The bmte command: Methods for the estimation of treatment effects when exclusion restrictions are unavailable

Abstract

We present a new Stata command, bmte (bias-minimizing treatment effects), that implements two new estimators proposed in Millimet and Tchernis (2013, Journal of Applied Econometrics 28: 982–1017) and designed to estimate the effect of treatment when selection on unobserved variables exists and appropriate exclusion restrictions are unavailable. In addition, the bmte command estimates treatment effects from several alternative estimators that also do not rely on exclusion restrictions for identification of the causal effects of the treatment, including the following: 1) Heckman’s two-step estimator (1976, Annals of Economic and Social Measurement 5: 475–492; 1979, Econometrica 47: 153–161); 2) a control function approach outlined in Heckman, LaLonde, and Smith (1999, Handbook of Labor Economics 3: 1865–2097) and Navarro (2008, The New Palgrave Dictionary of Economics [Palgrave Macmillan]); and 3) a more recent estimator proposed by Klein and Vella (2009, Journal of Applied Econometrics 24: 735–762) that exploits heteroskedasticity for identification. By implementing two new estimators alongside preexisting estimators, the bmte command provides a picture of the average causal effects of the treatment across a variety of assumptions. We present an example application of the command following Millimet and Tchernis (2013, Journal of Applied Econometrics 28: 982–1017).