A least-squares model specification test for a class of dynamic nonlinear economic models with systematically varying parameters

The problem of structural instability in estimated macroeconomic relationships has recently surfaced anew, due to a series of articles by the rational expectations school. A key explanation for the observed instability is said to be that the parameters appearing in modelled macroeconomic relationships, traditionally treated as constant or purely random, must realistically be viewed as the reflections of the demand and supply decisions of optimizing agents in the economy reacting rationally to changes in endogenous and exogenous variables, including changes induced by shifts in government policy decision rules. The present paper develops a least-squares measure for simultaneously testing the basic compatibility of prior dynamical, observational, and distributional model specifications against actual data for a class of dynamic nonlinear economic models with parameters explicitly modelled as nonlinear functions of endogenous and exogenous variables. Using invariant imbedding techniques, an algorithm is derived for sequentially updating the optimal least-squares estimates for parameters, endogenous variables, and squared residual modelling error sums as the duration of the process increases and new observations are obtained.Dedicated to R. BellmanThis work was partially supported by the National Science Foundation under Grant No. ENG-77-28432 and the National Institutes of Health under Grant No. GM-3732-03. A previous version of this paper (Ref. 1) was presented at the Econometrics Modelling Research Seminar, Department of Economics, University of Southern California, Los Angeles, 1979. The authors are grateful to numerous colleagues for helpful comments.