Richard Topol

Strong hysteresis versus zero-root dynamics

Abstract This paper presents the properties of remanence and of dependence on history pertaining to strong hysteresis through a foreign trade model. These properties reveal that it is impossible to assimilate zero-root dynamics to hysteresis.

Unit Root in the Wage‐Price Spiral Is Not Hysteresis in Unemployment

Hysteresis is one of the main concepts used in Layard, Nickell and Jackmans book, Unemployment: Macroeconomic Performance and the Labour Market. Attempts to clarify the concept of hysteresis, from its formal representation to its empirical applications. Emphasizes the idea that hysteresis refers back to a given set of formal properties, independently of the phenomenologies within which it is liable to be encountered. In economics, the fields concerned may indeed vary a lot (labour market, foreign trade, etc.). By highlighting all the formal properties of hysteresis, shows how the assimilation of phenomena characterized by a zero eigenvalue for linear systems (or unit-root systems for discrete-time processes) is wrong and, moreover, how the imprecise use of the concepts can lead to the particular constraints affecting unit-root econometrics being overlooked.

BUBBLES IN FOREIGN EXCHANGE MARKETS

We consider a model in which foreign and domestic traders buy the assets of both of two countries. Speculators in both countries use chartist or fundamentalist rules for forecasting the exchange rate. Demand for the assets of each country is determined by these forecasts. Perceptions of the fundamentals in each country are not necessarily the same. Rules are used with a certain probability depending on an agents previous experience with them. The demands of the fundamentalist and chartist agents in the two countries determine the temporary equilibrium exchange rate at each point in time. This is unique under certain assumptions. With traders of both nationalities there is no need, as in other models, for an exogenous supply of foreign exchange. The model produces realistic features of the equilibrium exchange rate series. Periods in which the exchange rate tracks the fundamentals of one of the countries alternate with others in which bubbles appear.

Deterministic macroeconomic dynamic equations from a stochastic microeconomic description: The role of time scales

Abstract In the present paper, we develop the ‘stochastic’ microeconomic approach to obtained a deterministic macrodynamic equation. Three time scales have to be introduced. To be valid, the dynamic equation has to be written on the meso-scopic time scale. ‘Discrete’ and ‘continuous’ time versions are given. On the other hand, the comparison between the ‘stochastic’ and the ‘average’ (all the agents have the same characteristics, the ‘average’ ones) approaches is presented. Both methods give the same form for the dynamic equation, nevertheless the ‘average’ approach gives conditions of validity which are not strict enough. An advantage of the ‘stochastic’ approach is to inforce this point and to propose a better framework for writing down deterministic macrodynamic equations and for making further developments if necessary.