Formal test for one-way versus two-way clustering

Develop and validate a formal statistical procedure to test one-way clustering against two-way clustering in linear regression models with clustered disturbances, and assess whether an adaptation of score-variance tests provides a correct and reliable solution.

Background

Determining whether dependence occurs along one or two clustering dimensions is crucial for valid inference. While two-way clustering methods exist, a formal test to choose between one-way and two-way clustering has not been established. The literature conjectures that score-variance tests might be adapted, but this remains to be shown rigorously.