Determinacy of Equilibrium in an Overlapping Generations Model with Heterogeneous Agents

We study the determinacy of perfect foresight equilibrium near a steady state in an overlapping generations model with production and both altruistic and non-altruistic agents having distinct utility functions. The proportion of each type of consumer is exogenously given. Our main results show that when there are positive stationary bequests, some standard assumptions on preferences and technology rule out local indeterminacy for any positive value of the proportions. In the particular case of a separable utility function for altruistic agents, we prove that the determinacy property does not depend on the size of the “infinite lived” altruistic dynasties. Journal of Economic Literature Classification Numbers: C62, D91, O21, O41.     

‘Double dipping’: the combined effects of social security and civil service pensions on employee retirement

How do macro variables such as aggregate consumption, aggregate money demand, prices, and interest rates vary in response to government attempts to redistribute income across agents through selective tax-transfer policies? This question is investigated for an overlapping generations model consisting of heterogeneously endowed three-period lived agents. In the presumably most favorable case for invariance (identical log-linear utility functions), it is shown that positive interest rate macro equilibria are invariant with respect to redistributions in social security benefits if and only if all agents initially exhibit qualitatively identical liquidity preference behavior, i.e. positive money holding only in youth, only in middle-age, or never.     

Optimal Monetary Policy in OLG Models with Long‐Lived Agents: A Note

This note reexamines Crettez, Michel, and Wigniolle ( 2002 ), who studied a two‐period overlapping generations model with cash‐in‐advance constraints and showed that a combination of saving tax and monetary policy involving positive nominal interest rates could achieve the first‐best allocation. The note shows that their result does not hold if agents live for three periods. The implementation of the first best requires the Friedman rule. If agents are long‐lived, saving tax cannot offset a distortion caused by the positive nominal interest rate.     

Existence of equilibria in the overlapping generations model: the nontransitive case

Summary This paper investigates the existence of competitive equilibria in dynamic exchange models with countably many periods and countably many agents. At each period the commodity space can be finite or infinite dimensional. The preferences of agents are not assumed to be transitive or complete. A first equilibrium existence theorem is established under the classical assumption that there exists a finite set of non-negligible agents. In the particular case of an overlapping generations model, a second existence theorem allows simultaneously for finite-lived assets and infinite-lived assets and limits the previous assumption to infinite-lived assets. This theorem covers obviously the standard case of an overlapping generations model where the agents have no endowment outside their lifetime.     

An integral equation representation for overlapping generations in continuous time

This paper develops a method for solving for the dynamic general equilibrium of a deterministic continuous time overlapping generations model with a finite-horizon life-cycle. The model has isoelastic preferences and allows for general assumptions about individual endowments and demographics. Solving for an equilibrium reduces to solving a nonlinear integral equation. In the special case of log utility, the integral equation is linear and global approximations to a solution are easily computed with linear algebra.     

Overlapping Generations or Infinitely-Lived Agents: Intergenerational Altruism and the Economics of Global Warming

Do we need an overlapping generations model for the economics of global warming? To answer this question, an infinitely-lived agent (ILA) approach and an overlapping generations (OLG) model are contrasted. ILA and OLG can be viewed as polar representations of intergenerational altruism. With ILA an immortal agent acts through his investment/savings decisions as trustee on the behalf of the future generations. With OLG, agents need not behave altruistic. They simply save during working years and dissave completely during retirement. Nevertheless, ILA and OLG must not differ in their implication for greenhouse policy. Greenhouse gas abatement is a straightforward alternative to physical capital formation and, even without altruism, each age cohort has an incentive to provide current abatement in order to reduce future damages attributable to climate change. Indeed, under reasonable assumptions and parameter values, our simulations reveal such an invariance result. Provided carbon taxes are the only policy tool and tax revenues are recycled through socially mandated rules, projections of economic growth, climate change and energy consumption are only insignificantly affected by the choice of approach.     

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.     

Intergenerational transfers and the social discount rate

This paper investigates the relationship between intergenerational asset transfers and the choice of the discount rate for use in cost-benefit analysis in a model of a competitive overlapping generations economy constrained by a socially managed exhaustible resource. Provided that there are no distortions in capital markets and that all agents hold perfect foresight, cost-benefit techniques will result in a Pareto efficient resource allocation if the discount rate is set equal to the market rate of interest. But since the path of the interest rate depends on the level of intergenerational transfers, cost-benefit techniques do not ensure a socially desirable distribution of welfare between generations; a social optimum will result only if intergenerational transfers are properly chosen and enforced. Decentralized private altruism may result in intergenerational transfers that both present and future individuals would agree are too small if members of the present generation attach positive weight to the general welfare of future generations, not simply their personal descendants. In a world where intergenerational transfers are non-optimal, second-best policy-making may imply a constrained optimum that is inefficient. Together, these findings suggest that cost-benefit analysis is at best a partial criterion to policy formulation that should be used only in conjunction with ethical principles that define the proper distribution of welfare between present and future generations.     

Cooperation in Stochastic OLG games

This paper builds on Cremer's (Quart. J. Econ. 101 (1986) 33) seminal analysis which shows that (almost) complete cooperation can be achieved as an equilibrium in a game played by overlapping generations of players if the institution in which players cooperate is infinitely lived.We analyze a similar model in which the costs of cooperation are subject to random shocks. Even if these random shocks are very small, the range of parameters for which cooperation can be sustained is decreased considerably in comparison to the deterministic case. Furthermore, we show how the efficient outcome can be approximated if the level of cooperation can be varied continuously and the cooperation technology has decreasing or constant returns to scale, while this is not possible in the case of increasing returns to scale.     

