Estimating the Causal Effect of A Digitally Native Retailer Opening a New Store: A New Two-Step Synthetic Control Method

Abstract

With the rapid growth of omnichannel retailing, digitally native retailers are increasingly opening physical stores. A critical issue for many digitally native retailers is to estimate the causal effect of a new store opening on their online sales. To assess the causal effect, a randomized control field experiment is infeasible, so quasi-experiments offer the best hope. Often, due to the non-availability of a readily matched control group, the use of synthetic control (SC) groups to estimate the causal effect is becoming popular. A crucial identifying assumption for the SC method is the parallel trends assumption, which states that the treatment unit would have followed a path parallel to the synthetic control group unit in the absence of treatment. However, this assumption may not hold in real data, in particular, in the omnichannel context. If this assumption is violated, current methods may yield incorrect and misleading estimates of causal effects. Unfortunately, no formal test of this assumption exists. We propose a new two-step synthetic control (TSSC) method that comprises a new test for the parallel trends assumption in the first step, and the application of an appropriate synthetic control method in the second step. Thus, our approach unifies the synthetic control and the modified synthetic control (MSC) methods. We examine the finite sample performance of our testing procedure using simulation. We apply this method to estimate the cross-channel effect of a digitally native retailer opening a physical showroom on its sales at two locations: Columbus, OH and Austin, TX. We demonstrate the value of our TSSC method by revealing that the cross-channel effect from the TSSC method for Columbus is positive and significant, contrary to the incorrect and misleading result from the traditional SC method that shows a negative and significant effect.

Keywords: retailing; omni-channel; cross-channel; quasi-experiment; synthetic control; treatment effects; nonlinear trend; parallel trend

JEL Classification: C1, C12, C13, C18, C120, C130, C150, C180, C190, C990, M0, M3, M30, M31, M390, L81, L810