------------------------------------------------------------------------------- name: log: /Users/carlosmendez/Documents/Github/starter-academic-v501/content > /post/stata_rd/analysis.log log type: text opened on: 24 Apr 2026, 08:19:38 . . *--------------------------------------------------- . * Section 1: Data loading and exploration . *--------------------------------------------------- . . use "https://github.com/quarcs-lab/data-open/raw/master/isds/tutoring.dta", c > lear . . * Describe variables . des Contains data from https://github.com/quarcs-lab/data-open/raw/master/isds/tuto > ring.dta Observations: 1,000 Variables: 5 6 Apr 2024 18:18 ------------------------------------------------------------------------------- Variable Storage Display Value name type format label Variable label ------------------------------------------------------------------------------- id int %8.0g ID of student entrance_exam float %9.0g Entrance exam score tutoring_text str8 %9s Enrolled in the tutoring program? exit_exam float %9.0g Exit exam score tutoring float %9.0g Enrolled in the tutoring program? (Yes = 1, No=0) ------------------------------------------------------------------------------- Sorted by: . . * Summary statistics . sum Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- id | 1,000 500.5 288.8194 1 1000 entrance_e~m | 1,000 78.1427 12.7265 28.8 99.8 tutoring_t~t | 0 exit_exam | 1,000 66.1646 7.625894 42.8 84.5 tutoring | 1,000 .241 .4279043 0 1 . . * Treatment distribution . tab tutoring Enrolled in | the | tutoring | program? | (Yes = 1, | No=0) | Freq. Percent Cum. ------------+----------------------------------- 0 | 759 75.90 75.90 1 | 241 24.10 100.00 ------------+----------------------------------- Total | 1,000 100.00 . . * Create treat variable (explicit copy for cleaner code below) . clonevar treat = tutoring . label var treat "Tutoring program (1 = Yes, 0 = No)" . . * Center running variable at cutoff . gen centered = entrance_exam - 70 . label var centered "Entrance exam centered at cutoff (70)" . . *--------------------------------------------------- . * Section 2: Verify sharp design . *--------------------------------------------------- . . * In a sharp RDD, treatment is a deterministic function . * of the running variable at the cutoff . . gen byte below_cutoff = (entrance_exam <= 70) . label var below_cutoff "Scored at or below cutoff (70)" . . tab below_cutoff treat, row +----------------+ | Key | |----------------| | frequency | | row percentage | +----------------+ Scored at | or below | Tutoring program (1 = cutoff | Yes, 0 = No) (70) | 0 1 | Total -----------+----------------------+---------- 0 | 759 0 | 759 | 100.00 0.00 | 100.00 -----------+----------------------+---------- 1 | 0 241 | 241 | 0.00 100.00 | 100.00 -----------+----------------------+---------- Total | 759 241 | 1,000 | 75.90 24.10 | 100.00 . . * Confirm: 100% treated below, 0% treated above . di _newline . di "If the table above shows 100% compliance," If the table above shows 100% compliance, . di "this is a sharp RDD." this is a sharp RDD. . . *--------------------------------------------------- . * Section 3: Figure 1 -- Scatter plot with cutoff . *--------------------------------------------------- . . twoway (scatter exit_exam entrance_exam if treat==1, /// > mcolor("106 155 204") msize(small) msymbol(circle)) /// > (scatter exit_exam entrance_exam if treat==0, /// > mcolor("217 119 87") msize(small) msymbol(circle)), /// > xline(70, lcolor(black) lwidth(medium) lpattern(dash)) /// > legend(order(1 "Tutored (score {&le} 70)" /// > 2 "Not tutored (score > 70)") /// > position(5) ring(0) col(1)) /// > title("Exit Exam Scores by Entrance Exam Score") /// > subtitle("Vertical dashed line at cutoff = 70") /// > xtitle("Entrance Exam Score") /// > ytitle("Exit Exam Score") /// > scheme(s2color) /// > name(scatter_raw, replace) . graph export "stata_rd_fig1_scatter_raw.png", replace width(2400) (file stata_rd_fig1_scatter_raw.png not found) file stata_rd_fig1_scatter_raw.png written in PNG format . . *--------------------------------------------------- . * Section 4: Figure 2 -- Histogram of running variable . *--------------------------------------------------- . . * Visual check for manipulation/bunching around cutoff . . histogram entrance_exam, /// > bin(30) /// > fcolor("106 155 204") lcolor(white) /// > xline(70, lcolor(black) lwidth(medium) lpattern(dash)) /// > title("Distribution of Entrance Exam Scores") /// > subtitle("Check for bunching at the cutoff (70)") /// > xtitle("Entrance Exam Score") /// > ytitle("Density") /// > scheme(s2color) /// > name(hist_running, replace) (bin=30, start=28.799999, width=2.3666668) . graph export "stata_rd_fig2_histogram_running.png", replace width(2400) (file stata_rd_fig2_histogram_running.png not found) file stata_rd_fig2_histogram_running.png written in PNG format . . *--------------------------------------------------- . * Section 5: Figure 3 -- RD Plot (rdplot) . *--------------------------------------------------- . . * Binned scatter with local polynomial fits on each side . . rdplot exit_exam entrance_exam, c(70) p(1) /// > graph_options(title("RD Plot: Exit Exam Score") /// > xtitle("Entrance Exam Score") /// > ytitle("Exit Exam Score") /// > legend(position(5) ring(0) col(1)) /// > name(rdplot_main, replace)) Mass points detected in the running variable. RD Plot with evenly spaced mimicking variance number of bins using polynomial r > egression. Cutoff c = 70 | Left of c Right of c Number of obs = 100 > 0 ----------------------+---------------------- Kernel = Unifor > m Number of obs | 237 763 Eff. Number of obs | 237 763 Order poly. fit (p) | 1 1 BW poly. fit (h) | 41.200 29.800 Number of bins scale | 1.000 1.000 Outcome: exit_exam. Running variable: entrance_exam. --------------------------------------------- | Left of c Right of c ----------------------+---------------------- Bins selected | 38 29 Average bin length | 1.084 1.028 Median bin length | 1.084 1.028 ----------------------+---------------------- IMSE-optimal bins | 8 9 Mimicking Var. bins | 38 29 ----------------------+---------------------- Rel. to IMSE-optimal: | Implied scale | 4.750 3.222 WIMSE var. weight | 0.009 0.029 WIMSE bias weight | 0.991 0.971 --------------------------------------------- . graph export "stata_rd_fig3_rdplot.png", replace width(2400) (file stata_rd_fig3_rdplot.png not found) file stata_rd_fig3_rdplot.png written in PNG format . . *--------------------------------------------------- . * Section 6: Parametric RDD (OLS) . *--------------------------------------------------- . . di _newline(2) . di "============================================" ============================================ . di " Parametric RDD Estimation" Parametric RDD Estimation . di "============================================" ============================================ . . * Model 1: Simple linear -- same slope on both sides . di _newline . di "--- Model 1: Simple linear RDD ---" --- Model 1: Simple linear RDD --- . reg exit_exam entrance_exam treat, robust Linear regression Number of obs = 1,000 F(2, 997) = 199.06 Prob > F = 0.0000 R-squared = 0.2685 Root MSE = 6.5288 ------------------------------------------------------------------------------ | Robust exit_exam | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- entrance_e~m | .5097654 .0260511 19.57 0.000 .4586441 .5608868 treat | 10.80043 .8063233 13.39 0.000 9.21815 12.38272 _cons | 23.72725 2.202253 10.77 0.000 19.40566 28.04883 ------------------------------------------------------------------------------ . estimates store m1_linear . . * Model 2: Different slopes on each side (interaction) . di _newline . di "--- Model 2: Linear with different slopes ---" --- Model 2: Linear with different slopes --- . gen interact = centered * treat . label var interact "Centered x Treat interaction" . reg exit_exam centered treat interact, robust Linear regression Number of obs = 1,000 F(3, 996) = 133.65 Prob > F = 0.0000 R-squared = 0.2685 Root MSE = 6.5321 ------------------------------------------------------------------------------ | Robust exit_exam | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- centered | .5102012 .032201 15.84 0.000 .4470116 .5733908 treat | 10.79696 .8157404 13.24 0.000 9.196192 12.39773 interact | -.0014004 .0545284 -0.03 0.980 -.1084041 .1056033 _cons | 59.40479 .5104966 116.37 0.000 58.40302 60.40656 ------------------------------------------------------------------------------ . estimates store m2_interact . . * Model 3: Quadratic specification . di _newline . di "--- Model 3: Quadratic specification ---" --- Model 3: Quadratic specification --- . gen centered2 = centered^2 . label var centered2 "Centered squared" . reg exit_exam centered centered2 treat /// > c.centered#c.treat c.centered2#c.treat, robust Linear regression Number of obs = 1,000 F(5, 994) = 87.66 Prob > F = 0.0000 R-squared = 0.2711 Root MSE = 6.527 ------------------------------------------------------------------------------ | Robust exit_exam | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- centered | .3280536 .1249398 2.63 0.009 .0828776 .5732295 centered2 | .0065482 .0042147 1.55 0.121 -.0017225 .0148189 treat | 9.223345 1.197548 7.70 0.000 6.873333 11.57336 | c.centered#| c.treat | .0216037 .1926001 0.11 0.911 -.3563458 .3995532 | c.centered2#| c.treat | -.0118178 .0060364 -1.96 0.051 -.0236634 .0000279 | _cons | 60.32171 .8138902 74.12 0.000 58.72457 61.91885 ------------------------------------------------------------------------------ . estimates store m3_quadratic . . * Compare all parametric models . di _newline . di "--- Comparison of parametric models ---" --- Comparison of parametric models --- . estimates table m1_linear m2_interact m3_quadratic, /// > b(%9.3f) se(%9.3f) stats(r2 N) -------------------------------------------------- Variable | m1_linear m2_inte~t m3_quad~c -------------+------------------------------------ entrance_e~m | 0.510 | 0.026 treat | 10.800 10.797 9.223 | 0.806 0.816 1.198 centered | 0.510 0.328 | 0.032 0.125 interact | -0.001 | 0.055 centered2 | 0.007 | 0.004 | c.centered#| c.treat | 0.022 | 0.193 | c.centered2#| c.treat | -0.012 | 0.006 | _cons | 23.727 59.405 60.322 | 2.202 0.510 0.814 -------------+------------------------------------ r2 | 0.268 0.268 0.271 N | 1000 1000 1000 -------------------------------------------------- Legend: b/se . . *--------------------------------------------------- . * Section 7: Nonparametric RDD (rdrobust) . *--------------------------------------------------- . . di _newline(2) . di "============================================" ============================================ . di " Nonparametric RDD Estimation (rdrobust)" Nonparametric RDD Estimation (rdrobust) . di "============================================" ============================================ . . * Default: MSE-optimal bandwidth, triangular kernel . * Note: rdrobust estimates the jump from left to right of the cutoff. . * Since tutored students are to the LEFT (score <= 70) and score higher, . * the RD effect is NEGATIVE (right minus left < 0). This is the same . * finding as the positive parametric coefficient on treat (~10.8), just . * with opposite sign convention. The magnitudes also differ because . * rdrobust uses only observations within the optimal bandwidth (~10 points . * around the cutoff), while the parametric model uses the full sample. . di _newline . di "--- Default (MSE-optimal, triangular kernel) ---" --- Default (MSE-optimal, triangular kernel) --- . rdrobust exit_exam entrance_exam, c(70) Mass points detected in the running variable. Sharp RD estimates using local polynomial regression. Cutoff c = 70 | Left of c Right of c Number of obs = 100 > 0 -------------------+---------------------- BW type = mser > d Number of obs | 237 763 Kernel = Triangula > r Eff. Number of obs | 144 256 VCE method = N > N Order est. (p) | 1 1 Order bias (q) | 2 2 BW est. (h) | 9.984 9.984 BW bias (b) | 14.578 14.578 rho (h/b) | 0.685 0.685 Unique obs | 155 262 Outcome: exit_exam. Running variable: entrance_exam. ------------------------------------------------------------------------------- > - | Point | Robust Inference | Estimate | z-stat P>|z| [95% Conf. Interval > ] -------------------+----------------------------------------------------------- > - RD Effect | -8.5793 | -4.3034 0.000 -12.1422 -4.5429 > 7 ------------------------------------------------------------------------------- > - Estimates adjusted for mass points