Three Essays on Semiparametric Methods for the Evaluation of Social Programs.

Abstract

This dissertation consists of three essays whose unifying topical theme is the study and application of semiparametric methods for the evaluation of social programs. The first essay evaluates the federal urban Empowerment Zone (EZ) program using an inverse probability weighting (IPW) difference-in-differences estimator. We use four decades of Census data on urban neighborhoods in conjunction with information on the proposed boundaries of rejected EZs. We find that neighborhoods receiving EZ designation experienced substantial improvements in labor market conditions and moderate increases in rents relative to rejected and future Empowerment Zones. No evidence exists of large scale gentrification.

The second essay explores the finite sample properties of several semiparametric estimators of average treatment effects, including IPW, matching and double robust estimators. We first show that all these estimators can be understood as weighted least squares. This result is used to explain the equivalency of these estimators. Then we study the implications of the assumption of strict overlap in the distribution of propensity scores for treatment and control units. When there is good overlap, IPW estimators are preferred on bias grounds and attain the semiparametric efficiency bound even for samples of size n=100. When overlap is close to failing, none of the estimators examined perform well, and standard asymptotics may be a poor guide to finite sample distribution of the estimators.

In the third essay I propose a variance estimator of IPW estimators of average treatment effects. I note that IPW is a sequential estimator which, in cases in which a parametric propensity score model is assumed, has a simple expression of the asymptotic variance. Using Monte Carlo simulations I find that tests based on the proposed variance estimator have good finite sample size and power compared to competing inference strategies. Tests based on the percentile-t bootstrap method have very similar size and power properties. I interpret this as an indication that the bootstrap percentile-t method is not providing any refinement to the proposed asymptotic variance, which indicates that the proposed variance estimator is a good enough approximation to the true variance of the treatment effect estimator.