Bootstrap Methods for Inference in a SUR model with Autocorrelated Disturbances

Although the Parks (1967) estimator for a SUR model with AR disturbances is efficient both asymptotically and in small samples, Kmenta and Gilbert (1970) and more recently Beck and Katz (1995) note that estimated standard errors tend to be biased downward as compared with the true variability of the estimates. This bias leads to tests that show over-rejection and to confidence intervals that are too small. We suggest bootstrapping the tests to correct this inference problem. After illustrating the over rejection associated with the estimated asymptotic standard errors, we develop a bootstrap approach to inference for this model, illustrate its use, and show using Monte Carlo methods that the bootstrap gives rejection probabilities close to the nominal level chosen by the researcher.