An Improved Consistent Conditional Moment Test for Regression Models in the Presence of Heteroskedasticity of Unknown Form
نویسنده
چکیده
The purpose of this paper is to propose a simple approach to consistent testing of specification of parametric regression models which is robust and efficient under heteroskedasticity of unknown form. We exploit the duality property of one class of weighting functions for both consistent specification testing and efficient estimation of regression models. An innovative residual empirical process is proposed, employing a projection-based transformation. It is shown that the new residual empirical process is not affected by the uncertainty from the parameter estimation, only a preliminary √ n-consistent estimator is needed. We establish its efficiency in the sense that the GMM estimator reaching the semiparametric efficiency bound under heteroskedasticity of unknown form is actually employed by the new empirical process under the null. Then a version of Bierens (1990) test based on the new empirical process is proposed, and its asymptotic properties are analyzed. Monte Carlo simulations are conducted to demonstrate the good finite sample properties of the new test statistic. JEL Classification: C12 C21
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