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 second-order asymptotic refinement in Rothenberg (1988) to determine critical values. We find substantial size improvements resulting from the second-order theory across a wide range of specifications, including substantial conditional heteroskedasticity. We also find that the size gains result in only moderate increases in the length of the associated confidence interval, which yields an increase in size-adjusted power. Finally, we note that the proposed test statistics do not require that the researcher specify the bandwidth or the kernel.