In this talk, I look at several methods for estimating average effects of a program, treatment, or regime, under unconfoundedness. The setting is one with a binary program. The traditional example in economics is that of a labor market program where some individuals receive training and others do not, and interest is in some measure of the effectiveness of the training. Unconfoundedness, a term coined by Rubin (1990), refers to the case where (nonparametrically) adjusting for differences in a fixed set of covariates removes biases in comparisons between treated and control units, thus allowing for a causal interpretation of those adjusted differences. This is perhaps the most important special case for estimating average treatment effects in practice. Under the specific assumptions we make in this setting, the population-average treatment effect can be estimated at the standard parametric root-N rate without functional form assumptions. A variety of estimators, at first sight quite different, have been proposed for implementing this. The estimators include regression estimators, propensity score based estimators, and matching estimators. Many of these are used in practice, although rarely is this choice motivated by principled arguments. In practice, the differences between the estimators are relatively minor when applied appropriately, although matching in combination with regression is generally more robust and is probably the recommended choice. More important than the choice of estimator are two other issues. Both involve analyses of the data without the outcome variable. First, one should carefully check the extent of the overlap in covariate distributions between the treatment and control groups. Often there is a need for some trimming based on the covariate values if the original sample is not well balanced. Without this, estimates of average treatment effects can be sensitive to the choice of, and small changes in the implementation of, the estimators. In this part of the analysis, the propensity score plays an important role. Second, it is useful to do some assessment of the appropriateness of the unconfoundedness assumption. Although this assumption is not directly testable, its plausibility can often be assessed using lagged values of the outcome as pseudooutcomes. Another issue is variance estimation. For matching estimators bootstrapping, although widely used, has been shown to be invalid. I discuss general methods for estimating the conditional variance that do not involve resampling.
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