A third order optimum property of the ML estimator in a linear functional relationship model and simultaneous equation system in econometrics (Q756349)

In this important paper the author shows that the maximum likelihood estimator and its modification in the linear functional relationship with incidental parameters are 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 estimator (LIML) 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.