Equilibria in an overlapping generations model with transfer policies and exogenous growth

For an overlapping generations economy with varying life-cycle productivity, non-stationary endowments, continuous time starting at $-\infty $ (hence allowing for full anticipation), constant-returns-to-scale production and ces utility, we fully characterise equilibria where output is higher than investment, which is strictly positive. Net assets (aggregate savings minus the value of the capital stock) are constant in any equilibrium, and, for balanced growth equilibria (bge, defined for an economy with stationary endowments), net assets are non-zero only in the golden rule equilibrium, in accord with Gale (1973). The number of bge is finite. Their parity, however, depends on the life-cycle productivity, in particular, on the relation between the intertemporal elasticity of substitution, the minimal working age and the minimal tax age.     

Signal-extracting education in an overlapping generations model

Summary. In order to get good positions in companies, people try to enter highly-ranked universities. However, abilities vary greatly between individuals. High-ability individuals have an incentive to send signals to firms by obtaining a higher level of education in order to distinguish themselves from low-ability individuals. This paper constructs an overlapping generations model in order to examine the macroeconomic consequences of such sorting behavior of individuals. There are two kinds of possible equilibria in our model. In one equilibrium, only the high-ability agent can obtain higher education and thus an elite society emerges. In the other equilibrium, all ability types have the chance to obtain higher education and thus a society with mass higher education emerges. We also discuss the possibility of multiple equilibria of these different steady states and the dynamic change in wage differentials.Received: 9 October 2002, Revised: 15 July 2003, JEL Classification Numbers: D82, J31, O10.The authors acknowledge Osamu Hayashida, Noriyoshi Hemmi, Hideshi Itoh, Michihiro Kandori, Toshihiro Matsumura, Takuya Nakaizumi, Osamu Nishimura, Ryoji Ohdoi, Tadashi Yagi, Noriyuki Yanagawa, and seminar participants at Doshisha University, the University of Tokyo, and Contract Theory Workshop at Kyoto University for helpful comments and suggestions. We would also like to thank an anonymous referee for valuable comments. This paper is part of the academic Project on Intergenerational Equity (PIE), funded by a scientific grant from Japans Ministry of Education, Culture, Sports, Science and Technology (grant number 603).     

Socially responsible investment in an environmental overlapping generations model

One of the problems associated with the conservation of the environment is that short-lived individuals fail to account for the long-term effects of pollution, which implies that future generations bear the costs imposed by the current generation. Such inter-generational externalities are usually tackled by (Pigovian) taxes, fiscal policy or environmental regulation. Alternatively, we propose that socially responsible investment funds create a role for the stock market to deal with intergenerational environmental externalities. We analyze the role of the stock market in an environmental overlapping generations model of the Diamond-type, in which agents choose between investing in “clean” government bonds or “polluting” firm equity. We show that although socially responsible investors are short-lived, the forward-looking nature of stock prices can help to resolve the conflict between current and future generations.     

Human capital and economic growth in an overlapping generations model

The paper describes an aggregative optimal growth model, the essential features of which are that individuals are mortal and obtain their labor skill through educational training. The process of human capital formation is described by an education function which relates the pass rate to the educational expenditure per student. Two alternative scenarios, private and public education regimes, are separately investigated. Under the decentralized education regime, risk-neutral individuals borrow to finance their education when young. Under the centralized education regime, the cost of education is financed by taxes imposed on the workers in the economy, and the central government maximizes a long-term social target function. The equilibria of both regimes are analyzed and various comparative static results derived. It is shown that educational investment in a decentralized equilibrium is higher than that in the centralized steady state. We also establish that there exists a time discount rate at which or above which the decentralized per capita consumption exceeds that of the centralized steady state whereas for time rates of discount sufficiently near the population growth rate, the above result will be reversed.     

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.     

Monetary equilibrium in an overlapping generations model with productive capital

Summary We study perfect foresight competitive equilibrium in an overlapping generations model with productive capital and a fixed nominal stock of money. We obtain almost-complete characterizations of (a) the existence of a monetary equilibrium from an arbitrary initial capital stock, and (b) the existence of anefficient monetary equilibrium from an arbitrary initial capital stock. When the initial capital stock is no larger than the golden rule stock, the necessary and sufficient condition for both (a) and (b) is the dynamic inefficiency (in the sense of Malinvaud) of the autarkic (or nonmonetary) equilibrium from the same initial stock. However, this condition, though necessary, isnot sufficient for the existence of a monetary equilibrium when the initial stock exceeds the golden rule stock (and still more conditions are needed for anefficient monetary equilibrium to exist). We provide characterizations for these cases, and as corollaries obtain examples in which (a) the nonmonetary equilibrium is inefficient but no monetary equilibrium exists, and (b) monetary equilibria exist but no efficient monetary equilibrium does.We are grateful to a co-editor and an anonymous referee for comments that greatly improved the exposition in the paper.     

