I recently read a paper in The Accounting Review (Vol 85, No. 2) titled “Correcting for Cross-Sectional and Time-Series Dependence in Accounting Research” by Ian Gow, Gaizka Ormazabal, and Daniel Taylor. The paper deals with how to adjust for clustering across two dimensions (normally firm and year).

After reading the paper I was was curious how a researcher could adjust for clustering across three dimensions. For example, a study on legal regimes usually has three sets of clusters: year, firm, and country. I contacted Dan Taylor to find out more. He told me that firm clustering is subsumed within country clustering. In other words, as long as you assume that a firm doesn’t change countries during the course of your study, cluster-adjusting by country automatically fixes the problem of lack of independence of observations within a firm.

I kept digging a bit and found a paper that deals with this idea (Gow et al. 2010 cite this paper): “Robust Inference with Multi-Way Clustering” by A. Colin Cameron, Jonah B. Gelbach and Douglas L. Miller, (c) 2006, an NBER working paper. To cite from their paper:

For two-way or multi-way clustering that is nested, one simply clusters at the highest level of aggregation. For example, with individual-level data and clustering on both household and state one should cluster on state.

So, long story short, if you have geographic locations in your study you should cluster on location and year and ignore firm.