Yong Cai, Ivan A. Canay, Deborah Kim, Azeem M. Shaikh
arXiv 17 Feb 2021 · Econometrics · publishedJournal of Econometric Methods (2022) · 6 citations (OpenAlex)
arXiv:2102.09058 · PDF · DOI · OpenAlex · Extracted main text
This paper provides a user's guide to the general theory of approximate randomization tests developed in Canay, Romano, and Shaikh (2017) when specialized to linear regressions with clustered data. An important feature of the methodology is that it applies to settings in which the number of clusters is small -- even as small as five. We provide a step-by-step algorithmic description of how to implement the test and construct confidence intervals for the parameter of interest. In doing so, we additionally present three novel results concerning the methodology: we show that the method admits an equivalent implementation based on weighted scores; we show the test and confidence intervals are invariant to whether the test statistic is studentized or not; and we prove convexity of the confidence intervals for scalar parameters. We also articulate the main requirements underlying the test, emphasizing in particular common pitfalls that researchers may encounter. Finally, we illustrate the use of the methodology with two applications that further illuminate these points. The companion {\tt R} and {\tt Stata} packages facilitate the implementation of the methodology and the replication of the empirical exercises.
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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., Romano, J. P. and Shaikh, A. M (2017) Randomization tests under an approximate symmetry assumption self | 1.000 | 15 | 5 | 100% |
| 2 | Munyo, I. and Rossi, M. A (2015) First-day criminal recidivism | 1.000 | 9 | 3 | 100% |
| 3 | Canay, I. A., Santos, A. and Shaikh, A. M (2021) small self | 1.000 | 7 | 3 | 100% |
| 4 | Meng, X., Qian, N. and Yared, P (2015) The institutional causes of china's great famine, 1959–1961 | 1.000 | 6 | 3 | 100% |
| 5 | Cameron, A. C., Gelbach, J. B. and Miller, D. L (2008) Bootstrap-based improvements for inference with clustered errors | 0.737 | 3 | 2 | 100% |
| 6 | Ibragimov, R. and Müller, U. K (2010) t-statistic based correlation and heterogeneity robust inference | 0.644 | 2 | 2 | 100% |
| 7 | Liang, K.-Y. and Zeger, S. L (1986) Longitudinal data analysis using generalized linear models | 0.644 | 2 | 2 | 100% |
| 8 | Canay, I. A., Romano, J. P. and Shaikh, A. M (2017) Supplement to ‘Randomization tests under an approximate symmetry assumption’ self | 0.511 | 2 | 1 | 100% |
| 9 | Bertrand, M., Duflo, E. and Mullainathan, S (2004) How much should we trust differences-in-differences estimates? | 0.405 | 1 | 1 | 100% |
| 10 | Canay, I. A. and Kamat, V (2018) Approximate permutation tests and induced order statistics in the regression discontinuity design self | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 13 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Combining Clusters for the Approximate Randomization Test | 0.874 | 5 | 2 |
| 2 | Network Cluster-Robust Inference | 0.737 | 3 | 2 |
| 3 | Inference with few treated units | 0.585 | 3 | 1 |
| 4 | Cluster-Robust Inference: A Guide to Empirical Practice | 0.405 | 1 | 1 |
| 5 | Randomization Inference: Theory and Applications | 0.405 | 1 | 1 |