Comparative Ambiguity Aversion in Intertemporal Decisions

• Date: 01 March 2020
• DOI: http://doi.org/10.1111/jori.12253
• Author: Jingyuan Li,Jianli Wang
• Published date: 01 March 2020

©2018 The Journal of Risk and Insurance. Vol.XX, No. XX, 1–18 (2018).

DOI: 10.1111/jori.12253

Comparative Ambiguity Aversion in Intertemporal

Decisions

Jianli Wang

Jingyuan Li

Abstract

This article examines the effects of ambiguity aversion on intertemporal

decisions when there is ambiguity about a future state. Compared to the

existing literature, we allow for a three-way separation between intertem-

poral substitution, risk aversion, and ambiguity aversion. Holding risk

preferences, beliefs, and time preferences fixed, we explore how a change

in ambiguity aversion increases the strength of the current willingness

to pay. We apply our results to saving, self-protection, and self-insurance

problems.

Introduction

In a two-period decision-making model, many decisions have a formal structure,

whereby a decision maker (DM) pays the current cost for stochastic improvements in

future risks. For example, a DM may sacrifice current consumption to improve wealth

distribution in the future, a DM may exert current effort to protect herself against the

risk of future loss, or a policyholder may pay a premium for an insurance policy to

improve the future wealth variable.

The phenomenon of ambiguity, or Knightian uncertainty (Knight, 1921), suggests

that DMs do not use subjectively chosen probability distributions to compute the

expected utility of the set of possible acts when making decisions. Several studies,

such as Segal (1987) and Klibanoff, Marinacci, and Mukerji (2005) (hereafter KMM),

Jianli Wang is at the College of Economics and Management, Nanjing University of

Aeronautics and Astronautics, Nanjing 211106, China. Wang can be contacted via e-mail:

jianliwang@nuaa.edu.cn. Jingyuan Li is at the Department of Finance and Insurance, Lingnan

University, Hong Kong. Li can be contacted via e-mail: jingyuanli@ln.edu.hk. The authors

are grateful to the Editor and three anonymous referees for constructive comments and

suggestions that led to significant improvement of an early manuscript. The research de-

scribed here was supported by the National Natural Science Foundation of China with

Grant Nos. 71401074 and 71231005, the Fundamental Research Funds for the Central

Universities under Research Project No. NS2018049, General Research Fund of the Hong

Kong Research Grants Council under Research Project No. LU13500717, and the Faculty

Research Grant of Lingnan University under Research Project Nos. DB18A9, DR17A6,

and DB16A1.

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focus on ambiguity aversion and propose models in which a DM does not engage in

a reduction of compound lotteries. The KMM model is particularly popular because

it provides a relatively simple distinction between risk and ambiguity.1

As a DM is ambiguous with regard to probability distributions in the future,the effect

of ambiguity attitudes on intertemporal decisions is important. How does a DM’s

attitude toward ambiguity relate to her current willingness to pay for a stochastic

improvement? For example, does a more ambiguity-averse DM, in the KMM sense,

always pay more for an insurance policy? The relationship between a DM’s current

willingness to pay for a general stochastic improvement and her ambiguity attitude

is intuitive but has never been formally established. There is also the question as to

which specific measure of ambiguity aversion is appropriate.

In this article, we use a recursive smooth ambiguity aversion model following KMM

(2009), Hayashi and Miao (2011), and other researchers. We consider two agents who

possess the same beliefs regarding ambiguity, the same time preferences, and the same

utility functions in evaluating risky acts. Using these two agents, we then investigate

how the strength of the DM’s ambiguity aversion affects her current willingness to

pay for a general stochastic improvement in future risk. Our work provides a set of

general sufficient conditions under which increasing the degreeof ambiguity aversion

causes an increase in the current willingness to pay for stochastic improvement. This

result also characterizes some very general measurementsof ambiguity aversion, such

as the absolute ambiguity aversion coefficient and the absolute ambiguity prudence

coefficient.

Weuse our results to study the effects of changes in ambiguity aversion on two funda-

mental economics problems. First, we qualitatively analyze the effects of ambiguity

aversion on saving. Our work is related to the literature on the effects of ambiguity

on the consumption-saving problem (see, among others, Hansen, Sargent, and Tal-

larini, 1999; Hansen, Sargent, and Wang, 2002; Miao, 2004; Berger, 2014; Osaki and

Schlesinger, 2014). We then characterize the effects of a change in ambiguity aversion

on the demand for self-insurance and self-protection (Ehrlich and Becker, 1972). Self-

insurance means that the effort of a DM reduces the size of a loss, whereas prevention

means that the effort of a DM reduces the probability of a loss. Our work is related

to the literature on the effects of ambiguity on self-insurance and self-protection de-

cisions (see, among others, Snow, 2011; Martinez-Correa, 2012; Alary, Gollier, and

Treich, 2013; Berger, 2013; Gollier, 2014).

This work proceeds as follows. Sufficient conditions for the comparative statics

of ambiguity aversion are derived in the “The Effect of Ambiguity Aversion on

Current Payments” section. The “Applications” section presents applications, and the

“Conclusion” section concludes the article. Proofs of the conclusions are provided in

the Appendix.

1For example, Gollier (2011), Snow (2011),Bergero (2014), Osaki and Schlesinger (2014), Huang

and Tzeng (2017), and others use a KMM model to explore many decision-making problems,

namely,portfolio choice, saving, and insurance.

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