Bayesian Estimation of Treatment Effects in Interactive Fixed Effects Models

In this study, we suggest an imputation approach for estimating treatment effect parameters when untreated potential outcomes follow a panel data model that has both interactive fixed effects (IFE) and additive two-way fixed effects. In settings with common treatment timing and staggered treatment adoption, we consider a hybrid approach involving classical and Bayesian methods. First, using the classical random sampling approach across units, we show that treatment effect parameters are identified in our setting under a selection on observables and unobservables assumption. We then suggest an efficient Gibbs sampler for estimating the treatment effect parameters using our suggested imputation approach. We consider two Bayesian methods for selecting the number of factors in the postulated model for untreated potential outcomes. We provide simulation evidence showing that our imputation approach performs satisfactorily. In an empirical application, we use our approach to study the causal effect of police presence on crime.