A theory of reverse retirement

• DOI: http://doi.org/10.1111/jpet.12458
• Published date: 01 September 2020
• Date: 01 September 2020
• Author: Gregory Ponthiere

J Public Econ Theory. 2020;22:1618–1659.wileyonlinelibrary.com/journal/jpet1618

|

© 2020 Wiley Periodicals LLC

Received: 19 September 2019

|

Accepted: 10 June 2020

DOI: 10.1111/jpet.12458

ORIGINAL ARTICLE

A theory of reverse retirement

Gregory Ponthiere

Université Paris Est (ERUDITE), Paris

School of Economics, Institut Universitaire

de France, Paris, France

Correspondence

Gregory Ponthiere, Paris School of

Economics, Institut Universitaire de

France, University of Paris‐Est (ERUDITE),

ENS, 48 Boulevard Jourdan, Office R3.66,

75014 Paris, France.

Email: gregory.ponthiere@ens.fr

Abstract

The retirement system is usually regarded as giving

a fair reward for a long working career. However,

only workers who have a sufficiently long life ben-

efit from that reward, but not workers who die

prematurely. To re‐examine the fairness of retire-

ment systems under unequal lifetime, this paper

compares standard retirement (i.e., individuals work

before being retired) with—hypothetical—reverse

retirement (i.e., individuals are retired before

working). We show that, under standard assump-

tions, an economy with reverse retirement, once in

place, converges towards a unique stationary equi-

librium. At the normative level, we show that, when

labor productivity declines with age, reverse retire-

ment cannot be optim al under the utilit arian cri-

terion (unlike standard retirement), whereas reverse

retirement can be optimal under the ex post egali-

tarian criterion (giving priority to the worst‐off in

realized terms). Finally, we show that there exists a

set of policy instruments that allow a government to

organize a successful transition from standard to

reverse retirement.

1|INTRODUCTION

Historical roots of retirement systems are old. These date back, in England, to the Poor Laws

(1599), which included dispositions for elderly individuals unable to work. In France, an édit

royal of 1604 required mine operators to dedicate 1/30th of their output to miners in need.

However, those early retirement systems differ from modern systems, on the grounds that these

were far from universal: Poor Laws were implemented at the parish level, whereas the French

édit royal concerned only the mining industry.

1

Universal pension systems are more recent:

Bismarck's old‐age insurance in Germany dates back to 1889, while Beveridge's pension system

in the UK dates back to 1942.

Retirement systems were introduced not only because of an insurance motive (protecting

individuals against the risk of being poor at the old age), but also, for redistributive reasons.

Retirement systems allow, in theory, for both vertical redistribution (from—potentially richer—

active young individuals toward inactive old individuals) and horizontal redistribution (from

richer to poorer retirees thanks to nonproportional replacement rates). Distributive aspects are

key elements in the design of a fair retirement system (see Cremer & Pestieau, 2011; Schokkaert

& Van Parijs, 2003; Schokkaert, Devolder, Hindriks, & Vandenbroucke, 2017).

Studying the fairness of retirement systems raises additional difficulties when individuals differ on

longevity. In particular, an important source of injustice lies in the fact that some proportion of the

workforce dies before reaching the retirement age. For instance, in France, about 10% of men and 4%

of women die before reaching the age of 60.

2

Those people obviously do not enjoy retirement. Thus,

although the retirement system is usually presented as giving a fair reward for a long working career,

the fairness of that system can be questioned, on the grounds that only workers who have a suffi-

cientlylonglifecanbenefitfromthatreward,whereas those who die prematurely are not rewarded.

The goal of this paper is to re‐examine the fairness of retirement systems in an economy

with unequal lifetime. In particular, we propose to study the capacity of retirement systems—

differing in terms of the ages of entry and exit of labor—to allow the society to achieve some

form of social justice despite longevity inequality.

From the perspective of social justice, a major requirement consists of compensating

disadvantages due to circumstances, that is, factors on which individuals have no control.

According to the Principle of Compensation (Fleurbaey, 2008 and Fleurbaey & Maniquet, 2004),

well‐being inequalities due to circumstances should be abolished by governments. Given that

longevity inequalities are largely due to circumstances (e.g., the genetic background), the

Principle of Compensation applies to the case of unequal lifetime.

3

Thus that principle provides

ethical support for the compensation of prematurely dead individuals.

