Capital accumulation,income distribution and endogenous fertility in an overlapping generations general equilibrium model

A study is conducted in attempts to increase the understanding of the links between macroeconomic effects and causes of population growth in formulating policy. An overlapping generations general equilibrium model is employed aggregating household decisions about fertility, savings, and investment in the human capital of children with the objective of studying intertemporal relationships among population growth, income distribution, inter-generation social mobility, skill composition of the labor force, and household income. As a result of endogenous fertility, the equilibrium path attains steady state from the second generation. Income tax transfer, child taxation, and social security taxation policies are also examined in the paper. A structural explanation is given for the inverse household income-child quantity and negative child quality-quantity relationships seen in developing countries. In a Cobb-Douglas economy, these relationships hold in the short-run, potentially working over the long-run in other economies. Overall, the model shows that group interests may hinder emergence of perfect capital markets with private initiatives. Where developing countries are concerned, these results have strong implications for population policy. A policy mix of building good quality schools, or subsidizing rural education, introducing a formal social security program, and providing high-yield, risk-free investments, banking, and insurance services to the poor is recommended.     

Capital Accumulation in an Economy with Dynasties and Uncertain Lifetimes

This paper studies how the lack of an annuities market affects savings behavior and intergenerational transfers in a dynastic overlapping generations economy. I find that the answer to this question depends crucially on altruism. On the one hand, if the altruistic bequest motive is operative, then the lack of annuity markets enhances capital accumulation. On the other hand, if the altruistic bequest motive is not operative, the absence of annuity markets can either increase or decrease aggregate savings. I characterize under which conditions capital accumulation is enhanced. I also prove that an overlapping generations economy with altruism and uninsurable lifetime risk faces capital overaccumulation relative to the modified Golden Rule. The efficient allocation corresponding to the modified Golden Rule can be decentralized as a competitive equilibrium by a pay-as-you-go social security system, and this can only be done if individuals are altruistic.     

Demographic change and long‐term growth in China: Past developments and the future challenge of aging

This paper explores the influence of demographic changes, particularly the sharp decline in fertility and the evolution of the population age structure, on economic development in China. A general equilibrium overlapping generations model with endogenous decisions on fertility, educational investment, and factor accumulation is employed for our analysis. The family support provided by children to the elderly, which is a component of traditional culture in Chinese society, is also considered. We find that technological changes matter most for growth. Demographic changes, on average, account for approximately 4% of the growth in China, while the effect is negative in the pre‐1980 period. With an extension to include population aging, we find that aging is not necessarily adverse to growth. This finding reflects the fact that a longer life expectancy requires more savings and makes educational investment in children more attractive, which accelerates physical capital and human capital accumulation. However, if the social norm of family support for aging parents is strict, aging will significantly increase the children's burden and crowd out physical and human capital accumulation.     

Jointly determined saving and fertility behaviour: theory,and estimates for Germany,Italy, UK and USA

This study uses new theories of capital accumulation and fertility in a comparative framework to test predictions with time-series data for Germany, Italy, the UK, and the US. The exogenous-fertility model is based on models of Barro and Becker. The endogenous-fertility models are based on models of Veall and Nishimura and Zhang. It is assumed that life cycle periods are youth, middle age, and old age. Several theoretical frameworks are tested with endogenous and exogenous fertility and altruism and nonaltruism. Data are obtained during 1950-90. Dependent variables are the total lifetime fertility rate and real per capita household savings. Explanatory variables include social security, the real social security deficit per capita, the real rate of interest, the real per capita disposable income, the average male real wage rate, the average female real wage rate, and the real child benefit rate. The explanatory variables are individually graphed to show differences by country over time. Findings suggest that fertility is endogenous in a nonaltruistic model. The only model not rejected by the data was the model in which fertility and intergenerational transfers were explained by nonaltruistic concerns. Fertility was positively affected by the male wage rate in all countries. Fertility was negatively affected by the female wage rate in all countries. Disposable income was insignificant in the UK and Germany and positive and significant in Italy and the US. The interest rate was significant in only 1 model. Child benefits had a positive and significant effect on fertility in the UK. In savings models, disposable income was significant and positive, and child benefits and wage rates were insignificant. Social security coverage had a negative effect on fertility and a positive effect on savings, except in Germany. Findings indicate that saving and fertility are jointly determined.     

