Asymptotic Properties of Instrumental Variables Statistics for Testing Non-Nested Hypotheses

Abstract

This paper develops Instrumental Variables statistics for testing non-nested hypotheses when the hypotheses considered are single equations from a system of linear dynamic simultaneous equations. Asymptotic distributions of those statistics and of comparable Maximum Likelihood statistics are derived under the null hypothesis, a local non-nested alternative hypothesis, and a local comprehensive alternative hypothesis. The asymptotic powers of the non-nested hypothesis tests are compared with those of tests of nested hypotheses, and a numerical application is given. This paper considers the asymptotic properties of two families of statistics for testing non-nested hypotheses, one based on the Maximum Likelihood (ML) estimator and the other based on the Instrumental Variables (IV) estimator. The models being considered are single equations, linear in their parameters, with serially uncorrelated identically distributed errors. For those statistics based on the IV estimator, each equation being estimated may be from a system of dynamic simultaneous equations with contemporaneously correlated but serially uncorrelated disturbances. For those statistics based on Maximum Likelihood, each model is a classical regression model with normally distributed errors. More explicitly, consider the two non-nested hypotheses,