Statistical Inference for the Factor Model Approach to Estimate Causal Effects in Quasi-Experimental Settings

Abstract

Causal inference using quasi-experimental data is of great interest to marketers. The factor model approach to estimate treatment effects accommodates a large number of control units and can easily handle a large number of treatment units while flexibly allowing for cases where the treatment is outside the range of the control units. However, the factor model method lacks formal inference theory, instead relying on bootstrap or permutation procedures with strong assumptions. Specifically, the extant Xu (2017) bootstrap procedure requires that the treatment and control error variances are equal. In this research the authors establish that when this assumption is violated, the bootstrap procedure results in biased coverage intervals. The authors develop a formal inference theory for the factor model approach to estimate the average treatment effects on the treated. The approach enables formal quantification of uncertainty through hypothesis testing and confidence intervals. The inference method is applicable to both stationary and nonstationary data. More importantly, the inference theory accommodates treatment and control unit outcomes with different distributions, which includes different error variances as a special case. The authors show the performance of the inference theory with simulated data. Finally, they apply the method to empirically quantify the uncertainty in the effect of legalizing recreational marijuana on the beer market and the sales effect of a digitally native online brand opening a physical showroom.