Intergenerational externalities,sustainability and welfare—The ambiguous effect of optimal policies on resource depletion

This paper studies an endogenous growth model with exhaustible resources, overlapping generations and human capital externalities. In the competitive equilibrium, selfish behavior and inefficient skills accumulation may prevent sustained growth. Implementing the utilitarian optimum likely induces sustainability via increased knowledge formation, but resource depletion may be faster or slower than under laissez-faire depending on the social discount rate. Heavy (modest) social discounting delays (anticipates) the achievement of net welfare gains for newborn agents and successors. The reason is that human capital accumulation magnifies the positive growth effects of policies that lower the rate of resource destruction, preserving the welfare of newborn agents. Resource-depleting policies, instead, hamper growth and reduce lifetime welfare of early-in-time generations—the first loser being the currently young.     

A SAVINGS SUBSIDISATION SYSTEM IN A MODEL OF ENDOGENOUS FERTILITY AND ENDOGENOUS GROWTH: AN EXTENSION OF WIGGER (1999)

Population ageing is now an established demographic characteristic of many economies. Economists working in the endogenous growth theory tradition have sought to model the relationship between public pensions, financed on a 'Pay-As-You-Go' basis, and the growth in per capita incomes. The resultant intergenerational wealth redistribution from young to older people seems to decrease private savings, diminish capital accumulation, and lower the growth of per capita incomes. The underlying transmission mechanism appears to be a crowding out effect in private capital markets contingent upon the introduction of public pension systems. A growing literature exists on the interrelationships between public pension schemes, fertility rates and endogenous growth. Following Wigger's (1999) pioneering overlapping generations endogenous growth model, we extend this model to examine the effects of a savings subsidisation system on the rate of per capita income growth, fertility and voluntary intrafamily wealth transfers, where parents view children both as an insurance good and a consumption good. Moreover, children care about the consumption levels of their parents. An increase in contributions to a savings subsidised public pension scheme will crowd out private intergenerational transfers from the young to the old and thereby negate the usefulness of children as an insurance good.     

Child policy ineffectiveness in an overlapping generations small open economy with human capital accumulation and public education

Motivated by the recent decrease in the number of children experienced in several developed countries, in this paper we consider a small open economy model with overlapping generations, endogenous fertility and human capital formation through public education, and look at the role the government can play in affecting fertility through the widely used child allowance policy. Contrary to conventional view, we show that the public provision of child allowances is fertility-neutral in the long run, that is it is not effective as a pro-natalist policy, while also reducing human capital accumulation. In contrast, the financing of the public education system is beneficial to both fertility and human capital. These results hold in the cases of both fixed and time cost of children.     

Dynamics of endogenous growth

Summary We present an overlapping generations model of endogenous fertility and growth. The cost of child rearing and the effect of population size on total factor productivity determine the dynamics of competitive equilibrium path of our model. The non-linear dynamics of the model generates a plethora of outcomes (depending on the functional forms, parameters and initial conditions) that include not only the neo-classical steady state with exponential growth of population with constant per capita income and consumption, but also growth paths which do not converge to a steady state and are even chaotic. Exponential, and even super exponential, growth of per capita output are possible in some cases.We would like to thank Mukul Majumdar, Kazuo Nishimura and an anonymous referee for many comments.     

Implementing Steady State Efficiency in Overlapping Generations Economies with Environmental Externalities

We consider in this paper overlapping generations economies with pollution resulting from both consumption and production. The competitive equilibrium steady state is compared to the optimal steady state from the social planner's viewpoint. We show that the dynamical inefficiency of a competitive equilibrium steady state with capital–labor ratio exceeding the golden rule ratio still holds. Moreover, the range of dynamically efficient steady state capital ratios increases with the effectiveness of the environment maintenance technology, and decreases for more polluting production technologies. We characterize some tax and transfer policies that decentralize as a competitive equilibrium outcome the transition to the social planner's steady state.     

