Market equilibrium with heterogeneous recursive-utility-maximizing agents

Summary This paper considers a heterogeneous agent Lucas style exchange economy. For a class of recursive utility functions containing the standard additive expected utility functions, I demonstrate that there exist market equilibria characterized by stationary (ergodic) Markov processes for consumption, portfolio holdings, asset prices and the unobserved utilities. No assumptions about market completeness are made, and there are no restrictions on the underlying information filtration.Other contributions of this paper include: (i) an existence and uniqueness theorem of intertemporal utility for the general class of recursive generators; (ii) the optimum principle as well as its corresponding Euler equation derived for the agent's consumption and portfolio choice problem under recursive utility, and (iii) a single-agent equilibrium asset pricing formula which generalizes that of Epstein and Zin (1989).This paper is a part of my PhD dissertation at the University of Toronto. I would like to thank Larry Epstein for his enthusiastic supervision, helpful discussion and valuable comments. Thanks also to Tan Wang and especially Darrell Duffie for valuable comments.     

Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment

Summary. We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics. Received: September 13, 2001; revised version: December 9, 2002 RID="*" ID="*" We are grateful to Tapan Mitra for pointing out errors as well as making very valuable suggestions. Thanks are due to Raouf Boucekkine and Jorge Duran for additional helpful discussions. We also thank an anonymous referee for his/her helpful comments. The second author acknowledges the financial support of the Belgian Ministry of Scientific Research (Grant ARC 99/04-235 “Growth and incentive design”) and of the Belgian Federal Goverment (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”). Correspondence to: C. Le Van     

Optimal unemployment insurance with heterogeneous agents

The framework of a general equilibrium heterogeneous agent model is used to study the optimal design of an unemployment insurance (UI) scheme and preferences for unemployment policy reforms. In a first step, the optimal defined benefit and defined replacement ratio UI systems are obtained in simulations. Then, the question whether switching to such an optimal system from the status quo would be approved by a majority of the population is explored. Finally, the transitional dynamics following a policy change are analysed. Accounting for this transition has an important influence on the support for a policy change.     

Endogenous market segmentation with heterogeneous agents

Summary. An explanation is provided for the evolution of segmented marketplaces in a pairwise exchange economy. Large traders operating in a pairwise exchange market prefer to meet other similar traders, because this enables them to trade their endowments in a smaller number of encounters. Large and small traders, however, cannot be distinguished a priori, and the existence of the small traders imposes a negative externality on the large traders. We show that, under conditions which are not very restrictive, establishing a separate market (perhaps with an entry fee) designated for the large traders induces the two types of traders to segment themselves. However, this segmentation is not necessarily welfare improving. Received: January 12, 2001; revised version: July 17, 2002 RID="*" ID="*" I wish to thank the participants in the Friday Theory Workshop at the University of Sydney, and the participants at the 17th Australian Theory Workshop at the University of Melbourne for comments and discussion. John Hillas and Stephen King pointed out an omission in an earlier version, and Catherine de Fontenay and Hodaka Morita made extensive comments on earlier drafts. This work was initiated while I was a short-term visitor at the University of Southern California.     

Quantal response equilibria with heterogeneous agents

This paper introduces a model of quantal response equilibrium with heterogeneous agents and demonstrates the existence of a representative agent for such populations. Except in rare cases, the representative agent?s noise terms cannot be independently and identically distributed across the set of actions, even if that is assumed for the individual agents. This result demonstrates a fundamental difference between a representative agent and truly heterogeneous quantal responders and suggests that when fitting quantal response specifications to aggregate data from a population of subjects, the noise terms should be allowed to be jointly dependent across actions. Even though this introduces additional degrees of freedom, it makes the model well specified. The representative agent inherits a regular quantal response function from the actual agents, so this model does impose falsifiable restrictions.     

