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Should We Adjust for the Test for Pre-trends in Difference-in-Difference Designs?

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  • Jonathan Roth

Abstract

The common practice in difference-in-difference (DiD) designs is to check for parallel trends prior to treatment assignment, yet typical estimation and inference does not account for the fact that this test has occurred. I analyze the properties of the traditional DiD estimator conditional on having passed (i.e. not rejected) the test for parallel pre-trends. When the DiD design is valid and the test for pre-trends confirms it, the typical DiD estimator is unbiased, but traditional standard errors are overly conservative. Additionally, there exists an alternative unbiased estimator that is more efficient than the traditional DiD estimator under parallel trends. However, when in population there is a non-zero pre-trend but we fail to reject the hypothesis of parallel pre-trends, the DiD estimator is generally biased relative to the population DiD coefficient. Moreover, if the trend is monotone, then under reasonable assumptions the bias from conditioning exacerbates the bias relative to the true treatment effect. I propose new estimation and inference procedures that account for the test for parallel trends, and compare their performance to that of the traditional estimator in a Monte Carlo simulation.

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  • Jonathan Roth, 2018. "Should We Adjust for the Test for Pre-trends in Difference-in-Difference Designs?," Papers 1804.01208, arXiv.org, revised May 2018.
    • Handle: RePEc:arx:papers:1804.01208
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    Cited by:

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    3. Indra Kurniawan, Muhammad, 2021. "Has access to health insurance through the Indonesian social security system improved peoples understanding of health issues? Evidence from a national survey," Warwick-Monash Economics Student Papers 14, Warwick Monash Economics Student Papers.
    4. 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.
    5. Mihai Alexandru Codreanu & Tom Waters, 2023. "Do work search requirements work? Evidence from a UK reform targeting single parents," IFS Working Papers W23/02, Institute for Fiscal Studies.

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