国有股权型社会保障研究

内容本文研究了一个存在股权交易的代际交叠模型中,国有股权型社会保障政策对经济长期均衡状态的影响。研究表明,在合理的参数设置下,国有股权型社会保障政策可以促进年轻人对资本积累的贡献,增加经济的均衡产出,提高年轻人和老年人的均衡消费;而一个向年轻人征收社会保障税补贴老年人的现收现付制社会保障税政策(PAYG,pay as you go)是劣于这种国有股权型社会保障政策的。模型的结论对中国社会保障事业发展以及国有股的减持和转持政策有一定的指导意义。     

Optimal steady-state in stationary consumption-loan type models

We consider a stationary overlapping generations economy, and prove that an optimal steady state exists. We show that if a government intervention is needed in order to implement the optimal steady state as a competitive equilibrium, it is necessary only in a finite number of periods. If the interest rate associated with the optimal steady state equals the population rate of growth, some outside money may be required in order to make the competitive equilibrium follow the optimal steady state. We show that our existence result enables us to construct Pareto optimal competitive equilibria in some important cases.     

On the emergence of competitive equilibrium growth cycles

A basic discrete-time heterogeneous capital goods competitive environment is considered, its potential for displaying steady growth solutions analyzed and the properties of the latter characterized. A first composite good may be used for consumption or investment on a one-to-one basis, while a second good is only used for accumulation, solely capital inputs being part of the production process. This framework is first considered from the allocative standpoint through the derivation of the frontier of the production possibility set. Having defined the perfect foresight competitive equilibrium that also describes a Pareto optimum over time, attention is then given to the potential for unbounded steady growth solutions. Under interiority, summability, and expansivity restrictions, there is a unique optimal steady growth rate. For unitary depreciation rates of both capital goods, locally there exists a unique convergent sequence to this steady growth solution that exhibits a saddlepoint structure. However, as soon as one of the depreciation rates of the capital goods is non-unitary and the profit share accruing to the first capital stock is greater in the second pure accumulation industry than in the first composite good industry, the steady growth solution shows a loss of stability, and competitive equilibrium growth cycles emerge through the occurrence of a flip bifurcation in its neighborhood. This is the first optimal cycles result based upon a production set that does not explicitly incorporate any exogenously determined primary labor input in its definition.     

Growth,fertility and human capital: A survey

This paper surveys recent work on endogenous fertility and endogenous growth. These models provide the building blocks for a theory of development. They are capable of explaining income and fertility differentials between rich and poor countries. They can produce switching behavior, countries that transform themselves from no growth economies into high growth economies. The fertility and growth effects of social security programs are also examined. Finally models with increasing returns to population are presented. They are capable of reproducing very long term relationships between human capital, fertility and economic growth.     

Demographic links to savings in life cycle models: identification of issues for LDCs

The author considers the potential for a link between the recent pattern of demographic transition and intertemporal and inter-country variations in savings rates. Fertility, infant mortality, life expectancy, and levels of female and child labor force participation are among the various demographic factors which affect national savings rates through their effects upon age structure, age-specific individual savings behavior, and their general equilibrium effects upon interest rates, wage rates, and income distribution. The author establishes a simple discrete time life cycle model of savings, explains the issues related to age structure, and discusses the effect of age-specific savings functions, the general equilibrium effects of demographic factors, the effects of life expectancies and child mortalities, and the nature of social security coverages in less developed countries, as well as issues which are especially important for less developed countries. A new strategy for empirically evaluating demographic policies is proposed. That is, one can estimate the age profile of earnings, saving and fertility rates from household survey data. The life tables can then be used to compute the aggregate savings rate and population size. Any demographic policy which affects the fertility rate, life expectancy, and investment in the quality of children will change the aggregate saving and population growth rates. These two aggregate effects could be compared to evaluate demographic policies. The author stresses, however, that changes in different demographic factors will have different short-run and long-run effects upon the savings rate which will also depend upon whether such changes are transitory or permanent.     