Rational expectations in the overlapping generations model

This paper reports results on the character of the rational expectations equilibria of a stochastic overlapping generations model with heterogenous markets. The model considered is a stationary overlapping generations model in which the endowments of young agents are subject to i.i.d. random shocks. The main result shown is that if there are l > 1 commodities traded in every period, then for most preferences, the rational expectations equilibrium stochastic process of prices and allocations necessarily exhibits serial correlation. This is in marked contrast to the one commodity model in which there always exists an equilibrium which is measure isomorphic to the endowment process.     

Asset bubbles in an overlapping generations model with endogenous labor supply

This paper examines the effects of asset bubbles in an overlapping generations model with endogenous labor supply. We show analytically that asset bubbles can lead to an expansion in steady-state capital, investment, employment and output under certain conditions.     

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.     

Consumption tax and economic growth in an overlapping generations model with money holdings

This paper examines the effect of a consumption tax on economic growth using an overlapping generations (OLG) model with money holdings. We show that the neutrality of the consumption tax does not hold in the money-in-the-utility-function model, because a change in consumption taxation induces the substitution of money holdings for consumption, and the money is the net wealth within the OLG structure. An increase in the consumption tax rate lowers (raises) the growth rate under a low (high) monetary expansion rate. On the other hand, in the cash-in-advance model and the money-in-the-production-function model, the neutrality of consumption taxation holds even within the OLG structure, because in these models there is no substitution of consumption and money holdings.     

Stationary equilibrium transition rules for an overlapping generations model with uncertainty

An overlapping generations model incorporating random production shocks is studied. Households have finite life spans. Futures markets are incomplete. Agents have full information in one case, and receive only a limited signal in another. In both instances the existence of a time-autonomous transition rule is proved such that if all agents forecast using it, the economy's actual growth will bear the predictions out. The rule corresponds to a steady state for a non-stochastic model. With limited information, it is seen to depend on all past signals. Several approximation theorems which may facilitate future applications are presented.     

Optimal tax rules and public sector efficiency with an externality in an overlapping generations model

This paper examines optimal tax rules and public sector efficiency, integrating them in a second-best world with pollution by using an overlapping generations model. The second-best world is characterized by the comparative statics of green preferences. The main results obtained are as follows. First, the marginal cost of public funds may be reduced by the externalities, regardless of the choice of taxes. Second, optimal environmental and non-environmental tax rules are additively and directly affected by the dynamic efficiency of capital accumulation per unit labour (DECAL), and indirectly by it, through the efficiency of the public sector. Environmental taxes going beyond Pigovian ones may be welfare-improving if the DECAL is improved by the environmental tax. Even optimal non-environmental tax rules should additively and directly counter the dynamics of pollution to consider the income effects of the optimal tax system for the future. Third, the “additivity property,” or the “principle of targeting,” does not hold even in the absence of incentive compatibility constraints. The essential reasons for this are clarified as follows: distortions that should be countered by taxes; that is, the income effects of the optimal tax system and the DECAL in this model, break the equality between optimal environmental taxes and the externalities measured by governments. Finally, growing environmental concerns may, in fact, increase pollution. The inverse relationship between environmental and labour income taxes may not hold.     

Sustainable government debt in a two-good,two-country overlapping generations model

The recent dramatic rise of government deficits in most advanced countries to counter the effects of the global financial crisis arouses renewed interest for one of the perennial topics of fiscal policy: the sustainability of government debt. This paper explores maximum sustainabile debt in a two-good, two-country overlapping generations (OLG) model and analyzes existence and dynamic stability of steady states as well as the transitional dynamics of private capital when government debt remains below the maximum sustainable level. We find that maximum government debt levels for both countries exist and are negatively related. Moreover, if sustainable government debt is unilaterally expanded, private capital is crowded out in both countries while the terms of trade of the debt-expanding country are unaffected if capital income shares are internationally equal.     

