Introduction to the stability of rational expectations equilibrium

This paper surveys the literature which examines the stability of the expectations that agents are assumed to have in a rational expectations equilibrium (REE). This issue is more complex than the usual statistical estimation problem because the relationship between observable variables and payoff relevant variables is endogenous. One approach taken in the literature yields convergence to a REE but requires agents to have extensive knowledge about the structure and dynamics of the model that prevails while they learn. A second approach does not assume that agents have correctly specified likelihood functions and finds that REE may not be stable.     

Learning in expectation formation with applications to cattle and beef exports

The paper briefly considers problems associated with rational expectations and formulates a more general model which allows for situations where economic agents do not immediately arrive at a fully rational solution. It incorporates a learning mechanism whereby agents can provisionally adopt hypothetically-derived expectations as a basis for comparison with the actual outturns. Utilizing the resultant past expectational errors as indicators of the likelihood of prospective future outcomes, agents make explicit allowance a rational solution. Thus, in situations where complete information is not freely available, rationality would be approximated over time by means of a dynamic learning process which is founded on a firm empirical approach. This essential empiricism requires that the problem be examined on the basis of direct observation of applied situations. Therefore the method is implemented and analysed with reference to Irish foreign trade in fat cattle, carcase and processed beef. Simultaneous equation models are specified for each of these markets and are tested econometrically for the period 1974–83. The results obtained indicate that the originally-derived estimates of rational expectations did not prove significant, while learning expectations overall mostly did so. In particular the expectational errors were highly significant where the markets were most volatile, i.e. in those for fat cattle and carcase beef.     

Random Walk or Bandwagon: Some Evidence From Foreign Exchanges in the 1980s

The predicitive performance of the bandwagon expectations model foe weekly spot exchange rates over the 1980–6 period is evaluated. Empirical results generally indicate the presence of significant bandwagon effects in the exchange rate dynamics, as found in survey expectations data. Specifically, we find the the bandwagon forecasting scheme can improve the forecasting accuracy in terms of both mean squared errors and market timing upon the random walk and vector autoregressive models. The results illustrate that bandwagon expectations can be rational, and the exchange rate appears to follow a more general integrated process than a random walk.     

Business cycle amplification with heterogeneous expectations

This paper studies the implications for business cycle dynamics of heterogeneous expectations in a stochastic growth model. The assumption of homogeneous, rational expectations is replaced with a heterogeneous expectations model where a fraction of agents hold rational expectations and the remaining fraction adopt parsimonious forecasting models that are, in equilibrium, optimal within a restricted class. Our approach nests the literature on rational expectations in business cycle models with a recent approach based on adaptive learning. We demonstrate that (i.) heterogeneous expectations can lead to substantial improvement in the internal propagation of equilibrium business cycle models and (ii.) the internal propagation depends on the degree of heterogeneity. A calibrated model with heterogeneity provides a closer fit to business cycle data than its representative agent, rational expectations counterpart.     

Model reference adaptive expectations in Markov-switching economies

This paper offers a theory of model reference adaptive beliefs as a selection device in Markov-switching economies under equilibrium indeterminacy. Consistent with the classical rational choice paradigm, our theory requires that endogenous expectations be replaced with a general-measurable function of the observable states of the model, to be determined optimally. This forecasting function is derived as the regime-independent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight state motion (the reference model). We show that model reference adaptive expectations always generate a rational expectations equilibrium, irrespective of the presence of nonlinearities and/or imperfect information. Under equilibrium indeterminacy, this forecasting mechanism enforces the unique mean-square stable solution producing nearly perfect-foresight dynamics.     

The acquisition of information in a dynamic market

Summary This paper models the information acquisition process in an intertemporal rational expectations framework. It demonstrates that equilibria do not generally exist in intertemporal economies in which agents are assumed to know the state-contingent price path and the information acquisition process is endogenous. In addition, an example of a fully revealing equilibrium in which agents pay a strictly positive amount for information is provided. Finally, we also show that it is possible for an equilibrium to exist in which agents choose to purchase information even if all agents, including the agents who purchased the information, are made strictly worse off by the purchase.The author would like to thank Kerry Back, Gerry Feltham Rich Kihlstrom, Vasant Naik, Bryan Routledge, Harald Uhlig and Josef Zechner for their comments and suggestions. A special note of thanks is due to the (anonymous) referee.     

Qualitatively Rational Expectations and Adjustment in the Specific-Factors Model

This paper considers adjustment in a dynamic specific-factors model with endogenous capital stocks. Investment is analyzed under the assumption that expectations are rational with respect to qualitative aspects of the adjustment process (qualitatively rational expectations, QRE). QRE leave considerable scope for systematic errors in expectations formation. Adjustment under rational expectations is similar to QRE adjustment; however, only in the former case is the speed of adjustment optimal. Overshooting of capital stocks is possible and may be optimal. Comparative-static analysis shows an asymmetry between inflows of labor and capital: only capital inflows may cause a Rybczynski effect.     

