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On the Consistency of Nonlinear FIML
P. C. B. Phillips
Abstract
Examples are given which show that normality is not necessary for the consistency of the quasi-maximum likelihood estimator in the nonlinear simultaneous equations model (nonlinear FIML) even when there are major departures from linearity. A possibility theorem is proved which demonstrates that when nonlinear FIML is consistent under normality it is always possible to find a nonnormal error distribution for which the consistency of nonlinear FIML is maintained. The procedure that is developed for finding a class of error distributions which preserve the consistency of nonlinear FIML can be applied more generally and may be useful in other contexts.
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