ZOOMING IN ON AMBIGUITY ATTITUDES

• DOI: http://doi.org/10.1111/iere.12331
• Author: Aurélien Baillon,Aysil Emirmahmutoglu
• Date: 01 November 2018
• Published date: 01 November 2018

INTERNATIONAL ECONOMIC REVIEW

Vol. 59, No. 4, November 2018 DOI: 10.1111/iere.12331

ZOOMING IN ON AMBIGUITY ATTITUDES∗

BYAUR ´

ELIEN BAILLON AND AYSIL EMIRMAHMUTOGLU1

Erasmus University Rotterdam, The Netherlands; ErasmusUniversity Rotterdam and Tinbergen

Institute, The Netherlands

Empirical studies of ambiguity attitudes to date have focused on events of moderate likelihood. Extrapolation

to rare events requires caution. In an Ellsberg-like experiment with very unlikely events, we measured ambiguity

attitudes with neither assumptions on subjects’ beliefs nor restrictions to specific ambiguity models. Very unlikely

events were overweighted, being weighted more strongly in isolation than when part of larger events. Using

latent profile analysis, we classified the subjects in terms of deviations from ambiguity neutrality. One third

behaved close to ambiguity neutrality. The others exhibited overweighting of rare events. Such behavior can

lead to money-pump situations.

1. INTRODUCTION

Ambiguous rare events are pervasive in various fields of economics. Ambiguous rare events

related to losses are events against which people may wish to insure. Policies for preventing or

coping with environmental catastrophes also concern ambiguous rare events. Neglect of rare

events can explain recent financial crises, as argued by Taleb (2007) in his book The Black Swan.

An example of a rare event in the gain domain is to find a so-called “unicorn,” a start-up whose

value exceeds one billion dollars. The occurrence of bubbles in the evaluation of high-tech

start-ups, such the “dot-com bubble” at the end of the 1990s or the more recent Silicon Valley

tech bubble, can be a sign that these rare events are overweighted by investors.

Kahneman and Tversky (1979) observe that rare events are typically either completely ne-

glected or overweighted. For decision making under risk, the common view in the literature

is that low-probability events are overweighted (e.g., Tversky and Kahneman, 1992; Gonzalez

and Wu, 1999). However, the picture is not so clear when we consider other decision paradigms.

Recent research in psychology has shown that if unlikely events are not described but rather

experienced by agents, such events tend to be partially neglected or underweighted (see, for

instance, Barron and Erev, 2003; Hertwig et al., 2004; Hertwig and Erev, 2009). Regarding am-

biguity, Ellsberg notes in his thesis (republished in 2011) that the common finding of ambiguity

aversion might be due to the focus on moderate-likelihood events and gains and that the results

might be reversed if unlikely events were to be considered. Several papers have confirmed this

conjecture for events with likelihoods in the range of 10%–30% (e.g., Ert and Trautmann, 2014;

Baillon and Bleichrodt, 2015; Dimmock et al., 2016), but Ert and Trautmann (2014) also show

that experiencing unlikely ambiguous events made them less attractive.

In this article, we zoom in on very unlikely events2in an Ellsberg-like experiment. Despite the

numerous studies on ambiguity attitudes conducted in recent decades (see Trautmann and Van

∗Manuscript received November 2016; revised August 2017.

1This research was made possible by a grant from the Netherlands Organization for Scientific Research. We thank

PhilippKoellinger, Paul Pelzl, Andreas Ferrara, and Peter P. Wakker for helpful comments. We are indebt to Emmanuel

Kemel and Vitalie Spinu for their advice on the analysis. Please address correspondence to: Aur´

elien Baillon, Erasmus

School of Economics, Erasmus University Rotterdam, P.O. Box 1738, Rotterdam, 3000 DR, The Netherlands. E-mail:

baillon@ese.eur.nl.

2Throughout the article, we use the terms “very unlikely event” and “rare event” interchangeably.

