Effect of social security on fertility and savings: an overlapping generations model

Old-age pension schemes do not exist in most developing countries, so adults bear children as security investments for the future. This phenomenon leads to unduly high rates of population growth. It has been hypothesized that introducing social security programs in such countries would increase savings rates and reduce the number of children born over the long term. The author studies the general equilibrium effects of some social security programs on rates of population growth and capital accumulation within an overlapping generations framework with endogenous fertility and savings. Specifically, Raul's overlapping generations growth model is extended to study the general equilibrium effects of payroll-tax-financed and child-tax-financed social security programs. It is shown that if the rate of intergenerational income transfers from young to old or child care cost is low, competitive equilibrium leads toward overpopulation and capital accumulation in a modified Pareto optimal sense; a social security program in such a case is therefore Pareto improving. A fully-funded system is not neutral when financed by child taxes. Finally, it is also shown that unlike in the case of exogenous fertility where competitive equilibrium attains steady state only asymptotically, fertility, when endogenous, may attain a unique globally steady state in finite time.     

A theory of competitive industry dynamics with innovation and imitation

Empirical evidence on industry life-cycle reveals a pattern in which innovation rates remain fairly stable or are perhaps even higher at early stages, while patenting increases sharply as the industry matures. This increase in patenting in later stages is accompanied by net exit and lower rates of output growth and price decline. In this paper, we develop a dynamic model of a competitive industry with innovation and imitation that is consistent with these stylized facts. We derive an equilibrium growth path, along which leading firms invest in increasing the stock of technological knowledge and choose not to prevent imitation by other firms as long as the industry remains relatively small. As the industry expands including new entry, the leaders' optimal amount of investment gradually declines. We show that under some rather general conditions, there would exist a scale of the industry where innovating firms would choose to start preventing free imitation, bringing further expansion of the industry through new entry to a halt and causing net exit.     

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.     

为结婚而储蓄?——来自中国家庭追踪调查①(CFPS)的经验证据

已有研究主要基于性别比失衡的竞争性储蓄动机解释了中国家庭的高储蓄之谜.文章把子女结婚这一自然事件作为处理变量,通过婚前和婚后的家庭储蓄变化识别出"婚姻效应",为竞争性储蓄动机理论和中国家庭的高储蓄之谜提供了微观证据.研究结果发现,在控制个人以及家庭特征后,相对于已婚家庭,未婚家庭储蓄显著更高.在排除地区性差异、教育储蓄动机、预防性储蓄动机和样本匹配等问题之后,未婚比已婚家庭具有更高储蓄水平的结论依然稳健.文章进一步分析识别出了城市和农村异质"婚姻效应"和婚后消费结构的变化,发现"婚姻效应"对不同收入水平的家庭都产生了影响,但"婚姻效应"对低收入家庭的消费抑制更为明显.文章的研究结果丰富了婚姻市场的竞争性储蓄动机理论.     

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.     

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.     

Interregional Fertility Differentials and Agglomeration

In this study, we construct an interregional trade model that includes endogenous fertility rates. The presented model shows that the agglomeration of manufacturing firms in a large region causes fertility rates to become lower than in a small region. We also find that a decrease in transportation costs results in the agglomeration of manufacturing firms, which lowers fertility rates in both large and small regions. In addition, comparing the competitive equilibrium with the optimal equilibrium, the fertility rates may be inefficiently small.     

Efficiency in overlapping generations economies with longevity choices and fair annuities

When individuals can influence their life-expectancies and save in annuities, suboptimal savings result from the lack of incentives to choose the optimal longevity, even when annuity returns can be made contingent to longevity-related choices. Specifically, the golden rule steady state maximizing the representative agent utility cannot be attained as a competitive equilibrium under laissez-faire, even with actuarially fair annuities contingent to longevity-enhancing choices. In order to decentralize through markets the golden rule, longevity-enhancing expenditures need to be taxed if the steady state old-age consumption exceeds the annuitized capital return, and subsidized otherwise—the government budget being balanced through lump-sum transfers or taxes. Interestingly, with positive population growth the expected net contribution is negative when longevity-enhancing expenditures are taxed, and positive when subsidized.     

