The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

Note on the non-existence of sunspot equilibrium

In this note, we emphasize the role of consumers’ risk aversion in the non-existence of sunspot equilibria in incomplete market economies. We prove that there are no sunspot equilibria if the fundamentals of the underlying economy admit a unique equilibrium for any distribution of endowments. This substantiates Mas-Colell’s (Economic analysis of markets and games: essays in honor of Frank Hahn. MIT, Cambridge, 1992) conjecture. We also prove that, in a two-consumer economy, no sunspot equilibrium exists under the more relaxed condition that the underlying economy admits a unique equilibrium for the initial endowment. This is a generalization of Corollaries 1 and 2 of Hens and Pilgrim (Econ Theory 24:583–602, 2004).      

Harmonic sequence paradox

Summary. Informal evidence suggests that individuals are willing to pay only a finite and, typically, very low price for a specific lottery that converges to an infinite payment with probability one. The established decision theories (expected value, expected utility theory, cumulative prospect theory) cannot satisfactorily explain this low willingness to pay. The presented paradox strengthens the original and the super St. Petersburg paradox.Received: 27 Spetember 2004, Revised: 15 January 2005, JEL Classification Numbers: C91, D81.I am grateful to Peter Wakker, whose suggestions helped to simplify significantly the exposition of the main idea, and to the participants of a brown-bag seminar at CERGE-EI (June 23, 2004, Prague), notably Dirk Engelmann and Andreas Ortmann, who suggested interesting testable explanations for the paradox.     

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.     

Manipulation of endowments and sunspot equilibria

We study the connection between occurrence of manipulation via reallocating endowments by coalitions and sunspot equilibria. The uncertainty about which coalition will form introduces extrinsic uncertainty into the economy. Under certain conditions, manipulation of endowments by coalitions can occur if and only if sunspots matter. We would like to thank Bill Ethier, Atsushi Kajii, Cuong Le Van, Karl Shell, Koji Shimomura, Nicholas Yannelis, an anonymous referee, as well as seminar participants at the Second Asian General Equilibrium Theory Workshop, 2005, Tokyo; Workshop on Uncertainty and Information, IMS, NUS, 2005; Kobe Institute of Economic Research; Public Economic Theory 2005 Conference, Marseille; and the South and South East Asia Econometric Society Meetings, 2006, Chennai for helpful discussions and comments.     

On the generic strategic stability of Nash equilibria if voting is costly

Summary. We prove that for generic plurality games with positive cost of voting, the number of Nash equilibria is finite. Furthermore all the equilibria are regular, hence stable sets as singletons.JEL Classification Numbers: C72, D72.We would like to thank Luisa Bassotto, Marco Celentani, Mamoru Kaneko, and participants at the 6 International Conference on Current Trends in Economics for helpful comments. We also thank an anonymous referee of this journal for precious advices that have substantially improved this paper. This paper was partially written while Francesco was visiting Tor Vergata University, which he thanks for hospitality and financial support. The usual disclaimer applies.     

Endogenous public policy and multiple equilibria

One of the well known roles of public policy in models with indeterminacy is to reduce the set of equilibria. However, agents' expectations regarding future policy may be self fulfilling when public policy is endogenized. We show that a simple overlapping generations economy with public education may yield multiple equilibria. Under a laissez-faire system, our model has a unique equilibrium. Thus, the presence of public policy may generate, rather than eliminate, multiple equilibria.     

The Simpson paradox of school grading in Italy

Data from the 2003 OECD-PISA Survey for Italy reveal a striking difference in the relationship between students’ competence (as measured by PISA score in Mathematics) and school grades across regions: a competence level granting bare sufficiency in the North yields excellence grades in the South. This has spurred a lively debate on education policy in the country, based on the inference drawn from this evidence that grading practices are excessively different in the two areas. We show in this note that this inference overlooks a Simpson paradox hidden in the data. After a more careful analysis, the above inference is seen to be wrong. The crucial omitted variable is the school-level average competence: schools with low-performing students, all over the country, inflate grades. Students in the South get higher grades simply because they are in weaker schools; grading policy is actually homogeneous across regions.     

