# Econometrica

## Journal Of The Econometric Society

### An International Society for the Advancement of Economic Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Sep, 1991, Volume 59, Issue 5

# Monte Carlo Methodology and the Finite Sample Properties of Instrumental Variables Statistics for Testing Nested and Non-Nested Hypotheses

Neil R. Ericsson

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.