Injecting rational bubbles

This paper proves two theorems about economies with a finite number of infinitely lived agents who trade a complete set of one-period Arrow securities and several infinitely lived securities at each date, subject to short-sales constraints. The first theorem in the paper considers an equilibrium to an economy of this kind. It proves that there exists another economy with perturbed short-sales constraints in which there is an allocation-equivalent equilibrium in which asset prices have a bubble. The second theorem extends to the result to the case in short-sales constraints are endogenously determined in the sense of Alvarez and Jermann [Efficiency, equilibrium, and asset pricing with risk of default, Econometrica 68 (2000) 775-797].     

Devaluation,long-term contracts and rational expectations

This paper considers the effects of devaluation and expected devaluation on output, prices and foreign exchange reserves in a small open economy with overlapping two period wage contracts and rational expectations. A devaluation has an expansionary effect on output provided it is unanticipated by at least some contracts when it occurs. Expected devaluations, however, have no effect on prices until they take place. If a devaluation is expected, but fails to take place, output is reduced. Reserves increase in response to all devaluations; but the expectation of a devaluation causes a loss of reserves prior to its expected date.     

Confident expectations, rational expectations and the optimal conduct of monetary policy

Under what conditions central banks can afford to deviate from announced targets without losing their reputation is analyzed. For this, the public must have something like ‘confident expectations' vis-a-vis monetary policy and central banks have to behave accordingly. The paper shows that it can be rational for the public and welfare-increasing for the society to retain ‘confident expectations' instead of switching to rational expectations, when central banks have gained long-run reputation. At the end of the paper, alternative optimal money supply rules are compared in a dynamic optimization framework. © 1998 Elsevier Science B.V. All rights reserved.     

Speculative trading with rational beliefs and endogenous uncertainty

Summary. This paper introduces the framework of rational beliefs of Kurz (1994), which makes the assumptions of heterogeneous beliefs of Harrison and Kreps (1978) and Morris (1996) more plausible. Agents hold diverse beliefs that are “rational” in the sense of being compatible with ample observed data. In a non-stationary environment the agents only learn about the stationary measure of observed data, but their beliefs can remain non-stationary and diverse. Speculative trading then stems from disagreements among traders. In a Markovian framework of dividends and beliefs, we obtain analytical results to show how the speculative premium depends on the extent of heterogeneity of beliefs. In addition, we demonstrate that there exists a unique Rational Belief Equilibrium (RBE) generically with endogenous uncertainty (as defined by Kurz and Wu, 1996) and that the RBE price is higher than the rational expectation equilibrium price (REE) under some general conditions Received: March 15, 2001; revised version: April 26, 2002 RID="*" ID="*" We are deeply grateful to Mordecai Kurz for his constant encouragement and inspiring guidance over the years. We wish to express our gratitude to an anonymous referee for the very valuable comments provided. We also thank Kenneth Arrow, Peter Hammond, Roko Aliprantis and Nicholas Yannelis for their helpful suggestions and Academia Sinica and the National Science Council of the R.O.C. for their indispensable support. Correspondence to: H.-M. Wu     

Asset price bubbles and crashes with near-zero-intelligence traders

Summary. We examine whether a simple agent-based model can generate asset price bubbles and crashes of the type observed in a series of laboratory asset market experiments beginning with the work of Smith, Suchanek and Williams (1988). We follow the methodology of Gode and Sunder (1993, 1997) and examine the outcomes that obtain when populations of zero-intelligence (ZI) budget constrained, artificial agents are placed in the various laboratory market environments that have given rise to price bubbles. We have to put more structure on the behavior of the ZI-agents in order to address features of the laboratory asset bubble environment. We show that our model of near-zero-intelligence traders, operating in the same double auction environments used in several different laboratory studies, generates asset price bubbles and crashes comparable to those observed in laboratory experiments and can also match other, more subtle features of the experimental data.Received: 15 July 2003, Revised: 28 September 2004, JEL Classification Numbers: D83, D84, G12. Correspondence to: John DuffyWe would like to thank an Anonymous referee, Guillaume Frechette, David Laibson, Al Roth and participants in Harvard Experimental and Behavioral Economics Workshop for their comments, and Charles Noussair for providing his data set.     

Interest-rate policy and rational expectations

The choice of monetary instrument under rational expectations is discussed in a general equilibrium model for the financial sector. It is shown that a supply rule leads to indeterminate asset prices, whereas the prices are determinate under an appropriately formulated interest-rate policy.     

Speculative bubbles,financial crises and convergence in global real estate investment trusts

We test for price bubbles in 14 national real estate investment trust (REIT) markets, and measure the degree of their convergence towards a common trend. Our methodology consists of the recently developed test of Phillips, Shi and Yu (2014) for mildly explosive processes, and the Phillips and Sul (2007) method for modelling convergence among random variables. We find evidence of explosive behaviour in index levels of seven of the 14 markets. In contrast, explosive dynamics are found in only one price/dividend ratio. More than half of the episodes of explosive behaviour are date-stamped to periods prior to the 2007–2009 financial crisis. We also discover a number of periods over which the markets converge towards a common trend. Interestingly, all of the convergence intervals coincide either with periods of crisis, or with periods of market exuberance. For instance, evidence of convergence is found during the 2000 dot-com crash, the 2007–2009 subprime crisis and the 2010–2013 European sovereign debt crisis, as well as over the bubble period of 2004–2005.     

