# 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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## Summary

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 phrases

Maximum likelihood estimator third-order efficiency linear functional relationship incidental parameter LIML estimator large econometric models## Preview

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© The Institute of Statistical Mathematics, Tokyo 1987