养老保险现收现付制的挤出效应——一个内生生育率模型

文章在一个内生经济增长的OLG模型框架下研究现收现付制养老保险计划的挤出效应。具体考察公共养老金税率变动对家庭的消费与储蓄、生育选择以及经济增长的长期影响。结果表明,存在向上利他动机的情况下,挤出效应的大小取决于养老基金的规模,适度规模的公共养老金计划不会挤出私人储蓄。而有利于消费增加与经济增长;较大规模的公共养老金计划会对私人自愿储蓄与消费产生负面影响,并且对储蓄的挤出作用要大于对消费的挤出。人口老龄化进程在一定程度上缓解挤出效应,促进资本积累与经济增长。     

Mixing Bismarck and child pension systems: an optimum taxation approach

Pensions with a strong tax–benefit link (Bismarck pensions) minimise the labour–leisure distortion of the public pension system. By contrast, pensions with a strong link of benefits to the number of children (child pensions) minimise the fertility distortion. When both types of distortion are present, we obtain a Corlett–Hague result regarding the optimal mix of the two pension formulae: the Bismack pension should be given a positive weight if and only if children are more complementary to leisure than consumption. Alternative fertility instruments such as child benefits turn out to be perfect substitutes to a child pension.     

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     

Fertility and PAYG pensions in the overlapping generations model

This article analyses how long-run pay-as-you-go public pensions react to a change in fertility in the Diamond overlapping generations model. While it might seem well established both in academic and political debates that the decline in fertility represents a “demographic time bomb” for the sustainability of public pensions, it is shown that a falling birth rate need not necessarily cause the fall of pensions in the long run.     

Fertility-related pensions and cyclical instability

In this paper, we study a general equilibrium model with overlapping generations, endogenous fertility and public pensions. By assuming Cobb–Douglas technology and logarithmic preferences, we show that the introduction of a fertility-related component in the pay-as-you-go pension scheme may destabilise the long-term equilibrium and cause endogenous fluctuations when individuals have static expectations. The possibility of cyclical instability increases (resp. reduces) when both the subjective discount factor and relative weight of individual fertility in pay-as-you-go pensions (resp. the parents’ taste for children) increase(s). Interestingly, when public pensions are contingent on the individual number of children, the financing of small-sized benefits may cause the occurrence of a flip bifurcation, two-period cycles and cycles of a higher order. In addition, we show through numerical simulations that these results hold in a more general setting with a constant inter-temporal elasticity of substitution utility function and a constant elasticity of substitution production function. Our findings identify a possible novel factor responsible for persistent deterministic fluctuations in a context of overlapping generations, while also representing a policy warning regarding the destabilising effects of fertility-related pension reforms, which are currently high in both the theoretical debate and the political agendas of several developed countries.     

Pensions with heterogenous individuals and endogenous fertility

We study the design of pension schemes when fertility is endogenous and parents differ in ability to raise children. Pay-as-you-go schemes require, under perfect information, a marginal subsidy on fertility to correct for the externality they create, equal pensions, and contributions that increase or decrease with the number of children. Under asymmetric information, incentive-related distortions supplement the Pigouvian subsidy. These require an additional subsidy or an offsetting tax depending on whether the redistribution is towards people with more or with less children. In the former case, pensions are decreasing in the number of children; otherwise, they are increasing.     

Growth and unemployment in an OLG economy with public pensions

This paper develops an overlapping generations model including (1) a productive externality as an engine of endogenous growth and (2) wage setting by trade unions as the cause of unemployment. Within this framework, the paper considers growth and unemployment affected by public pensions under the following two types of pension system: the proportionate pension system where only the contributors, that is, the employed, receive pensions, and the lump-sum pension system where both the employed and the unemployed receive pensions. It is shown that public pensions create a trade-off between growth and employment in the former system, whereas they produce no trade-off in the latter.     

Private versus public old-age security

We directly compare two institutions, a family compact—a parent makes a transfer to her parent in anticipation of a possible future gift from her children—with a pay-as-you-go, public pension system, in a life cycle model with endogenous fertility wherein children are valued both as consumption and investment goods. Absent intragenerational heterogeneity, we show that a benevolent government has no welfare justification for introducing public pensions alongside thriving family compacts since the former is associated with inefficiently low fertility. This result hinges critically on a fiscal externality—the inability of middle age agents to internalize the impact of their fertility decisions on old-age transfers under a public pension system. With homogeneous agents, a strong-enough negative aggregate shock to middle-age incomes destroys all family compacts, and in such a setting, an optimal public pension system cannot enter. This suggests the raison d’être for social security must lie outside of its function as a pension system—specifically its redistributive function which emerges with heterogeneous agents. In a simple modification of our benchmark model—one that allows for idiosyncratic frictions to compact formation such as differences in infertility/mating status—a welfare-enhancing role for a public pension system emerges; such systems may flourish even when family compacts cannot.     

