Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case

Summary. Suppose a large economy with individual risk is modeled by a continuum of pairwise exchangeable random variables (i.i.d., in particular). Then the relevant stochastic process is jointly measurable only in degenerate cases. Yet in Monte Carlo simulation, the average of a large finite draw of the random variables converges almost surely. Several necessary and sufficient conditions for such “Monte Carlo convergence” are given. Also, conditioned on the associated Monte Carlo -algebra, which represents macroeconomic risk, individual agents' random shocks are independent. Furthermore, a converse to one version of the classical law of large numbers is proved. Received: October 29, 2001; revised version: April 24, 2002 RID="*" ID="*" Part of this work was done when Yeneng Sun was visiting SITE at Stanford University in July 2001. An early version of some results was included in a presentation to Tom Sargent's macro workshop at Stanford. We are grateful to him and Felix Kübler in particular for their comments. And also to Marcos Lisboa for several discussions with Peter Hammond, during which the basic idea of the paper began to take shape. Correspondence to: P.J. Hammond     

Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium

In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist. This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.     

Evolutionary choice of markets

We consider an economy where a finite set of agents can trade on one of two asset markets. Due to endogenous participation the markets may differ in the liquidity they provide. Traders have idiosyncratic preferences for the markets, e.g.due to differential time preferences for maturity dates of futures contracts. For a broad range of parameters we find that no trade, trade on both markets (individualization) as well as trade on one market only (standardization) is supported by a Nash equilibrium. By contrast, whenever the number of traders becomes large, the evolutionary process selects a unique stochastically stable state which corresponds to the equilibrium with two active markets and coincides with the welfare maximizing market structure. We are grateful to Thorsten Hens, Fernando Vega-Redondo and a referee for valuable comments. We also thank seminar participants at the University of Zurich, the CES research seminar at the University of Munich, the Koc University in Istanbul as well as conference participants at the SAET conference in Ischia, the ESEM in Lausanne and the ESF workshop on Behavioural Models in Economics and Finance in Vienna. A first version of the paper was written while Marc Oliver Bettzüge was visiting the Institute for Empirical Research in Economics at the University of Zurich. Financial Support by the Swiss Banking Institute and by the National Centre of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK) is gratefully acknowledged. The NCCR FINRISK is a research program supported by the Swiss National Science Foundation.     

Dynamic and stochastic structures in tourism demand modeling

In this paper we consider a model for international tourism demand. The point of departure of the analysis is a utility function that is both dynamic and stochastic. In the model the stochastic component is interpreted as random changes in preferences for goods and services, while the dynamic component can be seen as either habit formation or as interdependent preferences. The resulting demand functions are estimated as a multivariate state space model, where the stochastic components enter the model as stochastic seasonal and trend components. An application is constructed for different segments of the Swedish tourism market. The results indicate the importance of including both dynamic and stochastic components in the utility function, and the importance of using disaggregate data to enable investigation of each market segment.I am grateful to two anonymous referees for useful comments. Much of the research was done while I was a visiting scholar at University of California Berkeley. The hospitality of the RIPM division is gratefully acknowledged. The research was supported by grants from the Wallander Foundation.First version received: January 2003/Final version received: February 2004     

State-owned enterprises as indirect instruments of entry regulation

In the context of mixed markets, Matsumura and Kanda (J Econ 84(1): 27–48, 2005) show that social welfare in free entry equilibrium is maximized when there exists a public firm in the market. En passant, these authors state that this outcome is connected to the entry-deterring influence of a public firm. In this way, they counter-act the excess entry problem of Mankiw and Whinston (Rand J Econ 17(1): 48–58, 1986). We explain this result arguing that the state-owned firm can be an indirect instrument to regulate entry. In fact, under free entry equilibrium welfare may be greater with the presence of a public firm than with a social planner.      

