MSE-Optimal Difference-in-Differences Estimator
TLDR
This paper introduces an MSE-optimal Difference-in-Differences estimator that selects pre-trend length to balance bias and variance, improving accuracy.
Key contributions
- Introduces an MSE-optimal DiD estimator by selecting the best pre-trend length.
- Minimizes mean squared error (MSE) by optimally balancing the bias-variance tradeoff.
- Addresses conventional DiD issues: small sample variance and weak parallel trend pre-tests.
- Practical applicability demonstrated through simulations and an empirical case study.
Why it matters
Conventional DiD methods often face accuracy issues, especially with small samples or weak pre-tests. This paper introduces an MSE-optimal estimator balancing bias and variance, leading to more robust and reliable causal inference.
Original 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.
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