A2040
Title: Nonparametric bootstrap correction for incidental parameter bias in GMM
Authors: Yitian Li - KU Leuven (Belgium) [presenting]
Geert Dhaene - KU Leuven (Belgium)
Abstract: The incidental parameter problem has been extensively studied in the context of parametric maximum likelihood estimation. In the last two decades, many methods have been developed to correct (or approximately correct) the bias of maximum likelihood estimates that arises when incidental parameters are present in the model. Nearly all these methods exploit the parametric likelihood structure of the model. In the more general context of GMM estimation, where a full parametric likelihood is lacking, the incidental parameter problem has been much less studied. We show that the nonparametric bootstrap can be used for approximate bias correction in the GMM framework. Our method also yields a novel bias correction in the likelihood setting as a special case. The bias correction can be applied directly to the GMM/ML estimator or to the estimating equations that define the GMM/ML estimator. We also show that the bias correction can be iterated, thereby reducing the asymptotic order of the bias and improving the coverage rate of confidence intervals at each iteration of the bootstrap. We discuss various numerical examples and simulations, including nonlinear models, and show that the method performs well.
