Estimation of Average Treatment Effects Using Panel Data when Treatment Effects Are Heterogeneous by Unobserved Fixed Effects

Abstract

This paper proposes a new approach to identifying and estimating the time-varying average treatment effect (ATE) using panel data to control for unobserved xed effects. The proposed approach allows for treatment effect heterogeneity induced by unobserved xed effects. Under such heterogeneity, while existing panel data approaches identify and estimate the ATEs only for limited subpopulations, the proposed approach identi es and estimates the ATE for the entire population. The proposed approach requires two conditions: (i) The proportion of additive unobserved xed effects terms in the treated and untreated potential outcome models is constant across units and time, and (ii) We have exogenous variables that correlate with unobserved xed effects conditional on the assigned treatment. Under these conditions, the approach rst identi es observed covariates parameters and the proportion of xed effects terms. The approach then identi es the ATE by combining observed data with them to predict and adjust unobserved potential outcome for each treated and untreated unit. Based on the identi cation result, this paper proposes an estimator of the ATE, which takes the form of a generalized method of moments. I apply the estimator to estimate the impact of a mother smoking during pregnancy on her child's birth weight.