The Maximum Likelihood Stage Least Squares Estimator in the Nonlinear Simultaneous Equations Model
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.
The author had stimulating discussions with David Belsley, Michio Hatanaka, and Jerry Hausman.
(Published as "The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model") Econometrica (1977).(Published as "The Maximum Likelihood, the Minimum Chi-Square and the
Bierens, Herman J. and A. Ronald Gallant (eds.) Nonlinear models. Volume 2 Elgar Reference Collection. International Library of Critical Writings in Econometrics, vol. 8. Cheltenham, U.K. and Lyme, NH: Elgar, 1997.