Inference for Average Treatment Effects

National Bureau Of Economic Research Inc, Cambridge MA

Investigators

Abstract

Estimation of causal effects of policy interventions such as job training programs is an important goal of much applied economic research. Often a reasonable starting point is the assume that assignment to the treatment is random given on sufficiently detailed observed pretreatment variables. Under that assumption one can identify the population average effect. This research will contribute to the literature on inference for average treatments effects under these assumptions in three parts. First, the research will develop large sample theory for matching estimators. By matching estimators we mean estimators where each treated unit is matched to one or a fixed number of controls, and each control is matched to one or a fixed number of treated units. Such pure matching estimators have considerable intuitive appeal and have been used widely in practice, without their large sample theory having been established other than for special cases. The result should be an asymptotic theory for such matching estimators that allows researchers to use these estimators in practice. In a second part, the research will investigate higher order properties of some of the estimators for average treatment effects that have been proposed. Many of these estimators have a nonparametric component. However, most of the literature is silent regarding the actual choice of smoothing parameters, beyond rate conditions. This makes it di .cult for practitioners to actually implement thse estimators. Here the plan is to develop a mean-squared-error based criterion to derive an explicit data-driven criterion for the smoothing parameter. In the third part, the research will compare a number of the estimators for average treatment effects. So far a number of estimators have been proposed, often with a small simulation study to investigate their properties. What this research accomplishes is a systematic comparison of various estimators. In many studies of social programs such as job training programs observational data are used to evaluate these programs. Statistical methods for such evaluations often rely on matching type methods that match trainees to similar controls, that is individuals who received the training to individuals who did not receive the training with similar background characteristics and labor market histories. A variety of such methods are currently used, with often the properties and reliability of such methods unknown. This research investigates the formal properties of such methods. In addition the research will develop automated procedures for implementing some of these methods. Currently these methods often require the researcher to make a number of choices in the implementation that potentially affect the final results substantially, without much guidance available to guide these choices. This should make these methods more transparent and easier to implement. Finally, the research will compare a number of these methods in settings where the correct answers are known so as to evaluate their performance and reach recommendations to inform the future use of such methods.