Central bank design with heterogeneous agents

We study alternative institutional arrangements for the determination of monetary policy in a general equilibrium model with heterogeneous agents, where monetary policy has redistributive effects. Inflation is determined by a policy board using either simple-majority voting, supermajority voting, or bargaining. We compare the equilibrium inflation rates to the first-best allocation.     

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.     

Collateral and growth cycles with heterogeneous agents

We investigate the effects of collateral and monetary policy on economic growth within a Ramsey equilibrium model where agents have different discount factors. Introducing liquidity constraints in segmented markets where (poor) impatient agents without collateral have limited access to credit, we study their implications in terms of welfare and business cycles (based on deterministic cycles through bifurcations and self-fulfilling prophecies). We find that an accommodative monetary policy may be growth-enhancing and welfare-improving (through the inequality reduction) while making unpleasant fluctuations more likely. Conversely, a regulation reinforcing the role of collateral and tempering the financial market imperfections may stimulate the economic growth while pursuing the goal of stabilization.     

On linking microsimulation and computable general equilibrium models using exact aggregation of heterogeneous discrete-choice making agents

Our paper contributes by bridging the gap between the (partial equilibrium) microsimulation and the computable general equilibrium (CGE) approaches, by making use of exact aggregation results from the discrete choice literature: heterogeneous individuals choosing within a set of discrete alternatives may be aggregated into a representative agent with (possibly multiple-level) constant elasticity-of-substitution/transformation preferences/technologies. These results therefore provide a natural link between the two policy evaluation approaches. We illustrate the usefulness of these results by evaluating potential effects of population ageing on the dynamics of income distribution and inequalities, using a simple overlapping generations model where individuals make leisure/work decisions, and choose a profession among a discrete set of alternatives.     

Monetary policy with heterogeneous agents and borrowing constraints

We show that the long-run neutrality of inflation on capital accumulation obtained in complete market models no longer holds when households face binding credit constraints. Borrowing-constrained households are not able to rebalance their financial portfolio when inflation varies, and thus adjust their money holdings differently compared to unconstrained households. This heterogeneity leads to a new precautionary savings motive, which implies that inflation increases capital accumulation. We quantify the importance of this new channel in an incomplete market model where the traditional redistributive effects of inflation are also introduced. We show that this model provides a quantitative rationale for the observed hump-shaped relationship between inflation and capital accumulation.     

A dynamic exchange rate model with heterogeneous agents

In this paper, we analyze a heterogeneous agent model in which the fundamental exchange rate is endogenously determined by the real markets. The exchange rate market and the real markets are linked through the balance of payments. We have analytically found that there exists at least a steady state in which the exchange rate is equal to its fundamental value and incomes of both countries are equal to the autonomous components times the multiplier (as in the Income-Expenditure model). This steady state can be unique and unstable when all agents act as contrarians, while when agents act as fundamentalists it is unique but its stability depends on the reactivity of actors of the market. Finally, we show that the (in)stability of the economic system depends on both the reactivity of the markets and that of different types of agents involved. Employing well-know functional forms, we show that the model can replicate some of the statistical features of the true time series of the exchange rate.     

Precautionary savings of agents with heterogeneous risk aversion

This article focuses on the estimation of the importance of the precautionary motive in the wealth accumulation decision. We use the micro data set of the De Nederlandsche Bank (DNB) Household Survey (DHS) (CentERdata, Tilburg University), a Dutch household survey containing information on wealth, a subjective measure of income uncertainty and subjective qualitative measures of risk aversion. We find that only a small share of wealth is accumulated for the precautionary motive by the Dutch households. This share of wealth is constant across assets with different degrees of liquidity. The economic downturn of the period 2008 to 2010 seems to affect risk attitudes and precautionary saving. Our findings also suggest that the more risk-averse individuals are those who hold less savings.     

Inequality and debt in a model with heterogeneous agents

We show that to account for the cross-sectional divergence in debt-to-income ratios in US data a DSGE model must assume a tax reallocation across the top- and bottom-income quantile of the population, rather than differential productivity growth, and low cost of access to financial intermediation.     

