MSE-Optimal Difference-in-Differences Estimator

TL;DR

This paper introduces an MSE-optimal difference-in-differences estimator that optimally selects pre-trend lengths to improve accuracy, addressing limitations of conventional DiD models especially in small samples.

Contribution

It develops a new DiD estimation method that minimizes mean squared error by choosing the optimal pre-trend length, enhancing validity and precision.

Findings

Simulation results show improved estimator accuracy.

Empirical application demonstrates practical usefulness.

Addresses bias-variance tradeoff in DiD estimation.

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.