Optimal age of retirement and population growth

The purpose of this paper is to study intergenerational optimal resources sharing when the social planer can choose the retirement age in addition to consumptions and investment. We use the extension of the Diamond analysis by Hu [1979] that incorporates endogenous retirement age. We found that the optimal retirement age is an increasing function of the population growth rate if the elasticity of substitution of old agents' labor for young agents' labor is lower than one. In the millian case, when the size of a population does not matter, and when the elasticity of substitution of old agents' labor for young agents' labor is strictly higher than one, the optimal retirement age is a decreasing function of the population growth rate. In the benthamite case, the change in the optimal retirement age is indeterminate. Received: 19 February 1999/Accepted: 27 February 2001 All correspondence to Bertrand Crettez. We would like to thank Jean-Pierre Vidal for very helpful comments on an earlier draft. An anonymous referee provided insightful comments on a previous version of this paper. Responsible editor: Alessandro Cigno.     

Rawlsian optimal population size

In this paper, I examine the implications of the Rawlsian maximin criterion for optimal population size and intergenerational allocation of resource when fertility is endogenous. I show that whenever children are better-off than their parents in laissez-faire, then the size of the population and parental bequests are also optimal according to the Rawlsian criterion. Otherwise, laissez-faire leads to overpopulation and suboptimal bequests. I then show that by using proper price-based corrective policies, society can achieve a Rawlsian optimal allocation. These policies involve either a combination of a subsidy to aggregate future consumption and a per-capita tax on children, or a subsidy to average future consumption.For their comments, I thank two anonymous referees. I also thank Assaf Razin and Efraim Sadka for their comments on an earlier draft.     

Population policy and individual choice

The general equilibrium implications of endogenous fertility for several social issues of population policy are examined. Laissez faire is found to lead to Pareto optimality within generations even in the presence of public goods and Malthusian diminishing returns. On the other hand, bequests emerge as a major potential source of Pareto inefficiency when parents care about the number and welfare of their offspring. Also considered are questions of intergenerational justice and equity using an intergenerational social welfare function. It is shown that maximizing the sum of utilities always leads to a larger population than maximizing per capita utility, but that the laissez-faire solution may lie outside the interval bounded by the two criteria.Invited Lecture at the First Annual Conference of the European Society for Population Economics, Rotterdam, 18–19 September 1987In preparing this paper, I have drawn heavily on joint work with Assaf Razin and Efraim Sadka, both of Tel-Aviv University, and on our book, Household and economy: Welfare economics of endogeneous fertility (Academic Press, New York 1987). I am indebted to two anonymous referees for helpful comments     

Optimal pension funding with demographic instability and endogenous returns on investment

This paper tries to explore some optimal funding policies for pension systems in a general equilibrium setting where funding affects returns on investment and wages through its impact on capital formation. This is done in the context of irregular demographic evolutions such as those expected in developed countries for the next century. Particular attention is given to the intergenerational welfare criterion which is used for designing optimal policies. It appears that funding receives low justification with a welfare criterion which assumes a high substitutability between consumptions of successive cohorts, implying a low concern for intergenerational equity. Funding is highly justified in the opposite case where a high level of consumption for some cohorts is not considered as a compensation for low consumption by others. However the optimal patterns of transfers and savings which are found in this latter case are not straightforward. Some simpler funding rules are explored in the last section of this paper, which show that non-optimal funding may imply, on the contrary, a high level of inequality between subsequent generations.Paper presented at the ISPE-conference Fiscal implications of an ageing population, May–June 1990 at Vaalsbroek, The Netherlands. We thank Pierre Pestieau for his remarks on a first draft of this paper. We also thank for their comments our two discussants Carol Propper and Lans Bovenberg, as well as other participants to the ISPE Conference. Any errors are, of course, ours.     

