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 non-nested 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 of the Wald statistic is favored over its $\chi^2$ form, and "large-$\sigma$" and small "effective" sample size strongly affect the test of over-identifying restrictions and the Cox-type test.