Hysteresis in economics has so far usually been based on a representation of a system with only a single input variable, which has a persistent effect on an economic outcome (i.e. the output variable). However, in general there is more than one factor influencing economic decision problems. As a result, the description of the path-dependency in relation to only one input variable may (possibly) be insufficient. The multidimensional path-dependence phenomenon is addressed (in mathematics and physics) by a vector-hysteresis system, with an input vector of two or more variables. Unfortunately, for practical purposes, these models are quite complicated in economics. However, since standard economic decisions are based on comparing economic values of alternatives (e.g. present values of investments), such models can be used to reduce the dimensions of the hysteresis system. This article outlines how the influence of several original input variables (e.g. price level and interest rate) is captured by the resulting variations of the present value of an investment. This economic value then can be used as a single signal/input variable of a modified hysteresis system. Since this system is dimensionally reduced to the standard hysteresis case with only a single input variable, the standard aggregation procedure for a situation with heterogeneous agents can be applied again.

KEY WORDS
vector-hysteresis, sunk-cost hysteresis, path-dependence, non-ideal relay, Mayergoyz/Preisach-model

CLASSIFICATION

JEL:

C61