Abstract: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. The proposed critical value guarantees third-order refinement, and it does not require resampling because it is a closed-form function of the estimated score skewness and kurtosis. Simulations show that our proposal can make a difference in size control with as few as 10 clusters.
Keywords: Cluster robust inference, Cramér-Edgeworth expansion, Asymptotic refinement
From: Bulat Gafarov [view email]
[v1]
Wed, 25 Mar 2026 20:00:38 UTC (175 KB)
[v2]
Tue, 2 Jun 2026 23:53:29 UTC (300 KB)
[v3]
Fri, 7 Aug 2026 18:25:30 UTC (71 KB)
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