Inference with Cluster Imbalance: The Case of State Corporate Laws

A workhorse research design identifies the effects of corporate governance by changes in state laws, clustering standard errors by state of incorporation. Asymptotic inference using these standard errors, however, dramatically understates false positives: in a typical specification, randomly generated placebo laws have 1/5/10%-level significant estimated treatment effects 9/21/30% of the time. This poor finite sample performance is due to unequal cluster sizes, especially Delaware's concentration of half of all incorporations. Bootstrap or permutation tests mostly fix the problem, common robustness checks less so. The placebo law approach can also be used to calculate power, which will be acceptably high only for substantial effect sizes.