Structural Instability in a Rational Expectations Model of a Small Open Economy with a J-Curve

Abstract

It is a now familiar feature of rational expectations models that their dynamic representation usually has associated eigenvalues that are in the conventional sense; that is, that their eigenvalues lie outside the unit circle in the case of discrete-time models, and that they have positive real parts in the case of continuous-time models. Some parts of the literature view this feature as posing problems of instability for rational expectations models.' However, following Sargent and Wallace (1973), it has been increasingly accepted that these unstable eigenvalues do not pose problems of instability provided that their number does not exceed the number of non-predetermined or free variables in the model.2 Indeed, their presence may be regarded as a useful feature, since the existence of a unique rational expectations solution depends on the unique saddle-point property, that the number of unstable eigenvalues is just equal to the number of non-predetermined variables.3 Experience with rational expectations suggests that this unique saddle-point property may often be satisfied over wide ranges of parameter values.4 This is true for models where, under alternative expectations schema (e.g. adaptive), instability is a feature.5 One may speculate that, as a broad generalization, rational expectations models are somewhat less susceptible than ordinary models to conventional problems of instability.6 The purpose of this paper is to highlight a different type of instability to which rational expectations models may be prone, namely a form of structural instability. By structural instability we mean the possibility that the solution to the model exhibits discontinuous changes in response to small changes in structural parameters of the model. In the neighbourhood of such discontinuities, the behaviour of the model will be very susceptible to parameter shifts. In such neighbourhoods, the assumption of parameter constancy and the fiction that agents have precise knowledge of parameters on which to base their rational forecasts have to be worked very hard for sense to be made of the rational expectations solution. It is more appropriate to recognize that, near to structural discontinuities of this kind, the rational expectations solution is not meaningful. This leaves scope for government macroeconomic policy to ensure, at minimum, that the system is placed in a region where such discontinuities are absent. The paper falls into two parts. Section I sets out a solution procedure (based on Dixit, 1980) for rational expectations models that makes transparent the potential for structural instability. Section II gives an example to demonstrate that this potential may be realized. The example is not without topical interest in its own right, since it is a small open economy analogue to the model of bond finance in a closed economy provided by Blinder and Solow (1973). In this context, with perfect capital mobility, we show the potential