The Maximum Likelihood Stage Least Squares Estimator in the Nonlinear Simultaneous Equations Model / Takeshi Amemiya.

By:

Amemiya, Takeshi

Contributor(s):

National Bureau of Economic Research

Material type: Text

TextSeries: Working Paper Series (National Bureau of Economic Research) ; no. w0090.Publication details: Cambridge, Mass. National Bureau of Economic Research 1975.Description: 1 online resource: illustrations (black and white)Online resources:

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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.

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June 1975.

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.