امنیت اجتماعی، سن بازنشستگی و مالیات بهینه از درآمد

It is often argued that implicit taxation on continued activity of elderly workers is responsible for the widely observed trend towards early retirement. In a world of laissez-faire or of first-best efficiency, there would be no such implicit taxation. The point of this paper is that, when first-best redistributive instruments are not available, because some variables are not observable, the optimal policy does imply a distortion of the retirement decision. Consequently, the inducement of early retirement may be part of the optimal tax-transfer policy. We consider a model in which individuals differ in their productivity and their capacity to work long and choose both their weekly labor supply and their age of retirement. We characterize the optimal non-linear tax-transfer that maximizes a utilitarian welfare function when weekly earnings and the length of active life are observable while individuals' productivity and health status are not observable.

A trend towards early retirement is currently observed in most European countries. Participation rates for men aged 60–64, which were above 70% in the early 1960s, have fallen to 57% in Sweden and to below 20% in Belgium, France Italy and the Netherlands. Similarly, the average labor participation in the age group 55–64 has declined and now ranges from 24% in Belgium, to 88% in Iceland, with the bulk of countries closer to Belgium than to Iceland. Early retirement per se is of course a blessing for a society, which values consumption of leisure. However, it also puts pressure on the financing of health care and pension schemes. This problem is made worse by growing longevity. In the European Union, life expectancy at age 65 has increased by more than 1 year per decade since 1950. As a consequence, instead of 45–50 years of work and 5–10 years of retirement of half a century ago, a young worker can now expect to work for 30–35 years and retire for 15–20 years. The effective retirement age varies across individuals and depends on features such as wealth, productivity and health. In addition, retirement decisions are likely to be affected by the pension system. When there is no pension system (utility maximizing) people retire when the marginal utility of inactivity is equal to their marginal productivity at work. People in poor health and with low productivity will retire earlier than people in good health and with high productivity. When there is a pension system, this tradeoff may or may not be affected, depending on the design of the benefit formula. In a first-best (full information) setting, an optimal retirement system would imply the same tradeoff. Such a pension system can be referred to as neutral or actuarially fair.1 In reality, pension systems are typically not neutral and they distort the retirement decision. As it has been shown by a number of authors, notably Gruber and Wise, 1999, Blondal and Scarpetta, 1998a and Blondal and Scarpetta, 1998b, the observed age of retirement is likely to be distorted downwards in a number of countries. The main explanation for this distortion appears to be the incentive structure implied by social protection programs aimed at elderly workers: pension plans but also unemployment insurance, disability insurance and early retirement schemes. The authors show that prolonged activity for elderly workers is subject to an implicit tax, which includes both the payroll marginal tax and forgone benefits. Consequently, social protection systems are far from being actuarially fair at the margin in countries such as Belgium, France, Germany or the Netherlands where people retire relatively early. On the other hand, in Japan, Sweden and the US the implicit tax is much lower so that the system tends to be rather neutral and people retire much later. These results are essentially positive. Nevertheless, they are often, at least implicitly, given a normative connotation and used to advocate reforms tending to remove the bias in the benefit formulas. This raises the question of whether a bias in the benefit formula in favor of early retirement is necessarily the sign of a bad policy. We show in this paper that this implicit tax on postponed retirement is not necessarily due to bad design but can be due to the desire by public authorities of using social security for redistribution when non-distortionary tools are not available. To address this issue, we determine in the line of Mirlees (1971) the social security benefits, payroll taxation and retirement age policy that are optimal from a utilitarian perspective. We consider a setting with heterogeneous individuals differing in two unobservable characteristics: level of productivity and health status. We study the design of a non-linear tax-transfer function depending upon two variables2: the weekly income and the retirement age. We show that, in a setting of asymmetric information, a distortion towards early retirement is desirable for some individuals. More precisely, the optimal policy in the two-type case induces highly productive and healthy workers to retire efficiently (namely when their labor disutility is marginally equal to their productivity) while less productive and less healthy workers are induced to retire earlier. We also show that the tradeoff between weekly labor supply and retirement age (for a given lifetime income) may or may not be distorted. When a distortion is called for, its sign depends on whether the “dominant” source of heterogeneity is health or productivity. When individuals differ mainly (or exclusively) in productivity, the distortion goes against weekly labor supply. When health differentials are dominant, the distortion goes against retirement age. The two dimensions of heterogeneity are a crucial ingredient of our analysis. When designing a redistributive social security system, it is important to take into account the wide variability in the capacity to work—a variability that is likely to widen as life expectancy increases. The practical issue is how to care for elderly workers who are in poor health without, at the same time, opening the door of retirement to those who would like to stop working but are quite capable of continuing. Consequently, a reform of social security ought to include a close connection between pensions systems and the system of disability insurance as well as the determination of a more flexible retirement age together with actuarial adjustment of yearly benefits. The ideal outcome would then be to have early retirees because of poor health receive relatively generous benefits while early retirees unwilling to continue working would receive actuarially low pensions. There exists a theoretical literature dealing with various aspects of the issue of social security, disability insurance and retirement. It focuses on long-term labor contracts encompassing retirement rules (Lazear, 1979) and the implicit inducement to retirement of existing public and private pension plans (Crawford-Lilien, 1981 and Fabel, 1994 see also Lumsdaire and Mitchell, 1999). This literature is mainly positive; it analyzes retirement behavior in order to explain the observed evolutions in retirement practice. Our paper uses a normative approach, which is intended to provide a benchmark against which the positive results can be assessed. In that respect, it is in the vein of Diamond and Mirrlees (1986) who derive disability contingent retirement rules. We shall further discuss the link between our approach and this earlier work in the concluding section. At this point, it is important to stress that we encompass income taxation, disability insurance, early retirement schemes and social security in our non-linear tax-benefit scheme. To pursue this rather ambitious endeavor, we admittedly have to simplify other aspects of the model. In particular, we essentially assume away the intertemporal aspects, which would bring in issues of uncertainty, commitment, liquidity constraints, etc. Unemployment insurance is not considered either as we assume full employment. The rest of the paper is organized as follows. Section 2 presents the basic model while the laissez-faire and the first-best solutions are studied in Section 3. In Section 4, the second-best policy is studied. We characterize the optimal (incentive compatible) utilitarian allocation and the implementing income tax and social security benefit functions. To keep the presentation simple, we focus on an economy with two types of individuals. Section 5 provides some numerical examples of a three-type setting. It also considers the possibility of (costly) auditing for the health status as additional departure from the theoretical model.

