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), which implements two new estimators proposed in Millimet and Tchernis (2012) designed to estimate the effect of treat-ment when there exists selection on unobserved variables 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: 1) Heckman’s two-step estimator (Heckman 1976, 1979); 2) a control function approach outlined in Heckman et al. (1999) and Navarro (2008); and 3) a more recent estimator proposed by Klein and Vella (2009) that exploits heteroskedasticity for identification. By implementing two new estimators alongside pre-existing 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 (2012)