Stata’s etregress allows you to estimate an average treatment effect (ATE) and the other parameters of a linear regression model augmented with an endogenous binary-treatment variable. You just specify the treatment variable and the treatment covariates in the treat() option. The average treatment effect on the treated (ATET) can also be estimated with etregress.
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We estimate the ATE of being a union member on wages of women with etregress. Other outcome covariates include wage, school, grade, and tenure. Indicators for living in an SMSA—standard metropolitan statistical area, being African American, and living in the southern region of the United States are also used as outcome covariates.
. webuse union3 (NLS Women 14-24 in 1968) . etregress wage age grade smsa black tenure, treat(union = south black tenure) Iteration 0: Log likelihood = -3140.811 Iteration 1: Log likelihood = -3053.6629 Iteration 2: Log likelihood = -3051.5847 Iteration 3: Log likelihood = -3051.575 Iteration 4: Log likelihood = -3051.575 Linear regression with endogenous treatment Number of obs = 1,210 Estimator: Maximum likelihood Wald chi2(6) = 681.89 Log likelihood = -3051.575 Prob > chi2 = 0.0000
| Coefficient Std. err. z P>|z| [95% conf. interval] | ||
| wage | ||
| age | .1487409 .0193291 7.70 0.000 .1108566 .1866252 | |
| grade | .4205658 .0293577 14.33 0.000 .3630258 .4781058 | |
| smsa | .9117044 .1249041 7.30 0.000 .6668969 1.156512 | |
| black | -.7882471 .1367078 -5.77 0.000 -1.05619 -.5203048 | |
| tenure | .1524015 .0369596 4.12 0.000 .0799621 .2248409 | |
| 1.union | 2.945815 .2749621 10.71 0.000 2.4069 3.484731 | |
| _cons | -4.351572 .5283952 -8.24 0.000 -5.387208 -3.315936 | |
| union | ||
| south | -.5807419 .0851111 -6.82 0.000 -.7475566 -.4139271 | |
| black | .4557499 .0958042 4.76 0.000 .2679771 .6435226 | |
| tenure | .0871536 .0232483 3.75 0.000 .0415878 .1327195 | |
| _cons | -.8855758 .0724506 -12.22 0.000 -1.027576 -.7435753 | |
| /athrho | -.6544347 .0910314 -7.19 0.000 -.832853 -.4760164 | |
| /lnsigma | .7026769 .0293372 23.95 0.000 .645177 .7601767 | |
| rho | -.5746478 .060971 -.682005 -.4430476 | |
| sigma | 2.019151 .0592362 1.906325 2.138654 | |
| lambda | -1.1603 .1495097 -1.453334 -.8672668 | |
The estimated ATE of being a union member is 2.95. The ATET is the same as the ATE in this case because the treatment indicator variable has not been interacted with any of the outcome covariates.
When there is a treatment variable and outcome covariate interaction, the parameter estimates from etregress can be used by margins to estimate the ATE. Now we use factor-variable notation to allow the tenure and black coefficients to vary based on union membership. We specify the vce(robust) because we need to specify vce(unconditional) when we use margins below.
. etregress wage age grade south i.union#c.(black tenure),
treat(union = south black tenure) vce(robust)
Iteration 0: Log pseudolikelihood = -3093.9289
Iteration 1: Log pseudolikelihood = -3069.8014
Iteration 2: Log pseudolikelihood = -3069.0214
Iteration 3: Log pseudolikelihood = -3069.0106
Iteration 4: Log pseudolikelihood = -3069.0106
Linear regression with endogenous treatment Number of obs = 1,210
Estimator: Maximum likelihood Wald chi2(8) = 445.85
Log pseudolikelihood = -3069.0106 Prob > chi2 = 0.0000
| Robust | ||
| Coefficient std. err. z P>|z| [95% conf. interval] | ||
| wage | ||
| age | .1547605 .020634 7.50 0.000 .1143186 .1952025 | |
| grade | .4328724 .0372888 11.61 0.000 .3597876 .5059572 | |
| south | -.5060951 .2009611 -2.52 0.012 -.8999716 -.1122186 | |
| union#c.black | ||
| 0 | -.4695395 .2009365 -2.34 0.019 -.8633677 -.0757112 | |
| 1 | -.8580219 .2893336 -2.97 0.003 -1.425105 -.2909385 | |
| union#c.tenure | ||
| 0 | .1802719 .0545018 3.31 0.001 .0734504 .2870934 | |
| 1 | .0848265 .0929442 0.91 0.361 -.0973408 .2669938 | |
| union | ||
| 1 | 3.060777 .9504098 3.22 0.001 1.198008 4.923546 | |
| _cons | -3.847881 .6560055 -5.87 0.000 -5.133628 -2.562133 | |
| union | ||
| south | -.5041281 .0932344 -5.41 0.000 -.6868642 -.321392 | |
| black | .4506167 .0953425 4.73 0.000 .2637489 .6374845 | |
| tenure | .0917203 .0260037 3.53 0.000 .040754 .1426867 | |
| _cons | -.9325238 .0811249 -11.49 0.000 -1.091526 -.7735219 | |
| /athrho | -.5750886 .3420724 -1.68 0.093 -1.245538 .095361 | |
| /lnsigma | .6978439 .0973047 7.17 0.000 .5071302 .8885576 | |
| rho | -.5190865 .2499007 -.8470277 .095073 | |
| sigma | 2.009416 .1955256 1.660519 2.43162 | |
| lambda | -1.043061 .5904939 -2.200407 .1142862 | |
The ATE of union membership is now estimated with margins. The “r.” notation tells margins to contrast the potential-outcome means for the treatment and control regimes.
. margins r.union, vce(unconditional) contrast(nowald) Contrasts of predictive margins Number of obs = 1,210 Expression: Linear prediction, predict()
| Unconditional | ||
| Contrast std. err. [95% conf. interval] | ||
| union | ||
| (1 vs 0) | 2.772613 .9382248 .933726 4.6115 | |
The estimate of the ATE is essentially the same as in the original model. Now we estimate the ATET of union membership with margins. We specify union in the subpop() option to restrict estimation to the treated subpopulation.
. margins r.union, vce(unconditional) contrast(nowald) subpop(union)
Contrasts of predictive margins Number of obs = 1,210
Subpop. no. obs = 253
Expression: Linear prediction, predict()
| Unconditional | ||
| Contrast std. err. [95% conf. interval] | ||
| union | ||
| (1 vs 0) | 2.70409 .9415886 .8586099 4.549569 | |
The estimated ATET and ATE are close, indicating that the average predicted outcome for the treatment group is similar to the average predicted outcome for the whole population.
