A third order optimum property of the ML estimator in a linear functional relationship model and simultaneous equation system in econometrics
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The maximum likelihood (ML) estimator and its modification in the linear functional relationship model with incidental parameters are shown to be third-order asymptotically efficient among a class of almost median-unbiased and almost mean-unbiased estimators, respectively, in the large sample sense. This means that the limited information maximum likelihood (LIML) estimator in the simultaneous equation system is third-order asymptotically efficient when the number of excluded exogenous variables in a particular structural equation is growing along with the sample size. It implies that the LIML estimator has an optimum property when the system of structural equations is large.
Key words and phrasesMaximum likelihood estimator third-order efficiency linear functional relationship incidental parameter LIML estimator large econometric models
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