National labor markets, international factor mobility and macroeconomic instability

We consider a standard two-country environment, where one of the two countries has a rigid labor market, and analyze how global economic integration affects the economies with respect to expectations-driven cycles and steady state welfare. We show that by allowing free capital mobility, equilibrium indeterminacy is exported from the rigid wage country to the world economy. If further liberalization is permitted, by allowing free movements of labor, the scope for indeterminacy is reduced and open labor markets may produce a stabilizing effect on the global macro-economy. Whether this also implies higher welfare in the long run depends on differentials in average firm size across countries, which determines the direction of migration flows.     

Renewable Resource Use and Nonseparable Amenity Benefits

We incorporate amenity benefits into an overlapping generations model with a renewable resource as a factor of production, source of amenity benefits and store of value. Unlike the conventional renewable resource problems studied under the assumption of additive consumption and amenity benefits, we let amenity benefits affect the utility of consumers in a nonseparable fashion. We examine the role that weights given to consumption and amenities have for harvesting and the resource stock. We characterize dynamics and stability of steady state equilibria with a logistic resource growth function. We demonstrate in parametric and numerical models that the weights given to consumption and amenities in the utility function matter substantially for the steady state equilibrium stock and its stability and dynamics. Both conventional saddle point equilibria and indeterminacy with infinite number of equilibria and saddle-node bifurcation is possible depending on the weights given to consumption and amenities. In addition, we show that for each inefficient equilibrium stock, there is a unique subsidy rate that can move the economy from an inefficient equilibrium to an efficient one. The presence of indeterminacy provides a challenge to resource policies, because the system becomes unpredictable. Therefore, expectations and market psychology may play an important role in resource utilization and provision of amenities.     

Real Indeterminacy of Stationary Monetary Equilibria in Centralized Economies

We show that real indeterminacy of stationary equilibria, by which the set of stationary equilibria is a continuum and the real allocation varies among equilibria, may arise in some general equilibrium models with fiat money. The conditions under which such equilibria arise are: (i) each household optimally saves a constant amount of money; and (ii) at least two households face different budget constraints. We present various models, including a decentralized money search model and a centralized model with a monopoly firm, to explain how these conditions lead to real indeterminacy. Finally, we present a policy that uniquely implements any desirable outcome.     

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.     

Global asymptotic stability of a competitive equilibrium with recursive preferences

Summary. This paper demonstrates global stability of a competitive equilibrium in a multi-sector model of many firms, each of which exhibits constant returns to scale technology, and of infinitely lived consumers, whose preferences are recursive but not necessarily additively separable. In the topology induced by a sup-norm, the dominant diagonal blocks condition (Araujo and Scheinkman (Econometrica 45, 1977)) allows us to apply the implicit function theorem to obtain continuity of the equilibrium path. If a stationary equilibrium is locally asymptotically stable, then the continuity of the equilibrium path and smoothness of a weight function on heterogeneous consumers imply that all equilibrium paths converge to the steady state. The dominant diagonal blocks condition is also shown to be sufficient for the local asymptotic turnpike property. Received: December 13, 1996; revised version: June 2, 1999     

Indeterminacy of equilibrium in stochastic OLG models

Summary. This paper studies the equilibria of a stochastic OLG exchange economies consisting of identical agents living for two periods, and having the opportunity to trade a single infinitely-lived asset in constant supply. The agents have uncertain endowments and the stochastic process determining the endowments is Markovian. For such economies, the literature has focused on studying strongly stationary equilibria in which quantities and prices are functions of the exogenous states of nature which describe the uncertainty: such equilibria are generalizations of deterministic steady states, and this paper investigates if they have the same special status as asymptotic limits of other equilibrium paths. The difficulty in extending the analysis of equilibria beyond the class of strongly stationary equilibria comes from the presence of indeterminacy: we propose a procedure for overcoming this difficulty which can be decomposed into two steps. First backward induction arguments are used to restrict the domain of possible prices; then if some indeterminacy is left, expectation functions are introduced to make the forward equilibrium equations determinate. The properties of the resulting trajectories, in particular their asymptotic properties, can then be studied. For the class of models that we study this procedure provides a justification for focusing on strongly stationary equilibria. For the model with positive dividends (equity or land) the justification is complete, since we show that the strongly stationary equilibrium is the unique equilibrium. For the model with zero dividends (money) there is a continuum of self-fulfilling expectation functions resulting in a continuum of equilibrium paths starting from any admissible initial condition: under conditions given in the paper, these equilibrium paths converge almost surely to one of the strongly stationary equilibria-either autarchy or the stochastic analogue of the Golden Rule. Received: November 19, 2001; revised version: March 22, 2002 RID="*" ID="*" We are grateful for the stimulating environment and research support provided by the Cowles Foundation at Yale University during the Fall 2000 when this paper was first conceived. We are also grateful to the participants of the SITE Workshop at Stanford University and the Incomplete Markets Workshop at SUNY Stony Brook during the summer 2001 for helpful discussions. Correspondence to: M. Magill     