in the running variable. . . * Store main results . local rd_coef = e(tau_cl) . local rd_se = e(se_tau_cl) . local rd_bw = e(h_l) . local rd_N = e(N_h_l) + e(N_h_r) . . di _newline . di "Summary of main RD estimate:" Summary of main RD estimate: . di " RD estimate: " %9.3f `rd_coef' RD estimate: -8.579 . di " Robust SE: " %9.3f `rd_se' Robust SE: 1.617 . di " Bandwidth (h): " %9.3f `rd_bw' Bandwidth (h): 9.984 . di " Effective N: " `rd_N' Effective N: 400 . . * Uniform kernel for comparison . di _newline . di "--- Uniform kernel ---" --- Uniform kernel --- . rdrobust exit_exam entrance_exam, c(70) kernel(uniform) Mass points detected in the running variable. Sharp RD estimates using local polynomial regression. Cutoff c = 70 | Left of c Right of c Number of obs = 100 > 0 -------------------+---------------------- BW type = mser > d Number of obs | 237 763 Kernel = Unifor > m Eff. Number of obs | 119 173 VCE method = N > N Order est. (p) | 1 1 Order bias (q) | 2 2 BW est. (h) | 7.223 7.223 BW bias (b) | 12.422 12.422 rho (h/b) | 0.582 0.582 Unique obs | 155 262 Outcome: exit_exam. Running variable: entrance_exam. ------------------------------------------------------------------------------- > - | Point | Robust Inference | Estimate | z-stat P>|z| [95% Conf. Interval > ] -------------------+----------------------------------------------------------- > - RD Effect | -8.2003 | -4.0141 0.000 -11.7749 -4.0486 > 7 ------------------------------------------------------------------------------- > - Estimates adjusted for mass points in the running variable. . . * Epanechnikov kernel for comparison . di _newline . di "--- Epanechnikov kernel ---" --- Epanechnikov kernel --- . rdrobust exit_exam entrance_exam, c(70) kernel(epanechnikov) Mass points detected in the running variable. Sharp RD estimates using local polynomial regression. Cutoff c = 70 | Left of c Right of c Number of obs = 100 > 0 -------------------+---------------------- BW type = mser > d Number of obs | 237 763 Kernel = Epanechni > kov Eff. Number of obs | 129 200 VCE method = N > N Order est. (p) | 1 1 Order bias (q) | 2 2 BW est. (h) | 8.179 8.179 BW bias (b) | 12.680 12.680 rho (h/b) | 0.645 0.645 Unique obs | 155 262 Outcome: exit_exam. Running variable: entrance_exam. ------------------------------------------------------------------------------- > - | Point | Robust Inference | Estimate | z-stat P>|z| [95% Conf. Interval > ] -------------------+----------------------------------------------------------- > - RD Effect | -8.3882 | -4.0224 0.000 -12.1749 -4.1973 > 5 ------------------------------------------------------------------------------- > - Estimates adjusted for mass points in the running variable. . . *--------------------------------------------------- . * Section 8: Bandwidth sensitivity . *--------------------------------------------------- . . di _newline(2) . di "============================================" ============================================ . di " Bandwidth Sensitivity Analysis" Bandwidth Sensitivity Analysis . di "============================================" ============================================ . . * Show all available bandwidth selectors . di _newline . di "--- Bandwidth selection methods ---" --- Bandwidth selection methods --- . rdbwselect exit_exam entrance_exam, c(70) all Mass points detected in the running variable. Bandwidth estimators for sharp RD local polynomial regression. Cutoff c = | Left of c Right of c Number of obs = 100 > 0 -------------------+---------------------- Kernel = Triangula > r Number of obs | 237 763 VCE method = N > N Min of entrance_exam | 28.800 70.000 Max of entrance_exam | 69.900 99.800 Order est. (p) | 1 1 Order bias (q) | 2 2 Unique obs | 155 262 Outcome: exit_exam. Running variable: entrance_exam. ------------------------------------------------------------------------------- > - | BW est. (h) | BW bias (b) Method | Left of c Right of c | Left of c Right of c -------------------+------------------------------+---------------------------- > - mserd | 9.984 9.984 | 14.578 14.578 msetwo | 11.558 10.041 | 17.057 14.759 msesum | 12.058 12.058 | 17.552 17.552 msecomb1 | 9.984 9.984 | 14.578 14.578 msecomb2 | 11.558 10.041 | 17.057 14.759 -------------------+------------------------------+---------------------------- > - cerrd | 7.068 7.068 | 14.578 14.578 certwo | 8.182 7.109 | 17.057 14.759 cersum | 8.536 8.536 | 17.552 17.552 cercomb1 | 7.068 7.068 | 14.578 14.578 cercomb2 | 8.182 7.109 | 17.057 14.759 ------------------------------------------------------------------------------- > - Estimates adjusted for mass points in the running variable. . . * Estimate at multiple manual bandwidths . di _newline . di "--- Manual bandwidth sensitivity ---" --- Manual bandwidth sensitivity --- . di "BW Coef SE p-value" BW Coef SE p-value . di "---- --------- --------- ---------" ---- --------- --------- --------- . . foreach bw in 5 7 10 12 15 20 { 2. quietly rdrobust exit_exam entrance_exam, c(70) h(`bw') 3. local coef_`bw' = e(tau_cl) 4. local se_`bw' = e(se_tau_cl) 5. local pv_`bw' = e(pv_cl) 6. di "`bw'" _col(10) %9.3f `coef_`bw'' /// > _col(23) %9.3f `se_`bw'' /// > _col(36) %9.3f `pv_`bw'' 7. } 5 -8.202 2.337 0.000 7 -8.237 1.919 0.000 10 -8.581 1.615 0.000 12 -8.675 1.486 0.000 15 -8.842 1.312 0.000 20 -9.157 1.131 0.000 . . *--------------------------------------------------- . * Section 9: McCrary density test (rddensity) . *--------------------------------------------------- . . di _newline(2) . di "============================================" ============================================ . di " McCrary Density Test" McCrary Density Test . di "============================================" ============================================ . . * Formal test: is there bunching at the cutoff? . * H0: density is continuous at the cutoff . * A non-significant p-value supports the RDD assumption . . rddensity entrance_exam, c(70) Computing data-driven bandwidth selectors. Point estimates and standard errors have been adjusted for repeated observation > s. (Use option nomasspoints to suppress this adjustment.) RD Manipulation test using local polynomial density estimation. c = 70.000 | Left of c Right of c Number of obs = 100 > 0 -------------------+---------------------- Model = unrestricte > d Number of obs | 237 763 BW method = com > b Eff. Number of obs | 208 577 Kernel = triangula > r Order est. (p) | 2 2 VCE method = jackknif > e Order bias (q) | 3 3 BW est. (h) | 22.444 19.966 Running variable: entrance_exam. ------------------------------------------ Method | T P>|T| -------------------+---------------------- Robust | -0.5521 0.5809 ------------------------------------------ P-values of binomial tests. (H0: prob = .5) ----------------------------------------------------- Window Length / 2 | =c | P>|T| -------------------+----------------------+---------- 0.300 | 9 11 | 0.8238 0.600 | 15 16 | 1.0000 0.900 | 20 21 | 1.0000 1.200 | 23 24 | 1.0000 1.500 | 29 32 | 0.7982 1.800 | 36 38 | 0.9076 2.100 | 43 47 | 0.7520 2.400 | 44 52 | 0.4752 2.700 | 47 57 | 0.3776 3.000 | 53 64 | 0.3553 ----------------------------------------------------- . . * Store p-value . local density_pval = e(pv_q) . di _newline . di "Density test p-value: " %9.4f `density_pval' Density test p-value: 0.5809 . di "If p > 0.05, no evidence of manipulation." If p > 0.05, no evidence of manipulation. . . * Figure 4: Density plot using lpdensity . * Generate density estimates on each side of the cutoff . * and plot them manually since rddensity plot can be fragile . . * Left side density . preserve . keep if entrance_exam <= 70 (759 observations deleted) . kdensity entrance_exam, generate(xL densL) nograph . save "_tmpL.dta", replace (file _tmpL.dta not found) file _tmpL.dta saved . restore . . * Right side density . preserve . keep if entrance_exam > 70 (241 observations deleted) . kdensity entrance_exam, generate(xR densR) nograph . save "_tmpR.dta", replace (file _tmpR.dta not found) file _tmpR.dta saved . restore . . * Combine and plot . preserve . use "_tmpL.dta", clear . append using "_tmpR.dta" . . twoway (line densL xL, lcolor("106 155 204") lwidth(medthick)) /// > (line densR xR, lcolor("217 119 87") lwidth(medthick)), /// > xline(70, lcolor(black) lwidth(medium) lpattern(dash)) /// > legend(order(1 "Below cutoff" 2 "Above