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Asymptotic Expansions and Higher Order Properties of Semi-Parametric Estimators in a System of Simultaneous Equations

By Naoto Kunitomo and Yukitoshi Matsushita

Abstract

Asymptotic expansions are made for the distributions of the Maximum Empirical Likelihood (MEL) estimator and the Estimating Equation (EE) estimator (or the Generalized Method of Moments (GMM) in econometrics) for the coefficients of a single structural equation in a system of linear simultaneous equations, which corresponds to a reduced rank regression model. The expansions in terms of the sample size, when the non-centrality parameters increase proportionally, are carried out to O(n-1). Comparisons of the distributions of the MEL and GMM estimators are made. Also we relate the asymptotic expansions of the distributions of the MEL and GMM estimators to the corresponding expansions for the Limited Information Maximum Likelihood (LIML) and the Two-Stage Least Squares (TSLS) estimators. We give useful information on the higher order properties of alternative estimators including the semi-parametric inefficiency factor under the homoscedasticity assumption.Revised version of CIRJE-F-237(2003); forthcoming in Journal of Multivariate Analysis

Topics: Asymptotic Expansions, Empirical Likelihood, Estimating Equation, Generalized Method of Moments, Limited Information Maximum Likelihood, Two-Stage Least Squares, Linear Simultaneous Equations, Reduced Rank Regression, 335
Publisher: University of Tokyo
Year: 2009
DOI identifier: 10.1016/j.jmva.2009.02.004
OAI identifier: oai:repository.dl.itc.u-tokyo.ac.jp:2261/25756
Provided by: UT Repository
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