Time-consistent fiscal policy and heterogeneous agents

This paper characterizes the time-consistency properties of the set of Pareto efficient (or second best) fiscal policies, in a two-class, stochastic economy similar to that in [Judd, K.L., 1985, Redistributive taxation in a simple perfect foresight model, Journal of Public Economics 28, 59–83]. The key finding is that the continuation of any Pareto efficient policy is always Pareto efficient. Hence, to require any policy revision to be approved by unanimity safeguards the time consistency of efficient fiscal policy. I also show that any Pareto efficient policy from a timeless perspective can be rendered time consistent by a policymaker whose objective function is given by a utilitarian social welfare function with precise welfare weights. These results link the policymaker's equity considerations with the credibility of efficient fiscal policy.     

A general equilibrium model of heterogeneous local property taxes

A formal model of an economy consisting of many production centres, each of which levies property taxes at a different rate, is developed and analyzed. In the context of the model, it is shown that holders of capital may have either a positive or negative willingness to pay for a heterogenous system of taxes relative to a uniform tax which raises the same revenue. Particular emphasis is placed on interpretation of the ‘new view’ of the property tax in light of this and other results which derive from the model.     

Market stability switches in a continuous-time financial market with heterogeneous beliefs

By considering a financial market of fundamentalists and trend followers in which the price trend of trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examine the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. These interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, sufficient conditions on the stability and global existence of the periodic solution are obtained.     

Foreign direct investment subsidy in a dynamic stochastic general equilibrium model with heterogeneous firms

This study analyzes the macroeconomic impacts of subsidies to attract multinational corporations when firms are determining whether to enter or how to serve foreign markets. We show that a small FDI subsidy scheme induces consumption gains and delivers short‐term welfare improvement for the FDI host country if firms differ in productivity. However, the subsidy generates a new problem and results in the wealth reallocation effect, leading to welfare deterioration for the host country in the long run. Moreover, we find that a subsidy program induces a welfare improvement for the host country if it is offered to all domestic producers instead of foreign producers only in the host country.     

A simple search model of money with heterogeneous agents and partial acceptability

Summary. Simple search models have equilibria where some agents accept money and others do not. We argue such equilibria should not be taken seriously. This is unfortunate if one wants a model with partial acceptability. We introduce heterogeneous agents and show partial acceptability arises naturally and robustly. There can be multiple equilibria with different degrees of acceptability. Given the type of heterogeneity we allow, the model is simple: equilibria reduce to fixed points in [0,1]. We show that with other forms of heterogeneity equilibria are fixed points in set space, and there is no method to reduce this to a problem in R¹.Received: 4 September 2002, Revised: 23 September 2002JEL Classification Numbers: C78, E40.A. Shevchenko, R. Wright: We thank seminar participants at the Federal Reserve Bank of Cleveland, Indiana University, Purdue University, University of Toronto, the 2002 Midwest Macroeconomics Conference at Vanderbilt University, and the 2001 Conference on Economic Dynamics at the University of Essex. The National Science Foundation and the Federal Reserve Bank of Cleveland provided financial support. Braz Ministerio de Camargo and Gabriel Camera provided some helpful suggestions. Correspondence to: R. Wright     

Market structure and competitive equilibrium in dynamic economic models

Recently theorists have analyzed economies which potentially contain both finite and infinite horizon overlapping generations, using “Arrow-Debreu” (complete) markets. Typically, applied models assume recursive spot and contingent securities markets, implying a different equilibrium concept. Indeed, if infinite horizon agents are present recursive equilibria cannot exist without some side conditions on debt. With the right side conditions, we show that every recursive market equilibrium allocation is a complete market equilibrium allocation and vice versa. This bridges a gap between theory and applications, and extends existing equivalence results on market structure.