# A Modified Randomization Test for the Level of Clustering

@inproceedings{Cai2021AMR, title={A Modified Randomization Test for the Level of Clustering}, author={Yong Cai}, year={2021} }

Suppose a researcher observes individuals within a county within a state. Given concerns about correlation across individuals, at which level should they cluster their observations for inference? This paper proposes a modified randomization test as a robustness check for their chosen specification in a linear regression setting. Existing tests require either the number of states or number of counties to be large. Our method is designed for settings with few states and few counties. While the… Expand

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#### References

SHOWING 1-10 OF 20 REFERENCES

Testing for the appropriate level of clustering in linear regression models

- Computer Science
- 2020

The overwhelming majority of empirical research that uses cluster-robust inference assumes that the clustering structure is known, even though there are often several possible ways in which a dataset… Expand

Randomization Tests Under an Approximate Symmetry Assumption

- Mathematics
- 2017

This paper develops a theory of randomization tests under an approximate symmetry assumption. Randomization tests provide a general means of constructing tests that control size in finite samples… Expand

Bootstrap-Based Improvements for Inference with Clustered Errors

- The Review of Economics and Statistics,
- 2008

Measuring Success in Education: The Role of Effort on the Test Itself

- Psychology
- 2017

Tests measuring and comparing educational achievement are an important policy tool. We experimentally show that offering students extrinsic incentives to put forth effort on such achievement tests… Expand

Inference with Few Heterogeneous Clusters

- Mathematics
- Review of Economics and Statistics
- 2016

Abstract Suppose estimating a model on each of a small number of potentially heterogeneous clusters yields approximately independent, unbiased, and Gaussian parameter estimators. We make two… Expand

Bias reduction in standard errors for linear regression with multi-stage samples

- Computer Science, Mathematics
- 2002

A User's Guide to Approximate Randomization Tests with a Small Number of Clusters

- Economics
- 2021

This paper provides a user’s guide to the general theory of approximate randomization tests developed in Canay et al. (2017a) when specialized to linear regressions with clustered data. Such… Expand

Asymptotic Theory for Clustered Samples

- Mathematics, Economics
- 2019

We provide a complete asymptotic distribution theory for clustered data with a large number of groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and… Expand

THE WILD BOOTSTRAP WITH A “SMALL” NUMBER OF “LARGE” CLUSTERS

- 2018

This paper studies the wild bootstrap–based test proposed in Cameron, Gelbach, and Miller (2008). Existing analyses of its properties require that number of clusters is “large.” In an asymptotic… Expand

When Should You Adjust Standard Errors for Clustering?

- Mathematics, Economics
- 2017

This paper argues that clustering is in essence a design problem, either a sampling design or an experimental design issue, and takes the view that this second perspective best fits the typical setting in economics where clustering adjustments are used. Expand