Consumption-loan type models the Samuelson case

This is a further study of the overlapping generations model with fixed amount of fiat money. We show that when the economy is Samuelsonian then there exists some Pareto optimal stationary competitive equilibrium from some initial money holdings. Moreover, if the steady-state interest factor is less than unity, then a non-monetary Pareto optimal equilibrium exists from any initial money endowments.     

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 interaction between risk sharing and capital accumulation in a stochastic OLG model with production

We analyze the interaction between risk sharing and capital accumulation in a stochastic OLG model with production. We give a complete characterization of interim Pareto optimal competitive equilibrium allocations. Furthermore, we provide tests of Pareto optimality/suboptimality based on (risky) rates of return only.     

Retrading in market games

When agents are not price takers, they typically cannot obtain an efficient real location of resources in one round of trade. This paper presents a non-cooperative model of imperfect competition where agents can retrade allocations, consistent with Edgeworth's idea of recontracting. We show (a) there are Pareto optimal allocations, including competitive equilibrium allocations, that can be approximated arbitrarily closely when trade is myopic, i.e., when agents play a static Nash equilibrium at every round of retrading; (b) any converging sequence of allocations generated by myopic retrading can be supported along some retrade-proof subgame perfect equilibrium path when traders anticipate future rounds of trading.     

Endogenous market power

In this paper we develop a framework to study markets with heterogeneous atomic traders. The competitive model is augmented as we provide traders with correct beliefs about their price impacts to define equilibrium with endogenously determined market power and show that such equilibrium exists in economies with smooth utility and cost functions and is generically determinate. Traders? price impacts depend positively on the convexity of preferences or cost functions of the trading partners and are subject to mutual reinforcement. Compared to the competitive model, the volume of trade is reduced, and hence is Pareto inefficient. The price effects of non-competitive trading depend on the convexity of marginal utility or cost function.     

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.     

The dynamics of efficient asset trading with heterogeneous beliefs

This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibrium when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and significant fluctuations in individual portfolios may be correct but it needs some qualifications. We consider an infinite horizon stochastic endowment economy populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying the portfolios that decentralize Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents believe that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the true process consists of i.i.d. draws from a common distribution and the support of some agent's prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.     

Computing DSGE models with recursive preferences and stochastic volatility

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences such as those in Epstein and Zin, 1989, Epstein and Zin, 1991 and stochastic volatility. Models with these two features have recently become popular, but we know little about the best ways to implement them numerically. To fill this gap, we solve the stochastic neoclassical growth model with recursive preferences and stochastic volatility using four different approaches: second- and third-order perturbation, Chebyshev polynomials, and value function iteration. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy. Our main finding is that perturbations are competitive in terms of accuracy with Chebyshev polynomials and value function iteration while being several orders of magnitude faster to run. Therefore, we conclude that perturbation methods are an attractive approach for computing this class of problems.     

On the nonexistence of recursive equilibrium in stochastic OLG economies

We study a class of stochastic Overlapping generations (OLG) economies that have one-memory equilibria, that is equilibria that are determined by the current and past realizations of the states of uncertainty. This class is negligible, but important. In particular, it contains all the known examples of nonexistence of recursive equilibrium. We show that, within this restricted domain, the existence of recursive equilibrium is actually typical, and such examples are therefore nonrobust. We thank Felix Kubler, Herakles Polemarchakis and Steve Spear for many useful discussions. This paper was started while the first author was visiting Columbia Business School.     

On optimality in intergenerational risk sharing

Summary. This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and give conditions under which introducing a pay-as-you-go system at an equilibrium would not lead to any Pareto improvement. Received: October 5, 1998; revised version: April 3, 2001     

Intergenerational Altruism and the Environment

We construct an overlapping generations model of pollution externality in which individuals are altruistically linked to their offspring as in Barro (1974). It is shown that steady-state consumption may be a decreasing function of the intergenerational degree of altruism. Despite individuals' altruism, the competitive equilibrium is not optimal. We thus study the social optimum and show that it can be decentralized.
JEL classification: D 62; D 64; D 91     

Competitive behavior in market games: Evidence and theory

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1973) [21]. Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market games.     

