Monte Carlo methodology and the finite sample properties of statistics for testing nested and non-nested hypotheses

Using recently developed Monte Carlo methodology, this paper investigates the effect of dynamics and simultaneity on the finite sample properties of maximum likelihood and instrumental variables statistics for testing both nested and non-nested hypotheses. Numerical-analytical approximations (response surfaces) to the unknown finite sample size and power functions of those statistics are obtained for dynamic one-and two-equation models. The results illustrate the value of asymptotic theory in interpreting finite sample properties and certain limitations for doing so. Two practical finite sample results arise: the F form of the Wald statistic is strongly favored over its chi-squared form; and the effects of "large-sigma" and a small effective sample size are particularly pronounced for Sargan's (1958) instrumental variables statistic and Ericsson's (1983) Cox-type instrumental variables statistic. Re-examining Pesaran and Deaton's (1978) empirical example illustrates the additional information gained from the instrumental variables statistics.