Design-Based Multi-Way Clustering

TL;DR

This paper extends the design-based framework to multi-way clustering, addressing variance estimation challenges and providing insights into inference validity under complex dependence structures.

Contribution

It introduces a framework for multi-way clustering with different sampling and assignment dimensions, analyzing variance estimators and inference validity.

Findings

Plug-in variance estimator is usually robust in simulations.

Conservative variance estimator tends to be overly cautious.

Multi-way clustering requires different inference approaches than one-way clustering.

Abstract

This paper extends the design-based framework to settings with multi-way cluster dependence, and shows how multi-way clustering can be justified when clustered assignment and clustered sampling occurs on different dimensions, or when either sampling or assignment is multi-way clustered. Unlike one-way clustering, the plug-in variance estimator in multi-way clustering is no longer conservative, so valid inference either requires an assumption on the correlation of treatment effects or a more conservative variance estimator. Simulations suggest that the plug-in variance estimator is usually robust, and the conservative variance estimator is often too conservative.