Source Dependence in Effort Provision

• Published date: 01 August 2024
• Author: Yiting Chen,Songfa Zhong
• Date: 01 August 2024
• DOI: http://doi.org/10.1111/iere.12698

INTERNATIONALECONOMIC REVIEW

Vol. 65, No. 3, August 2024 DOI: 10.1111/iere.12698

SOURCE DEPENDENCE IN EFFORT PROVISION∗

By Yiting Chen and Songfa Zhong

Lingnan University, Hong Kong SAR; The Hong Kong University of Science and Technology,

Hong Kong SAR and; National University of Singapore, Singapore

We examine source dependence in the setting of effort provision. Our first experiment elicits preference

over uncertain piece rate schemes to perform a real-effort task. Our second experiment elicits effort after re-

ceiving an uncertain gift. We vary the probability of winning and the familiarity of natural sources of uncer-

tainty. We show that subjects are averse to unfamiliar sources for moderate or high probability, but less so

for low probability. Moreover, effort exhibits more insensitivity to the probability under the unfamiliar source

compared with the familiar source. Our findings support the validity and generalizability of source dependence

in applied settings.

1. introduction

Keynes (1921) famously poses the following question: “If two probabilities are equal in de-

gree, ought we, in choosing our course of action, to prefer that one which is based on a greater

body of knowledge?” He exemplifies that people prefer betting on an urn with 50 white and

50 black balls over another urn with an unknown composition of white and black balls that

sum to 100. This two-urn example is later independently proposed by Ellsberg (1961) to il-

lustrate ambiguity aversion. Going beyond known and unknown probabilities, subsequent

studies explore variations on sources of uncertainty, in terms of competence, familiarity, and

so forth (Health and Tversky, 1991; Fox and Tversky, 1995). For example, Fox and Tversky

(1995) show that participants from the University of California at Berkeley prefer to bet on

the temperature in San Francisco over that in Istanbul. Tversky and Kahneman (1992) incor-

porate source dependence into cumulative prospect theory to account for the phenomenon

whereby the source of uncertainty affects probability weighting.

Although various theories have been developed to model source dependence and numer-

ous experimental studies provide evidence in support of its importance,1two questions remain

largely unexplored. The first question concerns the external validity. It is not clear whether

source dependence can go beyond traditional experimental paradigms such as binary lottery

choice, elicitation of certainty equivalent, and elicitation of probability equivalent, and can be

extended to applied settings. The second question concerns the generalizability. Trautmann

and van de Kuilen (2015) summarize a twofold pattern for ambiguity attitudes whereby in-

dividuals exhibit ambiguity aversion for gains with moderate and high probability and tend

∗Manuscript received February 2023; revised January2024.

We have benefited from the helpful comments from Soo Hong Chew, Jingcheng Fu, Lawrence Jin, and King King

Li. For financial support, Chen acknowledges National Natural Science Foundation of China (72303195) and Zhong

acknowledges Singapore Ministry of Education (Academic Research Fund Tier 1).

Manuscript received February 2023; revised January 2024. Please address correspondence to: Songfa Zhong, Depart-

ment of Economics, Lee Shau Kee (LSK) Business Building, The Hong Kong University of Science and Technology,

Hong Kong SAR, China. E-mail: zhongsongfa@gmail.com

1For theories, see Tversky and Fox (1995), Tversky and Wakker (1995), Nau (2006), Chew and Sagi (2008), Ergin

and Gul (2009), Abdellaoui et al. (2011), Gul and Pesendorfer (2015), and Cappelli et al. (2021). For experiments,see

Trautmannand van de Kuilen (2015) for a review.

1499

© 2024 The Authors. International Economic Review published by Wiley Periodicals LLC 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-NonCommercial-NoDerivs Li-

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1500 chen and zhong

to switch to ambiguity seeking for low probability. This pattern implies that individuals are

less responsive to changes in probability under ambiguity than risk, and suggests that likeli-

hood insensitivity is source-dependent. Whether this dependence can be generalized to natu-

ral sources of uncertainty requires further investigation.

We examine these two aspects of source dependence in effort provision when uncertain

payments involve different sources and probabilities. First, we propose a framework to link

source dependence with effort provision. Under certain payment schemes, individuals obtain

monetary and nonmonetary rewards from working and trade off against the cost of effort

(DellaVigna and Pope, 2018; DellaVigna et al., 2022). Under uncertain payment schemes, in-

dividuals assign source-dependent probability weights (Abdellaoui et al., 2011) to monetary

and nonmonetary rewards. Based on this framework, we show that sources of uncertainty

affect both the preference for uncertain payment schemes and effort provision, and we test

these hypotheses in two experiments.

Experiment 1 examines source dependence in binary choices between uncertain payment

schemes for effort, as well as between monetary lotteries. In Stage 1, subjects are informed of

a subsequent real-effort word encryption task and an uncertain payment scheme—a probabil-

ity of winning $0.1 for each correctly encrypted word. We randomly assign subjects to three

conditions with the winning probability being 90%, 50%, or 10%. Subjects learn that the un-

certainty is based on the future value of a stock, and they are asked to determine this source

of uncertainty by choosing between two stocks with different degrees of familiarity. In Stage

2, subjects are given a monetary lottery—a chance to win $4 (otherwise $0) with the winning

probability being 90%, 50%, or 10%, correspondingly. Similar to Stage 1, subjects make bi-

nary decisions among two stocks that differ in familiarity to determine the source of the un-

certainty of winning this extra $4. In the end, we randomly choose one of the selected stocks

in Stage 1 as the source of the uncertain payment scheme for subjects to provide effort in the

encryption task.

We observe source dependence in choices between uncertain payment schemes for effort

provision and between monetary lotteries. Subjects are less likely to choose payment schemes

and lotteries based on the unfamiliar stock for 90% or 50% winning probability, and this ten-

dency is weaker for 10% winning probability. More specifically, there is a twofold pattern in

which subjects exhibit unfamiliarity aversion and this aversion decreases as the probability of

winning gets smaller. Moreover, source dependence is correlated between uncertain payment

schemes and monetary lotteries. Subjects also exhibit source dependence in effort provision,

but we note that the assignment of sources is endogenous to their choices.

Different from Experiment 1 whereby subjects self-select the source of uncertain payment

schemes, Experiment 2 assesses source dependence in effort provision when uncertain pay-

ment schemes are exogenously provided. We randomly assign subjects to eight conditions by

varying the payment schemes to perform a real-effort word encryption task. The payment is

unexpected and independent of effort, which can be regarded as a gift (Akerlof, 1982; Fehr

et al., 1993; Gneezy and List, 2006; Falk, 2007; DellaVigna et al., 2022). In two baseline con-

ditions, subjects receive no additional payment in the No Gift condition and $2 for sure in the

Sure Gift condition. The six remaining treatment conditions use lotteries as gifts, which dif-

fer in terms of the winning probability for an additional $2 (otherwise $0) as 90%, 50%, or

10%, and the source of uncertainty based on the future value of either the New York Stock

Exchange Composite Index (NY) or the Laos Securities Exchange Composite Index (Laos).

Compared with Laos,NY is the more familiar source of uncertainty since 93% of our subjects

are American.

We observe source dependence of effort provision in response to uncertain gifts. Subjects

exert lower effort under Laos than NY when the winning probability is 90% or 50% and

higher effort under Laos than NY when the winning probability is 10%. That is, subjects

exhibit a twofold pattern of switching from unfamiliarity aversion to unfamiliarity seeking

when probability changes from large or moderate to small. This twofold pattern is significant

and is more pronounced among subjects who exert high effort and among American-based