Evaluating how predictable errors in expected income affect consumption

This article studies whether anomalies in consumption can be explained by a behavioural model in which agents make predictable errors in forecasting income. We use a micro-data set containing subjective expectations about future income. This article shows that the null hypothesis of rational expectations is rejected in favour of the behavioural model, since consumption responds to predictable forecast errors. On average, agents who we predict are too pessimistic increase consumption after the predictable positive income shock. On average, agents who are too optimistic reduce the consumption.     

A dynamic model of expectations equilibrium

This paper describes a dynamic information adjustment process which achieves (rational) expectations equilibria for stochastic exchange environments. An informational temporary equilibrium is an exchange equilibrium in which agents' expectations are conditioned on their initial information and market data generated in previous informational temporary equilibria. An equilibrium is a temporary equilibrium which reveals no further information. This process leads to an equilibrium even when the data observed by agents is insufficient to permit the existence of an expectations equilibrium.     

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     

Are more risk averse agents more optimistic? Insights from a rational expectations model

We analyse a model of partially revealing, rational expectations equilibrium with diverse information, endogenous beliefs formation and uncertain distribution of risk aversion. More risk averse agents are then more optimistic. Such a positive correlation is important for collective decision analysis.     

Learning process and rational expectations: An analysis using a small macro-economic model for New Zealand

The nature of expectations matters when conducting monetary policy. Models with a learning process can exhibit very different properties from models with other types of expectation rules. This paper draws on the work of Orphanides and Williams [Orphanides, A., Williams, J.C. 2002. Imperfect knowledge, inflation expectations and monetary policy, Federal Reserve Board Finance and Economics Discussion Series, 2002-27], extending it to allow for the possibility that the learning process may not be perpetual, but rather might be converging towards a rational expectations equilibrium. By modelling expectations using a learning process, we obtain that inflation expectations in New Zealand are moving towards rational expectations. The closer expectations are to rational, the more inflation can be reduced without costs, thus arguing for a rather tough policy aimed at anchoring expectations on the target.     

Strong convergence of least squares learning to rational expectations

Strong convergence to the rational expectations equilibrium is investigated for a discrete time stochastic model in conjunction with least squares estimation. It is shown that the possible convergence points of the resulting learning process are only the stable points of an associated differential equation and that the situation can converge almost surely to the rational expectations equilibrium.     

Random perturbations of deterministic equilibria

This paper examines whether a small random deviation from a non-random policy process will destabilize the equilibrium exchange rate. The results focus on exchange rate dynamics when the government maintains a target zone or makes unanticipated deviations from a policy rule. With rational expectations small random shocks do not create large deviations from the policy rule exchange rate. If agents are approximately rational large deviations between exchange rates are possible.     

Rational expectations in the overlapping generations model

This paper reports results on the character of the rational expectations equilibria of a stochastic overlapping generations model with heterogenous markets. The model considered is a stationary overlapping generations model in which the endowments of young agents are subject to i.i.d. random shocks. The main result shown is that if there are l > 1 commodities traded in every period, then for most preferences, the rational expectations equilibrium stochastic process of prices and allocations necessarily exhibits serial correlation. This is in marked contrast to the one commodity model in which there always exists an equilibrium which is measure isomorphic to the endowment process.     

Estimating the speed of adjustment of European banking efficiency under a quadratic loss function

This paper investigates the speed of adjustment of cost efficiency to equilibrium level in the European banking industry. Our analysis provides for the first time insights into the process of convergence across European banking markets as measured by the speed of adjustment of cost efficiency. In particular, we employ a quadratic loss function specification based on forward-looking rational expectations to model the underlying dynamics of efficiency scores in the banking industry of the EU-15 region over the period 1998–2005. Results show that there is considerable variation in the speed of adjustment across banking systems, while over time it appears that continuing efforts to advance financial integration have led to some improvement in the speed of adjustment to the long-run equilibrium.     

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.     

Information,trade and common knowledge

In any voluntary trading process, if agents have rational expectations, then it is common knowledge among them that the equilibrium trade is feasible and individually rational. This condition is used to show that when risk-averse traders begin at a Pareto optimal allocation (relative to their prior beliefs) and then receive private information (which disturbs the marginal conditions), they can still never agree to any non-null trade. On markets, information is revealed by price changes. An equilibrium with fully revealing price changes always exists, and even at other equilibria the information revealed by price changes “swamps” each trader's private information.     

Learning rational expectations: The finite state case

This paper is devoted to the question of whether traders can learn rational expectations from repeated observations of market data in a stationary environment with finitely many exogenous states of the world. The learning problem is placed in the context of an iterative adjustment process which achieves equilibrium if traders have rational expectations. The main result is that even if traders begin with no knowledge of their environment, there exists an estimation procedure which converges to rational expectations when the environment satisfies a certain regularity condition. The regularity condition is shown to be generic.