بازنشستگی، حقوق بازنشستگی و پیری

We study the effects of demographic shocks and changes in the pension system on the macroeconomic performance of an advanced small open economy facing a given world interest rate. We construct an overlapping-generations model which includes a realistic description of the mortality process. Individual agents choose their optimal retirement age, taking into account the time- and age profiles of wages, taxes, and the public pension system. The early retirement provision in most pension systems acts as a trap, inducing most workers to retire well before the normal retirement age. Simulations show that pension reform must be drastic for it to have any effects on the retirement behaviour of workers.

Population ageing is playing havoc with the public pension schemes of many western countries. In a celebrated sequence of international comparative studies, Gruber and Wise, 1999, Gruber and Wise, 2004 and Gruber and Wise, 2005 and their collaborators have established a number of stylized facts pertaining to a subset of OECD countries. These facts are: (SF1) For most developed countries, the pay-as-you-go social security system includes promises that cannot be kept without significant system reforms. In the absence of reform, current systems are fiscally unsustainable. (SF2) From the 1960s until the mid 1990s, the trend was for older people to leave the labour force at ever younger ages. Retirement is a normal good in the sense that the demand for years of retirement rises as agents' income rises ( Barr and Diamond, 2006, p. 27). (SF3) Only a very small fraction of the labour force retires before the earliest age at which public retirement benefits are available, the so-called early eligibility age (EEA hereafter). The EEA typically is in the range of 60–62 years of age. Similarly, only very few people work until the normal retirement age (NRA hereafter), which is typically 65 for most countries ( Duval, 2003, p. 35). Together this implies that most people retire either at the EEA or somewhere in between the EEA and the NRA. (SF4) Most social security programs contain strong incentives for older workers to leave the labour force. In most countries it simply does not pay to work beyond the EEA because adjustments are less than actuarially fair. The present value of expected social security benefits declines with the retirement age, so there is a high implicit tax on working beyond the EEA. (SF5) In many European countries disability programs and age-related unemployment provisions essentially provide early retirement benefits, even before the EEA. In our view, a formal analysis of issues surrounding ageing, retirement, and pensions can only be successful if it is able to accommodate at least some, but preferably all, of these stylized facts. In this paper we study the consumption, saving, and retirement decisions of individual agents facing lifetime uncertainty, or longevity risk. In addition, we also determine the macroeconomic consequences of individual behaviour and policy changes. We construct a simple analytical overlapping generations model and assume that the country in question is small in world capital markets and thus faces an exogenous world interest rate, which we take to be constant. Our analysis makes use of modelling insights from two important branches of the literature. First, in order to allow for overlapping generations, we employ the generalized Blanchard–Yaari model developed in our earlier papers (Heijdra and Romp, 2008a and Heijdra and Romp, in press). In this model disconnected generations are born at each instant and individual agents face an age-dependent probability of death at each moment in time. By allowing the mortality rate to depend on age, the model can be used to investigate the micro- and macroeconomic effects of a reduction in adult mortality, another well know phenomenon occurring in many western countries over the last century or so. Finitely-lived agents fully insure against the adverse affects of lifetime uncertainty by purchasing actuarially fair annuities. The second building block of our analysis concerns the labour market participation decision of individual agents. Following the seminal contribution by Sheshinski (1978) and much of the subsequent literature, we assume that labour is indivisible (the agent either works full time or not at all), that the retirement decision is irreversible, and that the felicity function is additively separable in consumption and leisure. All agents are blessed with perfect foresight and maximize an intertemporal utility function subject to a lifetime budget constraint. Workers choose the optimal retirement age, taking as given the time- and age profiles of wages, the fiscal parameters, and the public pension system. Not surprisingly, like Mitchell and Fields and many others we find that “the optimal retirement age … equates the marginal utility of income from an additional year of work with the marginal utility of one more year of leisure” (1984, p. 87). The two papers most closely related to ours are Sheshinski (1978) and Boucekkine et al. (2002).1 We extend the analysis of Sheshinski (1978) in two directions. First, as was already mentioned above, we incorporate a realistically modelled lifetime uncertainty process, rather than a fixed planning horizon. Second, we embed the model in the context of a small open economy and are thus able to study the macroeconomic repercussions of ageing and pension reform. We generalize the analysis of Boucekkine et al. (2002) by including a concave, rather than linear, felicity function, and by modelling a public pension system with realistic features such as an EEA which differs from the NRA and non-zero implicit tax rates. Furthermore, we conduct our theoretical analysis with a general description of the demographic process, whereas they use a specific functional form for this process throughout their paper. The remainder of this paper is organized as follows. In Section 2 we present the model and demonstrate its main properties. Consumption is proportional to total wealth, consisting of financial and human wealth. With a realistic demography, the marginal propensity to consume out of wealth is increasing in the agent's age because the planning horizon shortens as one grows older and the agent does not wish to leave any bequests. We derive the first-order condition for the optimal retirement age and show that it depends not only on the mortality process but also on the features of the fiscal and pension systems. The mortality process, in combination with the birth rate, also determines a unique path for the population growth rate. In Section 3 we abstract from the public pension system and study the comparative static effects on the optimal retirement age of various age-related shocks. A reduction in the disutility of working leads to an increase in the optimal retirement age. In contrast, an upward shift in the age profile of wages causes a negative wealth effect but a positive substitution effect, rendering the total effect on the optimal retirement age ambiguous. A reduction in adult mortality increases the expected remaining lifetime for everyone, though more so for older agents. We confirm the results of related papers by Chang (1991) and Kalemli-Ozcan and Weil (2002), in that the effect of increased longevity on the optimal retirement age is ambiguous in general. Intuitively, this is because the lifetime-income effect cannot be signed a priori. For realistic scenarios, however, the increased longevity only starts to matter quantitatively at ages exceeding the NRA so that the lifetime-income effect works in the direction of increasing the optimal retirement age. Section 3 also presents the graphical apparatus that we use throughout the paper. We demonstrate that the optimal retirement decision is best studied in terms of its consequences for lifetime income and the transformed retirement age. This transformed age is a monotonically increasing transformation of the calender age and captures the notion of an agent's economic (rather than biological) age. Our graphical apparatus has the attractive feature that indifference curves are convex and that the budget constraint is concave. We believe that our graphical representation is more intuitive than the conventional one based on biological years. In Section 4 we re-introduce the public pension system and determine its likely consequences for the retirement decision of individual agents. Using data from Gruber and Wise (1999) for nine OECD countries, we compute conservative estimates for standardized lifetime income profiles and find that these profiles are concave in the transformed age domain. For at least six of these countries, the lifetime income profile features a kink at the EEA as a result of non trivial implicit tax rates. Combined with convex indifference curves, it is not surprising that many agents choose to retire at the EEA, conform stylized facts (SF3) and (SF4). In Section 5 we take the concavity of lifetime income profiles for granted and discuss the comparative static effects on the optimal steady-state retirement age of various changes in taxes or the public pension system. We restrict attention to interior solutions because an optimum occurring at the kink in the lifetime income profile is insensitive to small changes. An increase in the poll tax leads to a reduction in lifetime income and an increase in the optimal retirement age. Retirement is thus a normal good in our model, conform stylized fact (SF2). Not surprisingly, an increase in the labour income tax has an ambiguous effect on the retirement age because the substitution effect is negative and the wealth effect is positive. Holding constant the slope of the pension benefit curve, an increase in its level unambiguously leads to a decrease in the retirement age—the wealth effect and the substitution effect operate in the same direction. In contrast, an increase in the slope of the benefit curve, holding constant its level, leads to an increase in the optimal retirement age as a result of the positive substitution effect. In Section 6 we calibrate the model to capture the salient features of a typical small open economy such as the Netherlands. Our postulated demographic process, when fitted to Dutch data, outperforms the one suggested by Boucekkine et al. (2002). The overall fit of our process is better and it also provides a better estimate for the population weight of older agents. We use this quantitative model to compute and visualize the general equilibrium effects of various large demographic shocks and several assumed policy reform measures. Conform stylized fact (SF3), we postulate that in the initial steady state individuals are stuck at the early retirement kink. Because both the shocks and the policy reform measures are inframarginal, we simulate a plausibly calibrated version of our model to compute the impact-, transitional-, and long-run effects on the macro-economy. Finally, in Section 7 we present some concluding thoughts and give some suggestions for future research. Heijdra and Romp (2008b) contains the key mathematical derivations, data on implicit tax rates and replacement rates for a number of OECD countries, as well as further supplementary material.

