Donor Altruism and the Transfer Paradox in an Overlapping Generations Model

This paper examines the transfer problem between two countries when a donor exhibits altruistic utility toward a recipient in a one‐sector overlapping generations model. We demonstrate that if the donor has a larger marginal propensity to save than the recipient, the donor's altruism never contributes to donor enrichment irrespective of the degree of the donor's altruism. Donor enrichment occurs only if the donor has a smaller marginal propensity to save and a sufficiently high level of altruism. These findings imply that the altruism of a donor toward a recipient does not necessarily explain the motivation to voluntarily provide a transfer.     

Aspirations and the transfer paradox in an overlapping generations model

This study examines the transfer problem between two countries when either the donor or the recipient has aspirations, based on parents’ standards of living, in a one-sector overlapping generations model. Focusing on whether and how aspirations impact the welfare effect of a transfer, we demonstrate the following results. First, when the donor forms aspirations, as the degree of his/her aspirations to their parents increases, a transfer is more likely to cause donor enrichment. However, this does not affect the recipient’s welfare at all. In contrast, when the recipient forms aspirations, whether the increase in the degree of these aspirations causes immiserization depends on whether the transfer raises the recipient’s consumption. Second, we show that if the donor’s or recipient’s marginal utility increases with their respective aspirations, the transfer is more likely to cause recipient immiserization. However, whether donor enrichment occurs depends on the situation. These results imply that there are two types of effects that aspirations can have on the welfare of both countries: effects caused by the aspirations, and effects that occur through the capital market. Furthermore, we find that these two effects on welfare do not necessarily work in the same direction.     

The Transfer Problem and Intergenerational Allocation in an Overlapping Generations Model

We investigate the transfer problem between two countries in the steady state in a one-sector overlapping generations model and explain how transfers should be shared between the young and old generations of the donor country and allocated across the generations of the recipient country. Except at the golden rule of capital accumulation, the ratios of the burden and distribution of transfers between the young and old generations affect welfare. We obtain the following results. First, the sharing of the transfer burden in the donor country depends on the relative size of two effects, namely, a negative direct effect and a positive indirect effect. If the former exceeds the latter, it is preferable for the donor country to allocate all of the transfer burden to the old generation and vice versa. Second, from the viewpoint of welfare maximization, it is preferable for the recipient country to distribute all of the transfers to the young generation. In contrast to the existing literature, these results suggest that the setting whereby the young generation of the donor country defrays all transfer costs may not be justifiable from the viewpoint of donor welfare maximization.     

Optimality and monetary equilibria in stationary overlapping generations models with long-lived agents: Growth versus discounting

This paper studies the relationship between the existence and optimality of a monetary steady state and the nonoptimality of nonmonetary steady states. We construct a sequence of stationary overlapping generations economies with longer and longer-lived generations in which all agents maximize a discounted sum of utilities with a common discount rate. Under some assumptions the following result is established: If the discount rate is greater (less) than the population growth rate, then eventually every nonmonetary steady state is optimal (nonoptimal) and a monetary steady state does not exist (exists and is optimal).     

Migration,Foreign Aid and the Welfare State

Aspects related to the links between international migration, foreign aid and the welfare state are highlighted in this paper. Migration is modeled as a costly movement from an aid‐recipient developing country with low income and no welfare state, towards a rich donor, developed country with a well‐developed welfare state. Within this model, it is found, among other things, that the best response of the developed donor country is to increase aid as the co‐financing rate by the recipient country increases. When the immigration cost decreases, e.g. as a result of greater economic integration between the two countries, it is beneficial for the donor country to increase aid and the recipient country to increase the co‐financing rate.     

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.     

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.     

Which countries show favour towards negative,zero or positive population growth?

This article develops an overlapping generations model with eldercare by migrants and children in the context of the ageing problem and examines what conditions cause people to prefer a negative, zero or positive population growth rate. We find that a wage ratio of around 0.7 for eldercare by migrants can explain well the coexistence of negative, zero and positive population growth rates in the European Union. A country that does not need eldercare and has an optimistic view of the future will have a positive population growth rate. Other countries will have zero or negative population growth rates.     

Money,inflation, and maximizing behavior: The case of many countries

This paper examines a world which is composed of countries each inhabited by a population of farsighted overlapping generations and in which the only assets are the national currencies that grow at constant proportional rates. It is shown that the world economy is unstable in the sense that, away from the steady state, either the real value of each country's stock of money goes to zero or the world monetary system eventually collapses. It is also shown that the dynamic paths of the price level and the real stock of money in each country may move nonmonotonically over time.     