Learning,estimation, and the stability of rational expectations

The stability of the rational expectations equilibrium of a simple asset market model is studied in a situation where a group of traders learn about the relationship between the price and return on the asset using ordinary least squares estimation, and then use their estimates in predicting the return from the price. The model which they estimate is a well-specified model of the rational expectations equilibrium, but a misspecified model of the situation in which the traders are learning. It is shown that for appropriate values of a stability parameter the situation converges almost surely to the rational expectations equilibrium.     

Taxation,rational expectations,and the neutrality of money

When progressive taxation of nominal income is introduced into a Barro-type monetary model with rational expectations, money may not be neutral even in the long run. In the short run, unanticipated money changes may cause output and prices to move either in the same or in opposite directions. The implications of this model are consistent with both the traditional inflation-output trade-off and the more recent phenomenon of “stagflation.”     

On non-revealing rational expectations equilibrium

It is shown that a non-revealing rational expectations equilibrium may not be coalitionally Bayesian incentive compatible, may not be implementable as a perfect Bayesian equilibrium and may not belong to the weak fine core and thus may not be fully Pareto optimal. These negative results lead us to conclude the non-revealing rational expectations equilibrium is not a sensible solution concept. We wish to thank Dr A. Hadjiprocopis for his invaluable help with the implementation of Latex in a Unix environment. We also thank a referee for several, constructive suggestions.     

Understanding Markov-switching rational expectations models

We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models and we develop an algorithm to check these conditions in practice. We use three examples, based on the new-Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov-switching with forward looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region.     

Unanticipated money, ‘disequilibrium’ modelling and rational expectations

This paper provides a synthesis of two recent approaches to macroeconomics, rational expectations and disequilibrium macromodelling. The unifying theme of the two approaches is the emphasis on the effects of the difference between actual and anticipated (or equilibrium) values of important variables such as the money supply.     

Refining linear rational expectations models and equilibria

This paper develops the case for forward convergence as a model refinement scheme for linear rational expectations models and an associated no-bubble condition as a solution selection criterion. We relate these two concepts to determinacy and characterize the complete set of economically relevant rational expectations solutions to the linear rational expectations models under determinacy and indeterminacy. Our results show (1) why a determinate solution is economically cogent in most, but not all, cases, and (2) that those models that are not forward-convergent have no economically relevant solutions.     

Empirical evidence on the rational expectations hypothesis using reported expectations

Zusammenfassung Die Arbeit versucht die Hypothese der Rationalen Erwartungen an Hand von empirisch erhobenen Erwartungsdaten zu testen. Diese Vorgangsweise stellt eine Alternative zu den indirekten Testmethoden dar, in denen die Rationalität der Erwartungen durch den Verlauf von objektiven Daten getestet wird (durch Überprüfung einer Erklärungshypothese, in der Erwartungen eine wohl definierte Rolle zukommt). In diesem Fall kann immer nur die gemeinsame Hypothese der Richtigkeit des Modells und der Rationalität der Erwartungen verifiziert werden. Bei Verwendung empirisch gemessener Erwartungen entfällt dieses Problem, doch kommt die Frage der Glaubwürdigkeit der gemessenen Erwartungen hinzu. Eine unvollständige Auskunft darüber gibt eine Untersuchung des Erklärungsbeitrags der Erwartungen und Antizipationen in Konsum und Investitionsfunktionen.Die Hypothese der rationalen Erwartungen kann erst empirisch getest werden, wenn man eine Annahme über die vorhandene Informationsmenge trifft. Als minimaler Informations-stand wird die Kenntnis der vergangenen Entwicklung der zu prognostizierenden Zeitreihe angenommen. Unter dieser Annahme lassen sich die Merkmale Unverzerrtheit, Effizienz, Suffizienz und Konsistenz aus dem Vergleich erwarteter und tatsächlicher Entwicklungen ableiten und empirisch untersuchen.Das empirische Material umfaßt 39 Zeitreihen über die erwartete (geplante) Entwicklung von Umsätzen, investitionen und Preisen aus mehreren Ländern, wobei teilweise Unternehmensbefragungen, teils Konsumentenbefragungen und teilweise Prognosen von Experten zugrundeliegen.     

Strict rational expectations equilibria with diffuseness

For smooth static pure-exchange economies under uncertainty, it is shown that a diffuseness condition on the distribution of traders' characteristics as the state of the world varies permits one to use only a weak dimensionality restriction in the proof of the genericity of existence of strict rational expectations equilibria. A generic result on the amount of information conveyed by equilibrium price functions and comparisons with some examples of nonexistence are given.     

Competitive equilibrium hyperinflation under rational expectations

This paper shows that a competitive equilibrium model, where a representative agent maximizes welfare, expectations are rational and markets are in equilibrium can account for several hyperinflation stylized facts. The theory is built by combining two hypotheses, namely, a fiscal crisis that requires printing money to finance an increasing public deficit and a predicted change in an unsustainable fiscal regime.We thank an anonymous referee for very helpful comments. A. B. Cunha acknowledges financial support from the Brazilian Council of Science and Technology (CNPq).