Dynamic treatment effect estimation with interactive fixed effects and short panels

Abstract

We study the estimation and inference of dynamic average treatment effect parameters when parallel trends holds conditional on interactive fixed effects and where units enter into treatment at different time periods. Our proposed generalized method of moments estimator consists of two parts: first, we estimate the unobserved time effects by applying the fixed-$T$ consistent quasi-long-differencing estimator of Ahn et al., (2013) to the never-treated group. Second, we estimate the interactive fixed effects for treated groups post-treatment to recover their unobserved counterfactual outcomes then subtract this quantity from the observed outcomes and average over group membership to estimate the Average Treatment Effect on the Treated. We also demonstrate the robustness of two-way fixed effects to certain parallel trends violations and describe how to test for consistency. We investigate the effect of Walmart openings on local economic conditions and demonstrate that our methods ameliorate pre-trend violations commonly found in the literature. We also provide statistical software to implement our estimator in Julia and R.