A theory of optimal denominations for government liabilities

Summary The design and implementation of monetary arrangements has important implications for the welfare and determinacy properties of equilibria that arise under competitive monetary exchange. In this paper we consider one particular feature of a monetary arrangement. We ask whether a government should issue its liabilities so that they are imperfectly divisible and whether they should at the same time regulate private intermediation. We argue that the answer is affirmative. We then consider the optimal minimum denomination for government liabilities given that the social planner would like to implement a particular equilibrium. We show that generically the steady state equilibria supported by minimum denominations that result in Pareto optimal allocations are indeterminate. We then pose the question, what is the best (in a Pareto sense) stationary equilibrium that can be supported, subject to the constraint that the equilibrium display certain minimal determinacy properties? The existence of an optimum in this sense is established. Such equilibria are supported by having the government issue indivisible liabilities with appropriately chosen minimum denominations.Research supported in part by NSF Grant SES-8921346. We have benefitted from conversations with Stan Engerman, Rod Garratt, Glenn MacDonald, Anne Villamil, Neil Wallace and Warren Weber, and from the comments of seminar participants at Cornell and Rochester. We are especially grateful to Ed Prescott for his suggestions.     

A note on the effects of market power distribution in Cordella and Gabszewicz's Ricardian model

We argue that it is the distribution of market power among agents, rather than the use of market power itself, that may force Ricardian economies into autarky. By applying Baldwin (1948) monopoly equilibrium concepts to the general equilibrium with imperfect competition model analyzed by Cordella and Gabszewicz (1997), we show that the monopoly equilibrium outcome Pareto dominates the oligopoly one. As a consequence, economic efficiency is higher when market power is concentrated in one agent than when it is evenly distributed among few agents.     

Balanced equilibrium in a consumption loans model

In a consumption loans model with many generations, Gale's theorem on the existence of balanced equilibrium is generalized, allowing more general preferences. The new theorem shows that there are plausible conditions under which there exists a Pareto optimal (non-optimal) balanced equilibrium whenever there exists (does not exist) a monetary golden rule equilibrium.     

Time inconsistency of benevolent government economies

A dynamic Walrasian economy is said to exhibit inconsistency if the competitive equilibrium path resulting from government reoptimization at some time τ>0 is not a continuation of the competitive equilibrium path resulting from the initial government optimization at time 0. The present paper establishes necessary and sufficient conditions for consistency for a general class of dynamic Walrasian economies. It is seen, for example, that reliance on nondistortionary policy instruments is neither necessary nor sufficient for consistency. It is also shown that Pareto optimal paths can be supported as optimal competitive equilibrium paths only if consistency prevails. However, consistent optimal competitive equilibrium paths need not be Pareto optimal.     

Social security and risk sharing

In this paper we identify conditions under which the introduction of a pay-as-you-go social security system is ex ante Pareto-improving in a stochastic OLG economy with capital accumulation and land. We argue that these conditions are consistent with realistic specifications of the parameters of the economy. In our model financial markets are complete and competitive equilibria interim Pareto efficient. Therefore, a welfare improvement can only be obtained if agents? welfare is evaluated ex ante, and arises from an improvement in intergenerational risk sharing. We also examine the optimal size of a given social security system as well as its optimal reform.     

Implementing the Mortensen rule in a frictional labor market

We show that, in settings where meetings can be multilateral, the allocation rule proposed by Mortensen (1982) can be relatively straightforward to implement: as a local auction conducted by sellers. The implications of using this mechanism in a simple model of the labor market are then explored. We characterize the equilibrium properties of this model, which include wage dispersion, and examine its implied Beveridge curve. A dynamic version of the model is calibrated to the US labor market, and we show that the model can account for observed vacancy rates, given parameters that are chosen to match the average wages and the natural rate of unemployment, although the implied wage dispersion is quite small. Finally, in the limit, as the time between offer rounds in the model approaches zero, the equilibrium approaches the Walrasian competitive equilibrium.     

On stationary overlapping generations models

Consider a stationary consumption–loan economy with fixed amount of fiat money. We show that although the economy is stationary if the number of goods and the number of ‘types’ of consumers are larger than one, there might be no Pareto optimal stationary competitive equilibrium.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.