## Statistical Inference in an Implicit, Nonlinear, Simultaneous
Equation Mode in the Context of Maximum Likelihood
Estimation

A. Ronald Gallant, Alberto Holly

*Econometrica*, Vol. 48, No. 3. (Apr., 1980), pp. 697-720.

### Abstract

Statistical inference for a system of simultaneous, nonlinear,
implicit equations is discussed. The discussion considers inference as
an adjunct to maximum likelihood estimation rather than in a general
setting. The null and non-null asymptotic distributions of the Wald
test, the Lagrange multiplier test (Rao's efficient score test), and
the likelihood ratio test are obtained. Several refinements in the
existing theory of maximum likelihood estimation are accomplished as
intermediate steps.