New evidence on the convergence of international income from a group of 29 countries

This paper updates and extends the time-series evidence on the convergence of international incomes using a set of 29 countries over the period 1900–2001. Time-series tests for stochastic convergence are supplemented with tests which provide evidence on the notion of “β-convergence” predicted by the Solow model. The evidence indicates that the relative income series of 21 countries are consistent with stochastic convergence, and that β-convergence has occurred in at least 16 countries at some point during the twentieth century. Further examination of the properties of the β-convergence test provides anecdotal evidence of conditional convergence in three additional countries for which the convergence hypothesis was initially rejected. Consideration of convergence clubs strengthens the evidence in favor of convergence. Analysis of the cross-country dispersion of incomes over time also suggests that convergence has occurred over the 1900–2001 period, particularly within certain clubs, with structural breaks associated with World War II in many countries causing a break in the convergence process.      

The dynamics of wealth distribution with asymmetric incentives and endogenous matching

In a dynastic economy with warm-glow bequest individuals can form firms in a frictionless matching market. Contracts within firms are subject to moral hazard. Production tasks differ in incentive intensity and the matching market is open until production takes place. The credit market is perfect. In a principal–agent context, we examine the long-run effects on the wealth distribution, and show the presence of hysteresis and poverty traps. The first draft of the paper was written in the Fall 2002 while I was visiting GSIA at Carnegie Mellon University. Subsequent developments were reached while I visited Columbia Business School in the Fall 2004. I want to thank Oded Galor, and especially Archishman Chakraborty for many valuable discussions.     

Mechanism Design with Interdependent Valuations: Surplus Extraction

If valuations are interdependent and agents observe their own allocation payoffs, then two-stage revelation mechanisms expand the set of implementable decision functions. In a two-stage revelation mechanism agents report twice. In the first stage - before the allocation is decided - they report their private signals. In the second stage - after the allocation has been made, but before final transfers are decided - they report their payoffs from the allocation. Conditions are provided under which an uninformed seller can extract (or virtually extract) the full surplus from a sale to privately informed buyers, in spite of the buyers’ signals being independent random variables. This research was started when I was visiting the Department of Applied Mathematics of the University of Venice, and continued while visiting the European University Institute in Florence. Their financial support is gratefully acknowledged.     

Moments of truncated <Emphasis Type="Italic">t</Emphasis> and <Emphasis Type="Italic">F</Emphasis> distributions

Truncated distributions commonly arise in economics and related areas, see, for example, Lee (Econ Lett 3:165–169, 1979), Lien (Econ Lett 19:243–247, 1985; Econ Lett 20:45–47, 1986), Burdett (Econ Lett 52:263–267, 1996), Sercu (Insur: Math and Econ 20:79–95, 1997), Abadir and Magdalinos (Econom Theory 18:1276–1287, 2002), and Horrace (J Econom 126:335–354, 2005). In this note, we consider the most commonly encountered truncated distributions with heavy tails: the truncated t distribution and the truncated F distribution. For each of these distributions, we derive explicit expressions for the moments and estimation procedures by the method of moments and the method of maximum likelihood. An application is illustrated to a popular data set in the econometric literature.      

Theory and practice of monetary policy

Summary. We consider an optimally managed renewable resource with stochastic non-concave growth function. We characterize the conditions under which the optimal policy leads to global extinction, global conservation and the existence of a safe standard of conservation. Our conditions are specified in terms of the economic and ecological primitives of the model: the biological growth function, the welfare function, the distribution of shocks and the discount rate. Our results indicate that, unlike deterministic models, extinction and conservation in stochastic models are not determined by a simple comparison of the growth rate and the discount rate; the welfare function plays an important role.Received: 20 October 2004, Revised: 28 February 2005, JEL Classification Numbers: D90, O11, O41, Q32.Santanu Roy: Correspondence toResearch on this paper was completed when the second author visited Cornell University in July, 2003. We thank the Center for Analytic Economics and the Department of Economics at Cornell University for making this research visit possible. The current version has gained considerably from the comments made by an anonymous referee.     

