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The Maximum Likelihood Stage Least Squares Estimator in the Nonlinear Simultaneous Equations Model

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  • Takeshi Amemiya

Abstract

The consistency and the asymptotic normality of the maximum likelihood estimator in the general nonlinear simultaneous equation model are proved. It is shown that the proof depends on the assumption of normality unlike in the linear simultaneous equation model. It is proved that the maximum likelihood estimator is asymptotically more efficient than the nonlinear three-stage least squares estimator if the specification is correct, However, the latter has the advantage of being consistent even when the normality assumption is removed. Hausrnan' s instrumental-variable-interpretation of the maximum likelihood estimator is extended to the general nonlinear simultaneous equation model.

Suggested Citation

  • Takeshi Amemiya, 1975. "The Maximum Likelihood Stage Least Squares Estimator in the Nonlinear Simultaneous Equations Model," NBER Working Papers 0090, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:0090
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    References listed on IDEAS

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    1. Dale W. Jorgenson & Jean-Jacques Laffont, 1974. "Efficient Estimation of Nonlinear Simultaneous Equations with Additive Disturbances," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 615-640, National Bureau of Economic Research, Inc.
    2. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
    3. Hausman, Jerry A, 1975. "An Instrumental Variable Approach to Full Information Estimators for Linear and Certain Nonlinear Econometric Models," Econometrica, Econometric Society, vol. 43(4), pages 727-738, July.
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