synthetic Difference-in-Differences Estimator ----------------------------------------------------------------------------- packsperca~a | ATT Std. Err. t P>|t| [95% Conf. Interval] -------------+--------------------------------------------------------------- treated | -15.60383 9.87941 -1.58 0.114 -34.96712 3.75946 ----------------------------------------------------------------------------- 95% CIs and p-values are based on large-sample approximations. Refer to Arkhangelsky et al., (2021) for theoretical derivations. . scalar sdid_se = e(se) . scalar sdid_cil = e(ATT_l) . scalar sdid_cir = e(ATT_r) . di as result "SDID ATT = " e(ATT) " SE = " sdid_se " 95% CI = [" sdid_cil "," sdid_cir "]" SDID ATT = -15.60383 SE = 9.87941 95% CI = [-34.967118,3.7594578] . . *------------------------------------------------------------------------------- . * 6. The three estimators in one framework: method(did|sc|sdid) . *------------------------------------------------------------------------------- . sdid packspercapita state year treated, method(did) vce(noinference) graph g1on /// > g1_opt(ylabel(-110(20)50) xtitle("")) /// > g2_opt(ylabel(0(25)150) ytitle("Packs per capita")) Difference-in-Differences Estimator ----------------------------------------------------------------------------- packsperca~a | ATT Std. Err. t P>|t| [95% Conf. Interval] -------------+--------------------------------------------------------------- treated | -27.34911 . . . . . ----------------------------------------------------------------------------- 95% CIs and p-values are based on large-sample approximations. . graph export "stata_sdid_did_panel.png", replace width(2000) file stata_sdid_did_panel.png written in PNG format . scalar did_att = e(ATT) . . sdid packspercapita state year treated, method(sc) vce(noinference) graph g1on /// > g1_opt(ylabel(-110(20)50) xtitle("")) /// > g2_opt(ylabel(0(25)150) ytitle("Packs per capita")) Synthetic Control ----------------------------------------------------------------------------- packsperca~a | ATT Std. Err. t P>|t| [95% Conf. Interval] -------------+--------------------------------------------------------------- treated | -19.61966 . . . . . ----------------------------------------------------------------------------- 95% CIs and p-values are based on large-sample approximations. . graph export "stata_sdid_sc_panel.png", replace width(2000) file stata_sdid_sc_panel.png written in PNG format . scalar sc_sdidframe_att = e(ATT) . . di as result "DiD(sdid)=" did_att " SC(sdid)=" sc_sdidframe_att " SDID=" sdid_att DiD(sdid)=-27.34911 SC(sdid)=-19.61966 SDID=-15.60383 . . *------------------------------------------------------------------------------- . * 7. Putting them side by side: one chart of California vs. every counterfactual . *------------------------------------------------------------------------------- . preserve . keep if state!="California" (31 observations deleted) . collapse (mean) ctrl_mean=packspercapita, by(year) . tempfile cm . save `cm', replace (file /var/folders/f_/4_1h2nwn2w91_4qmnp8p1snm0000gn/T//St11275.000009 not found) file /var/folders/f_/4_1h2nwn2w91_4qmnp8p1snm0000gn/T//St11275.000009 saved as .dta format . restore . . use `sdidser', clear . merge 1:1 year using `scser', nogen Result Number of obs ----------------------------------------- Not matched 0 Matched 31 ----------------------------------------- . merge 1:1 year using `cm', nogen Result Number of obs ----------------------------------------- Not matched 0 Matched 31 ----------------------------------------- . merge 1:1 year using `lamf', nogen Result Number of obs ----------------------------------------- Not matched 0 Matched 31 ----------------------------------------- . * DiD counterfactual: California's pre-level shifted by the controls' change . summ ca_actual if year<=1988, meanonly . local capre = r(mean) . summ ctrl_mean if year<=1988, meanonly . local copre = r(mean) . gen did_cf = `capre' + (ctrl_mean - `copre') . * SDID