We propose a factor-model imputation estimator using a common correlated effects model. This model allows to decompose treatment effects into a direct effect and effects mediated by covariates.
The present paper proposes a new treatment effects estimator that is valid when the number of time periods is small, and the parallel trends condition holds conditional on covariates and unobserved heterogeneity in the form of interactive fixed effects. The estimator also allow the control variables to be affected by treatment and it enables estimation of the resulting indirect effect on the outcome variable. The asymptotic properties of the estimator are established and their accuracy in small samples is investigated using Monte Carlo simulations. The empirical usefulness of the estimator is illustrated using as an example the effect of increased trade competition on firm markups in China.