Accurately Sized Test Statistics with Misspecified Conditional Homoskedasticity

We study the problem of obtaining accurately sized test statistics in finite samples for linear regression models where the error dependence is of unknown form. With an unknown dependence structure there is traditionally a trade-off between the maximum lag over which the correlation is estimated (the bandwidth) and the decision to introduce conditional heteroskedasticity. In consequence, the correlation at far lags is generally omitted and the resultant inflation of the empirical size of test statistics has long been recognized. To allow for correlation at far lags we study test statistics constructed under the possibly misspecified assumption of conditional homoskedasticity. To improve the accuracy of the test statistics, we employ the secondorder asymptotic refinement in Rothenberg (1988) to determine critical values. We find substantial size improvements resulting from the ∗Corresponding author †We thank the members of the Econometrics Lab at Santa Barbara for helpful comments.