Hysteresis means literally “that which comes later,” being derived from the Greek verb ύστερέω. Thus, hysteresis effects, generally defined, are those that persist after the initial causes giving rise to the effects are removed.During the course of the 1980s, it became increasingly fashionable to invoke hysteresis effects to explain economic phenomena. Two of the main areas of application were to unemployment and international trade. In the case of unemployment, distinctive features of labor markets, such as social norms that rule out wage-cutting in the face of rising unemployment, imply that “increases in unemployment have a direct impact on the ‘natural’ rate of unemployment” (Blanchard and Summers, 1988, p. 15). The implication for macroeconomic systems is that “temporary shocks can have a permanent effect on the level of employment” (Ibid., p. 307). In the case of international trade, hysteresis effects arise from the industrial economics of sunk costs: “the argument is that firms must incur sunk costs to enter new markets, and cannot recoup these costs if they exit.… thus foreign firms that entered the U.S. market when the dollar was high do not abandon their sunk cost investments when the dollar falls.” The implication for trade flows is “an effect which persists after the cause that brought it about has been removed” (Dixit, 1989, p. 205).
We introduce a class of agent-based market models founded upon simple descriptions of investor psychology. Agents are subject to various psychological tensions induced by market conditions, and endowed with a minimal 'personality'. This personality consists of a threshold level for each of the tensions being modeled, and the agent reacts whenever a tension threshold is reached. This paper considers an elementary model including just two such tensions. The first is 'cowardice', which is the stress caused by remaining in a minority position with respect to overall market sentiment, and leads to herding-type behaviour. The second is 'inaction', which is the increasing desire to act or re-evaluate one's investment position. There is no inductive learning by agents, and they are only coupled via the global market price and overall market sentiment. Even incorporating just these two psychological tensions, important stylized facts of real market data, including fat-tails, excess kurtosis, uncorrelated price returns and clustered volatility over the timescale of a few days, are reproduced. By then introducing an additional parameter that amplifies the effect of externally generated market noise during times of extreme market sentiment, long-time volatility correlations can also be recovered.
Economic analysis of adjustment behaviour often assumes continuous, but partial, adjustment by 'representative' agents (Holt et al., 1960, for example). These assumptions rule out the possibility that macroeconomic variables can be affected in a significant way by frictions of adjustment at the micro level. The alternative assumption of discontinuous, lumpy adjustment is more relevant to many situations (see Blinder, 1981; Hamermesh, 1989; for examples), and has been widely exploited in (S, s) models derived from the inventory control literature (Arrow, et al., 1951). Recent literature has investigated the macroeconomic implications of this more 'realistic' case of discontinuous adjustment by heterogeneous agents (Bertola and Caballero, 1990; Caplin and Leahy, 1991; for example). In such a world the whole history of nonsynchronised adjustments by different agents could, potentially, affect the paths taken by aggregate variables.The present paper contributes to this recent literature by applying the mathematical techniques invented by Krasnosel'skii and associates (Krasnosel'skii and Pokrovskii, 1989) to the problem of unravelling the macroeconomic implications of discontinuous adjustment by heterogeneous agents. The novel implication is that macroeconomic systems will contain a memory of only the non-dominated extremum values of the variables which drive adjustment at the micro level. This selective memory property is not only novel in relation to the literature on discontinuous adjustment, but could well prove to be extremely useful in empirical investigation of the properties of aggregate time series.The rest of this paper is organised as follows. Section I1 offers a brief review of the literature on discontinuous adjustment. Section I11 uses a simple model of two-way switching between foreign and domestic currency deposits by agents with different switching bands to illustrate how the selective memory property arises. Section IV discusses the implications and directions for future research. I1 DISCONTINUOUS ADJUSTMENTConvex adjustment costs are often assumed, as in the quadratic adjustment costs model of Holt et al. (1960), for example. The implication is that individ-
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