tailieunhanh - Book Econometric Analysis of Cross Section and Panel Data By Wooldridge - Chapter 18

Estimating Average Treatment Effects Introduction In this chapter we explicitly study the problem of estimating an average treatment effect (ATE). An average treatment e¤ect is a special case of an average partial effect: an ATE is an average partial e¤ect for a binary explanatory variable. | Estimating Average Treatment Effects Introduction In this chapter we explicitly study the problem of estimating an average treatment effect ATE . An average treatment effect is a special case of an average partial effect an ATE is an average partial effect for a binary explanatory variable. Estimating ATEs has become important in the program evaluation literature such as in the evaluation of job training programs. Originally the binary indicators represented medical treatment or program participation but the methods are applicable when the explanatory variable of interest is any binary variable. We begin by introducing a counterfactual framework pioneered by Rubin 1974 and since adopted by many in both statistics and econometrics including Rosenbaum and Rubin 1983 Heckman 1992 1997 Imbens and Angrist 1994 Angrist Imbens and Rubin 1996 Manski 1996 Heckman Ichimura and Todd 1997 and Angrist 1998 . The counterfactual framework allows us to define various treatment effects that may be of interest. Once we define the different treatment effects we can study ways to consistently estimate these effects. We will not provide a comprehensive treatment of this rapidly growing literature but we will show that under certain assumptions estimators that we are already familiar with consistently estimate average treatment effects. We will also study some extensions that consistently estimate ATEs under weaker assumptions. Broadly most estimators of ATEs fit into one of two categories. The first set exploits assumptions concerning ignorability of the treatment conditional on a set of covariates. As we will see in Section this approach is analogous to the proxy variable solution to the omitted variables problem that we discussed in Chapter 4 and in some cases reduces exactly to an OLS regression with many controls. A second set of estimators relies on the availability of one or more instrumental variables that are redundant in the response equations but help determine .