Correlates of Narrow Bracketing

• Date: 01 October 2019
• DOI: http://doi.org/10.1111/sjoe.12311
• Published date: 01 October 2019

Scand. J. of Economics 121(4), 1441–1472, 2019

DOI: 10.1111/sjoe.12311

Correlates of Narrow Bracketing*

Alexander K. Koch

Aarhus University,DK-8210 Aarhus V, Denmark

akoch@econ.au.dk

Julia Nafziger

Aarhus University,DK-8210 Aarhus V, Denmark

jnafziger@econ.au.dk

Abstract

Behavior often deviatesfrom standard predictions because individuals evaluate the consequences

of choices separately (i.e., narrow bracketing) rather than jointly. The main existing theories

classify different narrow bracketing phenomena as either (i) choice errors caused by cognitive

limitations,or (ii) strategies to achieve self-control. Using an online experiment, we find consistent

evidence for theory (ii): mental budgets and narrow goals are related to each other and to

measures of self-control, but are distinct from other forms of narrow bracketing. Evidence for

the complementary theory (i) is less consistent: few choice bracketing phenomena are related to

each other and to cognitive skills.

Keywords: Cognitive skills; mental accounting; narrow bracketing; risky choices; self-control

JEL classification:C91; D03; D81; D91

I. Introduction

It is a puzzle why people often evaluate consequences of choices separately

(i.e., narrow bracketing) rather than jointly (i.e., broad bracketing). Two

main, complementary explanations exist.

On the one hand, certain phenomena of narrow bracketing are

considered to be a choice error (Rabin and Weizs¨acker, 2009), explained by

cognitive limitations or cognitive inertia (Read et al., 1999). For example,

expected utility theory predicts that individuals are approximately risk

neutral for small stakes (Arrow, 1971). Yet, many people would reject

a favorable gamble with equal odds of winning $200 or losing $100 –

*We are grateful to Augenblick et al. (2015) for sharing their do-file, and we thank Kfir

Eliaz for helpful comments. Annette Mortensen, Thomas Stephansen, Mathias Barløse, Katrine

Poulsgaard,and Heidi Christina Thysen provided excellent research assistance. Financialsuppor t

from Aarhus Universitets Forskningsfond, AU IDEAS 2011, Grant number AUFF-E-201-FLS-

1-17, and the Danish Council for Independent Research – Social Sciences, FSE under grant

12-124835, is gratefully acknowledged.

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The editors of The Scandinavian Journal of Economics 2018.

1442 Correlates of narrow bracketing

suggesting implausibly high levels of risk aversion under expected utility

theory (Rabin, 2000). Narrow bracketing in conjunction with loss aversion

can explain this result. Loss-averse individuals suffer more from losing $100

than they gain from winning $200. Yet, the impact of loss aversion would be

attenuated if the individuals broadly bracketed the lottery with other risks

and wealth they face (Benartzi and Thaler, 1995). To see this, consider two

repetitions of the gain $200 or lose $100 gamble. If an individual aggregates

(broadly brackets) the outcomes of the gambles, then integrating a possible

loss of $100 in one gamble with a gain of $200 in the other gamble implies

that most outcomes of the aggregated gamble (three out of four) are in the

gain domain. Thus, loss aversion has little impact and the individual would

accept the aggregated gambles. In contrast, not integrating the two gambles

would lead to a rejection of each gamble, which can be considered an

error.

On the other hand, in some domains, narrow bracketing appears to be

beneficial. People bracket decisions narrowly to achieve self-control – a

phenomenon termed “motivational bracketing” (e.g., Shefrin and Thaler,

1988; Fudenberg and Levine, 2006; Koch and Nafziger, 2016). For example,

individuals who can choose their working hours, such as taxi drivers, often

appear to have narrow, daily income targets (Camerer et al., 1997). At

first glance, it seems suboptimal for taxi drivers to stop driving when

reaching their daily income target. They could earn more by working

longer when hourly earnings are high, and working fewer hours when they

are low. The reason that taxi drivers set narrow, daily income targets is

that these help to mitigate self-control problems, as Camerer et al. (1997)

conjecture.

The aim of this paper is to examine whether different phenomena

of narrow bracketing correlate with each other and with individual

characteristics, such as cognitive skills and self-control, as predicted by

the complementary theories that classify particular narrow bracketing

phenomena as a choice error (choice bracketing) or as a response to self-

control problems (motivational bracketing). Further, on a more exploratory

level, the correlations help to shed light on the question of whether choice

bracketing and motivational bracketing are distinct phenomena or whether

different bracketing phenomena can be captured by one parsimonious

model of narrow bracketing. For example, narrow bracketing can be seen

as a feature of the prospect theory of Kahneman and Tversky (1979).

It tightly links phenomena of narrow bracketing to reference-dependent

preferences and loss aversion, because the reference point against which

gains and losses are evaluated is often tied to a single, specific decision.

That is, the individual is assumed to bracket this decision narrowly

(e.g., Thaler, 1999).

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A. K. Koch and J. Nafziger 1443

We conduct an online survey experiment among university entrants at

Aarhus University. The survey includes questions and incentivized tasks

related to choice bracketing and motivational bracketing, as well as several

individual characteristics. We hypothesize (i) that the choice bracketing

phenomena are related to each other and to measures of cognitive skills,

and (ii) that the motivational bracketing phenomena are related to each

other and to measures of self-control.

We collect several measures related to choice bracketing, as follows.

Endowment Integration reveals the extent to which subjects integrate

their endowments when making risky choices. The remaining measures

capture phenomena where narrow bracketing goes hand-in-hand with

reference-dependent preferences that can be described by a value function

with three main features (Kahneman and Tversky, 1979): loss aversion,

s-shape, and a reference point.

Insurance counts how many categories of small-scale insurance (such

as insuring a laptop against theft and damage, or buying travel insurance)

a subject reports to have purchased. Paying a high insurance premium to

avoid such small risks is inconsistent with expected utility, but can be

explained by narrow bracketing in conjunction with loss aversion (Rabin

and Thaler, 2001).

Lottery Isolation builds on an incentivized version of a question by

Tversky and Kahneman (1981) that is designed to detect whether people

integrate multiple lotteries or view them in isolation. The question presents

two concurrent lotteries: one has outcomes in the gain domain and the

other has outcomes in the loss domain. A narrow bracketer with reference-

dependent preferences tends to make a risk-averse choice in the gain lottery

and a risk-seeking choice in the loss lottery – choices that are dominated

when considering the broadly bracketed compound lottery (Rabin and

Weizs¨acker, 2009).

Topical Account builds on two questions by Kahneman and Tversky

(1984) that reveal whether a subject narrowly brackets costs and benefits

associated with a particular consumption decision. Specifically, a narrow

bracketer will evaluate the loss of an already purchased theatre ticket

differently from losing an amount of money of equal value.

The variables Loss Aversion and S-Shaped relate to parameters of the

value function that we elicit with price lists. We predict a correlation with

the other choice bracketing phenomena not only because of the theoretical

link between reference-dependent preferences and narrow bracketing, but

also because of the elicitation procedure for the value function. One

can only observe reference-dependent preferences from choice lists if

individuals bracket the choices presented to them narrowly. Loss aversion,

for example, would play no role for decisions if individuals integrated the

experimental risk with their experimental endowment.

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