Using Monte Carlo methodology, this paper investigates the effect of dynamics and simultaneity on the finite sample properties of instrumental variables statistics for testing nested and nonnested hypotheses. Simple numerical-analytical formulae (response surfaces) are obtained which closely approximate the statistics' unknown size and power functions for a dynamic simultaneous-equations model. The analysis illustrates the value and limitations of asymptotic theory in interpreting finite sample properties. Two practical results arise. The F form and the Wald statistic is favored over its chi-squared form, and "large-sigma" and small "effective" sample size strongly affect the test of over-identifying restrictions and the Cox-type test.

This paper evaluates an empirical model of U.K. money demand developed by Milton Friedman and Anna J. Schwartz in Monetary Trends in the United States and the United Kingdom. Testing reveals misspecification and hence the potential for an improved model. Using recursive procedures on their annual data, we obtain a better-fitting, constant, dynamic error-correction (cointegration) model. Results on exogeneity and encompassing imply that our money demand model is interpretable as a model of money but not of prices, since its constancy holds only conditionally on contemporaneous prices.