FAIR RETIREMENT UNDER RISKY LIFETIME*

• Published date: 01 February 2016
• Date: 01 February 2016
• DOI: http://doi.org/10.1111/iere.12152

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 1, February 2016

FAIR RETIREMENT UNDER RISKY LIFETIME∗

BYMARC FLEURBAEY,MARIE-LOUISE LEROUX,PIERRE PESTIEAU,

AND GREGORY PONTHIERE1

Princeton University, U.S.A.; D´

ep. des Sc. Economiques, ESG-Universit´

eduQu

´

ebec `

a

Montr´

eal (UQAM), CIRPEE, Canada, CORE, Belgium; University of Liege and CORE,

Belgium, Paris School of Economics (PSE), France, CEPR, U.K.; University Paris East Cr´

eteil

and Paris School of Economics (PSE), France, Institut universitaire de France, France

A premature death unexpectedly brings a life and a career to their end, leading to substantial welfare losses. We

study the retirement decision in an economy with risky lifetime and compare the laissez-faire with egalitarian social

optima. We consider two social objectives: (1) the maximin on expected lifetime welfare, allowing for a compensation

for unequal life expectancies, and (2) the maximin on realized lifetime welfare, allowing for a compensation for

unequal lifetimes. The latter optimum involves, in general, decreasing lifetime consumption profiles as well as raising

the retirement age. This result is robust to the introduction of unequal life expectancies and unequal productivities.

1. INTRODUCTION

The continuous rise in life expectancy observed in industrialized economies in the last two

centuries hides a fundamental feature of human life. Despite major advances in medical sciences,

a human life remains a lottery, with a significant variance in longevity outcomes. This point is

well illustrated by survival curves, which give us the probabilities to reach all ages of life (based

on the age-specific mortality rates prevailing at the year under study). As shown by Figure 1

for French males, provided mortality rates remain constant, more than 13% of the cohort born

in 2010 will die before having reached the official retirement age of 62 years.2Moreover, about

20% will die before age 67.

Average life expectancy statistics therefore hide this important uncertainty and the induced

inequalities in longevity outcomes. Only 61% of French males will reach the average life

expectancy, equal to 78.04 years. The remaining 39% of the population will have a shorter life.

Premature deaths constitute a major source of human deprivation. Deprivation due to pre-

mature death looks even more severe once it is acknowledged that psychological well-being is

U-shaped through life, with a minimum in the middle age (see Blanchflower and Oswald, 2008).3

Provided the U-shaped lifetime happiness profile is a robust empirical finding, premature death

would not only prevent individuals from continuing their life, but it would also make them miss

some of the “best” years of their life.

Those observations are not without consequences for optimal policy making, in particular

when considering the design of optimal pension system. From a policy perspective, the ob-

served annual three-months increase in average life expectancy has often been used to justify

∗Manuscript received May 2013; revised June 2014.

1The authors are grateful to Benoit Decerf, Gabrielle Demange, Jean-Franc¸ois Laslier, John Leach, Alessandro

Lizzeri, Nicola Persico, Thomas Piketty, Pierre Yared, Stephane Zuber, and an anonymous referee for their comments

on this article. Marc Fleurbaey and Gregory Ponthiere acknowledge the financial support of the ANR Equirisk (Equity

in Risky Intertemporal Economic Environments; ANR-12-INEG-0006-01). Please address correspondence to: Gregory

Ponthiere, Ecole Normale Sup`

erieure (Paris), Paris School of Economics, 48, Boulevard Jourdan, 75014 Paris, France.

Phone: 0033143136302. E-mail: gregory.ponthiere@ens.fr.

2Sources: the Human Mortality Database (2012).

3Blanchflower and Oswald’s (2008) evidence of welfare being U-shaped through life is obtained while controlling

for cohort effects, for demographic variables, and for income.

177

C

(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

178 FLEURBAEY ET AL.

FIGURE 1

PERIOD SURVIVAL CURVES:FRENCH MALES (1816–2010)

postponing the legal retirement age in countries with pay-as-you-go pension systems. Indeed,

if individuals tend, “on average,” to live longer and if the retirement age remains the same, the

sustainability of the pension system requires, under a constant fertility, either to increase the

pension contributions or to reduce the replacement ratio.4

The problem is that such reasoning looks at things “on average.” In reality, there remain,

as shown above, large longevity inequalities, and it is not at all clear that policymakers should

concentrate on average outcomes. An obvious reason why more attention should be paid to

longevity inequalities is that a significant proportion of those inequalities are due to factors on

which individuals have no influence at all and, thus, are circumstances for which agents can

hardly be regarded as responsible.5For instance, Christensen et al. (2006) claim that about one-

quarter to one-third of longevity inequalities within a cohort can be explained by differences in

genetic background.

