An Encompassing Approach to Conditional Mean Tests with Applications to Testing Nonnested Hypotheses

A general class of tests designed to detect conditional mean misspecification for cross section or time series applications is proposed. The tests are derived from a particular application of the encompassing principle. The resulting conditional mean encompassing (CME) tests contain as special cases a version of the Lagrange Multiplier test for nested models, a new test in the presence of nonnested alternatives, and a version of the Durbin-Wu-Hausman test that compares two weighted nonlinear least squares estimators. The tests are valid without any assumption on the conditional variance of the dependent variable and can be computed using any /Tconsistent estimators. Moreover, CME tests for nonlinear, dynamic models are computable from linear least squares regressions.