Econometrica: Sep, 1982, Volume 50, Issue 5

On the Consistency of Nonlinear FIML

https://doi.org/0012-9682(198209)50:5<1307:OTCONF>2.0.CO;2-8
p. 1307-1324

P. C. B. Phillips

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.