Child mortality and fertility: public vs private education

How does the effect of child mortality reductions on fertility and education vary across educational systems? To answer this question, we develop an overlapping-generations model where altruistic parents care about both the number and human capital of their surviving children. We find that, under a private education system, if income is low initially, the economy converges to a Malthusian stagnation steady state. For a high level of initial income, the economy reaches a growth path in which children’s education rises and fertility decreases with income. In the growth regime under private education, exogenous shocks that lower child mortality are detrimental for growth: fertility increases and education declines. In contrast, under a public education system, the stagnation steady state does not exist, and health improvement shocks are no longer detrimental for growth. We therefore offer a new rationale for the introduction of public education.     

Fertility decisions when infant survival is endogenous

There is evidence that fertility is positively correlated with infant mortality, and that a child‘s chance of surviving to maturity increases with the level of nutrition, medical care, etc. received in the early stages of life. By modelling parental decisions as a problem of choice under uncertainty, the paper shows that fertility and infant mortality are most likely to move in opposite directions if, as implicitly assumed by existing economic theories, parents believe that there is nothing they can do to improve the survival chances of their own children. By contrast, if parents realize that those chances improve with the amount they spend for the health, nutrition, etc. of each child that they put into the world, then fertility and infant mortality may move in the same direction. Under such an assumption, the model has the strong policy implication that directly death-reducing public expenditures are most effective, but stimulate population growth, at low levels of development. By contrast, at high levels of development, such expenditures tend to crowd out parental expenditures, and are a factor in fertility decline. Received: 14 October 1996 / Accepted: 28 July 1997     

Growing old and staying young: population policy in an ageing closed economy

This paper analyses the relation between public pensions, fertility and child care in a closed-economy overlapping generations model with endogenous fertility. It is shown that raising a child involves two social externalities and that it is optimal to introduce child allowances if the government redistributes income from the young to the old. The optimal child allowance rises when longevity increases. If the costs of raising children depend positively on the wage, a third externality arises and the returns to savings should be taxed.

The effects of child-related benefits and pensions on fertility by birth order: A test on Hungarian data

Using aggregate time-series data from post-war Hungary, we investigated the effect of child-related benefits and pensions on overall fertility and fertility by birth order. The results indicate moderate effects that are robust across a wide range of specifications. According to our estimates, a 1-per-cent increase in child-related benefits would increase total fertility by 0.2 per cent, while the same increase in pensions would decrease fertility by 0.2 per cent. The magnitude of both effects increases by birth order; this is more robust for child-related benefits.     

Another Child? Fertility Ideals,Resources and Opportunities

Low fertility in most developed countries has prompted policy concern in relation to labour market supply, pensions, and expenditure on health and welfare services as well as policy debate about both the cost of children and the opportunity costs of parenthood. The extent to which family policy interventions can be effective in slowing or reversing fertility decline is much debated. This paper, based on a fertility module of the Scottish Social Attitudes Survey 2005, examines the current fertility, and ideal and expected fertility of a nationally representative sample of 455 parents of reproductive age and focuses on whether they plan to have another child. It compares the characteristics of those who intend to have another child with those who do not, and how parents with one child differ from those with more children. It addresses three questions about family size: (1) fertility ideals, (2) resources and the economic implications of childbearing, and (3) opportunities for childbearing and the effects of a late start on fertility expectations. It concludes that, despite a sustained period of low fertility in Scotland, childbearing ideals are robust and explanations of low fertility must derive from difficulties in realising those ideals. Difficulties in realising fertility aspirations are associated less with resources than with opportunities for childbearing, especially the timing of first birth. Those who delay their first birth are less likely to realise their ideal family size, and their lower fertility is associated with the opportunity costs of childbearing in terms of foregone qualifications, careers and earnings.     

Costs and benefits of children: implications for population policy

Family size preferences are strongly affected by parents' perceptions of the value, economic contributions, and costs of children. Better understanding of these factors can help policy-makers to improve the effectiveness of population IEC campaigns, design strategies to persuade couples to have smaller families, assess the relationship between economic development and family size preferences, and devise national population policies and family planning programs that reflect individual choices. Parents in high-fertility countries are more likely to perceive children as productive investments than those in low-fertility countries. Parents in the former countries maintain children are an economic advantage or provide practical assistance in the household; they are less likely to emphasize the psychological advantages of children. As economic development occurs, and parents no longer value children for their economic contributions, psychological and social reasons become more important. Changing fertility preferences is more complex than providing couples with family planning services. Similarly, efforts to persuade families that large families are a burden are successful only when families are already interested in reducing their family size. Efforts to persuade couples to have smaller families are likely to be more successful if there are alternative sources of old-age support available, for example, from increased household savings, public or private pensions, or greater contributions from 1st and 2nd children. Investments in education and training, especially for women and children, would also support these goals.     

