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MSE-Optimal Difference-in-Differences Estimator

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  • Yamato Igarashi

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.

Suggested Citation

  • Yamato Igarashi, 2026. "MSE-Optimal Difference-in-Differences Estimator," Papers 2605.05056, arXiv.org.
    • Handle: RePEc:arx:papers:2605.05056
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    References listed on IDEAS

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    1. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    2. Mario Fiorini & Wooyong Lee & Gregor Pfeifer & Gregor-Gabriel Pfeifer, 2024. "A Simple Approach to Staggered Difference-in-Differences in the Presence of Spillovers," CESifo Working Paper Series 11011, CESifo.
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    4. Shoya Ishimaru, 2026. "Estimating Treatment Effects in Panel Data Without Parallel Trends," Papers 2601.08281, arXiv.org.
    5. Clément de Chaisemartin & Xavier D’Haultfœuille, 2023. "Two-way fixed effects and differences-in-differences with heterogeneous treatment effects: a survey," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 1-30.
    6. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
    7. Jonathan Roth, 2022. "Pretest with Caution: Event-Study Estimates after Testing for Parallel Trends," American Economic Review: Insights, American Economic Association, vol. 4(3), pages 305-322, September.
    8. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.
    9. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
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    11. Kyle Butts, 2021. "Difference-in-Differences Estimation with Spatial Spillovers," Papers 2105.03737, arXiv.org, revised Jun 2023.
    12. Card, David & Krueger, Alan B, 1994. "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania," American Economic Review, American Economic Association, vol. 84(4), pages 772-793, September.
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