Ivtreatreg: a new STATA routine for estimating binary treatment models with heterogeneous response to treatment under observable and unobservable selection

This paper presents a new user-written STATA command called ivtreatreg for the estimation of five different (binary) treatment models with and without idiosyncratic (or heterogeneous) average treatment effect. Depending on the model specified by the user, ivtreatreg provides consistent estimation of average treatment effects both under the hypothesis of “selection on observables” and “selection on unobservables” by using Ordinary Least Squares (OLS) regression in the first case, and Intrumental-Variables (IV) and Selection-model (à la Heckman) in the second one. Conditional on a pre-specified subset of exogenous variables x – thought of as driving the heterogeneous response to treatment – ivtreatreg calculates for each model the Average Treatment Effect (ATE), the Average Treatment Effect on Treated (ATET) and the Average Treatment Effect on Non-Treated (ATENT), as well as the estimates of these parameters conditional on the observable factors x, i.e., ATE(x), ATET(x) and ATENT(x). The five models estimated by ivtreatreg are: Cf-ols (Control-function regression estimated by OLS), Direct-2sls (IV regression estimated by direct two-stage least squares), Probit-2sls (IV regression estimated by Probit and two-stage least squares), Probit-ols (IV two-step regression estimated by Probit and ordinary least squares), and Heckit (Heckman two-step selection model). An extensive treatment of the conditions under which previous methods provide consistent estimation of ATE, ATET and ATENT can be found, for instance, in Wooldgrige (2002, Chapter 18). The value added of this new STATA command is that it allows for a generalization of the regression approach typically employed in standard program evaluation, by assuming heterogeneous response to treatment.