counterfactual: e(series) Yco matches TRENDS not levels (unit FE absorbs . * the offset), so anchor it by the lambda-WEIGHTED pre-period gap -- exactly the . * baseline SDID differences against. Post-period (ca_actual - sdid_cf) then . * averages to the SDID ATT. . gen double pregap = lambda*(sdid_synth - ca_actual) if year<=1988 & lambda<. (12 missing values generated) . egen double offset_sdid = total(pregap) . gen sdid_cf = sdid_synth - offset_sdid . summ offset_sdid, meanonly . di as result "SDID lambda-weighted pre-period gap (anchor) = " r(mean) SDID lambda-weighted pre-period gap (anchor) = 25.352419 . drop pregap offset_sdid . order year ca_actual did_cf sc_synth sdid_cf sdid_synth ctrl_mean sc_effect lambda . export delimited using "web_app/data/series.csv", replace file web_app/data/series.csv saved . list year ca_actual did_cf sc_synth sdid_cf, sepby(year) noobs +--------------------------------------------------+ | year ca_act~l did_cf sc_synth sdid_cf | |--------------------------------------------------| | 1970 123 105.7252 117.3614 116.5335 | |--------------------------------------------------| | 1971 121 109.5042 119.7564 119.8504 | |--------------------------------------------------| | 1972 123.5 114.82 124.5763 124.4751 | |--------------------------------------------------| | 1973 124.4 117.1805 124.3053 123.7708 | |--------------------------------------------------| | 1974 126.7 120.3094 126.4153 124.8412 | |--------------------------------------------------| | 1975 127.1 122.5726 126.7159 125.064 | |--------------------------------------------------| | 1976 128 126.9015 128.4025 129.3823 | |--------------------------------------------------| | 1977 126.4 126.7305 126.6217 127.1502 | |--------------------------------------------------| | 1978 126.1 126.1147 126.0853 125.4456 | |--------------------------------------------------| | 1979 121.9 123.7278 122.8776 121.5677 | |--------------------------------------------------| | 1980 120.2 123.7305 120.1817 120.0172 | |--------------------------------------------------| | 1981 118.6 123.6278 119.6467 119.3115 | |--------------------------------------------------| | 1982 115.4 121.9357 116.4915 116.4296 | |--------------------------------------------------| | 1983 110.8 116.891 110.9973 111.7078 | |--------------------------------------------------| | 1984 104.8 110.5436 103.4059 103.7482 | |--------------------------------------------------| | 1985 102.8 108.7568 103.1442 101.8305 | |--------------------------------------------------| | 1986 99.7 106.2357 99.5867 98.58356 | |--------------------------------------------------| | 1987 97.5 103.2278 100.4232 97.31182 | |--------------------------------------------------| | 1988 90.1 99.46468 91.9269 91.14898 | |--------------------------------------------------| | 1989 82.4 95.30415 90.80379 87.24498 | |--------------------------------------------------| | 1990 77.8 91.30679 86.979 82.12582 | |--------------------------------------------------| | 1991 68.7 89.9831 81.3086 77.35355 | |--------------------------------------------------| | 1992 67.5 89.03574 81.2037 75.91912 | |--------------------------------------------------| | 1993 63.4 88.33573 80.9067 75.94547 | |--------------------------------------------------| | 1994 58.6 87.75942 80.6205 74.70623 | |--------------------------------------------------| | 1995 56.4 88.7989 79.2257 75.30577 | |--------------------------------------------------| | 1996 54.5 86.82521 78.4651 73.85014 | |--------------------------------------------------| | 1997 53.8 87.43047 80.0214 74.68352 | |--------------------------------------------------| | 1998 52.3 86.59889 75.5979 75.08157 | |--------------------------------------------------| | 1999 47.2 83.23573 74.6804 73.14493 | |--------------------------------------------------| | 2000 41.6 77.77521 68.1639 66.08488 | +--------------------------------------------------+ . . twoway (line ca_actual year, lcolor("$TREAT") lwidth(thick)) /// > (line