The Use of the Secant Method in Econometric Models

Abstract

In working with econometric models, it may be desired to find values of policy (instrument) variables which are consistent with specified levels of target variables. Tinbergen's work on economic policy,' for instance, frequently involves solving a set of linear structural equations for those values of the instrument variables which will produce desired levels of the target variables. Since Tinbergen worked with linear models, a straightforward matrix inversion is all that is needed to obtain the requisite values of the instrument variables. This approach cannot, however, be employed in mediumto large-sized nonlinear models such as the FRBMIT-PENN (FMP) model. The purpose of this note is to bring to the attention of researchers working with models of this sort a fairly simple means-the secant method-of finding values of instrument variables which are consistent with specified levels of target variables. This method is described in Section III. In Section II we discuss briefly an alternative method of solving this problem, by renormalization of relevant equations, which may be useful in some simple cases. We shall illustrate in each case by reference to our work with the FMP model (version 4.1). Descriptions of the model are available in the literature ;2 we need only note that it is a fairly large, nonlinear dynamic econometric model with 66 stochastic equations and 171 endogenous variables. When the Gauss-Seidel method3 is used in solving it,