Asymmetric information and rationalizability

We study how asymmetric information affects the set of rationalizable solutions in a linear setup where the outcome is determined by forecasts about this same outcome. The unique rational expectations equilibrium is also the unique rationalizable solution when the sensitivity of the outcome to agents’ forecasts is less than one, provided that this sensitivity is common knowledge. Relaxing this common knowledge assumption, multiple rationalizable solutions arise when the proportion of agents who know the sensitivity is large, and the uninformed agents believe it is possible that the sensitivity is greater than one. Instability is equivalent to existence of some kind of sunspot equilibria.     

Sufficient conditions for the existence of sunspot equilibria

This paper reports on conditions on agents' preferences and endowments sufficient to guarantee the existence of sunspot equilibria in a simple overlapping generations model of pure exchange. Sunspot equilibria are those in which uncertainty extrinsic to the economy operates through expectations to yield a fulfilled expectations competitive equilibrium in which the extrinsic randomness has real effects on prices and allocations. The paper also provides necessary and sufficient conditions for these equilibria to have agents trading in a fixed stock of valued fiat money. The condition derived can be interpreted as requiring that intertemporal income effects appropriately dominate substitution effects.     

Rationalizability, Strong Rationality, and Expectational Stability

We examine the connection between two stability concepts of rational expectations equilibria: expectational stability, based on the convergence of iterations of expectations, and strong rationality, based on uniqueness of the rationalizable solutions of an associated game with restrictions on beliefs. To compare the concepts we embed a standard expectations model in a game-theoretic framework. It is shown that the two stability concepts coincide when agents are homogeneous. For the general case of heterogeneous agents we show that expectational stability is a necessary condition for strong rationality and we provide a sufficient condition for the latter. Journal of Economic Literature Classification Numbers: C72, C62.     

Are Rational Expectations Equilibria with Private Information Eductively Stable?

The paper derives conditions for eductive stability of rational expectations equilibria in simple linear economic models with private information. Following Guesnerie (1992; 2002), the concept of eductive stability is used. It is shown that even in a private information setting, rational expectations equilibria might be justified as a result of mental process of reasoning of the agents. The paper considers an equilibrium concept, where the agents are unable to condition their forecasts on the actual market price. It is shown that eductive stability in this case requires that a condition is satisfied that is also relevant in the symmetric information case. This condition is compared to the respective stability condition that must hold if agents are able to use the current market price as an additional source of information. It turns out that the conditions for eductive stability that emerge under both equilibrium concepts differ.revised version received September 11, 2003     

The Structure of Sunspot Equilibria: The Role of Multiplicity

This paper examines the structure of sunspot equilibria in a standard two period exchange economy with real assets. We show that for a generic choice of utility functions and endowments, there exists an open set of real asset structures whose payoffs are independent of sunspots such that the economy with this asset structure has a regular sunspot equilibrium. An important implication of our result is that the multiplicity of non-sunspot equilibria is not necessary for the existence of sunspot equilibria. Our technique is general and can be applied to show the existence of sunspot equilibria in other frameworks.     

On the structure of Ramsey equilibrium: Cycles,indeterminacy, and sunspots

Summary We consider a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous households. Under the standard assumptions of strictly concave and time-additive utility functionals and a strictly concave production function we show that perfect foresight equilibria can be non-unique, even locally non-unique (indeterminate), and periodic of arbitrary long periodp. Moreover, we prove that there can exist non-trivial rational expectations (sunspot) equilibria when the agent's expectations about future factor prices depend on extrinsic uncertainty.Remarks made by an anonymous referee were extremely helpful in preparing the final draft of this paper.     

The genesis of expectations and of sunspot equilibria

The existence—under certain conditions—of sunspot equilibria in overlapping generations models is a well-known theoretical result, but a lot of research has still to be made to understand whether and how such equilibria may occur as a consequence of a dynamic process. In this paper, we explore a model with individuals having simple utility functions and discover situations in which the dynamic processes of expectations and observed prices do not converge in spite of the existence of static equilibria. In other words, unfounded beliefs do still have a permanent influence on the real economy but induce erratic evolutions.     

Trend inflation and macroeconomic stability in a small open economy

This paper estimates a small open economy New Keynesian model for Australia with positive trend inflation while allowing for multiple equilibria. We first show the extent to which positive trend inflation can shrink the determinacy region. We then conduct a Bayesian estimation over two separate periods: from 1983Q1 to 1993Q1, covering the pre-inflation-targeting regime, and from 1993Q2 to 2018Q4, covering the inflation-targeting regime. We find that Australian monetary policy before the adoption of inflation-targeting permitted multiple equilibria and self-fulfilling inflation expectations to arise, resulting in exacerbated macroeconomic volatility. The implementation of inflation-targeting in Australia in the early 1990s successfully eradicated equilibrium multiplicity and sunspot shocks, and thereby drove the economy towards greater stability.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems

This paper analyses the sustainability of inter-generational transfers in Samuelson's consumption-loan model when agents are imperfectly informed about past events. We find that with mild informational constraints, transfers cannot be supported by pure-strategy equilibria. Mixed strategies allow transfers to be sustained even if agents have little information, so that a version of the Folk theorem holds. However, these equilibria are not robust. If each agent's utility function is subjected to a small random perturbation as in Harsanyi (1973), these mixed strategy equilibria unravel, and only the zero-transfer allocation survives as the unique rationalizable outcome. This result is an example of mixed strategy equilibrium of an extensive form game which cannot be purified.     