did_cf year, lcolor(gs7) lpattern(dash)) /// > (line sc_synth year, lcolor("$CTRL") lpattern(shortdash) lwidth(medthick)) /// > (line sdid_cf year, lcolor("$TEAL") lpattern(solid) lwidth(medthick)), /// > xline(1989, lcolor(gs10)) /// > ytitle("Cigarette packs per capita") xtitle("") xlabel(1970(5)2000) /// > legend(order(1 "California (observed)" 2 "DiD counterfactual" /// > 3 "Synthetic control (synth2)" 4 "SDID counterfactual") /// > rows(2) pos(6) size(small)) /// > title("Four counterfactuals for California", size(medium)) /// > note("SDID counterfactual anchored to California by its {&lambda}-weighted pre-period gap." > ) . graph export "stata_sdid_compare_paths.png", replace width(2000) file stata_sdid_compare_paths.png written in PNG format . . * synth2 path + gap figures (built from the merged series) . twoway (line ca_actual year, lcolor("$TREAT") lwidth(thick)) /// > (line sc_synth year, lcolor("$CTRL") lpattern(dash) lwidth(medthick)), /// > xline(1989, lcolor(gs10)) ytitle("Packs per capita") xtitle("") /// > xlabel(1970(5)2000) /// > legend(order(1 "California" 2 "Synthetic California") pos(1) ring(0) cols(1) size(small)) / > // > title("Synthetic control fit (synth2)", size(medium)) . graph export "stata_sdid_sc_path.png", replace width(2000) file stata_sdid_sc_path.png written in PNG format . . twoway (line sc_effect year, lcolor("$INK") lwidth(medthick)), /// > yline(0, lcolor(gs10)) xline(1989, lcolor(gs10) lpattern(dash)) /// > ytitle("Gap: California - synthetic") xtitle("") xlabel(1970(5)2000) /// > title("Estimated gap (synth2)", size(medium)) . graph export "stata_sdid_sc_gap.png", replace width(2000) file stata_sdid_sc_gap.png written in PNG format . . * time-weight bar chart (SDID puts all pre-weight on 1986-1988) . preserve . import delimited "web_app/data/sdid_lambda.csv", clear (encoding automatically selected: ISO-8859-9) (2 vars, 31 obs) . twoway (bar lambda year if year<=1988, color("$CTRL") barwidth(0.8)), /// > ytitle("SDID time weight ({&lambda})") xtitle("") /// > xlabel(1970(2)1988) ylabel(0(.1).5) legend(off) /// > title("Where SDID looks: pre-period time weights", size(medium)) /// > note("Pre-period weight (1970-1988): zero until 1986, then 0.37, 0.21, 0.43 on 1986-198 > 8." /// > "Post-1989 years are omitted; SDID weights them uniformly at 1/12.") . graph export "stata_sdid_lambda.png", replace width(2000) file stata_sdid_lambda.png written in PNG format . restore . . *------------------------------------------------------------------------------- . * 8. Inference figure: SDID in-space placebo distribution . * Drop California; assign each control as the placebo-treated unit at 1989; . * re-estimate SDID; collect placebo ATTs. p = share with |placebo| >= |obs|. . *------------------------------------------------------------------------------- . use prop99_example.dta, clear . drop if state=="California" (31 observations deleted) . levelsof state, local(ctrls) `"Alabama"' `"Arkansas"' `"Colorado"' `"Connecticut"' `"Delaware"' `"Georgia"' `"Idaho"' `"Illinois" > ' `"Indiana"' `"Iowa"' `"Kansas"' `"Kentucky"' `"Louisiana"' `"Maine"' `"Minnesota"' `"Mississippi > "' `"Missouri"' `"Montana"' `"Nebraska"' `"Nevada"' `"New Hampshire"' `"New Mexico"' `"North Carol > ina"' `"North Dakota"' `"Ohio"' `"Oklahoma"' `"Pennsylvania"' `"Rhode Island"' `"South Carolina"' > `"South Dakota"' `"Tennessee"' `"Texas"' `"Utah"' `"Vermont"' `"Virginia"' `"West Virginia"' `"Wis > consin"' `"Wyoming"' . tempname pf . postfile `pf' str20 pstate double ptau using "_placebo.dta", replace (file _placebo.dta not found) . foreach s of local ctrls { 2. preserve 3. gen byte ptreat = (state=="`s'") & (year>=1989) 4. capture sdid packspercapita state year ptreat, vce(noinference) 5. if _rc==0 post `pf' ("`s'") (e(ATT)) 6. restore 7. } . postclose `pf' . . use "_placebo.dta", clear . local aatt = sdid_att . count if abs(ptau) >= abs(`aatt') 1 . local pc = r(N) . count 38 . local pn = r(N) . scalar sdid_pperm = `pc'/`pn' . di as result "SDID placebo permutation p-value = " sdid_pperm " (n=`pn')" SDID placebo permutation p-value = .02631579 (n=38) . export delimited using "web_app/data/placebo.csv", replace file web_app/data/placebo.csv saved . . local aatts : di %4.1f `aatt' . local pvals : di %5.3f sdid_pperm . twoway (histogram ptau, width(2) color("${CTRL}%70") lcolor(white)), /// > xline(`aatt', lcolor("$TREAT") lwidth(thick)) /// > xtitle("Placebo ATT among control states") ytitle("Density") /// > title("SDID placebo distribution", size(medium)) /// > note("Orange line: California's estimated ATT (`aatts'). Permutation p = `pvals'.") . graph export "stata_sdid_placebo_hist.png", replace width(2000) file stata_sdid_placebo_hist.png written in PNG format . . *------------------------------------------------------------------------------- . * 9. Summary table of every ATT estimate -> web_app/data/atts.csv . *------------------------------------------------------------------------------- . clear . set obs 5 Number of observations (_N) was 0, now 5. . gen str30 method = "" (5 missing values generated) . gen double att = . (5 missing values generated) . gen double se = . (5 missing values generated) . gen double ci_l = . (5 missing values generated) . gen double ci_r = . (5 missing values generated) . gen double note_pval = . (5 missing values generated) . replace method = "Raw 2x2 DiD" in 1 (1 real change made) . replace att = did2x2 in 1 (1 real change made) . replace method = "DiD (TWFE, sdid)" in 2 (1 real change made) . replace att = did_att in 2 (1 real change made) . replace method = "Synthetic control (synth2)" in 3 (1 real change made) . replace att = sc_att in 3 (1 real change made) . replace method = "SC (sdid framework)" in 4 (1 real change made) . replace att = sc_sdidframe_att in 4 (1 real change made) . replace method = "SDID" in 5 (1 real change made) . replace att = sdid_att in 5 (1 real change made) . replace se = sdid_se in 5 (1 real change made) . replace ci_l = sdid_cil in 5 (1 real change made) . replace ci_r = sdid_cir in 5 (1 real change made) . replace note_pval = sdid_pperm in 5 (1 real change made) . export delimited using "web_app/data/atts.csv", replace file web_app/data/atts.csv saved . list, noobs +----------------------------------------------------------------------------------------+ | method att se ci_l ci_r note_pval | |----------------------------------------------------------------------------------------| | Raw 2x2 DiD -27.349111 . . . . | | DiD (TWFE, sdid) -27.34911 . . . . | | Synthetic control (synth2) -19.481392 . . . . | | SC (sdid framework) -19.61966 . . . . | | SDID -15.60383 9.87941 -34.967118 3.7594578 .02631579 | +----------------------------------------------------------------------------------------+ . . *------------------------------------------------------------------------------- . * Clean up scratch file . *------------------------------------------------------------------------------- . capture erase "_placebo.dta" . . di as result _n "==================== KEY NUMBERS ====================" ==================== KEY NUMBERS ==================== . di as result "Raw 2x2 DiD = " %7.2f did2x2 Raw 2x2 DiD = -27.35 . di as result "DiD (sdid framework) = " %7.2f did_att DiD (sdid framework) = -27.35 . di as result "Synthetic control (synth2) = " %7.2f sc_att " (RMSE " %4.2f sc_rmse ")" Synthetic control (synth2) = -19.48 (RMSE 1.66) . di as result "SC (sdid framework) = " %7.2f sc_sdidframe_att SC (sdid framework) = -19.62 . di as result "SDID = " %7.2f sdid_att SDID = -15.60 . di as result "SDID placebo SE = " %7.2f sdid_se SDID placebo SE = 9.88 . di as result "SDID 95% CI = [" %6.2f sdid_cil ", " %6.2f sdid_cir "]" SDID 95% CI = [-34.97, 3.76] . di as result "SDID permutation p-value = " %5.3f sdid_pperm SDID permutation p-value = 0.026 . di as result "=====================================================" ===================================================== . end of do-file