During the last decades, a number of European countries, some more than others, have expanded their social security systems in ways which have discouraged labor market participation in old age and thus fostered early retirement. We raised the question whether these disincentives to continued activity are necessarily the result of a bad tax-transfer scheme design. Can they instead be an ingredient of an optimally designed redistributive policy in a world of asymmetric information? To address this issue, we have studied the design of retirement contributions and benefits in a setting where an optimal non-linear income tax is also available. Individuals differ in ability and/or health status (disutility of retirement age). Given the tax-transfer policy every individual chooses weekly labor supply (not observable) and retirement age (observable). As in the traditional income taxation literature, the optimal policy implies a positive marginal tax on the low ability (and/or less healthy) individual. More interestingly, the retirement benefit formula also introduces a bias towards early retirement in this individual's life cycle labor supply decisions. This distortion arises whatever the dominant source of heterogeneity (productivity or health). Finally, the relative distortion between weekly labor supply and retirement age (length of active life), if any, depends on the relative heterogeneity in ability and health. This paper has some rather ambitious features. It aims at dealing with the question of disability, early retirement and regular retirement within the same model with individuals differing in both productivity and health. To pursue this ambition, we admittedly had to simplify other aspects of the model. Two of the key assumptions are that of constant (though endogenous) labor supply during the active life and that of no liquidity constraint. These two restrictions allow us to reduce an otherwise dynamic model into a static one. Even though our paper deals in part with the issue of disability, its main focus is not disability insurance such as studied by Diamond and Mirrlees, 1978 and Diamond and Mirrlees, 1986. The difference is most easily shown for the case where people only differ in health status. Then considering that individuals ex ante do not know their Rj, our social security scheme can be viewed as a one period disability insurance. The healthier a worker is (lower Rj) the later he will retire and also the less he will receive as net benefits (−Tj). In Diamond and Mirrlees, all individuals are also identical ex ante but as time goes on they discover whether or not they are disabled. Truthtelling here implies that net benefits increase with the age of retirement. But clearly, this positive relation between benefit and retirement age is not the same as the negative relation one might observe in our one period model. We assume that not just productivity but also health (capacity to work long) are not observable. In the standard literature on disability, health is also not directly observable. However, some authors introduce the possibility of control, which at some cost reveals the health status; see, e.g., Diamond and Sheshinski (1995). Audit on health conditions can be introduced in our model and this will be the subject of a sequel to this paper. In the current paper, we have restricted ourselves to providing a few illustrative examples in Section 5. While the possibility of audit does bring in a number of additional interesting aspects, it does not appear to represent a fundamental challenge to the main findings of this paper. In particular, one can also expect that the optimal policy will continue to induce early retirement. As for the specific policy implications, one can conjecture that thanks to such audits early retirement benefits that are implicit to our optimal scheme will be higher than when audits are not available. Another possible and natural extension is to allow for some health spending to correct for a high Rj. In other words, the health status would continue to have an exogenous (adverse selection) component, but it would also be affected by some specific expenditure, which may or may not be observable. In particular public provision of such a private good could be used as an additional instrument along with our social security scheme. (See on this Cremer and Gavahri, 1997.) The underlying argument here would be to reduce the incidence of disability rather than simply redistributing towards the less able. One can conjecture that if this instrument can contribute to narrow the gap between Rh and Rl its availability would lead to a welfare improvement. Alternative specifications could lead to different outcomes. In particular, we deliberately assume that the utilitarian social planner takes into account differences in utilities without trying to correct them. In other words, it takes Rj as a health parameter and not as a taste parameter. People with Rh are unhealthy and ought to be compensated for that. If Rj were viewed as taste for leisure, then it would make sense to launder out differences in Rj. (See on this Boadway et al., in press.). With laundering out the result would change with tax inducement towards postponed activity for the Rh's workers now considered as “lazy”. In the same line, we could have assumed some myopic intertemporal preferences leading to overly early retirement. Again, if the social planner had less myopic time preferences, the tax design could have been different. Allowing for an explicit account of the time structure is clearly a priority on our research agenda. It is, however, a challenging objective in a setting with two, albeit correlated, factors of heterogeneity. Currently, there exists little work even on the separate issues of either health or productivity. On the health issue, there are naturally the papers by Diamond and Mirrlees, 1978 and Diamond and Mirrlees, 1986, which demonstrate the analytical difficulty of the question at hand. On the productivity issues, Britto et al. (1991) have shown how difficult is the issue of optimal non-linear income tax in a multiperiod setting. In view of these difficulties, it should not be surprising that the design an optimal tax-transfer scheme with intensive and extensive labor supply choices in a dynamic setting and with two characteristics is a formidable task. Our current paper clearly falls short of accomplishing this task. It is however a step in that direction which points at possible avenues for tackling more ambitious settings.