Inertia Risk: Improving Economic Models of Catastrophes*

• Published date: 01 October 2020
• DOI: http://doi.org/10.1111/sjoe.12381
• Date: 01 October 2020

Scand. J. of Economics 122(4), 1259–1285, 2020

DOI: 10.1111/sjoe.12381

Inertia Risk: Improving Economic Models of

Catastrophes*

Anne-Sophie Cr´epin

The Beijer Institute of Ecological Economics, SE-104 05 Stockholm, Sweden

asc@beijer.kva.se

Eric Nævdal

The Frisch Centre, NO-0349 Oslo, Norway

eric.navdal@frisch.uio.no

Abstract

We model endogenous catastrophic risk in a newway. We call it “inertia risk”, whichaccounts

for delays between physical variables and the hazard rate – a characteristic often observed in

reality. The added realism significantly affects optimal policies relative to the standard model

of catastrophic risk. The probability of a catastrophe occurring at some point in time can span

the entire interval [0,1], and is not 0 or 1 as is typical in standard models. Inertia risk can also

generate path dependences. Weillustrate the implications for policy in a simple model of climate

change.

Keywords: Catastrophic risk; climate change; lagged effects; resource management

JEL classification:C02; C61; Q20; Q54

I. Introduction

Recent years have seen growing awareness that human activity increases the

risk of regime shifts (substantial, persistent, and abrupt system changes;

Biggs et al., 2012a), some with potentially catastrophic effects (Steffen

et al., 2004, 2015; Rockstr¨om et al., 2009).1Given the tight social

and ecological interactions in many managed systems, economic models

focusing on regime shifts should incorporate processes likely to trigger

such shifts (Levin et al., 2012; Cr´epin and Folke, 2015). Economic analysis

of regime shifts leads to dynamic resource management problems where

stochastic processes can trigger rapid and dramatic changes. In continuous

*For funding, wethank the Ebba and Sven Schwartz Foundation, the European Commission FP7

projectArctic Climate Change Economy and Society (Dnr 265863), and the Norwegian Research

Council, Norklima project (no.196199). A.-S. Cr´epin is affiliated with the Stockholm Resilience

Centre at Stockholm University (Sweden). We are grateful to William Brock, Atle Seierstad,

William Sigurdsson, and four anonymous reviewersfor valuable comments.

1The effects might also be beneficial. In order to simplify the discussion, weonly discuss negative

effects.

C

2019The Authors. The Scandinavian Journal of Economics published by John Wiley& Sons Ltd on behalf of F ¨oreningen

f¨or utgivande av the SJE/The editors ofThe Scandinavian Journal of Economics.

This is an open access article under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivs License, which

permits use and distribution in any medium, provided the original work is properlycited, the use is non-commercial and no

modifications or adaptations are made.

1260 Inertia risk

time models, economists usually model catastrophic risk by assuming the

existence of a hazard rate that can depend on endogenous variables such

as CO2concentrations in the atmosphere or the size of fish stocks (Heal,

1984; Clarke and Reed, 1994; Tsur and Zemel, 1998; Gjerde et al., 1999).

The literature on the topic is largely theoretical, but with some empirical

applications (Cai et al., 2013; Lemoine and Traeger, 2014; Lontzek et al.,

2015).

The two most common approaches to modelling catastrophic risk in a

dynamic setting consider time-distributed catastrophes (TDCs, by far the

most common; e.g., Reed and Heras, 1992; Polasky et al., 2011) or state-

space-distributed catastrophes (SDCs; e.g., Tsur and Zemel, 1995; Nævdal,

2006).2These risk structures imply that either the catastrophe occurs with

probability 1 (TDCs) or the hazard rate is instantly responsive to changes

in control variables (SDCs). These properties are inadequate for many real-

world situations. We present an alternative risk structure that we call “inertia

risk”, which is a hybrid of both standard approaches. Inertia risk represents

real-life problems in a more realistic way, especially because it accounts

for dynamic lags between physical variables and the hazard rate, and it

allows for the possibility that substantial use of a resource at a certain level

might eventually be deemed safe.3This approach is particularly appropriate

for modelling renewable resource stocks such as fisheries (Polasky et al.,

2011), lakes (Scheffer and Carpenter, 2003), coral reefs (Hughes, 1994;

Norstr¨om et al., 2009), grasslands/savannah (Hirota et al., 2011), and global

phenomena such as planetary boundaries (Rockstr¨om et al., 2009; Steffen

et al., 2015). Some planetary boundaries relate to global-scale thresholds

linked to climate change, ocean acidification, and stratospheric ozone

depletion, while others – such as biogeochemical flows, land-system change,

and biodiversity loss – relate to regional thresholds (Rockstr¨om et al., 2009).

We study the implications of using our new risk structure, compared

with conventional models, in management models, using examples from

planetary boundaries and fisheries. However, we argue that the inertia risk

approach is applicable to other economic areas such as knowledge spillover

in relation to investments in R&D activities. The literature considers

different types of risk structures (Kamien and Schwartz, 1972; Doraszelski,

2003), but not inertia risk.

We show that inertia risk gives rise to optimal paths that differ from

the standard TDC approach in the following important respects.

2We introduce this terminology and are not aware of any alternative terminology for TDCs and

SDCs.

3We use the term “inertia” synonymously with “sluggishness”, and not in the technical sense

used in physics.

C

2019The Authors. The Scandinavian Journal of Economics published by John Wiley& Sons Ltd on behalf of F ¨oreningen

f¨or utgivande av the SJE/The editors ofThe Scandinavian Journal of Economics.