Theory of adaptive adjustment

Weihong Huang

doi:10.1155/s102602260000056x

Abstract

Conventional adaptive expectation as a mechanism of stabilizing an unstable economic process is reexamined through a generalization to an adaptive adjustment framework. The generic structures of equilibria that can be stabilized through an adaptive adjustment mechanism are identified. The generalization can be applied to a broad class of discrete economic processes where the variables interested can be adjusted or controlled directly by economic agents such as in cobweb dynamics, Cournot games, Oligopoly markets, tatonnement price adjustment, tariff games, population control through immigration <em>etc</em>.

Highlights

Adaptive expectations, as one of the main backward-looking expectations, has long been utilized by economists to stabilize a dynamical economic process
Instead of focusing the stability conditions under some specific economic processes, we shall turn to exploring the internal dynamical structure of an economic process that can be stabilized through adaptive expectations under a general framework
An adaptive adjustment scheme so defined can be applied to a broader class of discrete economic processes where the variables interested can be adjusted or controlled directly by economic agents, such as in cobweb dynamics, Cournot games, Oligopoly markets, tatonnement price adjustment, tariff games, population control through immigration etc

Summary

MOTIVATIONS

As one of the main backward-looking expectations, has long been utilized by economists to stabilize a dynamical economic process. Even though the adaptive expectation can be ensured to equate its realized counterpart in equilibrium, the convergence to such an equilibrium can not be guaranteed, especially in the case of a nonlinear multi-variables process It is the aim of this article to reconsider an adaptive expectations scheme as a means of stabilizing a nonlinear economic process from an angle different from conventional studies. We show that such adjustment succeeds in stabilizing type-I and typeII steady states (the steady states with all eigenvalues either greater than unity or less than unity). Possible areas for further research and concluding remarks are addressed in the last section

FROM ADAPTIVE EXPECTATIONS TO ADAPTIVE ADJUSTMENT

FROM CONVENTIONAL RANGE TO GENERALIZED RANGE

FROM ONE DIMENSION TO MULTI-DIMENSION

FROM JOINTLY AAM TO INDIVIDUALLY AAM

CONCLUDING REMARKS