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.
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