The taxation of capital returns in overlapping generations models

This paper shows that in the Diamond (1965) overlapping generations economy with production and capital savings, there is a period-by-period balanced fiscal policy supporting a steady state allocation that Pareto-improves upon the laissez-faire competitive equilibrium steady state (whether dynamically inefficient or efficient) without resorting to intergenerational transfers. The policy consists of taxing linearly (or subsidizing, in the dynamically efficient case) the returns to capital, while balancing the budget period by period through a lump-sum transfer (or tax, respectively) in second period. This intervention grants every generation the highest steady state utility attainable through markets (i.e. remunerating factors by their marginal productivities and without transfers) which under laissez-faire is not a competitive equilibrium outcome. A transition from the competitive equilibrium steady state to this other steady state is also Pareto-improving when the former is dynamically inefficient. The result disentangles from redistributive considerations the impact of the taxation of capital returns on steady state welfare, and thus provides a rationale for the taxation of capital returns that is based on efficiency considerations and not on redistributive goals.     

Growth and social security: the role of human capital

This paper studies the growth and efficiency effects of pay-as-you-go financed social security when human capital is the engine of growth. Employing a variant of the Lucas model [Lucas, R.E., 1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3–42.] with overlapping generations, it is shown that a properly designed, unfunded social security system leads to higher output growth than a fully funded one. Furthermore, the economy with an unfunded social security is efficient, while the other one is not. These results stand in sharp contrast to those obtained in models where the reason for economic growth is physical capital accumulation.     

Loss aversion and social security: a general equilibrium approach

Introducing an intertemporal model of loss aversion, I study the role of social security in determining intergenerational redistribution when consumers have reference-dependent preferences with loss aversion. Using a unified social security model in which different social security plans are specified via different degrees of fundedness, I examine the effect of the transition from a less funded system to a more funded one on savings, consumption, and capital accumulation for an OLG production economy. A general equilibrium analysis shows that the direction of intertemporal equilibrium is dependent on how the total savings responds to the interest rate change, but the effect of the payroll tax on capital accumulation is ambiguous. By deriving closed-form solutions, I find that an increase in fundedness intensity unambiguously increases capital accumulation in steady states, while the tax effects on consumption and savings are not conclusive. Moreover, simulation exercises show that when consumers are prone to over-consume because they care more about the contemporaneous gain utility, the fully funded system may help the individuals smooth out their lifecycle consumption.     

Conspicuous consumption and generation replacement in a model of perpetual youth

This paper investigates household decisions in an overlapping generations model in which individual utility depends on a weighted average of consumption of one's peers. In contrast to representative agent economies, the consumption externality generally affects savings and growth rates. The effects critically depend on the rate at which labor productivity changes with age. For a high (low) rate, the externality lowers (raises) the steady state propensity to consume out of total wealth. The optimal allocation can be decentralized by a (reverse) unfunded social security system if the rate of labor productivity decline is high (low). In contrast to discrete time OLG models, the optimal steady state capital income tax is zero, in spite of the externality.     

Physical and human capital,fertility, and childcare services

We shed light on a nexus between fertility transitions and economic growth patterns. We construct a two-sector overlapping generations (OLG) model with endogenous fertility, physical capital, and human capital, where one sector produces goods, and another produces childcare services. If the elasticity of fertility for expenditure on childcare services is zero, the economy experiences endogenous growth, and fertility does not depend on physical and human capital, but it increases with parental child-rearing time. On the other hand, if elasticity is positive, the economy converges to a steady state, and the number of children becomes the homogenous function of degree of elasticity (less than one). In other words, fertility is the decreasing-return-to-scale function of physical and human capital. We show that a subsidy policy for education is more desirable than a subsidy for childcare services.     

Low level equilibrium trap,unemployment, efficiency of education system,child labour and human capital formation

This paper builds an overlapping generations household economy model to examine the impact of adult unemployment on the human capital formation of a child and on child labour, as viewed through the lens of the adult’s expectations of future employability. The model indicates that the higher the adult unemployment rate in the skilled sector, the lesser is the time allocated by an unskilled adult towards schooling of her child. We also find that an increase in the unskilled adult’s wage may or may not decrease child labour in the presence of unemployment. The model predicts that an increase in child wage increases schooling and human capital growth rate only if the adults in the unskilled sector earn less than subsistence consumption expenditure. As the responsiveness of skilled wage to human capital increases, schooling and human capital growth rates increase. The model dynamics bring out the importance of education efficiency and parental human capital in human capital formation of the child. In the case of an inefficient education system, generations will be trapped into low level equilibrium. Only in the presence of an efficient education system, steady growth of human capital is possible. Suitable policies that may be framed to escape the child labour trap are discussed as well.