Edgeworth and Walras equilibria of an arbitrage-free exchange economy

Summary. In this paper, we first give a direct proof of the existence of Edgeworth equilibria for exchange economies with consumption sets which are (possibly) unbounded below. The key assumption is that the individually rational utility set is compact. It is worth noticing that the statement of this result and its proof do not depend on the dimension or the particular structure of the commodity space. In a second part of the paper, we give conditions under which Edgeworth allocations can be decentralized by continuous prices in a finite dimensional and in an infinite dimensional setting. We then show how these results apply to some finance models.Received: 15 April 2002, Revised: 25 February 2003, JEL Classification Numbers: C62, D58, G12. Correspondence to: Monique FlorenzanoThis paper was presented at seminars of the Economic Departments of Brown University, The Johns Hopkins University, The University of Alabama, Purdue University and at the Centro de Modelamiento Matematico de la Universidad de Chile at Santiago. The paper has benefitted of the comments of these diverse audiences. Part of this work was done while the authors were visiting respectively Brown University and the Centro de Modelamiento Matematico. We thank them for their hospitality.     

Generic inefficiency of equilibria in the general equilibrium model with incomplete asset markets and infinite time

Summary. We consider a Lucas asset-pricing model with heterogeneous agents, exogenous labor income, and a finite number of exogenous shocks. Although agents are infinitely lived, endowments and dividends are time-invariant functions of the exogenous shock alone and are thus restricted to lie in a finite-dimensional space; genericity analysis can be conducted on sets of zero Lebesgue measure. When financial markets are incomplete, that is, there are fewer financial securities than shocks, we show that generically in individual endowments all competitive equilibria are Pareto inefficient. Received: November 22, 1999; revised version: March 4, 2002 RID="*" ID="*" We are grateful to an anonymous referee for very insightful comments on earlier drafts.     

Multiple equilibria and hysteresis in simple exchange models

This paper presents a simple two-good general equilibrium model of exchange in which demands are linear functions of relative prices. The solution of the model is represented by a cubic equation which can have either a single root which corresponds to a unique equilibrium price or three roots corresponding to multiple equilibria. The major properties of the model are that the relative price can make large discrete jumps in response to small parameter changes, and can display hysteresis. The paper shows how recent developments in non-linear methods can be used to examine the equilibrium properties of the model and establish conditions under which multiple equilibria can arise. The model is compared with that used by Shapley and Shubik.     

Mixed equilibria in games of strategic complementarities

Summary. The literature on games of strategic complementarities (GSC) has focused on pure strategies. I introduce mixed strategies and show that, when strategy spaces are one-dimensional, the complementarities framework extends to mixed strategies ordered by first-order stochastic dominance. In particular, the mixed extension of a GSC is a GSC, the full set of equilibria is a complete lattice and the extremal equilibria (smallest and largest) are in pure strategies. The framework does not extend when strategy spaces are multi-dimensional. I also update learning results for GSC using stochastic fictitious play. Received: October 16, 2000; revised version: March 7, 2002 RID="*" ID="*" I am very grateful to Robert Anderson, David Blackwell, Aaron Edlin, Peter De Marzo, Ted O'Donoghue, Matthew Rabin, Ilya Segal, Chris Shannon, Clara Wang and Federico Weinschelbaum for comments and advise.     