We have studied the microeconomic and macroeconomic effects of ageing in the context of a small open economy populated by disconnected generations of finitely-lived agents facing age-dependent mortality and constant factor prices. From a policy perspective, our main finding is as follows. Most actual pension systems induce a kink in the lifetime income function which acts as an early retirement trap. Fiscal changes are not potent enough to get individuals out of the trap. Increasing the early entitlement age appears to be a low cost policy measure to counteract the adverse effects of the various demographic shocks. Our analysis is subject to a number of potentially important limitations, some of which we will address in the near future. First, in this paper the age profile of labour efficiency is exogenous, i.e. there is no endogenous human capital accumulation decision. In a companion paper we include an endogenous education decision taking place at the beginning of an agent's life; see Heijdra and Romp (in press). We have chosen to study start-up education and retirement in separate papers in order to obtain simple and intuitive results. It is, of course, quite feasible to combine the two decisions in a single computable general equilibrium (CGE). The results in our separate studies can then be of assistance in interpreting the effects of ageing, pensions, and taxes on the various macroeconomic variables. In our view, highly stylized analytical models and detailed CGE models are complementary tools for the public economist. Second, we have focused attention of mortality and have ignored the equally important issue of morbidity. One of the main functions of a social security system is to support people who are incapable of working due to old-age related diseases. Asymmetric information problems arise if health is not perfectly observable to the policy maker. The risk exists that either social security becomes too expensive because too many people make use of it, while they are perfectly capable of working, or that people who cannot work are kept out of the system.