Integrated Conditional Moment Tests for Parametric Conditional Distributions

This paper extends the Integrated Conditional Moment (ICM) test for the functional form of nonlinear regression models to tests for parametric conditional distributions. This test is formed on the basis of the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. This test is consistent, and has nontrivial power against √ n -local alternatives. To avoid numerical evaluation of the conditional characteristic function of the model distribution, a simulated integrated conditional moment (SICM) test is proposed, where each theoretical conditional characteristic function is replaced by a simulated counterpart, based on a single random drawing from the corresponding conditional distribution. All the properties of the exact ICM test carry over to the SICM test. ∗A previous version of this paper was presented by Herman Bierens at the ”Symposium on Nonparametric Testing in Econometrics”, March 21, 2008, Indiana University. The helpful comments of Juan Carlos Escanciano are gratefully acknowledged. †Support for research within the Center for the Study of Auctions, Procurements, and Competition Policy (CAPCP) at Penn State has been provided by a gift from the Human Capital Foundation