Social security in a general equilibrium model with endogenous government behavior

In this paper attention is focused on the economic and political effects of an aging population. For that purpose, a general equilibrium model is used that allows for an endogenous analysis of decisionmaking on government policies. We concentrate here on the effects of an aging population on expenditures and levels of social security benefits, the provision of public goods and services, the private output and intergenerational conflicts. Special attention will be paid to the effects of changes in the retirement age and in capital endowments. Furthermore, the effects of issues related to aging, as changes in the political influence structure and the motive of other-directedness by others, are investigated.The authors are grateful to the participants of the ISPE conference. They wish to thank in particular the discussants Jean Frijns, Pierre Pestieau and Harry van Dalen for their helpful comments.     

The old age security hypothesis and optimal population growth

The old age security approach is used to study the relationship between the rate of growth of the population and capital accumulation, within a Samuelson-Diamond overlapping generations framework. It is shown that a decentralized economy will fail, in general, to achieve the Pareto optimal path. However, a pay-as-you-go social security scheme in which the old get transfers which are proportional to the number of their children may restore optimality. On the other hand, child support systems or subsidies to capital can guarantee the optimal capital: labor ratio, but not the optimal population growth rate, while a lump sum social security system can guarantee the optimal population growth rate, but not the optimal capital: labor ratio. Finally, in a monetary economy any policy aimed at correcting the interest rate will restore full optimality.An earlier version of this paper was written during a visit to the University of California, San Diego. The paper benefited from the comments of two referees.     

The choice of factor mobility in a dynamic world

This paper compares the steady-state welfare implications of opening a two-country overlapping-generations world to international labor or capital mobility. By capturing the dual nature of labor mobility through the effect of migrants' savings on capital formation, this dynamic setting recovers the asymmetry between capital and labor denied to them in the existing static literature. It is shown that the optimal choice of factor mobility from a national viewpoint depends on the state of the economy with respect to the Golden Rule and on migrants' average savings ratio with respect to that of non-migrants.I would like to thank anonymous referees for useful comments.     

The fiscal impact of immigration to welfare states of the Scandinavian type

In this paper, we examine the potential of immigration to strengthen fiscal sustainability, which is under pressure by an ageing population in many European countries. We look at a particularly challenging case, namely that of Denmark, which has extensive tax-financed welfare programmes that provide a high social safety net. The analysis is based on a forecast of the entire Danish economy made using a dynamic computable general equilibrium model with overlapping generations. We present life cycle estimates of the potential fiscal impact of immigration considering the cost of immigration on the margin as well as on average. The main conclusion is that immigrants from Western countries have a positive fiscal impact, while immigrants from non-Western countries have a large negative one, which is also the case when considering only non-refugee immigrants. The negative effect is caused by both a weak labour market performance and early retirement in combination with the universal Danish welfare schemes.     

Social security reforms and early retirement

Many reform proposals of the social security systems in various OECD economies suggest to scale down the non-actuarial parts of the pension systems. These reforms have a flavor of increased efficiency at the costs of welfare losses for low-income individuals. Assessing the economic effects, we investigate five different reform proposals by means of a numerical overlapping generations model for the Norwegian economy. The model features an endogenous retirement age and heterogeneous individuals within generations. It turns out that the various reforms, which scale down the public non-actuarial pension system, lead to increases in the retirement age and steady-state welfare gains for all income classes. Received: 7 December 2000/Accepted: 29 January 2002 All correspondence to ?ystein Th?gersen. Financial support from the Research Council of Norway (The Economic Research Program on Taxation) is gratefully acknowledged. We are indebted to Lans Bovenberg, John Ermisch, Erling Steigum and two referees for valuable comments and useful discussion. Responsible editor: John F. Ermisch.     

