Tests for neglected heterogeneity in moment condition models - Jinyong Hahn; Whitney K. Newey; Richard J. Smith (Centre for Microdata Methods and Practice (cemmap), 2011)
The central concern of the paper is with the formulation of tests of neglected parameter heterogeneity appropriate for model environments specified by a number of unconditional or conditional moment conditions. We initially consider the unconditional moment restrictions framework. Optimal m-tests against moment condition parameter heterogeneity are derived with the relevant Jacobian matrix obtained as the second order derivative of the moment indicator in a leading case. GMM and GEL tests of specification based on generalized information matrix equalities appropriate for moment-based models are described and their relation to the optimal m-tests against moment condition parameter heterogeneity examined. A fundamental and important difference is noted between GMM and GEL constructions. The paper is concluded by a generalization of these tests to the conditional moment context.
Keywords: C13; C30; 330; GMM; GEL; Unconditional Moments; Conditional Moments; Score and LM Tests; Information Matrix Equality; Momentenmethode