Stationary Rational Expectations Equilibrium Research Articles

A stochastic optimal stopping model for storable commodity prices

In this paper, we propose a continuous time version of the well-known speculative storage model for commodity prices. But from the mathematical point of view this is not a trivial extension and needs careful consideration of the theory of stochastic stopping time combined with fixed point theory. We formulate the problem in a manner that the main objective of the storage model, known as the stationary rational expectations equilibrium (SREE), becomes a fixed-point of an operator which solves a free boundary problem and show that this operator under some conditions is a contraction. We also demonstrate the benefits of our continuous time model through a numerical algorithm.

The RPEs of RBCs and other DSGEs

In a broad class of non-linear representative agent models, represented by a system of difference equations, we replace rational expectations with linear forecast models conditioning on a predetermined set of regressors. Within this framework, a restricted perceptions equilibrium (RPE) corresponds to a forecast rule that is optimal within that class of models. Local uniqueness of a stationary rational expectations equilibrium (REE) near the non-stochastic steady state is shown to guarantee the existence, uniqueness and E-stability of an RPE local to that steady state. A benchmark RBC model with government spending shocks illustrates the theoretical results.

Commodity Price Modeling by Optimal Storage Time

We propose a modified version of the speculative storage model of Deaton and Laroque (1992) in a continuous-time framework. Unlike most of the literature, where either the demand or the price process are exogenously given, our framework models them endogenously for the storable commodities. This shows that how the commodities' economic characteristics like the demand elasticity and stylized facts like the price volatility can specify the prices. In addition, our model gives rise to the concept of the storage option and the optimal selling time. We prove the existence, and under very mild conditions, the uniqueness of the stationary rational expectations equilibrium (SREE), and introduce practical ways to approximate it. Finally, we conduct some sensitivity analysis to show the impact of the parameters on SREE.

Model Averaging and Persistent Disagreement

The authors consider the following scenario: Two agents construct models of an endogenous price process. One agent thinks the data are stationary, the other thinks the data are nonstationary. A policymaker combines forecasts from the two models using a recursive Bayesian model averaging procedure. The actual (but unknown) price process depends on the policymaker?s forecasts. The authors find that if the policymaker has complete faith in the stationary model, then beliefs and outcomes converge to the stationary rational expectations equilibrium. However, even a grain of doubt about stationarity will cause beliefs to settle on the nonstationary model, where prices experience large self-confirming deviations away from the stationary equilibrium. The authors show that it would take centuries of data before agents were able to detect their model misspecifications

Investor Expectations, Earnings Management, and Asset Prices

This paper examines the implications of investor expectations for the joint determination of earnings management and asset prices. I propose a dynamic stochastic model of financial reporting, in which a firm manager opportunistically shifts earnings in order to manipulate investor expectations, subject to a constraint on accumulated discretionary accruals. Four alternative investor expectation schemes are studied: rational expectations, constant-gain learning, regime-shifting beliefs, and accounting-information-system beliefs. The main findings are threefold. First, there does not exist a stationary rational expectations equilibrium; under the other three expectation schemes, optimal reporting decisions are characterized by threshold rules based on investor beliefs. Second, regression analysis using simulated data indicates that the relationships among earnings, discretionary accruals, and stock returns critically depend on investor expectations. Third, structural estimation uncovers considerable heterogeneity in investors' belief-formation processes, with accounting-information-system beliefs providing the best model fit for the majority of S&P 500 firms.

A Dynamic Model of Investor Expectations and Financial Reporting

This paper examines the implications of investor expectations for earnings management and asset prices. I propose a dynamic stochastic model of financial reporting, in which a firm manager opportunistically shifts earnings in order to manipulate investor expectations, subject to a constraint on accumulated accruals. Three investor expectations schemes with different levels of rationality are considered: rational expectations, adaptive learning, and misspecified Bayesian learning. In a stationary rational expectations equilibrium, whether the manager manipulates earnings depends on the real earnings process. Under adaptive learning and regime-shifting beliefs, earnings management exists to the extent that there is discrepancy between investor beliefs and the actual process of reported earnings. This model provides testable predictions for the joint impact of managerial opportunism and investor expectations on accounting-based return regularities. It also sheds light on the descriptive validity of different investor expectations schemes.

Monetary–Fiscal Policy Interactions under Implementable Monetary Policy Rules

This paper examines the implications of forward‐ and backward‐looking monetary policy rules in an environment with monetary–fiscal interactions. We find that the unique stationary rational expectations equilibrium (REE) is always non‐Ricardian under simple implementable monetary policy rules.

Rate-of-return dominance and efficiency in an experimental economy

One of the main challenges for monetary economics is to explain the use of assets that are dominated in rate-of-return as media of exchange.We use experimental methods to study howa fiat money might come to be used in transactions when an identically marketable, dividend-bearing asset, a consol, is also available. Our experimental economies, which have an overlapping generations structure, have the property that the only stationary rational expectations equilibria (SREE) require exclusive use of the consol as the medium of exchange. In a baseline treatment, agents use the consol exclusively, as would occur in an SREE. However, in other treatments, we observe episodes of rate-of-return dominance,with consistent use of fiat money as a medium of exchange. The results show that two properties of our economies are associated with the rate of return dominance anomaly. The first is a history of trading with fiat money, prior to the introduction of the consol. The second is the timing of the dividend payment; when the dividend payment follows the execution of trades between generations, hoarding of the consol occurs on the part of the old, who earn dividends by hoarding. In our economies, settling transactions with a dividend-bearing asset does not improve allocations over those resulting from trading with fiat money.

