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Inference for Factor Model Based Average Treatment Effects

In this paper we consider using a factor-model-based method, also known as the generalized synthetic control method, to estimate average treatment effects. This method is best suited for cases where there is only one (or a few) treated unit(s), a large number of control units, and large pre and post-treatment sample sizes (i.e., long panel). These settings of a long panel data are quite common in marketing due to the prevalence of daily and weekly data at the customer, store or company level. Existing inference methods lack theory and use a bootstrap or permutation procedure that either assumes that idiosyncratic errors have the same variance for the treated and control units or require that the treated units's error variances be the same during the pre and posttreatment periods. Our inference for the factor model based ATE addresses both issues, allowing the method to be more widely applied, and provides previously unknown distribution theory. We also propose a modified Bai and Ng model selection criterion to accurately select the number of factors even in finite samples. Simulations confirm our theoretical analysis, and an empirical application examines the effect of opening a showroom by e-tailer on its online sales.