Involuntary childlessness and voluntary fertility control during the fertility transition: Evidence from men who graduated from an American college

Abstract. Influences on the fertility of men during the American fertility decline are examined using a sample of about 1700 married men born between 1830 and 1880, all of whom attended Amherst College, Massachusetts. We consider two types of reduced fertility: involuntary childlessness as a function of health in early adulthood, and voluntary fertility control as a function of access to contraceptive technology. The relation between health, as measured by body mass index, and childlessness was nonlinear, with average sized men significantly more likely ever to father children than thin or bulky men. Among men who ever fathered a child, physicians fathered significantly fewer children while having probabilities of childlessness that were statistically indistinguishable from those of other men. Physicians may have had greater access to relatively new contraceptive technologies, which suggests a role for voluntary fertility control.     

Fertility and the economy

I relate the demand for children to parental incomes and the cost of rearing children — especially to the value of the time spent on child care and to public policies that change the cost of children. This paper also links the demand for children to investments in their human capital and other dimensions of the so-called quality of children. Fertility is shown to depend too on child and adult mortality, uncertainty about the sex of children — if there is a preference for boys, girls, or for variety — uncertainty about how long it takes to produce a conception, and other variables.Since biological necessity dictates that succeeding generations overlap, it is not surprising that fertility in one generation influences the fertility of succeeding generations. The overlapping generations approach provides a useful framework for relating fertility choices to population growth and macroeconomic changes.The modern approach to fertility leads to very different interactions between population growth and economic growth than is implied either by Malthusian or the usual neo-classical growth models. In particular, it provides a framework for analyzing how societies escape a Malthusian-like stagnating equilibrium and embark on the journey toward becoming modern economies, where per capita incomes, human capital, and physical capital all continue to grow, fertility declines to rather low levels, and married women participate extensively in the labor force.This essay was prepared for the Nobel Jubilee Symposium, Lund, Sweden, December 5–7, 1991. I have had valuable comments from James Heckman, Robert Willis and my discussants at the symposium: Allesandro Cigno and Richard Easterlin, and useful assistance from Becky Kilburn. I am indebted to the National Institute for Child Health and Human Development award R37-HD22054 and National Science Foundation award SES-90-10748.     

Population aging and PAYG pensions in the OLG model

This paper shows the effects on a pay-as-you-go pension system of the demographic change in the standard overlapping generations model. Firstly, we consider a setting with exogenous fertility and then a model with endogenous fertility. In both cases, population aging due to increased longevity implies a reduction in pensions payouts.     

Aging and political decision making on public pensions

In this paper decision making on public pensions in a representative democracy is modeled within the framework of the well-known two-overlapping-generations (OLG) general-equilibrium model with rational expectations. The model is used to analyze the effects of aging on the economy in general and on the evolution of public pension schemes in particular, where aging is interpreted as a combination of a decrease in the rate of population growth and an increase in the political influence of pensioners. Analytical results are derived for the long run as well as for the short run by the method of comparative statics and comparative dynamics respectively. It appears that an increase in transfers to the old is not guaranteed if due to aging their political power increases. JEL classification: J14, H55 Received April 5, 1995 / Accepted September 4, 1995     

Fertility estimation from open birth-interval data*

Censuses and surveys frequently collect information on period fertility through questions on the timing of last births. The standard approach to estimating fertility with open-interval data uses the proportion of women giving birth in the year before the interview. I propose a more efficient, maximum likelihood method for estimating fertility from open-interval data. I illustrate a mathematical derivation of the new method, perform sensitivity analyses, and conduct empirical tests with Brazilian census data. The new estimators have small biases and lower variance than standard estimators for open-interval data. Consequently, the new method is more likely to generate accurate results from small or moderately sized samples.     

The Projection Problem

While world population has continued to increase, fertility has been falling. Projections out to the year 2050 currently assume that fertility will continue to decline to, or below, replacement. 1) Past projections have been very wrong. Estimates of population growth have alternated between being far too low and far too high. 2) Similarly, public anguish has alternated between extreme fears of over- and under-population, neither supported by eventualities. 3) We do not understand the causes of the current fertility decline and so have little reason to project its continuation. 4) Many of the Asian countries, which are exemplars of the current decline, are exceptional because of coercion and/or vast infusions of Western capital. 5) The population decline may as readily plateau at 3 children as at 2 children. With an unknowable future, an emphasis on future population is misplaced. Concerns should be for the present. Poor families and a stressed environment are struggling with current population levels right now. Complacency about the future is unjustified by the facts and may derail efforts to ensure the continuation of the fertility decline.