History and Coordination Failure

An extensive literature discusses the existence of a virtuous circle of expectations that might lead communities to Pareto-superior states among multiple potential equilibria. It is generally accepted that such multiplicity stems fundamentally from the presence of positive agglomeration externalities. We examine a two-sector model in this class and look for intertemporal perfect foresight equilibria. It turns out that under some plausible conditions, positive externalities must coexist with external diseconomies elsewhere in the model, for there to exist equilibria that break free of historical initial conditions. Our main distinguishing assumption is that the positive agglomeration externalities appear with a time lag (that can be made vanishingly small). Then, in the absence of external diseconomies elsewhere, the long-run behaviour of the economy resembles that predicted by myopic adjustment. This finding is independent of the degree of forward-looking behavior exhibited by the agents.     

Economic planning for market economies : The optimality of planning in an economy with uncertainty and asymmetrical information

The paper is based on a disequilibrium model which is Keynesian in the ‘short run’, ie with given expectations, but which admits of a continuum of equilibria when expectations are rational. Expectations are adaptive (so that they are rational only in the long run) but can be influenced by an indicative plan. The government and the private sector have differing information sets, each knowing some things the other sector does not (spontaneously) know. It is shown that in this world, an optimal plan dominates a self-fulfilling plan, which in turn dominates a no-planning equilibrium.     

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.     

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).      

Local Sunspot Equilibria Reconsidered

We generalize the usual notion of local sunspot equilibria. We say such equilibria exist around a steady state of an OLG economy whenever stationary sunspot equilibria of arbitrarily close economies exist within any neighborhood of the steady state. Unlike the usual notion, this generalization allows to address the following identification problem: Can an analyst distinguish empirically small fluctuations due to small shocks to the fundamentals from pure expectations-driven fluctuations? We study conditions under which these generalized local sunspot equilibria exist in OLG economies, and show that they may exist around not only indeterminate but also determinate steady states.     

A note on conspicuous leisure,animal spirits and endogenous cycles

This paper investigates general equilibrium effects of conspicuous leisure. It finds that leisure externalities reduce the degree of other market imperfections needed to generate indeterminacy or sunspot equilibria - endogneous cycles become empirically more plausible. Sunspot equilibria are possible with a downward-sloping labor demand schedule. The economic reasoning behind the result is that with conspicuous-externalities, labor is drawn more easily in and out of leisure to help fulfill agents expectations.Received: June 2003, Accepted: January 2004, JEL Classification: E32Mark Weder: I thank Paulo Brito (the Editor), Michael Burda and an anonymous referee for very helpful comments and suggestions. All remaining errors are my own. Support by the Deutsche Forschungsgemeinschaft in the form of a Heisenberg Fellowshipis gratefully acknowledged.     

Robust equilibria under non-common priors

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogeneous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.     

Incomplete markets and individual risks

Summary This paper studies the incomplete markets model with financial assets when the only missing markets are for individual risks. There are no aggregate risks in the economy. Assuming the individual risks are only privately observable, the only equilibria that are implementable by anonymous mechanisms are those in which prices do not vary across states of the world. Such equilibria always exist. Generically, they are locally unique and depend continuously on the parameters of the economy, just like complete-markets equilibria. Generically, there is also an infinite-dimensional manifold of equilibria in which prices do vary across states of the world. These equilibria are isomorphic to sunspot equilibria.I am grateful to Dave Cass for several helpful discussions and to Darrell Duffie for his comments on an earlier draft.     

The information content of market-based measures for the long-term inflation expectations of professionals: evidence from a midas analysis

Long-term inflation expectations taken from the Survey of Professional Forecasters are a major source of information for monetary policy. Unfortunately, they are published only on a quarterly basis. This article investigates the daily information content of market-based measures, such as inflation-linked swaps and breakeven inflation rates, for the next survey outcome. Using a mixed data sampling approach, we find that professionals account for the daily dynamics of market-based measures when they submit their long-term inflation expectations. We propose a daily indicator of professionals’ inflation expectations that outperforms alternative indicators that ignore the high-frequency dynamics of market-based measures. To illustrate the usefulness of the new indicator, we provide new evidence on the (re-)anchoring of U.S. inflation expectations.     

Correlated equilibrium and sunspot equilibrium

Summary We show by an example that the sunspot equilibria of a competitive economy are not equivalent to the correlated equilibria if sunspots generate transfers between (extrinsic) states of nature (through a contingent commodities market). Nevertheless, we prove that the sunspot equilibrium allocations of a standard overlapping generations economy coincide with the (strategic form) correlated equilibrium allocations of a natural market game mimicking the economy.