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Under the null of valid specification, pre-tests cannot make post-test inference liberal

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  • Cl'ement de Chaisemartin
  • Xavier D'Haultf{oe}uille

Abstract

Consider a parameter of interest, which can be consistently estimated under some conditions. Suppose also that we can at least partly test these conditions with specification tests. We consider the common practice of conducting inference on the parameter of interest conditional on not rejecting these tests. We show that if the tested conditions hold, conditional inference is valid, though possibly conservative. This holds generally, without imposing any assumption on the asymptotic dependence between the estimator of the parameter of interest and the specification test.

Suggested Citation

  • Cl'ement de Chaisemartin & Xavier D'Haultf{oe}uille, 2024. "Under the null of valid specification, pre-tests cannot make post-test inference liberal," Papers 2407.03725, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2407.03725
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    References listed on IDEAS

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    1. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
    2. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    3. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    4. 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.
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