Optimal population and exhaustible resource constraints

A large literature considers the optimal size and growth rate of the human population, trading off the utility value of additional people with the costs of a larger population. In this literature, an important parameter is the social weight placed on population size; a standard result is that a planner with a larger weight on population chooses larger population levels and growth rates. We demonstrate that this result is conditionally overturned when an exhaustible resource constraint is introduced: if the discount rate is small enough, the optimal population today decreases with the welfare weight on population size. That is, a more total-utilitarian social planner could prefer a smaller population today than a more average-utilitarian social planner. We also present a numerical illustration applied to the case of climate change, where we show that under plausible real-world parameter values, our result matters for the direction and magnitude of optimal population policy.     

Optimal fertility under age-dependent labour productivity

In the so-called Rapport Sauvy (1962), the French demographer Alfred Sauvy argued that Wallonia’s fertility rate was socially suboptimal, and recommended a 20 % rise of fertility, on the grounds that a society with too low a fertility leads to a low-productive economy composed of old workers having old ideas. This paper examines how Sauvy’s intuition can be incorporated in the Samuelsonian optimal fertility model (Samuelson, Int Econ Rev 16:531–538, 1975). We build a four-period OLG model with physical capital and with two generations of workers (young and old), the skills of the latter being subject to some form of decay. We characterize the optimal fertility rate and show that this equalizes, at the margin, the sum of the capital dilution effect (Solow effect) and the labour age-composition effect (Sauvy effect) with the intergenerational redistribution effect (Samuelson effect). Numerical simulations show that it is hard, from a quantitative perspective, to reconcile Sauvy’s recommendation with facts. This leads us to examine other potential determinants of optimal fertility, by introducing technological progress and a more general social welfare function.     

Does time preference change with age?

This study looks at compensating differentials in the National Longitudinal Survey of Youth (NLSY) to derive estimates of the levels of time preference for labor force participants in each of 15 waves of data from 1979 to 1994. With these estimates the evolution of time preference over the life course is described. Future utility among labor force participants appears to be valued more highly by subjects who are older, more schooled, white, or male. Controlling for schooling level, a higher IQ is associated with a preference for more immediate rewards.If social rates of time preference are correlated with individual rates of time preference then population aging could create intergenerational asymmetries in the social rate of time preference.This phenomenon could make the optimal investments of young populations appear selfish to future generations that are older.Support from Hopkins Population Center (R24) is gratefully acknowledged. I am thankful for helpful comments received from Jim Burgess, Mike Grossman, Bruce Hamilton, Fritz Laux, Athanasios Orphanides, Katie Roche, and Eric Slade. All errors are my own. Responsible editor: Alessandro Cigno.     

Social time preference revisited

The article reconsiders the implications of the choice of pure social time preference for intergenerational equity in the presence of a time-consistent utilitarian social welfare criterion. The analytic framework is a setting with overlapping generations, lifetime uncertainty, population growth and technical progress. The analysis identifies upper and lower bounds for the feasible range of social discount rates and draws a corresponding distinction between “gerontocratic” and “Stalinist” optimal plans. The paper corrects a number of inaccurate propositions in a related earlier contribution by Marini and Scaramozzino (2000) to this journal.

Population aging, health care, and growth

This paper constructs a small open two-sector (health care and non-health care) overlapping generations model and investigates how changes in the demand for health care induced by population aging influence the economy’s employment structure and per capita income growth rate. We show that population aging induces a shift in labor from the non-health care sector to the health care sector and lowers the per capita income growth rate. This paper also investigates public policy for child care and demonstrates the existence of an intergenerational conflict between current and future generations concerning public policy on child care.     

Education and income inequality: The role of a social protection system

In this paper we aim to understand the role a welfare state can play in stimulating risky but profitable activities like investment in education, and in reducing income inequality. We analyze how unemployment benefits may affect investment in education when the latter is characterized by uncertain returns. This is done in an overlapping generations model in which endogenous growth is introduced through human capital accumulation. We develop a numerical example of the model in order to reproduce some key differences between the European versus the North American economy; differences that, according to this model, result from the different degree of social protection characterizing both economies. Received: 02 June 1999/Accepted: 22 February 2000     

