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

This paper proposes a new approach to identifying and estimating the time-varying average treatment effect (ATE) using panel data to control for unobserved fixed effects. The proposed approach allows for treatment effect heterogeneity induced by unobserved fixed effects. Under such heterogeneity, while existing panel data approaches identify and estimate the ATEs only for limited subpopulations, the proposed approach identifies and estimates the ATE for the entire population. The proposed approach requires two conditions: (i) The proportion of additive unobserved fixed 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 fixed effects conditional on the assigned treatment. Under these conditions, the approach first identifies observed covariates parameters and the proportion of fixed effects terms. The approach then identifies the ATE by combining observed data with them to predict and adjust unobserved potential outcome for each treated and untreated unit. Based on the identification results, 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.