Indeterminacy of intertemporal equilibria under imperfect competition

Summary. It is known that overlapping generations models with imperfectly competitive firms may exhibit a continuum of stationary equilibria. The reason of this indeterminacy is that different price expectation functions of consumers lead to different objective demand functions against which firms maximize. All these expectation functions fulfill perfect foresight in the equilibrium, but they can be arbitrary off the equilibrium. In this paper it is shown that it is not this arbitrariness which is responsible for the indeterminacy, but that the continuum of stationary equilibria emerges even if expectation functions are rational. Received: March 25, 1999; revised version: February 16, 2000     

Optimal growth with many consumers

A method is described for constructing all Pareto-optimal allocations for a dynamic economy with many heterogeneous consumers, under certainty, in which both the technology and consumer preferences are recursive but preferences need not be additively separable over time. Optimal (perfect foresight competitive equilibrium) allocations are obtained through the study of a dynamic program. For an economy with one consumption good, sufficient conditions are given for the existence of a unique interior stationary distribution of consumption and wealth. For a two-person exchange economy, sufficient conditions are given for the global asymptotic stability of the unique interior stationary point.     

Does commodity money eliminate the indeterminacy of equilibrium?

Previous studies have shown that a random-matching model with divisible fiat money and without constraint on agents’ money inventories possesses a continuum of stationary single-price equilibria. Wallace (J. Econom. Theory 81 (1998) 223) conjectures that the indeterminacy can be eliminated by the use of commodity money. Instead, I find that in a similar random-matching model with dividend-yielding commodity money, a continuum of stationary single-price equilibria exists when the utility of dividend is not too high. This result casts doubt on the conventional belief that the indeterminacy of monetary equilibrium is be caused only by the nominal nature of money.     

ON THE ROLE OF TAX SUBSIDY SCHEME IN MONEY SEARCH MODELS*

This article investigates the roles of policy in search models with divisible money. Recently, real indeterminacy of stationary equilibria has been found in both specific and general search models with divisible money. Thus if we assume the divisibility of money, it would be quite difficult to make accurate predictions of the effects of simple monetary policies. Therefore, in this article, we introduce a certain tax subsidy scheme and show that this is effective in selecting a determinate efficient equilibrium. In other words, for a given efficient equilibrium and for any real number δ > 0 , a certain tax subsidy scheme induces a locally determinate equilibrium within the δ‐neighborhood of the given equilibrium. Moreover, the size of the tax subsidy can be arbitrarily small.     

Model reference adaptive expectations in Markov-switching economies

This paper offers a theory of model reference adaptive beliefs as a selection device in Markov-switching economies under equilibrium indeterminacy. Consistent with the classical rational choice paradigm, our theory requires that endogenous expectations be replaced with a general-measurable function of the observable states of the model, to be determined optimally. This forecasting function is derived as the regime-independent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight state motion (the reference model). We show that model reference adaptive expectations always generate a rational expectations equilibrium, irrespective of the presence of nonlinearities and/or imperfect information. Under equilibrium indeterminacy, this forecasting mechanism enforces the unique mean-square stable solution producing nearly perfect-foresight dynamics.     

The determinacy of equilibrium in economies of overlapping generations

We study the problem of uniqueness of equilibrium paths in the overlapping generations model. We show that, despite local calculation based on counting equations and unknowns, the equilibrium path may be unique. We do this by constucting an example of an economy of overlapping generations with just one equilibrium up to time shift, beside the steady states. Time is either discrete or continuous; in either case, it extend into the infinite future and, possibly, the infinite past. There is one, non-storable commodity at each date. The economy is stationary; intertemporal preferences are logarithmic; the endowments and discount factors of individuals need not depend continuously on time. With continuous time, equilibrium paths of prices are smooth; this, even for endowments and discount factors of individuals that do not depend continuously on time. With discrete time, as the number of periods in the life-span of individuals increases, equilibrium paths converge to the continuous time solutions. If time extends infinitely into the infinite past as well as into the infinite future, in continuous time, all non-stationary equilibrium paths of prices are time-shifts of a single path; in addition, there are two stationary solutions; in discrete time, there is a one dimensional family of non-stationary solutions, up to time-shift; however, the indeterminacy vanishes as the number of periods in the life span of individuals tends to infinity. If, alternatively, time has a finite starting point, in discrete time the degree of indeterminacy increases with the life-span of individuals, and, in continuous time, it is infinite; however, these are families of exponentially decreasing oscillations which, although they may exhibit pseudo-chaotic behaviour for a while, as time tends to infinity they all get damped, and asymptotic behaviour is that of the economy that originates in the infinite past. Stefano Lovo made interesting comments.     

