arXiv 6 Feb 2025 · Econometrics
arXiv:2502.03865 · PDF · DOI · OpenAlex · Extracted main text
This paper develops procedures to combine clusters for the approximate randomization test proposed by Canay, Romano, and Shaikh (2017). Their test can be used to conduct inference with a small number of clusters and imposes weak requirements on the correlation structure. However, their test requires the target parameter to be identified within each cluster. A leading example where this requirement fails to hold is when a variable has no variation within clusters. For instance, this happens in difference-in-differences designs because the treatment variable equals zero in the control clusters. Under this scenario, combining control and treated clusters can solve the identification problem, and the test remains valid. However, there is an arbitrariness in how the clusters are combined. In this paper, I develop computationally efficient procedures to combine clusters when this identification requirement does not hold. Clusters are combined to maximize local asymptotic power. The simulation study and empirical application show that the procedures to combine clusters perform well in various settings.
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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 | Canay, I. A., J. P. Romano, and A. M. Shaikh (2017) a): Randomization Tests under an Approximate Symmetry Assumption | 1.000 | 8 | 5 | 100% |
| 2 | Dincecco, M. and G. Katz (2016) State Capacity and Long-run Economic Performance | 0.874 | 6 | 3 | 67% |
| 3 | Cai, Y., I. A. Canay, D. Kim, and A. M. Shaikh (2023) On the Implementation of Approximate Randomization Tests in Linear Models with a Small Number of Clusters | 0.874 | 5 | 2 | 100% |
| 4 | Hagemann, A (2022) Permutation inference with a finite number of heterogeneous clusters | 0.874 | 5 | 2 | 100% |
| 5 | Cao, J., C. Hansen, D. Kozbur, and L. Villacorta (2022) Inference for Dependent Data with Learned Clusters | 0.737 | 3 | 2 | 100% |
| 6 | Bester, A., T. Conley, and C. Hansen (2011) Inference with dependent data using cluster covariance estimators | 0.644 | 2 | 2 | 100% |
| 7 | Cameron, A., J. Gelbach, and D. Miller (2008) Bootstrap-Based Improvements for Inference with Clustered Errors | 0.644 | 2 | 2 | 100% |
| 8 | Hoeffding, W (1952) The Large-Sample Power of Tests Based on Permutations of Observations | 0.644 | 2 | 2 | 100% |
| 9 | Ibragimov, R. and U. K. Müller (2016) Inference with Few Heterogeneous Clusters | 0.644 | 2 | 2 | 100% |
| 10 | Abadie, A., S. Athey, G. W. Imbens, and J. M. Wooldridge (2022) When Should You Adjust Standard Errors for Clustering? | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 32 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Cluster-robust inference with a single treated cluster using the t-test | 0.644 | 2 | 2 |
| 2 | Inference with few treated units | 0.405 | 1 | 1 |