Given that longevity inequalities are, to a significant extent, independent of individual be-

havior, there is a strong ethical support for a social security system that does not penalize the

short-lived. The goal of this article is to examine the design of the optimal retirement sys-

tem in an economy with risky lifetime, with a social objective that incorporates a concern for

inequalities.

In the context of risk, there are two main ways of taking account of inequalities. One can

first focus on inequalities in expected lifetime utility and in particular give priority to people

having lower life expectancy. This connects well to the policy proposal of making retirement

age depend on working conditions that affect longevity. But one can also look at the final

distribution of longevity and realized utility across individuals and thereby take account of the

residual inequalities due to good or bad luck in the lottery of longevity. This relates to the policy

discussions about giving less priority to the (lucky) elderly people who had their “fair innings.”

The former approach we call ex ante egalitarianism and the latter ex post egalitarianism.

From an ethical perspective, both ex ante and ex post egalitarianism are attractive, but

for different reasons. Ex ante egalitarianism aims at providing equal welfare chances to all

4On the potential gains from postponing the age at retirement, see Cremer and Pestieau (2000, 2003).

5See Fleurbaey (2008) on the distinction between circumstances and responsibility characteristics.

FAIR RETIREMENT AND RISKY LIFETIME 179

individuals and respects their attitudes toward risk. However, ex post egalitarianism is also

quite intuitive. It can be argued that from the perspective of individual well-being, what really

matters to people is what they achieve in their lives, and not what they expected to achieve. The

inequalities between the lucky who enjoy a long life and the unlucky who die prematurely are

recorded only by the ex post approach.

The choice between ex ante and ex post egalitarian views is of ethical nature. The goal of

this article is not to argue that one approach is superior to another but, rather, to derive and

compare the corollaries of these two distinct egalitarian approaches for the design of a fair

retirement system.

Here is a brief summary of our results. We first study the retirement decision in a two-

period economy with identical agents and a risky lifetime. In such a simple framework, the

laissez-faire allocation coincides with the ex ante egalitarian social optimum, but not with the ex

post egalitarian optimum because of the remaining longevity inequalities. The latter optimum

involves a declining consumption profile over the life cycle and a later retirement than in the

laissez-faire. We then focus on the result that the ex post approach implies a later retirement,

and we show that the opposite result can be obtained when mortality occurs mostly after

retirement. The reason is that when mortality occurs early, a late retirement helps providing

high consumption to the young in order to help those among them who will have a short life.

In contrast, when death strikes after retirement, it helps the short-lived to give them an early

retirement. Finally, we study a model with heterogeneity in life expectancy and in productivity,

and we show that the ex ante and ex post approaches still differ regarding the optimal retirement

age under perfect and asymmetric information.

In sum, the present article suggests that adopting an ex post egalitarian social objective would

lead to a strong reorganization of the life cycle in terms of consumption and labor. As such,

the present study complements the existing literature in several ways. First, it complements the

existing positive literature on optimal labor and retirement age (see Sheshinski, 1978; Crawford

and Lilien, 1981; Kahn, 1988) by applying a model of labor and retirement decisions in a

context of risky lifetime. Second, this article also complements the normative literature on

(socially) optimal labor and retirement age (see Cremer et al., 2004), which relies on classical

(Benthamite) utilitarianism, unlike the present, egalitarian ethical framework.6In particular, it

complements recent theoretical works on the design of efficient pensions systems (see Shourideh

and Troshkin, 2012; Golosov et al., 2013; Hosseini, 2014).7Third, our article also complements

recent attempts to apply ex post egalitarian social criteria to economies with risky lifetimes,

but which did not consider labor and retirement decisions (see Fleurbaey and Ponthiere, 2013;

Fleurbaey et al., 2014).

The rest of the article is organized as follows: Section 2 presents the basic framework where

individuals who are identical ex ante turn out to have unequal longevity and compares the

laissez-faire with the social optimum under ex ante and ex post egalitarianism. Section 3 com-

pares the ex ante and the ex post approaches under different assumptions about when mortality

strikes in the life cycle. Section 4 introduces a more general model with double heterogeneity:

life expectancy and labor earnings. Section 5 concludes.

2. IDENTICAL INDIVIDUALS FACING MORTALITY RISK

We consider a two-period model with risky lifetime. The population is a continuum of agents,

with a measure normalized to 1. Agents live either one period or two periods. The old age

(second period) is reached with a probability π. During the young age (first period), agents

supply their labor inelastically, consume, and save resources for the old age. At the old age,

6Utilitarianism also prevails in optimal retirement age studies in a dynamic setting (see Crettez and Le Maitre, 2002;

Michel and Pestieau, 2002; Lacomba and Lagos, 2006).

7Those recent articles pay particular attention to the design of an optimal pension system in a second-best environ-

ment, because of a limited set of policy instruments (Shourideh and Troshkin, 2012; Golosov et al., 2013) or because of

adverse selection (Hosseini, 2014).