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 two-sector overlapping generations model with heterogeneous capital

Summary. This paper characterizes the existence and stability properties of steady state solutions as well as the nature of transition paths of a two-sector growth model with heterogeneous capital. It compares the properties of a Cobb-Douglas–Leontief economy with heterogeneous capital with the properties of the same economy with homogeneous capital. The model with heterogeneous capital reveals a set of characteristics different to those of the model with homogeneous capital. These include the saddle-path stability of the non-trivial steady state as well as the possibility of overshooting and in contrast to the homogeneous capital case, the possibility of damped oscillations along the transition path for realistic parameter values. Received: September 21, 2001; revised version: November 21, 2002 RID="*" ID="*" We thank Costas Azariadis, and Laurie Conway for helpful comments on a previous draft. The paper has substantially benefited from the feedback of an anonymous referee. Correspondence to: R. Wendner     

Equilibrium cycles in an overlapping generations economy with production

Perfect foresight equilibrium trajectories of an overlapping generations model with production may include stable or unstable invariant closed curves. These orbits are detected using the Hopf bifurcation theorem, where the parameter of bifurcation is purely technological. The paper also proves that there is a stabilization policy that completely eliminates the cycle. Finally, using a C.E.S. production function, it is shown that the range of values of the elasticity of substitution between capital and labor for which cycles may exist is bounded above.     

Identifying optimal contingent fiscal policies in a business cycle model

Optimal fiscal policy is indeterminate in a dynamic and stochastic environment. The complete characterization of the fiscal policy requires the use of identification constraints. In the literature either capital taxes or debt have been restricted to be not contingent on the state of nature. We propose a different type of identification constraints to have both policy variables state-contingent. Three alternative identification conditions are considered: (i) restrictions on the dynamic and stochastic behavior of the debt path; (ii) an exogenous debt path, and (iii) an exogenous belief function. The main result indicates that the optimal capital tax is zero and constant over the business cycle for any of the identification conditions used, suggesting that is optimal for the government to use debt return as a shock absorber, keeping capital taxes constant. The result is quite different from the previous literature, which obtains very volatile capital taxes. JEL Classification: E62, H21. We are grateful to Alfonso Novales, Víctor Ríos-Rull, Javier Vallés and two anonymous referees for helpful comments and suggestions. We acknowledge financial support from Spanish Ministerio de Ciencia y Tecnología (Ruiz and Pérez: BEC 2003-039; Manzano: BEC 2002-01995). Baltasar Manzano also acknowledges support from Xunta de Galicia (PGIDIT03PXIC30001PN, PGIDIT03CSO30001PR).     

Existence and uniqueness of steady-state equilibrium in a two-sector overlapping generations model

In his seminal paper Galor [A two-sector overlapping generations-model: a global characterization of the dynamical system, Econometrica 60 (1992) 1351-1386] establishes conditions for the existence of equilibrium in the two-sector overlapping generations (OLG) model. Although appealing theoretically, these conditions are implicit and not easy to apply. This paper develops new theorems on the existence and uniqueness of steady-state equilibrium in the two-sector OLG model. We provide explicit conditions on the utility and production functions for the existence and uniqueness of equilibrium, with which one only needs to check the derivatives of the production and utility functions and their interactions, without requiring solving for the savings function and its derivatives. We present detailed steps to check the existence and uniqueness of equilibrium and provide illustrative examples.     

Exchange market reform,inflation, and fiscal deficits

This paper examines the effects of exchange market reform on inflation and quasifiscal deficits in developing countries. The first part presents the conceptual framework, which identifies a variety of implicit taxes and subsidies that must be taken into account (in addition to implicit taxes on exports, as emphasized by Pinto (1991)) in assessing the fiscal and inflationary effects of exchange market reform. A formula that attempts to capture explicitly these taxes and subsidies is derived. The second part applies the formula to six countries (Guyana, India, Jamaica, Kenya, Sierra Leone, and Sri Lanka). The results suggest that exchange market reform may lead to a significant reduction in reliance on the inflation tax.     

Sunspot-like equilibria in an overlapping generations economy with strategic interactions

In this paper I analyze the effect of market uncertainty in an overlapping generations economy with strategic interactions among agents. I demonstrate the existence of sunspot-like equilibria, in which arbitrarily small amounts of intrinsic uncertainty in agents’ offers generate large fluctuations in equilibrium bids and prices. I would like to express my gratitude to Stephen Spear for his guidance during the realization of this project. I thank an anonymous referee for providing insightful comments and suggestions. I have benefited from comments by Alexander Elbittar, Cesar Guerrero, and Vivek Ramachandran.