A pure hedonic theory of utility and status: Unhappy but efficient invidious comparisons

• Published date: 01 August 2019
• Date: 01 August 2019
• DOI: http://doi.org/10.1111/jpet.12364
• Author: Pascal Courty,Merwan Engineer

Received: 13 July 2018

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Revised: 3 December 2018

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Accepted: 18 January 2019

DOI: 10.1111/jpet.12364

ORIGINAL ARTICLE

A pure hedonic theory of utility and status:

Unhappy but efficient invidious comparisons

Pascal Courty

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Merwan Engineer

Department of Economics, University of

Victoria, Victoria, Canada

Correspondence

Merwan Engineer, Department of Economics,

Business and Economics Building, University

of Victoria, Victoria, British Columbia,

Canada, V8W 2Y2.

Email: menginee@uvic.ca

Funding information

Social Science and Humanities Research

Council (Canada), Grant/Award Number:

SSHRC grant 410‐2100‐1256

Abstract

We examine status preferences where agents compare their

own utility relative to the utilities of others. As long as

status utility comparisons are not too intense, they do not

affect either the competitive equilibrium or the set of

efficient allocations. However, status utility comparison may

substantially reduce average utility and dramatically in-

crease utility inequality. Equating utility with happiness

operationalizes the theory and provides an explanation of

why invidious comparisons can generate so much unhappi-

ness without much inefficiency. Our theory has very

different welfare implications from other status theories,

even when reduced form representations appear observa-

tionally equivalent.

Our envy always lasts longer than the happiness of those we envy.

La Rochefoucauld (1678/1827)

Apart from economic payoffs, social status seems to be the most important incentive and motivating force

of social behavior.

Harsanyi (1976, p. 204)

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INTRODUCTION

There is now a substantial body of economic theory and empirical studies that incorporate interpersonal

comparisons into economic models. This literature typically locates the status preference on a single variable, such

as leisure (Veblen, 1899/1953), consumption income (Duesenberry, 1949), or positional goods (Hirsch, 1976). Such

status preferences, where relative comparisons are made for a subset of variables in the utility function, generate

allocation distortions that reduce welfare. Layard (1980) and Frank (1985) have long urged us to accept the sad

J Public Econ Theory. 2019;21:601–621. wileyonlinelibrary.com/journal/jpet © 2019 Wiley Periodicals, Inc.

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reality that relative comparisons impose major negative externalities that, like pollution, could be taxed to public

benefit.

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This paper proposes an alternative theory of status preferences that have very different welfare and policy

implications. Our theory is grounded on a hedonic foundation where the status function involves comparisons of

cardinal utilities across individuals. We name this class of status function “status utility”because utilities are

compared instead of leisure, income, or consumption as is done in the literature. Status utility captures how well an

individual is doing in utility terms relative to their reference group. For status‐conscious individuals, where

maximizing own utility is their end goal, utility comparison is the ultimate basis for comparing individuals. Equating

cardinal utility with measures of happiness from the subjective well‐being (SWB) literature operationalizes the

theory. Happier people have higher status and are happier for it.

In the model, each agent’s utility is a function of their primary utility and their status utility. Primary utility is the

standard cardinal utility function defined on consumption goods, leisure, and so on. Status utility is a linear function

of the difference between own utility and the weighted sum of utilities of other agents in the reference group. The

utility functions are, therefore, implicit functions of each other. With this system, and assuming status comparisons

are not too intense, we derive the following key results: (a) Utility can be expressed as a function of the primary

utilities of all agents. (b) The set of Pareto‐efficient allocations is unaffected by the introduction of status utility, and

the competitive equilibrium is unaffected by status utility. (c) Status utility can help explain what appear to be

positional concerns over goods without resort to positional preferences over goods. (d) Status utility generates

network effects that typically magnify utility inequality. (e) In the most relevant cases, status utility is negative sum

and equity policy increases average utility. (f) Utilitarian allocations reduce negative status externalities by

allocating more to those who compare themselves more intensely to others.

Including relative utility comparisons into the standard model need not alter key positive and normative results.

The utility equivalence result (a) boils down to each agent’s utility ultimately depending positively on their own

primary utility, and the efficiency and equilibrium results (b) depend on not being able to manipulate others’

primary utilities.

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In contrast, the status literature departs from the standard model by incorporating status goods,

where a subset of goods, termed positional goods by Hirsch (1976), generate negative consumption externalities.

The more positional the good, the greater the externality and distortion. To this conclusion, Arrow and Dasgupta

(2009) provide a major qualification. They show that if all goods are equally positional, then the externalities cancel

out.

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In their economy, each good is separable in the utility function and there is a negative externality from the

absolute level of average consumption of each good. The market equilibrium has no allocation distortions when

good externalities are proportionally symmetric across consumption goods. In our model, the balance is naturally

struck as agents in effect maximize primary utility. Allocations and primary utilities are the same as in the standard

model. This neutrality result survives recursive utility comparisons and all specifications of reference groups.

Our model offers other contrasting perspectives to the literature. Solnick and Hemenway (1998, 2005) and

others find dramatic survey evidence for positional concerns. For example, about half of those surveyed prefer a

world where they get a lower absolute income when it improves their relative income position. However, for

vacations only a few respondents choose less vacation time. The result that income is far more positional than

leisure in the utility function is at odds with the requirement of Arrow and Dasgupta (2009) that goods be equally

positional for externalities to cancel out. In contrast, we show that the survey evidence is consistent with standard

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Clark, Frijters, and Shields (2008) review the empirical and theoretical literature. Easterlin (1974, 2013) argues that relative comparisons are a key

culprit that explain his controversial claim that income growth has not improved the human lot in developed nations. Consideration of relative

consumption can dramatically alter optimal tax policy (e.g., Aronsson & Johansson‐Stenman, 2018; Slack & Ulph, 2018).

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We relate our utility equivalence results to the work of Bergstrom (1999) on interdependent nonpaternalistic altruistic preferences in Section 2.2, and in

Section 3.1, we relate our neutrality results to the general analysis of other‐regarding preferences in Dufwenberg, Heidhues, Kirchsteiger, Riedel, and

Sobel (2011).

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Layard (1980) briefly discusses offsetting externalities. For recent work on offsetting externalities, see Aronsson and Johansson‐Stenman (2013) and

Johansson‐Stenman and Sterner (2015).

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COURTY AND ENGINEER