Multiple Optima and Asymptotic Approximations in the Partial Adjustment Model

This paper examines statistical problems which arise in empirical applications of the partial adjustment model with autoregressive errors when the model is nearly nonidentified. The results of Monte Carlo experiments show that the NLS estimation criterion function is multipeaked with high probability when the model is nearly nonidentified. In the cases examined the finite-sample distributions of the NLS estimators and the Wald test statistics are poorly approximated by their asymptotic distributions. The asymptotic approximation works better for the likelihood ratio (LR) test statistics, but still can be unsatisfactory. When the Wald and LR tests are based on bootstrap critical values the size distortions are effectively eliminated