Inference about clustering and parametric assumptions in covariance matrix estimation

Selecting an estimator for the covariance matrix of a regression’s parameter estimates is an important step in hypothesis testing. From less robust to more robust, the available choices include: Eicker/White heteroskedasticity-robust standard errors, cluster-robust standard errors, and multi-way cluster-robust standard errors. The rationale for using a less robust covariance matrix estimator is that tests conducted using a less robust covariance matrix estimator can have better power properties. This motivates tests that examine the appropriate level of robustness in covariance matrix estimation. In this paper we propose a new robustness testing strategy, and show that it can dramatically improve inference about the proper level of robustness in covariance matrix estimation. In the leading empirically relevant example, the placebo treatment application introduced by Bertrand, Du‡o and Mullainathan (2004), power of the proposed robustness testing strategy against the null hypothesis “no clustering”is 0.82 while power of the existing robustness testing approach against the same null is only 0.04. We also show why the existing clustering test and other applications of the White (1980) robustness testing approach often perform poorly, which to our knowledge has not been well understood. The insight into why this existing testing approach performs poorly is also the basis for the proposed robustness testing strategy. Keywords: covariance matrix estimator; cluster-robust; heteroskedasticity-robust; power; size, …nite samples. JEL Classi…cation Codes: C10, C12, C13, C52. We thank two anonymous referees for their useful comments and suggestions which has led to an improved presentation of the paper. We also thank Jay Bhattacharya (Stanford University) for numerous discussions on the early versions of the paper. The usual disclaimer applies. yDepartment of Economics, University of Waterloo, Canada. Email: [email protected]. zDepartment of Statistics & Actuarial Science and School of Accounting & Finance, University of Waterloo, Canada. Email: [email protected].