International trade and capital accumulation in an overlapping generations model with a public intermediate good

We investigate the effects of a public intermediate good on trade patterns, capital accumulation, and the gains from trade in a two‐country, three‐sector overlapping generations model. A public intermediate good affects not only the productivity of private production but capital accumulation; thus, the results differ from those obtained in previous studies. First, opening to trade may accelerate capital accumulation in the higher‐savings country. Additionally, the country producing a public intermediate good more (which is labor‐intensive) may be the importer of the investment good (which is the most capital‐intensive). Finally, the lower‐savings country may have lower steady‐state welfare under trade.     

COMPETITIVE GROWTH IN A LIFE‐CYCLE MODEL: EXISTENCE AND DYNAMICS*

The dynamic behavior of the capital growth rate is analyzed using an overlapping‐generations model with continuous trading. Assuming a technology satisfying constant social returns to capital, the equilibrium growth rate is piecewise‐defined by functional differential equations with both delayed and advanced terms. The main result concerns the existence of a solution expressed as a series of exponentials, which is shown to crucially depend on the initial wealth distribution among cohorts. Upon existence, the dynamics of the capital growth rate has a saddle‐point trajectory that converges to a unique steady state. Along the transition path, the growth rate exhibits exponentially decreasing oscillations.     

Capital income taxation in a growing world economy

This paper deals with dynamic adjustment in large economies to changes in the rate of capital income taxation or in the rate of investment tax credit in one country. The framework applied in the paper is a continuous-time, overlapping generations model with two countries. It features population growth and debt non-neutrality. We address impact and steady state effects of capital income tax and investment subsidy changes in the home country on consumption per capita, the capital intensity, and the per capita net foreign asset position in both countries. We also briefly consider individual welfare consequences of these policies.     

Family allowances as welfare improvements

The present paper studies the equilibria of a simple overlapping generations model of pure exchange in which money is traded. There is a continuum of agents in each generation and population growth is endogenous via voluntary decisions on children. Any monetary steady state has to satisfy the golden rule that the interest rate equals the growth rate. Still such a monetary steady state may be inefficient. If raising children is not excessively profitable, then there exists a transfer scheme, in favor of those who raise children, which improves upon the steady state.     

A model of the optimal allocation of government expenditures

Government expenditures can be used for various socioeconomic objectives, including public education, consumption of public goods and services, and social protection. This paper analyzes the optimal allocation of public expenditures among these competing functions. We establish an overlapping generations model with heterogeneous individuals in which the government optimally chooses income tax, transfer payment, educational spending, and public consumption. Our model characterizes the transitional dynamics and the steady state of each function with and without a pay‐as‐you‐go intergenerational contract. We also conduct a simulation illustrating that the presence of an intergenerational contract may raise public consumption and social welfare in the steady state.     

Transfers, the terms of trade, and capital accumulation

Abstract .  In the context of a two-sector overlapping-generations model it is demonstrated that a steady-state transfer paradox may arise under commodity trade with stability and without distortions or bystanders. The existence of the paradox is due to the effect of the transfer on world capital accumulation, which is shown to always (i.e., for any ranking of factor intensities and savings rates) improve the donor's terms of trade. Transfers may also improve steady-state welfare for both donor and recipient and produce paradoxical welfare results along the transition path.     

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.     

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.     

A CLOSED‐FORM SOLUTION FOR DETERMINING THE BURDEN OF PUBLIC DEBT IN NEOCLASSICAL GROWTH MODELS

This paper develops a new approach, termed as the stock approach, to calculate the steady‐state output loss caused by public debt in neoclassical growth models. The novelty of our stock approach is that it provides a closed‐form solution to the steady‐state output‐debt relationship. The main conclusion of the paper is that the steady‐state burden of public debt is country‐specific in neoclassical growth models and it decreases with the private saving rate and increases with the population growth rate, with the exception of the special case where Ricardian equivalence holds.     

Educational Policy in a Credit Constrained Economy with Skill Heterogeneity*

An overlapping‐generations model where agents choose whether to become educated when young is presented. Education enhances productivity, but needs to be financed by borrowing. Because of the possibility of default, lenders may ration credit. We characterize the steady‐state equilibrium with and without credit constraints and show that credit constraints are associated with lower education and a lower real interest rate. We then study the role of public policy in remedying the inefficiency which occurs with credit market imperfections and examine whether public education can improve on the constrained equilibrium.     

Logic of Aid in an Intertemporal Setting

The paper studies the welfare implications of temporary foreign aid in the context of a simple two‐country model of trade. In addition to its usual effects, a transfer of income in one period is assumed to influence the preferences of the recipient country in the following period. The implied changes in the terms of trade over the two periods are consistent with a number of possible outcomes with respect to the intertemporal welfare of the donor, the recipient, and the world as a whole. Particular attention is devoted to the conditions for strict Pareto improvement and the circumstances under which temporary aid transactions are likely to occur.