Generalized C(α) tests for estimating functions with serial dependence

Abstract

We propose generalized C(α) tests for testing linear and nonlinear parameter restrictions in models specified by estimating functions. The proposed procedures allow for general forms of serial dependence and heteroskedasticity, and can be implemented using any root-n consistent restricted estimator. The asymptotic distribution of the proposed statistic is established under weak regularity conditions. We show that earlier C(α)-type statistics are included as special cases. The problem of testing hypotheses fixing a subvector of the complete parameter vector is discussed in detail as another special case. We also show that such tests provide a simple general solution to the problem of accounting for estimated parameters in the context of two-step procedures where a subvector of model parameters is estimated in a first step and then treated as fixed.