Fair optimal tax with endogenous productivities

• Date: 01 December 2018
• Published date: 01 December 2018
• Author: Giacomo Valletta,Marc Fleurbaey
• DOI: http://doi.org/10.1111/jpet.12318

Received: 31 October 2016 Accepted: 20 May 2018

DOI: 10.1111/jpet.12318

ARTICLE

Fair optimal tax with endogenous productivities

Marc Fleurbaey1Giacomo Valletta2

1PrincetonUniversity, Princeton, NJ

2EDHECBusiness School, Roubaix, France

Correspondence

GiacomoValletta, EDHEC Business School, 24

AvenueGustave Delory,59100 Roubaix, France.

Email:giacomo.valletta@edhec.edu

We consider a model where agents differ in their preferences about

consumption, labor,and human capital. Moreover, choosing a certain

level of human capital, agents can differently affect their endoge-

nous earning ability. Finally,agents differ in their human capital dis-

position: different agents face a different cost to acquire a certain

amount of human capital. In this framework we study the problem of

assessing tax reforms when a policy maker wants to reduce inequal-

ities due to unequal skills while accepting inequalities due to diverse

preferences. Consistent with the findings of the fair income taxation

literature, when evaluating a tax reform, in order to obtain a social

improvementone should always give priority to agents with the most

disadvantaged characteristics who work full time. However, in our

framework, this corresponds to a whole rangeof earnings depending

on the corresponding levelof human capital. We show how subsidies

on human capital affect the level of earnings that gets most priority

in order to single out more precisely the population that should be

the focus of the reform. Relying on these findings we also study the

shape of the optimal tax function.

1INTRODUCTION

The literature on optimal taxation has recently started to study nonutilitarian social objectives, on the grounds that

utilitarian social welfare functions fail to incorporate important value judgments that are part of current public

debates. Boadway (2012), Piketty and Saez (2013) , Lockwood and Weinzierl(2014), and, most comprehensively, Saez

and Stantcheva (2016) provide a list of relevant considerationsof equity that are ignored by the classical approach. In

particular,Piketty and Saez (2013) stress that the maximization of a (possibly weighted) utilitarian social welfare func-

tion would fall short in producing two desirable fairness properties. First, utility should be equalized when all agents

have the same preferences (a property more generally known as the compensation objective). Second, when all agents

havethe same productivity, then laissez-faire should be the social optimum (the laissez-faire objective). These two prop-

erties are a particular case of the more general (and popular) idea that, unlike disadvantageous circumstances (i.e.,

personal characteristics that are beyond individual responsibility), personal preferences and effort should not be a

target of redistribution. This idea of fair taxation has been applied to the problem of optimal taxation by Fleurbaey

and Maniquet (2006, 2007, 2011, forthcoming), who defined social welfare functions that embody the compensation

and the responsibility objective through the use of special money-metric individual utility functions, and used them to

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Journal of Public Economic Theory. 2018;20:849–873. wileyonlinelibrary.com/journal/jpet © 2018 Wiley Periodicals, Inc.

evaluate taxes. Related approaches have been developed by Boadway, Marchand, Pestieau, and Racionero (2002),

Jacquet and VanDe Gaer (2011), and Lockwood and Weinzierl (2015).1

A controversial aspect of all these approaches, however,is that they assume that the workers'earnings abilities are

exogenousand hence totally a matter of circumstances, while their preferences over consumption and labor are totally

a matter of responsibility.This may be viewed as a convenient starting point, but, apart from being unrealistic, it is also

problematic from a normative point of view: a model where productivity is exogenous does not allow to distinguish

between a low-skilled agent who has chosen her lower productivity and another low-skilled agent who has instead suf-

fered from various impediments that haveprevented her from acquiring a higher skill. Similarly, one cannot distinguish

between a low earner who has chosen to work few hours because it was too costly for her to invest in human capital

(and have access to a better job)and a low earner who has voluntarily chosen to work few hours. In this paper, we pro-

pose to examine how the analysis is modified when individuals can be held partly responsible for their earning abilities

(due to their training or health choices) and partly nonresponsible for their preferences.

In order to tackle this issue we introduce a third dimension, alongside consumption and leisure, namely,human cap-

ital, which is meant to encapsulate both skills and health conditions and has a positive impact on earning ability.2Indi-

vidualshave heterogeneous preferences over consumption, labor, and human capital (people do care about their health

condition, beyondthe fact that health may affect their productivity, and they also care about their education, given that

it provides cultural and social opportunities and status beyond earning potential3) and they will choose their human

capital in addition to their labor time and consumption, under a budget constraint.

The richness of our model allows us to analyze the normative implications of a wide range of situations. Allowing

agents to choose their level of human capital makes them partly responsible for their earning ability. Theyare only

partly responsible because they may have a different human capital disposition namely, they have to face different

costs of human capital (due to genetic and epigenetic characteristics,4social background, health contingencies). Also,

the impact of human capital on earning ability can vary across agents and such heterogeneity might be due to innate

factors, or social connections, which are beyond their responsibility.

Moreover,adding human capital as an argument of individual utility allows us to make a distinction between situa-

tions where agents choose a high level of human capital just because they care about it (theycare about being healthy

and/or cultivated), or because they only care about consumption (a higher levelof human capital increases their pro-

ductivity) and so explain, among other things, certain differences in preferences between consumption and leisure.

For example, certain individuals may be forced to choose their labor time at a point where the marginal rate of sub-

stitution between consumption and labor is particularly high because of their personal circumstances: An apparent

aversion to work may be actually due to circumstances likebad health disposition, or capability to learn, giving access

to low-quality jobs. On the contrary, certain individuals may choose their labor time at a point where their marginal

rate of substitution between consumption and labor is particularly low because they have decided to invest a lot in

human capital (even if this was costly to them). Insofar as the choice of a certain amount of human capital is partly

due to circumstances, the individuals'consumption–leisure preferences can also be taken to be only partly a matter of

responsibility.5

1Boadway et al. (2002) and Lockwood and Weinzierl (2015) propose weighted utilitarian social welfare functions. Jacquet and VanDe Gaer (2011) adopt

Fleurbaey–Maniquetsocial criteria and focus on the extensive margin.

2Thisis true not just for education but also for health care as shown, among others, by Mushkin (1962), Grossman and Benham (1974), and Luft (1975).

3Unlikehealth, there is no clear empirical association between education and happiness, as documented in Abel and Kruger (2005), Michalos (2008), Phillips

andHempstead (2017), and Pompili et al. (2013). There are many reasons why education can be associated with unhappiness, for example, through increased

expectationsand responsibilities. However, this is compatible with people having a genuine preference for being educated rather than not.

4Christensen, Holm, Mcgue, Corder,and Vaupel (1999) show that approximately a quarter of the variation in self-reported health and in the number of hos-

pitalizationscould be attributed to genetic factors. Currie (2011) studies the epigenetic determinants of human capital.

5Inthe literature (e.g., Roemer, 2012), it is sometimes argued that individuals should not be held responsible for the part of their preferences that is influenced

by their circumstances (e.g.,their upbringing). This sort of reasoning makes sense when the goal is to give people equal access to a material outcome such as

income, because an upbringing that makesone less hardworking is indeed an obstacle on the road to income. But in our paper, welfare is at stake, so we stick

tothe idea that individual preferences are equally respectable no matter how they were formed, and leave the study of paternalism for another occasion.

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