Econometrica: Apr, 1980, Volume 48, Issue 3

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

https://doi.org/0012-9682(198004)48:3<697:SIIAIN>2.0.CO;2-5
p. 697-720

A. Ronald Gallant, Alberto Holly

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.