MSE-Optimal Difference-in-Differences Estimator

Abstract: This paper develops a difference-in-differences (DiD) estimation method that selects the optimal length of pre-trends by minimizing the mean squared error (MSE). Conventional DiD regression models, such as the two-way fixed effects model or the event study model, may suffer from accuracy and validity concerns. If the sample size is small, the estimator may have a larger variance. Also, pre-tests often lack power to detect violations of the parallel trends assumption as Roth (2022) highlights. By focusing on the bias and variance tradeoff, the proposed method derives the MSE-optimal estimator from the optimal length of pre-trends. Simulation results and an empirical application demonstrate the practical applicability of the proposed method.