Social security policy with public debt in an aging economy

This paper analyzes a social security policy with public debt in an overlapping generations growth model. In particular, the paper considers a situation in which population aging causes a heavy burden of social security payments where public debt is issued by the government to finance the payment. In the model presented below, an economy with an aging population may achieve two dynamically inefficient equilibria. Under certain conditions, the effects of pension reform and population aging on capital accumulation are entirely different between the two equilibria. Received: 23 July 2001/Accepted: 22 August 2002 I am deeply grateful to an anonymous referee and Professor A. Cigno, the Editor of this journal, for their valuable comments and suggestions. I am also grateful to Kazuyo Tanimoto and Kiheiji Nishida for their research assistance. Any remaining errors are my own. The research reported here was conducted as part of a larger study, the “Project on Intergenerational Equity” at the Institute of Economic Research, Hitotsubashi University. Financial support from Kani Hoken Bunka Zaidan is also gratefully acknowledged. Responsible editor: Alessandro Cigno.     

人口年龄结构变动下的最优退休年龄动态模型构建与应用——以陕西省为例

文章主要以社会福利最大化为基本前提,假定社会福利最大化条件下的退休年龄为最优平均退休年龄,通过建立人口年龄结构变动下的最优退休年龄动态模型,以陕西省人口数据和养老保险相关数据为基础,测算了社会福利最大化条件下的陕西省最优平均退休年龄。得出结论:满足社会福利最大化时,陕西省最优平均退休年龄将会从2010年的58.4岁,逐步提高到2020年的59.6岁,进而提高到2030年的61.3岁。     

The intergenerational transmission of fertility in contemporary Denmark: The effects of number of siblings (full and half), birth order,and whether male or female

Using the Danish Fertility Database, we investigate intergenerational fertility transmission, including the relationship between the number of children born to those aged 25 and 26 years in 1994 and the number of their full sibs and half-sibs. We find that the fertility behaviour of parents and their children is positively correlated, and that half-sibs and full sibs have broadly similar effects. We do not find, in this complete national population, the strong birth order effects reported in some earlier studies. Nor do we find evidence of a weakening of intergenerational fertility transmission over time, perhaps because the greater flexibility of lifestyles in this post-transitional phase provides the extended social space within which intergenerational continuities can manifest themselves. We show that members of large families are over-represented in subsequent generations - that they have far more kin than those from smaller families - and that intergenerational continuities in fertility behaviour play a substantial role in keeping fertility higher than it would be in the absence of such transmission.     

The intergenerational transmission of fertility in contemporary Denmark: the effects of number of siblings (full and half), birth order,and whether male or female

Using the Danish Fertility Database, we investigate intergenerational fertility transmission, including the relationship between the number of children born to those aged 25 and 26 years in 1994 and the number of their full sibs and half-sibs. We find that the fertility behaviour of parents and their children is positively correlated, and that half-sibs and full sibs have broadly similar effects. We do not find, in this complete national population, the strong birth order effects reported in some earlier studies. Nor do we find evidence of a weakening of intergenerational fertility transmission over time, perhaps because the greater flexibility of lifestyles in this post-transitional phase provides the extended social space within which intergenerational continuities can manifest themselves. We show that members of large families are over-represented in subsequent generations - that they have far more kin than those from smaller families - and that intergenerational continuities in fertility behaviour play a substantial role in keeping fertility higher than it would be in the absence of such transmission.     

International labor migration and social security: Analysis of the transition path

This paper numerically simulates a two-country overlapping-generations model to study international labor migration when the two countries are characterized by different social-security systems. The present analysis extends previous work beyond steady-state considerations. The most striking result is that in all cases considered, dynamically efficient and inefficient economies in autarkic steady-state, migration leads to temporary welfare losses in both countries. In all cases, the transition path is characterized by temporary dynamic inefficiency in one country.All correspondence to Doris Geide-Stevenson. We would like to thank an anonymous referee for very helpful comments. We are responsible for any remaining errors. Responsible editor: Christoph M. Schmidt.