Continuity properties of the private core

Let be a sequence of differential information economies, converging to a limit differential information economy (written as ). Denote by the set of all ε-private core allocations, ε ≥ 0 (for ε=0 we get the private core of Yannelis (1991), denoted by ). Under appropriate conditions, we prove the following stability results

North–South Trade and Pollution Migration: The Debate Revisited

The paper examines the effect of freer North–South trade in goods on pollution, commodity terms-of-trade and national welfare, utilizing a factor endowment framework. North and South are distinguished in terms of the relative endowment of a pollution causing natural resource: South is relatively more resource abundant. Compared to the analysis of Copeland and Taylor (1994)—which is the central work so far on this subject—this paper internalizes the commodity terms-of-trade impact of individual environment policies. It is derived that if countries specialize completely in the free-trade equilibrium, both are induced to reduce their pollution as compared to autarky. It is interesting and paradoxical that the South also reduces its pollution, despite specializing in the pollution-intensive good. Again, contrary to common perception, free trade may entail an overall terms-of-trade loss for the North, while South will always have a positive change in the terms-of-trade. Finally, inspite of better environment, free trade may cause both the countries to gain or lose in terms of aggregate welfare. This research has benefitted from comments received at the conference on International Dimension of Environment Policy organized by the European Science Foundation and Tilburg University, October 7–12, 2000 Kerkrade, The Netherlands and the International Conference on Environment and Development organized by CITD, School of International Studies, JNU, April 7–8, 2005, New Delhi, India, as well as those received from two anonymous referees. A small section of this research was published in Mehra and Das (2002).     

Arrow's theorem on the optimality of deductibles: A stochastic dominance approach

Summary We provide a new proof for the optimality of deductible insurance that does not depend on the expected-utility hypothesis. Our model uses only first- and second-degree stochastic dominance arguments.This paper was partially written while Schlesinger was visiting at the University of Toulouse. Financial support for this visit from the Fédération Francaise des Société d' Assurance is gratefully acknowledged. The authors also thank Louis Eeckhoudt, Ed Schlee and an anonymous referee for helpful comments.     

Endogenous fluctuations in the demand for education

Abstract. Enrollment rates to higher education reveal a quite large variation over time which cannot be explained by productivity shocks alone. We develop a human capital investment model in an overlapping generations framework that features endogenous fluctuations in the demand for education. Agents are heterogeneous in their beliefs about future wage differentials. An evolutionary competition between the heterogeneous beliefs determines the fraction of the newborn generation having a certain belief. Costly access to information on the returns to education induces agents to use potentially destabilizing backward looking prediction rules. Only if previous generations experience regret about their human capital investment decisions, will agents choose a more sophisticated prediction rule that dampens the cycle. Access to information becomes key for stable flows to higher education. RID="*" ID="*"We would like to thank Cars Hommes, Florian Wagener, seminar participants at the University of Amsterdam, participants of the workshop on ‘Skill Needs and Labor Market Dynamics’ at the Wissenschaftszentrum Berlin für Sozialforschung (WZB) for helpful discussions, and an editor of this Journal and three anonymous referees for their comments. Tuinstra's research is supported by the Netherlands Organisation for Scientific Research (NWO) under a MaG-Pionier grant. Neugart acknowledges financial support from the German Ministry of Education. Parts of the research were done while Tuinstra was visiting the WZB and when Neugart was visiting CeNDEF. Correspondence to: The research for this paper was done while the first author was affiliated with the Wissenschaftszentrum Berlin für Sozialforschung.     

Uniqueness of asset prices in an exchange economy with unbounded utility

Summary. This paper studies conditions under which the price of an asset is uniquely determined by its fundamental value – i.e., no bubbles can arise – in Lucas-type asset pricing models with unbounded utility. After discussing Gilles and LeRoy's (1992) example, we construct an example of a two-period, representative agent economy to demonstrate that bubbles can arise in a standard model if utility is unbounded below, in which case the stochastic Euler equation may be violated. In an infinite horizon framework, we show that bubbles cannot arise if the optimal sequence of asset holdings can be lowered uniformly without incurring an infinite utility loss. Using this result, we develop conditions for the nonexistence of bubbles. The conditions depend exclusively on the asymptotic behavior of marginal utility at zero and infinity. They are satisfied by many unbounded utility functions, including the entire CRRA (constant relative risk aversion) class. The Appendix provides a complete market version of our two-period example. Received: January 22, 1996; revised version: February 18, 1997     

