A0992
Title: Nuisance parameters, modified profile likelihood and Jacobian prior
Authors: Guangjie Li - Cardiff University (United Kingdom) [presenting]
Roberto Leon-Gonzalez - GRIPS (Japan)
Abstract: In a model with nuisance parameters, the maximum likelihood estimators (MLE) of the parameters of interest can be biased. One can reduce the bias due to the presence of the nuisance parameters by removing the $O(1)$ bias of the profile likelihood score. To achieve this, the Jacobian integrated likelihood (JIL) is proposed obtained by using a prior consisting of the Jacobian determinant of the new nuisance parameters, which are functions of the original nuisance parameters and are independent of the dependent variable. The adjusted MPL is proposed, which is easier to be computed and can also remove the $O(1)$ bias of the profile likelihood score. For panel fixed effects models, both the JIL and the adjusted MPL can remove the bias of order $O(T^{-1})$ in the MLE as the cross-sectional size ($N$) increases. The conditions when the estimators from the adjusted MPL and the JIL are the same and consistent with $N$ being large relative to $T$ are given. Although the adjusted MPL and the JIL do not always exist, one can use their first-order conditions to obtain bias-reduced estimators. The theoretical results are demonstrated by panel binary choice models and dynamic panel linear models with exogenous and predetermined regressors.