GROWTH AND BUBBLES WITH CONSUMPTION EXTERNALITIES*

This paper explores the role of consumption externalities in an overlapping generations economy with capital accumulation. If consumers in each generation are concerned with other agents’ consumption behaviours, there exist intergenerational as well as intragenerational consumption externalities. It is the presence of intergenreational consumption externalities that may produce fundamental effects both on equilibrium dynamics and on steady‐state characterization of the economy. This paper demonstrates this fact in the context of a simple model of endogenously growing, overlapping‐generations economy with or without asset bubbles.     

Specialization in a dynamic trade model: An overlapping generations case

Abstract

We explore a small open economy with overlapping generations to show that demographic structure is an important factor for the determination of a production pattern in the dynamic trade theory. In the representative agent model, Baxter (1992) shows that even if there are two commodities and two production factors, there is a Ricardian implication that opening up to trade leads to perfect specialization in a small open economy. In contrast, using the overlapping generations model, we find that the heterogeneity of the economic agents generally makes imperfect specialization occur. We also find that whether the stability condition holds or not is crucial for the determination of the long-run production pattern.     

Population growth and the transfer paradox in an overlapping generations model

This study investigates whether the transfer paradox (donor enrichment and/or recipient impoverishment) occurs when a donor and a recipient have different population growth rates by using a one‐sector, two‐country overlapping generations model. We show that if the population growth rates differ, neither donor enrichment nor recipient impoverishment occurs in the steady state under dynamic efficiency. This result is in stark contrast to the existing results that the transfer paradox might occur when a donor and a recipient country have different marginal propensities to save, assuming that both have the same population growth rate. Furthermore, we present the condition for the transfer problem to occur on the transition path and show that the transfer paradox is less likely to occur as the economy converges to the steady state. Our result shows that the prevailing finding that the transfer paradox can occur in an overlapping generations model is limited to the special case of countries having the same population growth rate.     

CLIMATE CHANGE AND OVERLAPPING GENERATIONS

This paper examines the interplay between discounting and the distribution of welfare between generations in formulating climate change response strategies. The analysis shows that one can understand Nordhaus's (1994) standard representative agent model for climate policy analysis as a reduced form of an overlapping generations model that embodies more realistic demographic assumptions. In this setting, alternative Pareto efficient allocations may be supported as competitive equilibria given appropriate sets of income transfers between generations. Numerical simulations establish that increased intergenerational transfers entail reduced monetary discount rates and increased rates of greenhouse gas emissions abatement. Short-run policy choices are highly sensitive to normative judgments concerning the relative weight attached to the welfare of future generations.     

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.     

Discrete time dynamics in a random matching monetary model

Summary. Under take-it-or-leave-it offers, dynamic equilibria in the discrete time random matching model of money are a “translation” of dynamic equilibria in the standard overlapping generations model. This formalizes earlier conjectures about the equivalence of dynamic behavior in the two models and implies the indeterminacy of dynamic equilibria in the random matching model. As in the overlapping generations model, the indeterminacy disappears if an arbitrarily small utility to holding money is introduced. We introduce a different pricing mechanism, one that puts into sharp focus that agents are forward-looking when they interact. Received: January 18, 2001; revised version: May 25, 2001     

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.     

Learning stability in economies with heterogeneous agents

An economy exhibits structural heterogeneity when the forecasts of different agents have different effects on the determination of aggregate variables. We study the important case of economies in which agents' behavior depends on forecasts of aggregate variables and show how different forms of heterogeneity in structure, forecasts, and adaptive learning rules affect the conditions for convergence of adaptive learning towards rational expectations equilibrium. Results are applied to an overlapping generations model and a New Keynesian model of monetary policy.     

Does Money Always Make People Happy?

This paper presents an overlapping generations model with private information, in which the use of fiat money and the rampant moral hazard incentives sustain each other. It is shown that there is a monetary equilibrium, despite the fact that the rate of return on the nonmonetary asset is significantly higher than the rate of economic growth in the nonmonetary case; the valuation of money is not necessarily Pareto-improving, but rather can be harmful to almost all generations; an inflationary policy can improve the welfare of all generations except the initial one. Journal of Economic Literature Classification Number: E41.     

Precautionary saving or denied dissaving

Precautionary saving in response to uninsurable income risk can in principle explain the stylized fact that aggregate saving increases with the variance of income, but it is controversial how much of the observed variation in incomes is, in fact, unpredictable. Borrowing constraints offer an alternative explanation that does not require consumers to be uncertain about their future income. This paper employs a three-cohort, overlapping generations model with quadratic utility and no capital to show that, if agents are patient enough, heterogeneity alone can account for more than half the decrease in the equilibrium interest rate caused by a borrowing constraint. The possibility of facing a binding borrowing constraint in the future induces saving, and this saving increases with the cross-sectional variation in income. Another channel that pushes down the interest rate is the direct effect caused by currently constrained agents not being allowed to dissave. For patient agents, the two channels have roughly the same impact on the interest rate.     

Optimal climate and fiscal policy in an OLG economy

This paper develops a climate–economy model to study the joint design of optimal climate and fiscal policies in economies with overlapping generations (OLGs). I demonstrate how capital taxation, if optimal, drives a wedge between the market costs of carbon (the net present value of marginal damages using the market interest rate) and the Pigouvian tax (the net present value of marginal damages using the consumption discount rate of successive OLGs). In contrast to deterministic infinitely lived representative agent models, at the optimum, the capital income tax is positive, the carbon price equals the market costs of carbon but it falls short of the Pigouvian tax when (i) preferences are not separable over consumption and leisure; and (ii) labor income taxes cannot be age-dependent. I also show that restrictions on climate change policy provide a novel rationale for positive capital income taxes.