PERFORMANCE OF RATIONAL AND BOUNDEDLY RATIONAL AGENTS IN A MODEL WITH PERSISTENT EXCHANGE-RATE VOLATILITY

The model is a two-country overlapping generations economy with boundedly rational agents who update their decision rules using a version of the stochastic replicator dynamic. The results show that stationary rational expectations equilibria of this model are unstable under this type of evolutionary adaptation. The paper also derives a two-period-ahead forecast of the values of average fractions of savings placed in each of the two currencies. This forecast is used in decisionmaking of a rational agent who has a full knowledge of the evolutionary economy. The performance of the rational agent is compared to the performance of boundedly rational agents, based on the average utility received over time. Results show that the difference between utilities earned by rational and boundedly rational agents is small. In addition, the average utility of the best-performing boundedly rational agents is higher than the average utility of the rational agents.

Exponentially fading memory learning in forward-looking economic models

In this paper we analyze forward-looking economic models under bounded rationality. We consider a learning mechanism characterized by exponentially fading memory with a learning step not vanishing in the limit. The dynamics of the model under bounded rationality can be parametrized with respect to the memory of the learning mechanism. We show that memory plays a stabilizing role in a local sense: it induces local convergence towards a stationary rational expectations equilibrium and in some cases it does not allow for nonperfect foresight attractors obtained through local bifurcations. We discuss this learning mechanism in pure exchange overlapping generations models. We also analyze models with predetermined state variables, in this setting the effect of memory on the learning dynamics is controversial.

Stationary Ramsey Equilibria under Uncertainty

Deterministic dynamic equilibrium models with borrowing constraints and heterogeneous agents exhibit stationary solutions where the most patient household owns the economy's capital stock. An example shows that this result does not carry over to stationary stochastic environments. We prove, under some conditions, the existence of a stationary rational expectations equilibrium in two related setups. The first is the existence of a stationary Nash equilibrium where each agent's payoff depends on his capital process and the capital processes of the remaining agents. The second existence theorem applies to a stationary competitive equilibrium model.Journal of Economic LiteratureClassification Numbers: E13, E21, D80.

On aggregation of information in competitive markets: The dynamic case

This article examines, in the spirit of Hellwig (1980), how a dynamic competitive security market aggregates and communicates information between various market participants at every instant. It employs a continuous time economy consisting of a large number of heterogeneous agents who are endowed with noisy private signals about the risky asset payoff of differing precision. It yields a stationary rational expectations equilibrium in which at every instant the agents use information contained in the market prices without rendering their private information redundant. It shows that the market price reflects only that part of private information which is common to many signals and, thus, extends Hellwig's single-period results to a multi-period model.

A Theory of Commodity Price Fluctuations

This paper studies the price fluctuations of storable commodities that are traded in open markets and are subject to random shocks to demand or, more particularly, to supply. It relaxes the common assumption that the shocks are identically and independently distributed in favor of temporally dependent and periodic disturbances. The existence of a unique stationary rational expectations equilibrium is demonstrated for each of the models analyzed, and testable implications of the models are derived. An illustrative empirical investigation is then undertaken for the model with periodic disturbances using monthly time-series observations for seven commodities over the period 1960-93.

Ignorance may be optimal? Some welfare implications of rational versus non-rational expectations

We compare the lifetime utility of agents in a stationary non-rational expectations equilibrium to that obtained in a stationary rational expectations equilibrium. When government expenditures are financed by an inflationary tax, and agents in the non-rational expectations equilibrium underestimate inflation, it is shown that the non-rational expectations equilibrium is Pareto superior to the rational expectations equilibrium.

Indeterminacy of Equilibria in a Hyperinflationary World: Experimental Evidence

The authors design and study an OLG experimental economy where the government finances a fixed real deficit through seigniorage. The economy has continua of nonstationary rational expectations equilibria and two stationary rational expectations equilibria. The authors do not observe nonstationary rational expectations paths. Observed paths tend to converge close to, or somewhat below, the low inflation stationary state. The adaptive learning hypothesis is consistent with the data in selecting the low inflation stationary state rational expectations equilibrium as a long-run stationary equilibrium. Nevertheless, simple adaptive learning models do not capture the market uncertainty or the biases observed in the data. Copyright 1993 by The Econometric Society.

Sequential elections with limited information

We develop an incomplete information model of a sequence of elections in a one-dimensional policy space, where voters have no contemporaneous information about candidate positions, and candidates have no information about voter preferences. The only source of information is contemporaneous endorsement data and historical data on the policy positions of previous winning candidates. We define a notion of “stationary rational expectations equilibrium”, and show that such an equilibrium results in outcomes which are equivalent to those that would occur under full information.

Sequential Elections with Limited Information

We develop an incomplete information model of a sequence of elections in a one-dimensional policy space, where voters have no contemporaneous information about candidate positions, and candidates have no information about voter preferences. The only source of information is contemporaneous endorsement data and historical data on the policy positions of previous winning candidates. We define a notion of “stationary rational expectations equilibrium”, and show that such an equilibrium results in outcomes which are equivalent to those that would occur under full information.