**Working Paper Series**
# No 132:

A General FIML Estimator for a Certain Class of Models that are Non-Linear in the Variables

*Erik Mellander*
**Abstract:** 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:** Full information maximum likelihood (FIML); non-lionear model; multi-equation model; (follow links to similar papers)

**JEL-Codes:** C30; C50; (follow links to similar papers)

33 pages, September 1984

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