Estimating the natural rates in a simple New Keynesian framework

The time-varying natural rate of interest and output and the implied medium-term inflation target for the US economy are estimated over the period 1983–2005. The estimation is conducted within the New Keynesian framework using Bayesian and Kalman-filter estimation techniques. With the model-consistent estimate of the output gap, we get a small weight on the backward-looking component of the New Keynesian Phillips curve—similar to what is obtained in studies which use labor share of income as a driver for inflation (e.g., Galí, Eur Econ Rev 45(7):1237–1270, 2001; Eur Econ Rev 47(4):759–760, 2003). The turning points of the business cycle are nevertheless broadly consistent with those of CBO/NBER. We find considerable variation in the natural rate of interest while the inflation target has been close to 2% over the last decade.     

Corrigendum to “On randomized matching mechanisms” [Economic Theory 8(1996)377–381]

Ma (in Econ. Theory 8, 377–381, 1996) studied the random order mechanism, a matching mechanism suggested by Roth and Vande Vate (Econometrica 58, 1475–1480, 1990) for marriage markets. By means of an example he showed that the random order mechanism does not always reach all stable matchings. Although Ma's (1996) result is true, we show that the probability distribution he presented – and therefore the proof of his Claim 2 – is not correct. The mistake in the calculations by Ma (1996) is due to the fact that even though the example looks very symmetric, some of the calculations are not as “symmetric.” We thank two anonymous referees for their helpful comments. B. Klaus’s and F. Klijn’s research was supported by Ramón y Cajal contracts of the Spanish Ministerio de Ciencia y Tecnología. The work of the authors was also partially supported through the Spanish Plan Nacional I+D+I (BEC2002-02130 and SEJ2005-01690) and the Generalitat de Catalunya (SGR2005-00626 and the Barcelona Economics Program of CREA).     

Production, interest, and saving in deterministic economies with additive endowments

Stationary equilibria are constructed for a series of nonstochastic production economies in which the decisions of producers, wage earners, shareholders, and savers modulate, via a “production function”, the endowment variables in an additive manner. The efficiency of each model is compared to that of a single agent who produces for personal consumption.Most of this work was carried out during the spring of 2004, while Sudderth was visiting the Cowles Foundation at Yale University. The work of Karatzas was supported by the National Science Foundation under grant NSF-DMS-06-01774, and by the Institute for Mathematics and Its Applications (IMA) which made possible a visit to the University of Minnesota during a week in May 2004. The support of these foundations is gratefully acknowledged.     

Quasi-fundamental exchange rate variation

Summary. This paper uses a general equilibrium model to study the determination of the exchange rate in an economy with fundamental uncertainty. The model has steady state equilibria in which the exchange rate is constant. These equilibria may coexist with “quasi-fundamental” equilibria – nonstationary equilibria in which the exchange rate displays stochastic fluctuations that are correlated with the fluctuations in fundamental random variables. The quasi-fundamental equilibria are Pareto dominated by the corresponding constant-exchange-rate steady states. They also converge to these steady states, inevitably or with positive probability. Received: October 2, 1999; revised version: March 26, 2002 RID="*" ID="*" This paper began as a joint project with Alex Mourmouras, who has made many helpful comments and suggestions but is not responsible for any errors or deficiencies. In addition, I thank an anonymous referee for helpful comments.     

Market power, survival and accuracy of predictions in financial markets

In a standard General Equilibrium framework, we consider an agent strategically using her large volume of trade to influence asset prices to increase her consumption. We show that, as in Sandroni (Econometrica 68:1303–1341, 2000) for the competitive case, if markets are dynamically complete and some general conditions on market preferences are met then this agent’ long-run consumption will vanish if she makes less accurate predictions than the market, and will maintain her market power otherwise. We thus argue that the Market Selection Hypothesis extends to this situation of market power, in contrast to Alchian (J Pol Econ 58:211–221, 1950) and Friedman (Essays in Positive Economics, University of Chicago Press, Chicago, 1953) who claimed that this selection was solely driven by the competitiveness of markets. I would like to thank T. Hens, A. Kirman and A. Sandroni for many stimulating conversations and encouragements. Two anonymous referees also provided very valuable comments.