Rod Cross

A Test for Strong Hysteresis

The mathematical definition of systems withhysteresis, that is nonlinear input-output systemswith memory, is different from the definition usuallyapplied to economic systems. Economic theory andmodelling practice have almost always specified simpledynamic systems with regular leads and lags in theirresponses, corresponding to input-output systems withunit or zero (or at least stable) roots. These modelscannot capture the ‘selective memory’ feature ofhysteretic behaviour, that is, the influence only ofcertain past events (typically, non-dominatedsequences of previous peaks and troughs). There istherefore a difficulty in testing for and validatingeconomic models containing hysteretic behaviour;appropriate empirical tests have not been developed.In particular, the usual unit vs. zero (or stable)root tests used in econometric analysis are unable todetect hysteretic behaviour or to distinguish it frommore conventional economic behaviour. The purpose ofthis paper is to propose a new way of testing forhysteresis, by drawing on some ideas in themathematical/control theory literature and adaptingthem to fit into the economic frameworks with elementsof hysteresis.

Hysteresis and economics

The goal of this article is to explore the rationale underlying the application of hysteresis to economic models. In particular, we explain why many aspects of real economic systems are hysteretic. The aim is to be explicit about the difficulties encountered when trying to incorporate hysteretic effects into models that can be validated and then used as possible tools for macroeconomic control. The growing appreciation of the ways that memory effects influence the functioning of economic systems is a significant advance in economic thought and, by removing distortions that result from oversimplifying specifications of input-output relations in economics, has the potential to narrow the gap between economic modeling and economic reality. Static hysteresis input-output systems, hysterons, and Preisach models are defined, and the form that macroeconomic models with hysteresis typically take is described. Then some relevant economics background is sketched, and the distinctive nature of models in economics is discussed in detail. In the following central section of the article the results of approximately two decades of hysteresis modeling in economics are summarized.

Hysteresis and Emu

We consider how differences between the way firms react to a common monetary policy affect the performance of a monetary union. A model is presented in which heterogeneous firms respond discontinuously to monetary shocks. The implication is that the level of economic activity has a selective memory of the extremum values of the shocks experienced, and depends on the distribution of switching values for entry and exit.

Memory of recessions

This paper reviews the evidence on the effects of recessions on potential output. In contrast to the assumption in mainstream macroeconomic models that economic fluctuations do not change potential output paths, the evidence is that they do in the case of recessions. A model is proposed to explain this phenomenon based on an analogy with water flows in porous media. Because of the discrete adjustments made by heterogeneous economic agents in such a world, potential output displays hysteresis with regard to aggregate demand shocks and thus retains a memory of the shocks associated with recessions.

Stylized facts from a threshold-based heterogeneous agent model

Abstract.A class of heterogeneous agent models is investigated where investors switch trading position whenever their motivation to do so exceeds some critical threshold. These motivations can be psychological in nature or reflect behaviour suggested by the efficient market hypothesis (EMH). By introducing different propensities into a baseline model that displays EMH behaviour, one can attempt to isolate their effects upon the market dynamics. The simulation results indicate that the introduction of a herding propensity results in excess kurtosis and power-law decay consistent with those observed in actual return distributions, but not in significant long-term volatility correlations. Possible alternatives for introducing such long-term volatility correlations are then identified and discussed.

A mean-field model of investor behaviour

In this note we investigate the ability of a mean-field model distilled from a heterogeneous agent model to simulate stylized facts of financial times series.

On entry and exit in response to aggregate shocks

This note extends the Dixit-Pindyck analysis of investment, in the form of market entry and exit under sunk costs, to the case of heterogeneous sunk costs. The implication is that the market displays full hysteresis, in the form of remanence and dependence on the nondominated extremum values of the aggregate shocks experienced. These implications are illustrated by numerical simulations.

Uncertainties Surrounding Natural Rate Estimates in the G7

It is four decades since Phelps (1967) and Friedman (1968) unveiled the natural rate of unemployment hypothesis, and the concept of an equilibrium rate of unemployment is central to the prevailing theories of labour market behaviour and the relationship between unemployment and inflation. Moreover, the natural rate and associated unemployment gaps are seen as important reference points, typically as part of a broad range of indicators, by policy makers who need to assess short-term inflation developments and/or consider appropriate decompositions of fiscal balances into their structural and cyclical components. Yet, as surveys and symposia have illustrated (Bean 1994, Cross 1995, Journal of Economic Perspectives 1997), there remains much uncertainty both about which factors do and do not determine equilibrium rates of unemployment, and about the corresponding numerical values.

MEASURES OF SHORTAGE AND MONETARY OVERHANG IN THE POLISH ECONOMY

This paper attempts to cast light on the debate about the existence and size of a monetary overhang in household money balances in command economies. Four measures of shortage or price deformation are constructed for the Polish economy and used to test for the existence of shortage money balances in Poland 19651989. The approach involves estimating relationships for household money balances 19651993, a period that spans both central planning and the post-1990 period of liberalised prices. The principal finding is that the evolution of household money balances in Poland cannot be explained without invoking measures of shortage and an overhang during the planning period. The estimates suggest an overhang with a maximum of just over 40 of money balances.

Metaphors and time reversibility and irreversibility in economic systems

This paper deals with the way metaphors carried over from physical or biological systems condition the analysis of economic systems. The metaphors drawn from Newtonian mechanics, or from conservative fields of force, by neoclassical economists are discussed. Alternative metaphors which involve non-homeostasis and time irreversible processes are then outlined. Particular attention is paid to thermodynamics, evolutionary biology, and non-conservative or hysteretic force fields as sources of such metaphors. It is argued that these metaphors provide illumination to aspects of economic systems which are not consistent with the homeostatic, time reversible metaphors conventionally employed in economics.