It is far from trivial to design retirement systems favoring the compensation of the short‐

lived. In a recent paper, Fleurbaey, Leroux, Pestieau, and Ponthiere (2016)examinedhow

varying the age at retirement could achieve such a compensation. Fleurbaey et al. (2016)

characterized the optimal retirement age while adopting an ex post egalitarian social wel-

fare criterion, which gives absolute priority to the worst‐off in realized terms (who is, in

general, the short‐lived). Fleurbaey et al. (2016) showed that the compensation of the un-

lucky short‐lived pushes toward postponing retirement in comparison with the utilitarian

social optimum. The underlying intuition is that postponing retirement allows to transfer

moreresourcestowardtheyoungage,and,hence,toincreasethewell‐being of all young

individuals (including those who will turn out to die prematurely).

Although Fleurbaey et al. (2016) casts some light on how taking care about the compensation of

the short‐lived can affect the optimal age at retirement, it remained based on the standard view on

retirement. Actually, Fleurbaey et al. (2016) assumed the usual life cycle, where individuals work at

1

In France, another édit royal published in 1673 created a pension for officers of the Marine Royale, while pensions were

introduced for soldiers and civil servants in, respectively, 1831 and 1853 (see Lavigne, 2013).

2

See the Human Mortality Data Base.

3

On the impact of genes on longevity inequalities, see Christensen, Johnson, and Vaupel (2006).

PONTHIERE

|

1619

the young age, and become retiree as they reach some (older) age. But can we think about

alternative retirement systems that would be more fair?

To re‐examine the fairness of retirement systems under unequal lifetime, this paper pro-

poses to go beyond the standard representation of retirement systems, in which individuals are

first workers at the young age, and, then, if they survive to sufficiently high ages, retirees. We

propose to consider also what we call a “reverse”retirement system, where individuals would—

unlike in existing societies—be first retirees at the young age, and, then, workers at the old age.

This paper examines the conditions under which such a—purely hypothetical—reverse re-

tirement system dominates the standard retirement system.

At this early stage of our explorations, it should be stressed that reverse retirement does not

exist in actual economies, and is thus a pure theoretical abstraction. Reverse retirement is a

kind of “utopia,”in the same way as standard retirement was regarded as an utopia during the

longest part of History. Note, however, that, in the common language, the term “reverse re-

tirement”refers to the behavior of a minority of retirees who go back to work. In some sense,

the reverse retirement system that we consider is a generalization of this behavior to the entire

society. We propose to compare existing standard retirement systems with the—purely

hypothetical—reverse retirement system.

For that purpose, we develop a 4‐period overlapping generations model (OLG) with unequal

lifetime. That dynamic framework will allow us to examine not only the social desirability of reverse

retirement, but also, its economic feasibility. We assume that: (a) production involves physical

capital as well as young and/or old labor; (b) there is a perfect substitutability between young and

old labor (but with age‐dependent labor productivity); (c) older workers face a higher marginal

disutility of labor than younger workers. We first study the temporary equilibrium, and the long‐run

dynamics of the economy, under either standard or reverse retirement. Those two kinds of economy

differ from a qualitative perspective: under standard retirement, young individuals work and save

for their old days (during which they will be retired), whereas, under reverse retirement, young

individuals do not work, borrow resources, and pay these back at the old age (during which they

work). In a second stage, we examine the social desirability of standard and reverse retirement

under two social welfare criteria: utilitarianism and ex post egalitarianism.

Our results are threefold. First, at a positive level, we show that, under standard assumptions on

technology and preferences, an economy with reverse retirement, once in place, converges toward a

unique stationary equilibrium. Thus an economy with reverse retirement is sustainable in the long‐

run. Second, at the normative level, we show that, when labor productivity declines with age,

reverse retirement is never optimal under the utilitarian criterion, but can, under some conditions,

be optimal under the ex post egalitarian criterion. From the ex post egalitarian perspective, standard

retirement dominates reverse retirement in less developed economies (characterized by harsh

working conditions, a steep age‐productivity profile and a lower probability of survival to age 50),

but reverse retirement dominates in advanced economies (characterized by less harsh working

conditions, a flatter age‐productivity profile, and a higher probability of survival to age 50). Third,

we show that, although the transition from standard to reverse retirement leads to the collapse of

the economy in the laissez‐faire, there exists a set of policy instruments that allow governments to

organize a successful transition from standard to reverse retirement.

This paper is related to several branches of the literature. First, it is related to the literature on

retirement and distribution (Cremer & Pestieau, 2011;Schokkaert&VanParijs, 2003; Schokkaert

et al., 2017), which focuses on standard retirement, unlike this paper, which also examines reverse

retirement. Second, this paper is also related to the literature on fairness and compensation under

unequal lifetime (see Fleurbaey & Ponthiere, 2013; Fleurbaey et al., 2016,2014). Fleurbaey et al.

1620

|

PONTHIERE