This paper examines some implications of the observation that the same Lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses. A characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification, and the consequences for finite sample power properties are examined by Monte Carlo experiments.

L. G. Godfrey, M. R. Wickens; Testing Linear and Log-Linear Regressions for Functional Form, The Review of Economic Studies, Volume 48, Issue 3, 1 July 1981, Pa