Inference about Clustering and Parametric Assumptions in Covariance Matrix Estimation

Selecting an estimator for the variance covariance matrix is an important step in hypothesis testing. From less robust to more robust, the available choices include: Eicker/White heteroskedasticity-robust standard errors, Newey and West heteroskedasticity-and-autocorrelation- robust standard errors, and 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. 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. Our main focus is on inference about clustering although the proposed robustness testing strategy can also improve inference about parametric assumptions in covariance matrix estimation, which we demonstrate for the case of testing for heteroskedasticity. We also show why the existing clustering test and other applications of the White (1980) robustness testing approach 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.