Hysteresis losses in the Preisach framework

Abstract

Hysteresis is a nonlinear and path-dependent phenomenon which is used to model the “wait-and-see” behaviour of firms in times of uncertainty. Important applications are found on the labour market and foreign trade. Reasons for hysteresis in foreign trade are sunk costs e.g. for market entry and/or exit, learning-by-doing or demand carry over effects. Recent studies have shown that hysteresis losses are proportional to the area within the loop which represents the hysteresis model in a micro- or macroframework. Taking up this idea, a first hysteresis loss indicator was developed which was able to identify hysteresis losses empirically based on the play hysteresis model. This study develops a new hysteresis loss indicator based on the Preisach procedure. The hysteresis loss indicator reports dynamic losses which occur during the adjustment process towards a new equilibrium. In the case of foreign trade, these losses occur when a firm exits an export market due to writing off sunk entry and/or exit costs. To illustrate this new welfare loss indicator, an example of German exports to Great Britain is studied. The losses found relate to the financial crisis and the Brexit decision.