cutoff") /// > position(5) ring(0) col(1)) /// > title("Density of the Running Variable") /// > subtitle("No bunching at the cutoff supports the RDD assumption") /// > xtitle("Entrance Exam Score") /// > ytitle("Density") /// > scheme(s2color) /// > name(density_test, replace) . graph export "stata_rd_fig4_density_test.png", replace width(2400) (file stata_rd_fig4_density_test.png not found) file stata_rd_fig4_density_test.png written in PNG format . restore . . * Clean up temp files . capture erase "_tmpL.dta" . capture erase "_tmpR.dta" . . *--------------------------------------------------- . * Section 10: Placebo cutoffs (robustness) . *--------------------------------------------------- . . di _newline(2) . di "============================================" ============================================ . di " Placebo Cutoff Tests" Placebo Cutoff Tests . di "============================================" ============================================ . . * If the effect is real, only the true cutoff (70) . * should show a significant discontinuity . . * Use postfile to collect results for plotting . tempname pf . tempfile placebo_results . postfile `pf' cutoff coef se pval using `placebo_results', replace (file /var/folders/3h/bdq32hpj7ln850s11fd2qvqw0000gn/T//St60985.000004 not found) . . di _newline . di "Cutoff Coef SE p-value" Cutoff Coef SE p-value . di "------ --------- --------- ---------" ------ --------- --------- --------- . . foreach c in 50 55 60 65 70 75 80 85 90 { 2. capture quietly rdrobust exit_exam entrance_exam, c(`c') 3. if _rc == 0 { 4. local pc = e(tau_cl) 5. local ps = e(se_tau_cl) 6. local pp = e(pv_cl) 7. if `c' == 70 { 8. di "`c' *" _col(10) %9.3f `pc' /// > _col(23) %9.3f `ps' /// > _col(36) %9.3f `pp' 9. } 10. else { 11. di "`c'" _col(10) %9.3f `pc' /// > _col(23) %9.3f `ps' /// > _col(36) %9.3f `pp' 12. } 13. post `pf' (`c') (`pc') (`ps') (`pp') 14. } 15. else { 16. di "`c'" _col(10) " (insufficient data)" 17. } 18. } 50 12.728 21.302 0.550 55 0.557 3.052 0.855 60 0.569 3.193 0.859 65 3.296 1.742 0.058 70 * -8.579 1.617 0.000 75 -1.548 1.691 0.360 80 -1.095 1.472 0.457 85 0.817 1.605 0.611 90 -0.540 1.900 0.776 . . postclose `pf' . . * Figure 5: Placebo cutoff plot . preserve . use `placebo_results', clear . . gen ci_upper = coef + 1.96 * se . gen ci_lower = coef - 1.96 * se . gen byte is_true = (cutoff == 70) . . twoway (rcap ci_upper ci_lower cutoff if is_true==0, /// > lcolor("106 155 204")) /// > (scatter coef cutoff if is_true==0, /// > mcolor("106 155 204") msymbol(circle)) /// > (rcap ci_upper ci_lower cutoff if is_true==1, /// > lcolor("217 119 87") lwidth(thick)) /// > (scatter coef cutoff if is_true==1, /// > mcolor("217 119 87") msymbol(diamond) msize(large)), /// > yline(0, lcolor(black) lpattern(dash)) /// > legend(order(2 "Placebo cutoffs" 4 "True cutoff (70)") /// > position(5) ring(0) col(1)) /// > title("Placebo Cutoff Test") /// > subtitle("Only the true cutoff should show a significant effect") /// > xtitle("Cutoff Value") /// > ytitle("RD Estimate") /// > scheme(s2color) /// > name(placebo_cutoffs, replace) . graph export "stata_rd_fig5_placebo_cutoffs.png", replace width(2400) (file stata_rd_fig5_placebo_cutoffs.png not found) file stata_rd_fig5_placebo_cutoffs.png written in PNG format . restore . . *--------------------------------------------------- . * End of analysis . *--------------------------------------------------- . . di _newline(2) . di "============================================" ============================================ . di " Analysis complete." Analysis complete. . di " Sharp RDD: tutoring at entrance_exam <= 70" Sharp RDD: tutoring at entrance_exam <= 70 . di " Estimand: LATE at the cutoff" Estimand: LATE at the cutoff . di " See the tutorial for interpretation." See the tutorial for interpretation. . di "============================================" ============================================ . . log close name: log: /Users/carlosmendez/Documents/Github/starter-academic-v501/content > /post/stata_rd/analysis.log log type: text closed on: 24 Apr 2026, 08:19:44 -------------------------------------------------------------------------------