Expectations and the multiplier-accelerator model

Abstract

In this paper we investigate how a simple expectations mechanism modifies the basic dynamical structure of the multiplier-accelerator model due to Samuelson (1939). Consumption depends on the expected value of present income rather than lagged income. National income is determined as a nonlinear mix of extrapolative and reverting expectations formation rules (prototypical predictors used in recent literature on financial markets). The total level of economic activity depends endogenously on the proportion of agents using the predictors. The very simplicity of Samuelson's descriptive macroeconomic model makes it an excellent candidate for studying the effects of introducing expectations without changing the emphasis of the formalization. That is, agents' expectations are not part of an optimization problem and the resulting framework remains in the class of descriptive models. (For bibliographical references of past and recent extensions to Samuelson's model see Westerhoff (2005) and the bibliographies in other chapters of this volume.) The expectations hypotheses follow in the style of Kaldor. Some destabilizing force exists for values near the equilibrium but the economy neither explodes nor contracts indefinitely due to a global stabilizing mechanism that is activated when the economy deviates too much from its equilibrium. These interacting forces permit a greater variety of attracting sets including point equilibria above and below the (unique) Samuelsonian equilibrium and closed curves on which lie both quasiperiodic and periodic cycles. Moreover, under realistic values for the multiplier and coefficient of acceleration, a larger area of the parameter space is characterized by stable limit sets and much of that is dominated by solutions with persistent fluctuations. © Springer-Verlag BerHn Heidelberg 2006.