Title: Solving Nonlinear Economic Models Accurately Via a Linear Representation

Author: K.R. Pearson

Abstract

This paper focuses on one way a linearized representation of a nonlinear economic
model can be used to obtain arbitrarily accurate solutions to simulations. The key is a
method for translating a simulation problem directly to a so-called initial value
problem. Since many different methods for solving initial value problems are known and
well understood, and since each one converts to an algorithm for solving simulation
problems, this insight greatly expands the computational tool kit for conducting
simulations. This paper contains a survey of the theoretical results guaranteeing
convergence and forming the basis for extrapolations of two important methods for solving
initial value problems. Theoretical considerations suggest that the faster rate of
convergence of one of these methods (the modified midpoint method) is likely to cause it
to dominate the other (Euler's method) in many situations faced by applied general
equilibrium modellers. The other main points of the paper are:

(a) to emphasize that linearized (symbolic) representations of models lead naturally
to efficient algorithms which can be used to compute solutions having any desired degree
of precision; and

(b) to suggest that such accurate methods (rather than Johansen's method) should be
the default when solving models (especially applied general equilibrium models)
represented in linearized form.

JEL classification: C63, C68

This version (June 2002) of IP-55 is a revised version. The original version was
published in July 1991. The revisions made in June 2002 are minor. A small number of
typographical errors were corrected. The paging and positioning of diagrams are slightly
different from the original July 1991 version.