A General FIML Estimator for a Certain Class of Models that are Non-Linear in the Variables - Erik Mellander (The Research Institute of Industrial Economics (IUI), 1984)
Most econometric multi-equation models estimated are assumed to be linear in both the variables and the parameters. One reason is that, in general, methods of linear algebra cannot be applied to nonlinear systems. In this paper a certain class of nonlinear models is defined, however, the members of which can be formulated in matrix terms. Particular interest is focused upon nonlinearities in the variables. An algorithm for full information maximum likelihood (FIML) is described, including the linear model as a special case. Neither the likelihood function presented, nor its first order derivates are overly complicated relative to the usual (linear) FIML case. The latter makes the suggested approach particularly attractive compared to 'derivative-free' methods when dealing with systems containing many parameters. It is also shown how the efficiency in the actual computations can be greatly increased by exploiting certain properties of the involved matrices.
Keywords: C30; C50; 330; Full information maximum likelihood (FIML); non-lionear model; multi-equation model