Contracting with private rewards

• Published date: 01 June 2020
• DOI: http://doi.org/10.1111/1756-2171.12326
• Date: 01 June 2020
• Author: René Kirkegaard

RAND Journal of Economics

Vol.51, No. 2, Summer 2020

pp. 589–612

Contracting with private rewards

René Kirkegaard∗

The canonical moral hazard model is extended to allow the agent to face endogenous and non-

contractible uncertainty. The agent works for the principal and simultaneously pursues outside

rewards. The contract offered by the principal thus manipulates the agent’s work–life balance.

The participation constraint is slack whenever it is optimal to distort the agent’s work–life bal-

ance away from life comparedto a symmetric-information benchmark. Then, the agent’sexpected

utility is high and he faces flatter incentives. Such contracts may be optimal when the two activi-

ties are strong substitutes in the agent’s cost function or when reservation utility is low.

1. Introduction

The principal–agent model has been tremendously influential in economics. However, by

treating leisure as an exogenous black box, the canonical model in many ways ignores that a

rich part of the agent’s life takes place outside the office. In reality, workers are not just passive

consumers when they are off the job. For instance, Bryson and MacKerron (2017) document that

the leisure activities that people are the most happy engaging in all involve physical or mental

exertion.1More broadly, nonwork activities include home production, see, for example, Becker

(1965). The agent devotes time and attention to a range of activities from the mundane to the

extraordinary, like a complicated do-it-yourself renovation. Moonlighting represents yet another

relevant activity.

Hence, it is more accurate to think of the agent as multitasking: He invests effort in two

arenas, summarized here as “work” and “life.” In this article, the latter more broadly refers to

whatever activities the agent is pursuing when he is not working for the principal (leisure, home

production, moonlighting).

This article proposes a multitasking model in which the agent decides how hard to work on

the job and how hard to pursue noncontractible outside rewards. Rewards from the two sources

are substitutes. Likewise, effort devoted to the two activities are substitutes in the agent’s cost

function. A key point then is that the contract manipulates the agent’s entire work–life balance.

This is enough to twist familiar intuition, with important consequences.

∗University of Guelph; rkirkega@uoguelph.ca.

Kirkegaard thanks the Canada Research Chairs programme and SSHRC for funding this research. He is grateful to

the Editor, David Martimort, as well as two anonymousreferees for substantial and constr uctive comments that greatly

improved the article. He is also grateful for comments and suggestions from seminar audiences at Queen’sUniversity,

the University of Guelph, and the Canadian Economic Theory Conference.

1Examples include going to a concert, exercising, gardening, hiking, pursuing a hobby.Passive activities such as

watching TV or browsing the internet are much further down the list.

© 2020, The RAND Corporation. 589

590 / THE RAND JOURNAL OF ECONOMICS

For instance, under normal circumstances the principal can calibrate a reduction in the wage

schedule in a way that does not alter incentives on the job, although doing so may discourage

participation. However, in the current model declining wages spur the agent to substitute effort

toward “life” and away from “work.” Similarly, a steepening of the wage schedule is normally

taken to imply stronger incentives for work effort. Although this direct effect still exists, there

is now an additional countervailing indirect effect. Specifically, a steep wage schedule implies

more risk, which causes the job to become less attractive to the risk averse agent. This effect

again encourages a substitution of effort away from work. The latter effect dominates if the two

activities are strong substitutes. Steepening the contract is then self-defeating as effort on the

job declines.

The principal cares about work–life balance to the extent that it influences the cost of in-

centivizing work. It may be optimal to keep the wage schedule relatively flat. With less risky

labor income, the incentive to supplement with private rewards diminishes. As the agent is less

distracted by life, he may nowincrease effort at work despite the flatter wage schedule. The aver-

age wage can then be decreased. However, as previously explained, wages cannot be reduced too

much without destroying incentives. Thus, the agent may earn rent in excess of his reservation

utility. In summary, (i) the wage schedule is relatively flat and (ii) the agent earns high expected

utility. Much of the article is devoted to formalizing this intuition and understanding when these

features are optimal.

These properties set the model apart from more standard models and may help resolve some

common criticisms of the latter. First, standard models predict a binding participation constraint.

This is arguably somewhat puzzling in light of amble evidence that employed people are hap-

pier than unemployed people, see, for example, Clark and Oswald (1994). Second, a common

objection is that real-world incentives appear weaker than what the standard model suggests.

Englmaier and Leider (2012) develop a reciprocity-based model in which the agent becomes

“intrinsically motivated” to repaythe principal’s kindness when he is offered a generous contract.

Thus, flatter extrinsic incentives are needed and they go hand in hand with higher expected utility.

The current article’s explanation is instead based on endogenizing the agent’s work–life balance.

The formal analysis requires an examination of the interplay between participation and in-

centive constraints. The symmetric-information benchmark is a useful starting point. Here, the

principal can dictate effort toward both work and life all while offering a fixed wage. Given the

wage and work effort, it is optimal to permit the agent to pursue the level of life that maximizes

his utility. The participation constraint can then be satisfied at the lowest possible wage.

Under asymmetric information, however, the participation constraint interacts with the in-

centive constraint on life. At low levels of life, the job must be made more attractive in order

to compensate for low private rewards and secure participation. This is consistent with disincen-

tivizing life because private rewards are less of a draw when the job is attractive. Hence, the two

constraints are compatible. Note that a job with a low expected wage may still be attractive to

the agent if it entails very little risk. Under reasonable assumptions, the incentive constraint is

the stricter constraint. Thus, the only way to entice the agent to reduce his level of life below the

symmetric-information level is by granting him utility above reservation utility. In contrast, the

two constraints conflict when the aim is to induce the agent to aggressivelypursue life. Participa-

tion requires very high rewards to compensate for high effort costs, but this tends to disincentivize

life. In some cases, it is impossible to write a contract that resolves this conflict.

The purpose of distorting life is to minimize the cost of incentivizing work. There is a trade-

off. Pushing the agent to lower his pursuit of private rewards tightens the incentive constraint

on life as he must be persuaded to divest from life. However, this leads to a weakening of the

incentive constraint on work as the agent’s marginal cost of effort is reduced. The second effect

is stronger when the two activities are strong substitutes. Then, it is optimal to skew the agent’s

work–life balance away from life. Flat incentives now serve a dual purpose. First, they make the

job attractive. Wages can then be lowered to the principal’s benefit while still disincentivizing

life. Second, as the agent is not pursuing life too hard, flat incentives are sufficient to incentivize

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