Should we do more when we know less? The effect of technology risk on optimal effort

• Published date: 01 September 2021
• Author: Lu Li,Richard Peter
• Date: 01 September 2021
• DOI: http://doi.org/10.1111/jori.12339

J Risk Insur. 2021;88:695–725. wileyonlinelibrary.com/journal/jori

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695

Received: 7 June 2020

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Revised: 24 December 2020

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Accepted: 25 February 2021

DOI: 10.1111/jori.12339

ORIGINAL ARTICLE

Should we do more when we know less? The

effect of technology risk on optimal effort

Lu Li

1

|Richard Peter

2

1

Institute for Risk Management and

Insurance, Ludwig‐Maximilians‐

Universitaet Munich, Munich, Germany

2

Department of Finance, University of

Iowa, Iowa City, Iowa, USA

Correspondence

Richard Peter, Department of Finance,

University of Iowa, 108 Pappajohn

Business Bldg, Iowa City, IA 52242, USA.

Email: richard-peter@uiowa.edu

Abstract

Technology risk arises when the effectiveness of self‐

insurance and self‐protection activities depends on exo-

genous factors or is only imperfectly known. It affects

optimal behavior via a preference channel and a technol-

ogy channel. In this paper, we identify conditions for un-

ambiguous comparative statics with respect to the

presence of, as well as various stochastic changes in

technology risk. These conditions involve prudence, re-

lative risk aversion, relative prudence, and several new

measures of mitigation efficacy. We highlight cases where

technology risk raises the optimal level of effort, consistent

with the precautionary principle. We discuss several ap-

plications of our results.

KEYWORDS

prudence, risk aversion, self‐insurance, self‐protection,

technology risk

JEL CLASSIFICATION

D61, D81, D91, G22

1|INTRODUCTION

Risk‐averse decision‐makers are negatively affected by the presence of risk and seek strategies

to mitigate it. In doing so, they are often unable to predict the precise effectiveness of their

effort, which we refer to as technology risk in this paper. Using a subjective expected utility

framework (Savage, 1954), we analyze how technology risk affects risk mitigation behavior.

Specifically, we provide conditions under which technology risk leads to more effort.

© 2021 American Risk and Insurance Association

Most loss control decisions are characterized by technology risk because benefits are only

imperfectly known to the decision‐maker. While people are generally aware of the benefits of a

balanced diet and regular exercise, they are often unable to quantify by how much such

activities actually reduce their health risk. At the beginning of the outbreak of a novel in-

fectious disease, there are debates about the effectiveness of preventive activities such as mask

wearing and canceling social events. Other examples of technology risk include personal in-

surance decisions and climate change mitigation. Many models of insurance demand assume a

precise indemnity payment in the loss state (see Schlesinger, 2013), but the role of non-

performance risk (see Clarke, 2016; N. Doherty & Schlesinger, 1990; Peter & Ying, 2020) and

people's lack of trust in the insurance mechanism (see Courbage & Nicolas, 2020;

Tennyson, 1997) have been emphasized as well. For climate change mitigation, there is a fair

amount of scientific disagreement on the effectiveness of mitigation and adaptation effort (see

Berger et al., 2017). Broadly speaking, technology risk may arise from the presence of unknown

exogenous risk factors, lack of information or data errors (Bai et al., 2012), inattention on behalf

of the decision‐maker (Golman et al., 2017; Schwartzstein, 2014), lack of confidence or so-

phistication with a particular mitigation decision (Li et al., 2021; Lusardi & Mitchell, 2011;

Neumuller & Rothschild, 2017), or measurement error associated with the quantification of

risks (Delage & Li, 2017). We show that technology risk has profound implications for behavior.

For our analysis, we build on the distinction between self‐insurance and self‐protection

pioneered by Ehrlich and Becker (1972).

1

Self‐insurance or loss reduction refers to a costly

activity that reduces the size of loss whereas self‐protection or loss prevention refers to a costly

activity that reduces the probability of loss. While both forms of risk mitigation lower expected

losses, there is a broad array of dissimilarities between them. We analyze the optimal demand

for each type of preventive effort. Our central question is whether the presence of technology

risk increases or decreases the optimal effort. In addition, we also study the intensive margin by

performing various stochastic changes in technology risk. We discuss higher‐order extensions,

delineate our results from the background risk literature, and extend our main result to cases

where risk mitigation affects both probability and severity of loss.

Our analysis produces a set of new results and identifies restrictions on preferences and

technologies that yield unambiguous comparative statics. The preference conditions involve

prudence, relative risk aversion and relative prudence. The technology conditions are new in

the literature because we explicitly allow for nonlinearity. Other papers on precautionary

behavior mainly consider linear technologies. Technology risk compromises the effectiveness of

risk mitigation and at the same time introduces a precautionary motive to do more. This trade‐

off may be resolved in either direction depending on preferences and how uncertainty interacts

with the risk mitigation technology. We highlight those cases where knowing less does indeed

suggest doing more, consistent with the precautionary principle.

2

Similar to previous research, the distinction between self‐insurance and self‐protection

matters. Expected utility is linear in probabilities, so if risk mitigation reduces the likelihood of

adverse outcomes and technology risk only increases the variation in probability reduction, it

will have no effect on the decision‐maker's objective. For self‐insurance instead, we find

1

See Courbage et al. (2013) for a survey. We discuss some related literature in Section 7.

2

Principle 15 of the Rio declaration calls for a wide application of the precautionary approach, especially in those cases where full scientific certainty is lacking,

see http://www.un.org/documents/ga/conf151/aconf15126-1annex1.htm.“In order to protect the environment, the precautionary approach shall be widely

applied by States according to their capabilities. Where there are threats of serious or irreversible damage, lack of full scientific certainty shall not be used as a

reason for postponing cost‐effective measures to prevent environmental degradation.”

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