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.     

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.     

Uncertain lifetime, fertility and social security

Investigating the effects of population aging on fertility and economic growth, we show that an increase in life expectancy lowers the fertility rate and raises life-cycle savings, and that a pay-as-you-go social security does not reverse the effect on fertility. Received: 10 March 2000/Accepted: 28 April 2000     

Intergenerational redistribution in a small open economy with endogenous fertility

For pay-as-you-go financed pension systems, claims may be calculated according to individual contributions (income) or the number of children of a family. We analyse the optimal structure of these parameters in a model with endogenous fertility. It is shown that for both structural determinants there exists no interior solution of the problem of intragenerational utility maximisation. Thus, pure systems are always welfare maximizing. Furthermore, children-related pension claims induce a fiscal externality that tends to be positive. The determination of the optimal contribution rate shows that the widely accepted Aaron-condition is in general a misleading indicator for the comparison of fully funded and pay-as-you-go financed pension systems. Received March 12, 1996 / Accepted January 27, 1997     

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.     

Pareto improving transition from a pay-as-you-go to a fully funded pension system in a model of endogenous growth

In this paper we investigate the possibility of Pareto improving social security reforms within a framework of endogenous growth. Belan et al. (1998) propose a transition from a pay-as-you-go (PAYG) pension system to a system of savings–subsidization. We follow this approach and prove that a Pareto improving conversion from the PAYG system to a fully funded one is possible. Finally, we compare the subsidy system with the fully funded system and discuss the problem of implementing the transition to the fully funded system. Received: 07 March 1999/Accepted: 13 December 1999     

Pay-as-you-go financed public pensions in a model of endogenous growth and fertility

Employing an overlapping generations endogenous growth model in which parents derive utility from having children and, additionally, expect children to support them in old age, this paper explores the interrelation between growth, fertility, and the size of pay-as-you-go financed public pensions. It is shown that small sized public pensions stimulate per capita income growth, but further increases in public pensions eventually reduce it. Fertility, on the other hand, falls by an increase in public pensions if they are either small or large. Medium sized public pensions, however, may stimulate fertility. Received: 9 September 1997 / Accepted: 10 April 1998     

The macroeconomics of fertility in small open economies: A test of the Becker-Barro model for The Netherlands and New Zealand

Becker and Barro (1988) formulated a theoretical model which identified a range of macroeconomic variables which can temporarily or permanently affect fertility in small open economies. This article tests the Becker-Barro model with relevant data which covers most of the 20th century for two small open economies, namely The Netherlands and New Zealand. The results show that government subsidies for having children have a strong positive effect on fertility, while the provision of public pensions has a strong negative effect. The degree of intergenerational altruism appears to have been declining. Moreover, there is only weak support for the hypothesis that real interest rates positively influence fertility. Received: 2 March 1998/Accepted: 1 September 1999     

The allocation of time and goods in household activities: A test of separability

In this paper, we test for the weak separability hypothesis imposed by the household production model between goods and time inputs used in the production of different commodities. Our data come from a French survey which reports both expenditures and time that households devote to some activities. The results allow us to show that the weak separability assumption cannot be rejected only when households are strongly time constrained. In the opposite case, home time uses are found to be nonseparable. Received: 24 November 1999/Accepted: 16 November 2000     

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     

Estimating intrahousehold allocation in a collective model with household production

The purpose of this paper is to estimate the intra-family distribution of income and the individual demand for leisure and household production from Swedish cross-sectional household data. As a basis for the analysis, we use a collective model where each individual is characterized by his or her own utility function and divides total time between leisure, household production and market work. For the purpose of comparison, we also estimate a version that is consistent with a more traditional model of labor supply, the unitary model. Received: 14 April 2000/Accepted: 12 January 2001     

Time preference, international migration, and social security

This paper analyzes both the formation of long-run migration incentives and the consequences of a regime change from “autarky” to “free migration” in an overlapping-generations framework with two countries. Under autarky the countries may differ with respect to their aggregate savings rate or with respect to their pension-wage ratio. It is shown that an individual prefers to live in a country where the capital-labor ratio is close to the Golden Rule level and where his characteristics are relatively scarce. Both the migration incentives and the consequences of free migration are determined by these two effects. Received: 2 March 1998/Accepted: 10 February 1999     

Inheritance, land, and capital mobility linked to labour mobility

This paper presents a two-country migration model, following Galor (1986), in which the world population consists of two types individuals. Individuals with a high (low) degree of altruism give to their children a high (low) level of bequest. Production uses three inputs: immobile land, mobile labour, and capital. Capital mobility is linked to labour mobility since individuals move with their inheritance. The model shows that countries are homothetic in the post-migration equilibrium with equal factor prices and equal densities of population. Migration flows are bilateral and the number of each type of migrants is uniquely determined. In some cases, migration leads to a Pareto improvement in both countries. Received: 8 July 1999/Accepted: 7 April 2000     

Altruism and international labour migration

This paper investigates the effect of altruism on the pattern of labour migration in a two-country overlapping generations model. We show that differences in degrees of altruism across countries lead to bilateral migration flows. Starting from the autarkic steady-state equilibrium, restrictions on labour migration are relaxed. In temporary post-migration equilibrium factor prices are equal across countries. We then characterize the unique stable steady-state equilibrium: both countries are populated and this equilibrium is not a Pareto improvement. Some individuals prefer to live in autarky, others in an integrated world economy. Received: 6 July 1998/Accepted: 11 February 1999     

