Econometrica: May, 1977, Volume 45, Issue 4

The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model

https://doi.org/0012-9682(197705)45:4<955:TMLATN>2.0.CO;2-5
p. 955-968

Takeshi Amemiya

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. Hausman's instrumental-variable interpretation of the maximum likelihood estimator is extended to the general nonlinear simultaneous equation model.