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.     

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 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     

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.     

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.     

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.     

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).     

On multiple equilibria and the rational expectations hypothesis

Summary This paper analyzes through a simple two-period model the fact that, if some agents hold inside money intertemporally, the second-period normalization matters. Thus, there are several equilibria of the second-period economy, indexed by the level of inflation. A concept of equilibrium acknowledging this fact, and requiring that agents put some weight on any of the possible second-period equilibrium price vectors is developed. Such an equilibrium is shown to exist, and is illustrated by an example.This a revised version of chapter three of my Ph.D. dissertation. I would like to thank David Cass, Atsushi Kajii, George Mailath and Shinichi Suda for helpful discussions and comments. Thanks are also due to Jean-Michel Grandmont who pointed out mistakes in a previous version. All remaining mistakes are of course my own. Financial support from a CARESS scholarship at the University of Pennsylvania is gratefully acknowledged.     

Learning rational expectations in an asset market

Will traders in a risky asset market learn Muthian expectations when they initially lack the necessary information? If some traders learn from their observations, will market dynamics depend only on “fundamentals,” as implied by the Efficient Market Hypothesis? This paper shows that at any finite point in time the answer to these questions is “no”. The context is a constant absolute risk aversion model with two kinds of traders and asymmetric information. The market converges asymptotically to a rational expectations equilibrium where prices depend only on fundamentals and the market is efficient.     

Money demand, the Cagan model, testing rational expectations vs adaptive expectations: The case of Turkey

This paper estimates the Cagan type demand for money function for Turkish economy during the period 1986:1–1995:3 and tests whether Cagan's specification fits the Turkish data using an econometric technique assuming that forecasting errors are stationary. This paper also tests the hypothesis that monetary policy was implemented in aiming to maximize the inflation tax revenue. Finally, the Cagan model is estimated with the additional assumption of rational expectations for Turkey for the considered period. First version received: March 1998/final version received: October 1998     

Functional rational expectations equilibria in market games

The rational expectations equilibrium (REE) has been criticized as an equilibrium concept in market game environments. Such an equilibrium may not exist generically, or it may introduce unrealistic assumptions about an economic agent’s knowledge or computational ability. We define an REE as a probability measure over uncertain states of nature which exploits all available information in a market game, and which exists for almost all economies. Furthermore, if retrading is allowed, it is possible for agents to compute such a ‘functional rational expectations equilibrium’ using straightforward numerical fixed point algorithms. The approach is demonstrated in a detailed numerical example.     

A test for rational bubbles in stock prices

This paper presents two necessary conditions for the absence of rational bubbles on the assumption that the discount rate is stationary. One condition is that real stock prices and real dividends are cointegrated with the time-varying cointegrating vector. The other is that the order of integration of real stock prices is equal to that of real dividends. The first condition is different from that proposed on the assumption of a constant discount rate. In contrast, the second condition is the same as that presented on this assumption. Examining the second condition using Japanese data, we find that Japanese stock prices and dividends satisfy the necessary condition. First version received: May 2000/Final version accepted: April 2001     

Speculative bubbles in the ff/DM parity during the 1980s

It is often argued that exchanged rates volatility during the 1980s was too excessive to be attributed only to market fundamentals. This paper investigates for speculative bubles in the franc–mark exchange rate applying direct tests for determinate bubbles and indirect ones(according to the issues of integration and cointegration)for stochastic bubbles, in the context of a sticky price monetary model. No clear-cut conclusions can be drawn from these tests although all of them indicate that the no-bubble hypothesis cannot be easily accepted. However, any evidence for bubbles should be interpreted with caution, since a possible misspecification of the model may produce misleading inferences.