Fiscal policies, environmental pollution and economic growth

This paper develops a model of endogenous economic growth with special consideration to the role of productive public expenditure and environmental pollution; and analyses the properties of optimal fiscal policy in the steady state growth equilibrium. We consider the level of consumption as the source of pollution. Government allocates its tax revenue between pollution abatement expenditure and productive public expenditure. Optimum ratio of productive public expenditure to national income is equal to the competitive output share of the public input, when productive public expenditure is depicted as tax revenue minus abatement expenditure. However, the proportional income tax rate exceeds the competitive output share of the public input. There is no conflict between the social welfare maximizing solution and the growth rate maximizing solution in the steady state growth equilibrium. The unique steady state growth equilibrium appears to be a saddle-point when the growth rate is above a critical level and the steady state equilibrium growth rate in the market economy is not necessarily lower than the socially efficient growth rate.     

Firm-specific cost savings and market power

Summary. We report a policy experiment that illustrates a potential problem of using historical pass-through rates as a means of predicting the competitive consequences of projected firm-specific cost savings in antitrust contexts, particularly in merger analysis. The effects of cost savings on welfare can vary vastly, depending on how the savings affect the industry supply schedule. In a capacity-constrained price-setting oligopoly, we observe that cost savings can overwhelm behaviorally salient market power incentives when the savings affect marginal (high cost) units. However, cost savings of the same magnitude on an infra-marginal unit leave market power unchanged.     

Consumption externality, efficiency and optimal taxation in one-sector growth model

In an economy with consumption externalities, existing studies find that a competitive equilibrium is efficient in the long run and remains efficient in transitions if preferences are homothetic. This paper revisits the efficiency issue in an otherwise standard one-sector growth model where consumption externalities affect a utility via their effects on the time preference. We find that even if preferences are homothetic, the externality changes the marginal rate of substitution between now and future and leads to a disparity in the intertemporal elasticity of substitution between the centrally planned economy and a decentralized economy. As a result, a competitive equilibrium is inefficient in transition dynamics. We characterize an optimal tax/subsidy structure that enables the allocation in a decentralized economy to replicate the social optimum.     

Capacity Utilization,Foreign Portfolio Investment and International Debts and Deficits

This paper develops a long-run equilibrium growth model, in the tradition of Keynes, Kalecki and Steindl, involving international capital flows between a debtor and a creditor country, and in which capacity utilization is variable. This latter assumption implies that the shares of savings by capitalists and workers will vary with capacity utilization. Profit rates will also vary with capacity utilization rates, so that the establishment of a common warranted rate of growth requires that the rates of profit in the creditor and the debtor countries must vary inversely. The long-run equilibrium shares of ownership of the two stocks of capital must therefore vary as the utilization rates vary. Taking the international interest rate as given, steady growth in each country at near full employment is shown to be accommodated, to some extent, through variations in the degree of capacity utilization. Even if income distribution remains unchanged, the variability of capacity utilization allows the existence of a range of growth rates consistent with the long-run equilibrium conditions of the model.     

ENDOGENOUS HEALTH CARE, LIFE EXPECTANCY AND ECONOMIC GROWTH

We study the endogenous relationship between health care, life expectancy and output in a neoclassical growth model. Although health care directly diverts resources away from goods production, it prolongs life expectancy, which in turn leads to higher savings and, hence, capital formation through a private annuity market. We show that savings and health care are complements in equilibrium, with both rising with economic development. Our model is therefore consistent with several observed stylized development patterns across countries. Moreover, through the longevity-enhancing channel, health care and health production technology are found by simulation to be growth and welfare promoting.     

High growth and low consumption in East Asia: How to improve welfare while avoiding financial failures

This paper analyzes certain policies that are typical of a number of rapidly growing East Asian countries in which a fixed exchange rate, combined with a surplus labor market, has made domestic assets relatively inexpensive, generating high rates of FDI as well as domestic capital formation. This “investment hunger” can lead to unanticipated declines in the returns to investment, and resulting financial insolvencies. Private consumption remains low and there are concerns that high savings rates cannot be sustained.We construct a dynamic general equilibrium model and apply it to a stylized Asian economy, loosely based upon China. We calibrate a benchmark equilibrium, and carry out various counterfactual simulations to analyze alternative policies, in particular tax cuts and exchange rate revaluations, as instruments in increasing private consumption while avoiding bank failures.     

