Subjective well‐being, consumption comparisons, and optimal income taxation

• Published date: 01 August 2018
• DOI: http://doi.org/10.1111/jpet.12281
• Author: David Ulph,Sean Slack
• Date: 01 August 2018

Received: 28 March 2017 Accepted: 16 October 2017

DOI: 10.1111/jpet.12281

ARTICLE

Subjective well-being, consumption comparisons,

and optimal income taxation

Sean Slack David Ulph

Universityof St. Andrews

SeanSlack, School of Economics & Finance, Uni-

versityof St. Andrews, Castlecliffe, The Scores,

St.Andrews, Fife, KY16 9AR, Scotland, U.K.

(sean.ses34@gmail.com).

DavidUlph, School of Economics & Finance, Uni-

versityof St. Andrews, Castlecliffe, The Scores,

St.Andrews, Fife, KY16 9AR, Scotland, U.K.

(du1@st-andrews.ac.uk).

Financialsupport from the AXA Research Fund

isgratefully acknowledged. We also thank John

Ashworthand Durham University for hosting us

duringthis research. Finally, we greatly appreci-

atethe detailed feedback from the referees.

We introduce reference consumption into the standard utility func-

tion from optimal tax analysis. Individuals compare their consump-

tion “narrowly” with those of the same productivity, or “broadly”

with the average consumption across society. In both narrow and

broad equilibria reference consumption is an increasing function of

the tax parameters, so generating new theoretical results. Individual

well-being decreases with the net wage (net-of-tax) rate for low pro-

ductivity workers under narrow (broad) comparisons, thus adjusting

redistributive taxation considerations. Further, in both cases refer-

ence consumption distorts labor supply away from the social opti-

mum level, giving a distortion-correcting role for taxation.

1INTRODUCTION

The standard optimal income tax framework (i.e., Mirrlees, 1971;Sheshinski, 1972) assumes that individual well-being

is independent of the outcomes of others. This is in contrastwith the substantial body of empirical work suggesting that

income and consumption comparisons are a key driver of one's subjective well-being (Blanchflower & Oswald, 2004;

Clark, Frijters,& Shields, 2008; Clark & Oswald, 1996; Ferrer-i Carbonell, 2005; Layard, 2005; Layard, Mayraz, & Nick-

ell, 2009; Senik, 2009).1Much of this research is based on survey evidence in which the main socioeconomic variable

available to the researcher is income: it is an open question whether it is income or consumption comparisons that are

relevant, but in the context of the frameworkin this paper the two coincide. With this in mind, our paper analyzes the

optimal income tax problem when individual preferences are defined very generally overown-consumption and labor

time (as in the standard model) and the averageconsumption of some reference group.

Our question is as follows: How do the conventional results from the optimal linear income tax framework change

when individual well-being is decreasing in the average consumption of some reference group and, further,the level

of reference group consumption may be an argument of individual choices, thus generating keeping up with the Joneses

behavior? In answering this question, we are also responding to recommendations that public economic theory should

1Thisliterature has largely spawned from the well documented “Easterlin Paradox”: substantial increases in real income per capita across developedcountries

have not been accompanied by markedincreases in average reported well-being; though within-country higher income individuals tend to be happier than

lower income individuals (Easterlin, 1974, 1995, 2001). Relativeincome theory (Duesenberry, 1949) provides a possible resolution: if individual preferences

aredefined over consumption relati ve to the unweightedaverage in society, a ceteris paribus increase in a given individual's income will increase their well-being,

butan increase in the average national income will generate no such increase in individual well-being (see also van de Stadt, Kapteyn, & van de Greer, 1985).

Journal of Public Economic Theory.2018;20:455–476. wileyonlinelibrary.com/journal/jpet c

2017 Wiley Periodicals,Inc. 455

456 SLACKAND ULPH

incorporate key insights from the extensive literature on subjective well-being (Layard, 2006; O'Donnell, Deaton,

Durand, Halpern, & Layard,2014).