2107

C

(2018) The Authors. International Economic Review published by Wiley Periodicals, Inc. on behalf of the Economics

Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research

Association

This is an open access article under the terms of the Creative Commons Attribution License, which permits use,

distribution and reproduction in any medium, provided the original work is properly cited.

2108 BAILLON AND EMIRMAHMUTOGLU

De Kuilen, 2016, for a survey), rare events have been virtually ignored to date because of three

major challenges. The first challenge is to provide sufficiently high incentives to consider such

rare events.3In our experiment, subjects could either lose an initial endowment of €300 (loss

frame) or win an equal amount (gain frame). The second challenge lies in identifying ambiguity

attitudes generated on top of risk attitudes when moving from decision making under risk to

decision making under uncertainty. We use matching probabilities to address this issue. The

matching probability for an event Eis the objective probability pthat makes a decision maker

indifferent between receiving a nonzero outcome €300 with probability pand receiving €300

if event Eoccurs. Dimmock et al. (2016) formally show that matching probabilities can directly

capture ambiguity attitudes without requiring correction for utility or probability weighting.

We generalize their result and develop an approach that is valid for all ambiguity models

and all decision models under risk. The third challenge is related to controlling for people’s

unknown beliefs. A decision maker may truly believe that an event is impossible, and we should

not misinterpret such behavior as neglecting a rare event. Therefore, we do not use arbitrary

benchmarks to assess overweighting or ignorance of very unlikely events. Instead, we compare

matching probabilities only with themselves and study their internal consistency, as proposed

by Baillon et al. (forthcoming). We do this through the use of additivity measures. Intuitively, if

an unlikely event is neither ignored nor overweighted, it should be assigned the same subjective

value (matching probability) either in isolation or as part of a larger event. Hence, matching

probabilities should be additive under ambiguity neutrality. If unlikely events are weighted

more strongly in isolation (overweighting), then the matching probabilities will be said to be

subadditive. Neglecting or underweighting would result in the opposite violation of additivity

(superadditivity).4

Below, we begin by defining the theoretical framework and highlighting its advantages

(Section 2). We show that our approach is as general as possible and does not rely on any strong

assumptions. After describing the experiment (Section 3), we pursue our minimal-assumption

approach for empirical analysis as well (Section 4). We first use nonparametric tests to examine

whether additivity is violated and, if so, whether it is violated differently in the gain frame and

in the loss frame. Our analysis reveals that very unlikely events were not ignored but rather

were overweighted overall, and more so in the loss frame. Second, to study heterogeneity of

behavior, we use latent profile analysis (LPA) with completely free parameters. This approach

allows us to extract several behavioral profiles from the data without ex ante assumptions re-

garding what these profiles should be. Simultaneously, subjects are classified in accordance with

these profiles. One of these profiles is close to ambiguity neutrality and represents approxi-

mately one-third of the subjects. The other profiles consist of mild and extreme deviations from

ambiguity neutrality, all in the sense of the overweighting of rare events. Finally, we discuss the

interpretation and possible consequences of our results (Section 5). Agents who assign greater

weight to events in isolation than combined might be exploited in the form of money pumping,

for instance, by splitting an insurance contract into subcontracts. The conclusion is presented

in Section 6.

2. THEORETICAL FRAMEWORK

2.1. Notation and Matching Probabilities. The state space is finite and is denoted by S.It

contains all possible states of nature. Only one state is realized, but it is unknown which one.

Subsets of Sare called events, and each event is denoted by E. The complementary event to Eis

denoted by EC. The possible outcomes are monetary amounts from the set {−300, 0, 300}. Bets

assign a nonzero outcome to an event and a zero outcome to the complement of that event. An

3Einhorn and Hogarth (1986) simply avoid this problem by conducting a hypothetical survey.

4Thus far, the only study to address the first challenge (incentives) of which we are aware was conducted by Schade

et al. (2012). However, they do not address the two other challenges and cannot draw clear conclusions about ambiguity

attitudes.