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Analytic inference with two-way clustering

Laurent Davezies, Xavier D'Haultfœuille, Yannick Guyonvarch

arXiv 25 Jun 2025 · Econometrics

arXiv:2506.20749 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper studies analytic inference along two dimensions of clustering. In such setups, the commonly used approach has two drawbacks. First, the corresponding variance estimator is not necessarily positive. Second, inference is invalid in non-Gaussian regimes, namely when the estimator of the parameter of interest is not asymptotically Gaussian. We consider a simple fix that addresses both issues. In Gaussian regimes, the corresponding tests are asymptotically exact and equivalent to usual ones. Otherwise, the new tests are asymptotically conservative. We also establish their uniform validity over a certain class of data generating processes. Independently of our tests, we highlight potential issues with multiple testing and nonlinear estimators under two-way clustering. Finally, we compare our approach with existing ones through simulations.

Citation extraction

18
references
45
in-text mentions
18
distinct cited
1
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8,820
main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Menzel, Konrad (2021) Bootstrap with cluster-dependence in two or more dimensions0.693131100%
2Kallenberg, Olav (1989) On the representation theorem for exchangeable arrays0.5114150%
3Aldous, D. J (1981) Representations for partially exchangeable arrays of random variables0.51121100%
4Hoover, D. N (1979) Relations on probability spaces and arrays of random variables0.51121100%
5Cameron, A Colin and Gelbach, Jonah B and Miller, Douglas L (2011) Robust inference with multiway clustering0.51121100%
6Davezies, L. and D'Haultfœuille, X. and Guyonvarch, Y (2021) Empirical Process Results for Exchangeable Arrays self0.51121100%
7MacKinnon, James G and Nielsen, Morten Ørregaard and Webb, Matthew D (2024) Jackknife inference with two-way clustering0.51121100%
8Miglioretti, Diana L and Heagerty, Patrick J (2007) Marginal modeling of nonnested multilevel data using standard software0.51121100%
9Thompson, Samuel B (2011) Simple formulas for standard errors that cluster by both firm and time0.51121100%
10Chen, Jiahua and J.N.K. Rao (2007) Asymptotic Normalityunder Two-Phase Sampling Designs0.4052150%

Showing the top 10 of 18 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Jackknife Inference with Two0.04167em–0.08333em Way Clustering0.92843
2Gaussian Approximation for Maximum Score and Non-Smooth M-Estimators with Multiway Dependence0.64422
3Bootstrap Inference under General Two-way Clustering with Serially and Spatially Dependent Common Effects0.64422
4Robust Inference for Dyadic Data with Dependent Ordered Nodes0.64422
5Cross-Fitting-Free Debiased Machine Learning with Multiway Dependence0.51121
6When Can We Trust Cluster-Robust Inference?0.51121
7Inference in High-Dimensional Panel Models: Two-Way Dependence and Unobserved Heterogeneity0.40511
8Two-way Clustering Robust Variance Estimator in Quantile Regression Models0.40511