Efficiency of Average Treatment Effect Estimation When the True Propensity Is Parametric

Kyoo Il Kim

doi:10.3390/econometrics7020025

Abstract

It is well known that efficient estimation of average treatment effects can be obtained by the method of inverse propensity score weighting, using the estimated propensity score, even when the true one is known. When the true propensity score is unknown but parametric, it is conjectured from the literature that we still need nonparametric propensity score estimation to achieve the efficiency. We formalize this argument and further identify the source of the efficiency loss arising from parametric estimation of the propensity score. We also provide an intuition of why this overfitting is necessary. Our finding suggests that, even when we know that the true propensity score belongs to a parametric class, we still need to estimate the propensity score by a nonparametric method in applications.

Highlights

Estimating treatment effects of a binary treatment or a policy has been one of the most important topics in evaluation studies
We find that a nonparametric sieve estimation of the propensity score has two roles in the efficient estimation of average treatment effects
This suggests that, even though we know the true propensity score belongs to a parametric class, we still need to estimate the propensity score by a nonparametric method. Our intuition behind this result is that the nonparametric sieve estimation of the propensity score plays two roles in the estimation of the treatment effect. It approximates the true propensity score, and second it approximates the conditional expectation of the derivative of the moment condition for the treatment effect with respect to the propensity score

Summary

Introduction

Estimating treatment effects of a binary treatment or a policy has been one of the most important topics in evaluation studies. A nonparametric method of estimating the propensity score may require a large data set, especially when covariates or pre-treatment variables are high dimensional For this reason, many empirical researchers estimate the propensity score parametrically using the probit or logit specification, given the idea that these parametric models are still good approximations to the true propensity score. We find that a nonparametric sieve estimation of the propensity score has two roles in the efficient estimation of average treatment effects It approximates the true propensity score, and second it approximates the conditional expectation of the derivative of the moment function for the treatment effect with respect to the propensity score.

Estimation of Average Treatment Effect

Efficient Estimation When the True Propensity Score Is Parametric

Generalization to Estimating the Weighted Average Treatment Effect

Conclusions