Friday, June 15, 2012

F-tests Based on the HC or HAC Covariance Matrix Estimators

We all do it - we compute "robust" standard errors when estimating a regression model in any context where we suspect that the model's errors may be heteroskedastic and/or autocorrelated.

More correctly, we select the option in our favourite econometrics package so that the (asymptotic) covariance matrix for our estimated coefficients is estimated, using either White's heteroskedasticity-consistent (HC) estimator, or the Newey-West heteroskedasticity & autocorrelation-consistent (HAC) estimator.

The square roots of the diagonal elements of the estimated covariance matrix then provide us with the robust standard errors that we want. These standard errors are consistent estimates of the true standard deviations of the estimated coefficients, even if the errors are heteroskedastic (in White's case) or heteroskedastic and/or autocorrelated (in the Newey-West case).

That's fine, as long as we keep in mind that this is just an asymptotic result.

Then, we use the robust standard error to construct a "t-test"; or the estimated covariance matrix to construct an "F-test", or a Wald test.

And that's when the trouble starts!