Modelling economic hysteresis losses caused by sunk adjustment costs

ABSTRACT

Transition from one economic equilibrium to another as a consequence of shocks is often associated with sunk adjustment costs. Firm-specific sunk market entry investments (or sunk market exit costs) in case of a reaction to price shocks are an example. These adjustment costs lead to a dynamic supply pattern similar to hysteresis. In analogy to “hysteresis losses” in ferromagnetism, the authors explicitly model dynamic adjustment losses in the course of market entry and exit cycles. They start from the micro level of a single firm and use explicit aggregation tools from hysteresis theory in mathematics and physics to calculate dynamic losses. The authors show that strong market fluctuations generate disproportionately large hysteresis losses for producers. This could give a reason for the implementation of stabilizing measures and policies to prevent strong (price) variations or, alternatively, to reduce the sunk entry and exit costs.

KEYWORDS:

• Adjustment costs
• dynamic losses
• option value of waiting
• path-dependence
• persistence
• sunk-cost hysteresis

JEL CLASSIFICATIONS:

• B59
• C61
• D21
• D69

Notes

¹Hysteresis originally stems from physics (ferromagnetism, plasticity, etc.) and also occurs in several phenomena in chemistry, biology, engineering (see Visintin, 2006, p. 3), and in economics, especially in international trade and unemployment (see Göcke, 2001). Amable et al. (1992), Cross (1993a), Setterfield (1993, 2009), Göcke (2002) Cross, Grinfeld, and Lamba (2009), and Cross et al. (2010) provided an overview of hysteresis in economics. The term hysteresis is derived from a Greek verb hysteros meaning “lagging behind” or “that which comes later” (Cross, 1993a, p. 53) and describes an effect that persists after the cause that brought it about has been removed.

²As pointed out by Setterfield (2009, 2010), hysteresis is a special case of path-dependency and also a special form of the principle “history matters,” among others discussed by Robinson (1974). To what extent hysteresis is relevant to the Post Keynesian understanding of economic processes is from time to time discussed in the literature. Paul Davidson and Rod Cross had one of the first discussions regarding this topic (see Cross, 1993b, and Davidson, 1991, 1993). We further on rely on the arguments of Rod Cross that support the relevance of the hysteresis concept to the Post Keynesian economics.

³The intertemporal optimization techniques are commonly believed to be at odds with conceptual foundations of the Post Keynesian economics—specifically, it’s focus on fundamental uncertainty. However, the use of them can be tolerated in the context of Post Keynesian economics, since they explain the purpose of the exercise and thus, are only means to a useful end.

⁴Moreover, integrating stochastic risk in future revenues will generate option value effects on the trigger values. This results in a widening of the “band-of-inaction” between entry and exit-trigger (see Dixit, 1989; Pindyck, 1991). Thus, including risk effects into the investor’s calculation will further curtail the direct one-to-one interpretation of the enclosed area inside the hysteresis loop as the sum of lost sunk adjustment cost. For attempts to include Knightian uncertainty in sunk costs hysteresis models, see, for example, Bassi (2016).

⁵The distribution of firms in the entry-exit diagram determines the curvature of the aggregated hysteresis loop.

⁶For a detailed aggregation procedure see e.g., Amable et al. (1991), Göcke (2002).

⁷We assume one-product and one-unit firms with the same time horizon and no possibility to re-enter or re-exit the market.

Additional information

Funding

This work was supported by the German Research Foundation (DFG) [Project No. 62201369].

Notes on contributors

Jolita Adamonis

Jolita Adamonis and Matthias Göcke are both in the Faculty of Economics and Business Studies at Justus Liebig University Giessen.