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Robust Post-Matching Inference

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  • Alberto Abadie
  • Jann Spiess

Abstract

Nearest-neighbor matching is a popular nonparametric tool to create balance between treatment and control groups in observational studies. As a preprocessing step before regression, matching reduces the dependence on parametric modeling assumptions. In current empirical practice, however, the matching step is often ignored in the calculation of standard errors and confidence intervals. In this article, we show that ignoring the matching step results in asymptotically valid standard errors if matching is done without replacement and the regression model is correctly specified relative to the population regression function of the outcome variable on the treatment variable and all the covariates used for matching. However, standard errors that ignore the matching step are not valid if matching is conducted with replacement or, more crucially, if the second step regression model is misspecified in the sense indicated above. Moreover, correct specification of the regression model is not required for consistent estimation of treatment effects with matched data. We show that two easily implementable alternatives produce approximations to the distribution of the post-matching estimator that are robust to misspecification. A simulation study and an empirical example demonstrate the empirical relevance of our results. Supplementary materials for this article are available online.

Suggested Citation

  • Alberto Abadie & Jann Spiess, 2022. "Robust Post-Matching Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 983-995, April.
  • Handle: RePEc:taf:jnlasa:v:117:y:2022:i:538:p:983-995
    DOI: 10.1080/01621459.2020.1840383
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    1. Dechezleprêtre, Antoine & Nachtigall, Daniel & Venmans, Frank, 2023. "The joint impact of the European Union emissions trading system on carbon emissions and economic performance," Journal of Environmental Economics and Management, Elsevier, vol. 118(C).
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    3. de Rassenfosse, Gaétan & Pellegrino, Gabriele & Raiteri, Emilio, 2024. "Do patents enable disclosure? Evidence from the invention secrecy act," International Journal of Industrial Organization, Elsevier, vol. 92(C).
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    5. Görg, Holger & Lehr, Jakob, 2024. "Short and medium-term effects of foreign acquisitions on manufacturing firms: Evidence from Germany," Open Access Publications from Kiel Institute for the World Economy 302104, Kiel Institute for the World Economy (IfW Kiel).
    6. Vu, Khoa & Dao, Vu & DeJaeghere, Joan & Glewwe, Paul, 2024. "Collaborative learning in the Vietnam Escuela Nueva Model and students’ learning behaviors: A mixed methods longitudinal study," International Journal of Educational Development, Elsevier, vol. 106(C).
    7. Glazer Amanda K. & Pimentel Samuel D., 2023. "Robust inference for matching under rolling enrollment," Journal of Causal Inference, De Gruyter, vol. 11(1), pages 1-19, January.
    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. Shaojie Wei & Chao Zhang & Zhi Geng & Shanshan Luo, 2024. "Identifiability and Estimation for Potential-Outcome Means with Misclassified Outcomes," Mathematics, MDPI, vol. 12(18), pages 1-19, September.

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