arXiv 25 Mar 2026 · Econometrics
arXiv:2603.24786 · PDF · DOI · OpenAlex · Extracted main text
It has become standard for empirical studies to conduct inference robust to cluster dependence and heterogeneity. With a small number of clusters, the normal approximation for the $t$-statistics of regression coefficients may be poor. This paper tackles this problem using a critical value based on the conditional Cramér-Edgeworth expansion for the $t$-statistics. Our approach guarantees third-order refinement, regardless of whether a regressor is discrete or not, and, unlike the cluster pairs bootstrap, avoids resampling data. Simulations show that our proposal can make a difference in size control with as few as 10 clusters.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Cameron, A Colin and Gelbach, Jonah B and Miller, Douglas L (2008) Bootstrap-based improvements for inference with clustered errors | 1.000 | 6 | 3 | 100% |
| 2 | Bertrand, Marianne and Duflo, Esther and Mullainathan, Sendhil (2004) How much should we trust differences-in-differences estimates? | 1.000 | 5 | 3 | 100% |
| 3 | Bhattacharya, Rabi N and Rao, R Ranga (1976) Normal Approximation and Asymptotic Expansions | 0.843 | 4 | 4 | 75% |
| 4 | Hall, Peter (1983) Inverting an Edgeworth expansion | 0.843 | 4 | 3 | 75% |
| 5 | Hall, Peter (2013) The Bootstrap and Edgeworth Expansion | 0.843 | 4 | 3 | 75% |
| 6 | Djogbenou, Antoine A and MacKinnon, James G and Nielsen, Morten Ørre… (2019) Asymptotic Theory and Wild Bootstrap Inference with Clustered Errors | 0.814 | 13 | 4 | 54% |
| 7 | Cameron, A Colin and Miller, Douglas L (2015) A practitioner's guide to cluster-robust inference | 0.644 | 2 | 2 | 100% |
| 8 | Cameron, A Colin and Miller, Douglas L (2025) Inference for Regression with Clustered or Spatially Correlated Data | 0.644 | 2 | 2 | 100% |
| 9 | Bhattacharya, Rabi N and Ghosh, Jayanta K (1978) On the validity of the formal Edgeworth expansion | 0.511 | 5 | 2 | 20% |
| 10 | Angst, Jürgen and Poly, Guillaume (2017) A weak Cramér condition and application to Edgeworth expansions | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 25 scored citations.