Sunspot cycles

Summary. This paper shows new properties about the equilibria of a stationary OG economy by establishing a connection between its stationary equilibria and those of a finite economy, with and without extrinsic uncertainty. Specifically, it shows the countability and local uniqueness with respect to the sup metric of the so-called sunspot cycles introduced here, that encompass both the deterministic cycles and the usual finite Markovian stationary sunspot equilibria. These sunspot cycles are, moreover, able to generate, at a lower cost in terms of assumptions than other sunspot equilibria, time series with the recurrent but irregular fluctuations typical of economic time series. Received: July 26, 2001; revised version: March 5, 2002 RID="*" ID="*" I want to thank an anonymous referee for comments that have helped greatly to improve this paper, as well as the comments about its contents received from several audiences in different seminars and conferences (the Economic Theory seminar of the University of Pennsylvania, the 2001 Meeting of the Econometric Society held at New Orleans, the 2000 Econometric Society World Congress, the 2000 Society for Economic Design Conference) and from comments to a previous paper, Dávila [10], specially from Jim Peck at the 1997 Workshop on General Equilibrium held at the University of Venice, that eventually lead to this one.     

The effects of risk preferences in mixed-strategy equilibria of games

We consider the effects of risk preferences in mixed-strategy equilibria of 2×2 games, provided such equilibria exist. We identify sufficient conditions under which the expected payoff in the mixed equilibrium increases or decreases with the degree of risk aversion. We find that (at least moderate degrees of) risk aversion will frequently be beneficial in mixed equilibria.     

The productivity paradox and the new economy: The Spanish case

This paper studies the impact of the information and communication technologies (ICT) on economic growth in Spain using a dynamic general equilibrium approach. Contrary to previous works, we use a production function with six different capital inputs, three of them corresponding to ICT assets. Calibration of the model suggests that the contribution of ICT to Spanish productivity growth is very relevant, whereas the contribution of non-ICT capital has been even negative. Additionally, over the sample period 1995–2002, we find a negative TFP growth and productivity growth. These results together aim at the hypothesis that the Spanish economy could be placed within the productivity paradox.     

Creditworthiness and thresholds in a credit market model with multiple equilibria

Summary. The paper studies creditworthiness in a model with endogenous credit cost and debt constraints. Such a model can give rise to multiple candidates for steady state equilibria. We use new analytical techniques such as dynamic programming (DP) with flexible grid size to find solutions and to locate thresholds that separate different domains of attraction. More specifically, we (1) compute present value borrowing constraints and thus creditworthiness, (2) locate thresholds where the dynamics separate to different domains of attraction, (3) show jumps in the decision variable, (4) distinguish between optimal and non-optimal steady states, (5) demonstrate how creditworthiness and thresholds change with change of the credit cost function of the debtor and (6) explore the impact of debt ceilings and consumption paths on creditworthiness.JEL Classification Numbers: C61, C63, D91, D92, E51, G12, G32.An earlier version of this paper has been prepared for the 1998 North American Winter Meeting of the Econometric Society, January 1998, Chicago. We want to thank Jess Benhabib, Buz Brock, Gustav Feichtinger, Franz Wirl, Michael Woodford, Wolf-Jürgen Beyn and Thorsten Pampel for helpful discussions and comments on various versions of the paper. We also want to thank participants in a workshop at the University of Technology, Vienna, the Macroeconomic Workshop at Columbia University, and the SCE conference, at Yale University, June 2001. We are also grateful for comments from a referee of the journal.     

Multiple equilibria, coordination, and transitional growth

We study a small open economy with two sectors and two factors of production. In one of the sectors, external economies of scale are generated through the industry-level capital input. This leads to a divergence between private and social production possibility frontiers as well as to multiple equilibria. The equilibrium selection problem that arises is solved by agents who follow a simple trial-and-error learning rule. The growth path of the economy as agents learn lies below the production possibility frontier and may display cyclical transitional dynamics. We also show that coordination problems which may prevent the economy from attaining the “good” equilibrium may be alleviated by the temporary use of policy instruments that shape the allocation of resources.     

Correlated equilibria in continuous games: Characterization and computation

We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of departure functions. We use these characterizations to construct effective algorithms for approximating a single correlated equilibrium or the entire set of correlated equilibria of a game with polynomial utility functions.