Non-parametric counterfactual analysis in dynamic general equilibrium

In this paper, we examine non-parametric restrictions on counterfactual analysis in a dynamic stochastic general equilibrium model. Under the assumption of time-separable expected utility and complete markets all equilibria in this model are stationary. The Arrow-Debreu prices uniquely reveal the probabilities and discount factor. The equilibrium correspondence, defined as the map from endowments to stationary (probability-free) state prices, is identical to the equilibrium correspondence in a standard Arrow-Debreu exchange economy with additively separable utility. We examine possible restriction on this correspondence and give necessary as well as sufficient conditions on profiles of individual endowments that ensure that associated equilibrium prices cannot be arbitrary. Although restrictions on possible price changes often exist, we show that results from a representative-agent economy usually do not carry over to a setting with heterogeneous agents.     

Growth and equilibrium indeterminacy: the role of capital mobility

Summary. The paper presents a human capital driven endogenous growth model which, in general, permits a multiplicity of equilibrium balanced growth paths. It is shown that allowing for perfect capital mobility across countries increases the range of parameter values for which the model permits equilibrium indeterminacy. As opposed to the closed capital markets case, simple restrictions on preferences are no longer sufficient to eliminate the indeterminacy. Intuitively, under perfect capital mobility agents are able to smooth consumption completely. This induces an economy with open capital markets to behave like a closed economy with linear preferences thereby increasing the possibility of equilibrium indeterminacy. Received: 18 November 1998; revised version: 10 August 1999     

Journey into the Unknown? Economic Consequences of Factor Market Integration under Increasing Returns to Scale

What are the dynamic consequences of comprehensive integration shocks? The answer to this question appears all but trivial. A dynamic macroeconomic model is set up of a small open economy with capital mobility, migration and increasing returns to scale. The model features multiple equilibria as well as (local and global) indeterminacy. Despite its simplicity, the model creates a rich set of plausible implications. This paper clarifies the mechanics that may lead an integrating economy to the good or to the bad equilibrium by showing how fundamentals and expectations interact in the process of equilibrium selection. The model is applied to replicate two striking empirical characteristics of macroeconomic development in East Germany since 1990.     

On the consistency of stationary Markov equilibria with an exogenous distribution

A technique to show the existence of stationary Markov equilibria is provided by Duffie, Geanakoplos, Mas-Colell and McLennan Econometrica 62 (1994) 745-781. In many applications, a state space is constructed as the product of a space of exogenous variables and a space of endogenous variables. In addition, the exogenous shock is given and is a Markov process with a transition probability and an initial distribution. Then their theorem does not ensure the existence of a stationary Markov equilibrium that is consistent with the exogenous distribution. In this paper, we give a sufficient condition for settling the inconsistency problem.     

A Characterization of the Dynamical System in a Two-sector Overlapping-generations Model: The Case of Unbounded Growth

This paper characterizes perfect-foresight equilibria in a two-sector overlapping-generations economy for the case of unbounded growth. The analysis demonstrates that gross substitutability in consumption is not sufficient to ensure the determinacy of equilibrium. Unlike Boldrin and Rustichini (1994), indeterminacy of equilibria can arise within the framework of an overlapping-generations model with convex technology. The finite time horizon of agents is the source of such indeterminacy.
JEL Classification Number: 041.     

Global and local determinacy in a one-step forward looking New Keynesian model

In this paper we consider a New Keynesian model for optimal monetary policy in a staggered fashion. We provide the relations of a non linear model of general economic equilibrium, implementing a suitable Taylor-type interest rate rule. We characterize the conditions that guarantee local determinacy and explore conditions under which local bifurcations of the target equilibrium may occur. Afterwards, we argue how local determinacy might be associated with global indeterminacy, providing some numerical examples.     

Correlated equilibrium in evolutionary models with subpopulations

We study a version of the multipopulation replicator dynamics, where each population is comprised of multiple subpopulations. We establish that correlated equilibrium is a natural solution concept in this setting. Specifically, we show that every correlated equilibrium is equivalent to a stationary state in the replicator dynamics of some subpopulation model. We also show that every interior stationary state, Lyapunov stable state, or limit of an interior solution is equivalent to a correlated equilibrium. We provide an example with a Lyapunov stable limit state whose equivalent correlated equilibrium lies outside the convex hull of the set of Nash equilibria. Finally, we prove that if the matching distribution is a product measure, a state satisfying any of the three conditions listed above is equivalent to a Nash equilibrium.     

Sraffian Indeterminacy in General Equilibrium

The indeterminacy claim for competitive price systems made by Sraffa (1960) is examined by placing Sraffa's work in an intertemporal general equilibrium model. We show that indeterminacy occurs at a natural type of equilibrium. Moreover, the presence of linear activities instead of a differentiable technology is crucial and the indeterminacy is constructed, as in Sraffa, by fixing some or all of the economy's aggregate quantities. On the other hand, an extra condition, that some factors have inelastic excess demand is necessary, and, unlike Sraffa's model, relative prices must be allowed to vary through time. Sraffian indeterminacy and the generic finiteness of the number of equilibria are reconciled by showing that indeterminacy occurs at a measure-zero set of endowments. We use an overlapping-generations model to show that these endowments nevertheless arise systematically and that indeterminacy does not occur when relative prices are constant through time.