Frontiers: A Simple Forward Difference-in-Differences Method

The difference-in-differences (DID) method is the most widely used tool to answer causal questions from quasiexperimental data in marketing and the broader social sciences. Because assignment to treatment in quasiexperiments is not random, the selection of proper control units is critically important for estimating the causal effect. DID requires that the treatment unit's outcomes would have been parallel to the average of the control units' outcomes in the absence of treatment. However, this DID parallel trends assumption is likely to be violated when assignment to the treatment and control groups is not random. We propose a simple forward difference-in-differences (Forward DID) method that uses a forward selection algorithm to flexibly select a relevant subset of control units. The Forward DID has several advantages. First, it can be widely applied and suitable even when DID is too restrictive. Second, Forward DID can accommodate any number of control units. Third, there are no overfitting concerns because Forward DID only needs to estimate one parameter after identifying a subset of control units. Fourth, Forward DID has computational advantages over algorithms that consider all possible subsets of control units. Finally, we establish consistency and develop inference theory, which is applicable to both stationary and non stationary data. We demonstrate the usefulness of the Forward DID method and compare it with the alternative methods using simulations and an application to store openings.