Robust post-matching inference
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.
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Bootstrapping allows for consistent standard errors for matching without replacement but not for matching with replacement.
“For example, bootstrapping allows for consistent standard errors for matching without replacement (Abadie and Spiess, 2022), but not for matching with replacement (Abadie and Imbens 2008).”
From The joint impact of the European Union emissions trading system on carbon emissions and economic performance (2023) · cites this paper as Abadie and Spiess, 2022
The result of Abadie and Spiess (2022) only holds for matching without replacement.
“However, the result of Abadie and Spiess (2022) only holds for matching without replacement.”
From The joint impact of the European Union emissions trading system on carbon emissions and economic performance (2023) · cites this paper as Abadie and Spiess (2022)
Abadie and Spiess (2022) demonstrate that the standard errors of regression coefficients in matched samples without replacement are consistent provided that they are clustered at the level of the matched sets.
“Abadie and Spiess (2022) demonstrate that the standard errors of regression coefficients in matched samples without replacement are consistent provided that they are clustered at the level of the matched sets.”
From The joint impact of the European Union emissions trading system on carbon emissions and economic performance (2023) · cites this paper as Abadie and Spiess (2022)
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- Authors
- Abadie, A., & Spiess, J.
- Affiliations
- Massachusetts Institute of Technology (US)
- Stanford University (US)
- Corresponding author
- Abadie, Alberto
- ORCID
- Spiess, Jann
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2021-01-14
- Volume
- 117
- Issue
- 538
- Pages
- 983-995
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2912110689
- Cited by
- 169
- References
- 31
- Citations by year
- 2026: 19 · 2025: 30 · 2024: 38 · 2023: 25 · 2022: 20 · 2021: 13 · 2020: 10 · 2019: 5 · 2018: 6 · 2017: 3
- FWCI
- 12.03
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- NSF (SES 0961707)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- nearest neighbor matching, standard errors, confidence intervals, model misspecification, treatment effect estimation, matched data, asymptotic validity, robust inference, observational studies, covariate balance
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