Social security,social welfare and the aging population

This study examines the effects of pay-as-you-go social security programs in aging economies when the middle-aged both educate their dependent children and subsidize the retirement of the old. Using an overlapping generations framework in which agents are three-period lived but timing of death in the third period is uncertain, we analyze the effects of social security tax schemes, under various demographic assumptions, on capital accumulation, education expenditures, social welfare, and economic growth. We find that in many cases social security crowds out education, and reduces economic growth and social welfare. Received: 29 April 1998/Accepted: 3 March 1999     

Population size and environmental quality

This paper presents a simple general equilibrium analysis of first best allocations in an economy where a consumption good is produced using labor. Production results in pollution, which is a public bad. Pollution abatement can be achieved either by restricting production or by using additional labor. We consider how the first best allocation and Pigouvian tax vary with population size. Consumers are unambiguously worse off when the population is larger, but not necessarily due to increased pollution. In fact, optimal policy on how pollution and labor should vary with population size is very sensitive to preferences and technology. The best response to an increase in population size might be either to increase or to decrease emissions and/or labor, depending on functional forms and parameters. However, given separable preferences and some convexity, the optimal emissions tax increases, and the first best level of per-capita consumption decreases with population size. The paper also considers the extent to which exogenous technical progress can overturn these conclusions. Received August 28, 1996 / Accepted January 27, 1997     

Modeling female fertility using inflated count data models

For modeling complete female fertility we propose a zero-and-two-inflated count data model, which accounts for a relative excess of both zero and two children. As the underlying distribution of counts we use the standard Poisson distribution and the more general Gamma count distribution. We compare our proposed model with standard count data models by using data on complete fertilities for a sample of Swedish women. The preferred specification for Swedish fertility data is the zero-and-two inflated Gamma count data model. The estimated “extra” probabilities of zero and two children, when modelled as individual specific probabilities, vary substantially across individuals, with mean of 0.05 and 0.16, respectively. These extra probabilities show that women who formed a family later in life have a higher probability of being childless, and women of our youngest cohort have a higher probability of forming a two-child family. Received: 7 January 1999/Accepted: 19 May 1999     

Who takes care of the children? The quantity-quality model revisited

We study the Becker and Lewis (1973) quantity-quality model of children adding an explicit child care time constraint for parents. Parents can take care of the children themselves or purchase day care. Our results are: (i) If there only is own care, a quantity-quality trade-off, different from that of Becker and Lewis (1973), arises. The income effect on fertility is positive if child quantity is a closer complement than child quality to the consumption of goods. (ii) If, instead, there is a combination of purchased and own care, the effect of income on fertility is ambiguous, even if quantity of children is a normal good in the standard sense. This is the Becker and Lewis (1973) result extended to a situation with a binding child care time constraint. The conclusion is that the Becker and Lewis (1973) result holds as long as at least some child care is purchased. Received: 12 November 1999/Accepted: 1 September 2000     

Brother correlations in earnings in Denmark, Finland, Norway and Sweden compared to the United States

The correlation in economic status among siblings is a useful “omnibus measure” of the overall impact of family and community factors on adult economic status. In this study we compare brother correlations in long-run (permanent) earnings between the United States, on one hand, and the Nordic countries (Denmark, Finland, Norway and Sweden) on the other. Our base case results, based on very similar sample criteria and definitions for all countries, show that this correlation is above 0.40 in the United States and in the range 0.14–0.26 in the Nordic countries. Even though these results turn out to be somewhat sensitive to some assumptions that have to be made, we conclude that the family and community factors are more important determinants of long-run earnings in the United States than in the Nordic countries. Received: 27 July 2000/Accepted: 7 March 2001 All correspondence to: Anders Bj?rklund. Comments from two referees, conference participants at ESPE2000 and the Canadian Employment Research Forum, seminar participants in Aarhus, Uppsala, Bonn, and Stockholm are gratefully acknowledged. We thank NOS-S for financial support. The Swedish data collection was also supported by HSFR and SFR. The Finnish data were obtained with support from the Yrj? Jahnsson Foundation. We thank Tom Erik Aab? for preparing the Norwegian data, and Esben Agerbo for computational assistance with the Danish data. Responsible editor: John F. Ermisch.     

Pensions as a portfolio problem: fixed contribution rates vs. fixed replacement rates reconsidered

Pay-as-you-go (PAYG) pension schemes can contribute to better intergenerational risk-sharing and diversification. However, different variants of PAYG schemes entail different properties in these respects. In a stochastic 2-OLG model we compare PAYG schemes with fixed contribution rates and such with fixed replacement rates. The literature has shown that the former are preferable to the later from an ex ante perspective. We derive the opposite result for the ex post perspective. Here, schemes with fixed replacement rates are unambiguously preferable: they enhance intergenerational risk-sharing, lead to a higher savings and higher utility levels. We further show that, from an ex ante (veil-of-ignorance), perspective both schemes are non-comparable if the effect that fixed-replacement schemes serve as an insurance device for old-age income is properly accounted for. Received: 7 December 2000/Accepted: 17 May 2001