Demographics and real interest rates: Inspecting the mechanism

The demographic transition can affect the equilibrium real interest rate through three channels. An increase in longevity—or expectations thereof—puts downward pressure on the real interest rate, as agents build up their savings in anticipation of a longer retirement period. A reduction in the population growth rate has two counteracting effects. On the one hand, capital per-worker rises, thus inducing lower real interest rates through a reduction in the marginal product of capital. On the other hand, the decline in population growth eventually leads to a higher dependency ratio (the fraction of retirees to workers). Because retirees save less than workers, this compositional effect lowers the aggregate savings rate and pushes real rates up. We calibrate a tractable life-cycle model to capture salient features of the demographic transition in developed economies, and find that its overall effect is a reduction of the equilibrium interest rate by at least one and a half percentage points between 1990 and 2014. Demographic trends have important implications for the conduct of monetary policy, especially in light of the zero lower bound on nominal interest rates. Other policies can offset the negative effects of the demographic transition on real rates with different degrees of success.     

Has the capital accumulation in the Asian miracle economies been fuelled by growth?

The Asian growth miracle is often attributed to factor accumulation under the implicit assumption that savings, broadly defined, have been high and increasing due to exogenous forces. Using data for India, Indonesia, Korea, Singapore and Taiwan over the period 1870–2011 this article examines the causal relationship between growth and saving. The response of growth to savings is first estimated using instruments to generate exogenous variation in savings rates. The residual variation in growth that is not driven by savings is then used as an instrument to estimate the effect of growth on savings. The estimates show that the spectacular saving rates in the Asian miracle economies have been fuelled by growth, and not the other way around.     

Control and the management of a spreading invader

We consider the problem of management of an aquatic invader spreading in a lake system. We assume that each year the invader can be removed from a certain proportion of invaded lakes, which depends on the selected intensity of control. Control decisions are generated and compared for an optimally controlled system and for a static optimization across asymptotic steady states. Control close to eradication of the invasive species is always optimal for invasions with relatively high damages, low rates of density dependent spread and/or low chance of additional random introductions. Control to a highly invaded steady state is optimal for those invasions with low relative damages, high chances of random introduction and high levels of uncertainty in species location. In all other cases the optimal outcome depends upon initial conditions. Comparing the relative performance of the optimally controlled system and the static optimization demonstrates situations when the differences are small and when not. When invasions are acted upon in their later stages and across certain parameter combinations a static optimization provides a reasonable approximation of an optimally controlled system. The flip-side is that optimal policies directed at an invasion in its early stages tend to provide significantly savings. The savings vary across parameter combinations, yet in these situations little useful insight will be generated without consideration of a dynamically optimized system.     

Costly structural change and optimal growth

Summary This paper studies the optimal growth of a developing economy that has a choice to expend a fixed amount of resource for a structural change that advances its production technology. It is shown that structural change is undertaken if capital stock is above a critical level. Economies undertaking structural change converge to a larger steady state and economies not undertaking structural change converge to a smaller steady state. The optimal policy correspondences and growth paths are characterized. The social optimum is shown implementable by a competitive equilibrium with lump-sum taxation.We are grateful to Francis Cheung, Carmen Menezes, Peter Mueser, Don Schilling, two anonymous referees and an associate editor for their valuable suggestions.     

INDUSTRIAL RELATIONS AND ECONOMIC GROWTH IN KOREA

The wage rate, labour productivity, and labour share are examined as they relate to changing industrial relations over the last four decades in the Korea. The results imply that the labour share is greater than that of Korea's competitive equilibrium in the 1990s. We analyse the effect of industrial relations on economic growth through a theoretical model comparing the growth rate of the competitive equilibrium with that of the bargaining equilibrium. The bargaining growth rate is lower than that of the competitive equilibrium. Among bargaining equilibria, the growth rate decreases as the labour share increases.     

Optimal growth in the two-sector neoclassical growth model

This article analyzes optimal growth in the neoclassical two-sector model. First, the optimal savings ratio is derived corresponding to that growth path which maximizes consumption at each point of time. Secondly, it can be shown that this optimal savings ratio is the limit for the optimal savings ratio as derived by Pontryagin's maximum principle for an optimal policy, when the social discount rate for future per capita consumption approaches zero.This work was supported by the Deutsche Forschungsgemeinschaft, West-Germany.