An empirical literature helps inform the appropriate choice of theoretical framework, in particular providing evi-

dence on the composition of reference groups, the size of income/consumptionexternalities, and the behavioral impli-

cations of income comparisons. First, Clark and Senik (2010) elicit from the European Social Survey (Wave 3) that

a majority of individuals compare their income with others and, further, of those who compare, colleagues are the

most prevalently reported reference group. Second, a number of studies suggest that an increase in reference group

income or corresponding reduction in own-income reduces well-being bysimilar magnitudes (Ferrer-i Carbonell, 2005;

Luttmer,2005). Third, there is evidence that income comparisons have an upward effect on labor supply: an individual

who whose income falls behind that of the reference group may increase their work hours in a bid to “keepup with the

Joneses” (Pérez-Asenjo, 2011). This is also consistent with the prevailing view that individuals do not compare their

leisure with that of others (Layard, 2006).2

There is also experimental evidence that individuals may trade–offincome for higher relative standing in choosing

their preferred society: this is illustrated, for example, in Johansson-Stenman, Carlsson, and Daruvala (2002), where

individuals compare societies of equal income inequality but different relative positions for their hypothetical grand-

children (also see Alpizar,Carlsson, & Johansson-Stenman, 2005; Fehr & Schmidt, 1999).

In our framework individuals may compare their consumption “narrowly” with those of the same productivity, or

“broadly” with the average consumption across society as a whole.3Individuals choose their Marshallian labor supply

taking as given the reference consumption level; but in both the narrow and broad cases the equilibrium level of ref-

erence consumption will be a function of the tax parameters (and in the narrow case also a function of productivity).

Consequently,a number of new theoretical results arise relative to the conventional theory.

Our first result concerns well-being and the net wage/net-of-tax rate. In the conventional theory an increase in

the net wage (net-of-tax) rate increases the well-being of workers at a rate proportional to labor supply (gross earn-

ings). In our framework, there is also a second opposing effect. Under narrow comparisons an increase in the net wage

rate increases averagepeer consumption, which acts to lower well-being because reference consumption is a negative

externality. Forworkers with productivity close to the reservation productivity—and so very low labor supply—this

second effect dominates the conventional effect and well-being falls with the net wage rate. The implication is that,

in contrast to the conventional theory,the worst-off in society are no longer the voluntarily unemployed or those of

lowest productivity, but instead workersof low productivity. Next, under broad comparisons average consumption is

independent of productivity and so well-being is unambiguously increasing in individual productivity.4However,an

increase in the net-of-tax rate is well-being–reducing for workersof low productivity. The intuition is analogous to the

narrow comparison case: the negative externality of increased reference consumption offsets the traditional effect.

In the broad comparison case we must thus distinguish between changes in individual productivity and the net-of-

tax rate, whereas in the narrow case both arguments are summarized via the net wage rate.5Finally,these well-being

results hold for both the cases where labor supply is independent of reference consumption (the pure negative exter-

nality case) and where labor supply is an increasing function of the reference consumption level.

This first result has implications for the how the social marginal welfare weight (smww) changes with individual pro-

ductivity.In modern tax analysis, the smww captures the value, in units of public funds, that society places on awarding

a given individual an additional one unit of income (Piketty & Saez, 2012). In the conventional theory the smww is

2Though since Veblen (1899) it has been recognized that leisure may play a role in “displaying”relative consumption disparities: individual consumption

is time-consuming and so higher consumption may require more leisure, while individuals taking leisure may notice more the consumption of others (see

Aronsson& Johansson-Stenman, 2013).

3Ourframework is static and so income is equivalent to consumption.

4Wethink of this as a cross-sectional result.

5Theresult that an individual'swell-being falls with the net-of-tax rate continues to hold in a Piketty and Saez (2012)–style framework where individuals differ

inboth their preferences and earnings ability. However, because such a frameworkdoes not permit interpersonal comparisons all we can say is that the sign of

theinequality has changed relative to the standard theory. For this reason, a framework with homogenous preferences affords us more theoretical insight.