Differential mortality and social security

Abstract

This paper studies the normative problem of redistribution between individuals who differ in their lifespans. We discuss aspects related to the objective function and argue that aversion to multiperiod inequality should be taken into account. Then, we study the properties of the social optimum both with full information and with asymmetric information. We highlight the role of aversion to multiperiod inequality and show that it has substantial consequences on the design of Social Security schemes. In particular, we show that for a low (resp. high) aversion to multiperiod inequality, a negative (resp. positive) implicit tax rate on continued activity is desirable. JEL classification: D63, H55, H23, I31Mortalité différentielle et sécurité sociale. Ce mémoireétudie le problème normatif de la redistribution entre individus qui ont des durées de vie différentes. On discute certains aspects reliésà la fonction objective et on montre que l'aversionà l'inégalité sur plusieurs périodes doitêtre prise en compte. Onétudie les propriétés de l'optimum socialà la fois dans les cas d'information complète et d'information asymétrique. On souligne le rôle de l'aversionà l'inégalité sur plusieurs périodes, et on montre qu'elle a des conséquences importantes sur le design des régimes de sécurité sociale. En particulier, on montre que pour une faible (haute) aversionà l'inégalité, un taux d'imposition implicite négatif (positif) sur la continuation des activités est désirable.

Evidence on individual preferences for longevity risk

“…Note that measures of the risk attitude are strongly 6 Kapteyn and Teppa (2011) finds similar results using Dutch data, except for income, which is not significant in their study. Yet, they find a negative relation between risk aversion and wealth.…”

“…in income and in education. 6 In both studies, male are found to be less risk averse. These papers off course, study a different kind of risk aversion, since they are about individual preferences over monetary risks while our paper focuses on the risk of longevity.…”

Endogenous differential mortality, non-contractible effort and non-linear taxation

“…As shown by Gruber and Wise (1999), Social Security systems typically provide replacement rates which are lower than one. 3 Our theoretical model supports such a feature of the pension design, as a way to limit longevity-enhancing behavior.…”

“…4 Our paper might however complete his work as we consider a special case of non-monetary investment in longevity; we also assume a population with different disutility from effort so that our results are not only about efficiency but also about equity. 3 For example, they estimate that the replacement rate at early retirement age ranged from 20% in Canada to 91% in France and in the Netherlands. 4 Chapter 7 pp.53 in "The economic theory of annuities".…”

Designing benefit rules for flexible retirement: Welfare vs. redistribution

“…Probably we are the first who -following Mirrlees (1971) -explicitly formulate pension mechanism design as an isoperimetric optimal control problem. Independently of our work, Bommier et al (2011) analysed a similar model, where the distribution function of life expectancy is continuous rather than discrete, the disutility of labour is increasing with the age rather than being constant or two-valued, the contribution rate is type-dependent and the social welfare function is generalised utilitarian. Their results are qualitatively similar to ours but they do not present numerical examples.…”