Rational Expectations Model Research Articles

Information rigidities in survey data: Evidence from dispersions in forecasts and forecast revisions

Predictable forecast errors in survey data documented in the existing literature suggest a deviation from the rational expectations hypothesis and are in favor of imperfect information models such as sticky and noisy information models. This article assesses the validity of the imperfect information models by establishing a linkage between dispersions in survey forecasts and survey forecast revisions. We find that the dynamics of dispersion in survey forecasts are consistent with the prediction of sticky information models, but at odds with that of conventional noisy information models as well as full information rational expectations models, both of which assume agents’ continuous updating of their information sets.

Transaction Risk, Derivative Assets, and Equilibrium

We describe a rational expectations model in which there is not only asymmetric information about payoffs but also asymmetric information about the preference, proportion and precision of private information of investors. We define this payoff-irrelevant risk as transaction risk, which is described by market state variables unrelated to payoffs. When derivative assets are introduced, the prices of the derivative assets can reveal information about transaction risk. Due to the informational role of derivative-asset prices, introducing derivative assets can increase social welfare and the price of the underlying asset even though no investors are trading in these derivative assets.

A dynamical systems model of price bubbles and cycles

Various markets exhibit growth and collapse in prices that are sometimes called bubbles, and cycles if the phenomenon repeats. Rational expectations models have been proposed to explain these phenomena; however, such models suffer from a number of criticisms, including lack of experimental support. Moreover, they assume unbiased forecasts without explaining how the investors form their forecasts. In this paper, we provide a model of asset price forecasts and market prices that can be calibrated with experimental data and that can capture various behavioural characteristics of investors such as confidence and panic. We study the resulting dynamical system and show that asset price bubbles may result from seemingly reasonable forecasts and decisions of investors. The model attempts to provide insight into the qualitative connection between investors’ forecasting behaviour and the formation of bubbles and cycles. We present results on the convergence of the process to a fixed point, or to an attractor that describes a price cycle, or to long-run behaviour that seems unpredictable, and we consider where in the cycles most time is spent.

Modeling speculative bubbles with diverse investor expectations

We construct a model of asset market exuberance, collapse and recovery using subjective investor-based rational expectations about the impact of fundamentals on the market price. Investors are assumed to have heterogeneous market sentiments, allowing them to be exuberant, cautious, or fundamentalist via boundary conditions that describe their respective views of the market impact of the same economic fundamentals. Equilibrium solution paths of the model take varying forms, depending on the parameter settings that reflect the importance of each type of market participant. This rational expectations model of asset pricing is shown to be consistent with a simple explosive continuous time autoregression when exuberant sentiment dominates the market. The model explains asset price bubbles, including expansion and subsequent collapse, together with long-term recovery. Extensions of the model allow for contagion effects in which market sentiments are transmitted from a primary market to a secondary market, reproducing speculative behavior and corrections in the secondary market. Some of the implications of the model for empirical work are explored.

System Reduction and Finite-Order VAR Solution Methods for Linear Rational Expectations Models

This paper considers the solution of a large class of linear rational expectations (LRE) models and its characterization via finite-order VARs. The solution of the canonical LRE model can be cast in state-space form and solved for by the method of undetermined coefficients. In this paper I propose an approach that simplifies the systematic characterization of the solution into finite-order VAR form and checks existence and uniqueness based on the solution of a companion Sylvester equation. Solving LRE models with a finite-order VAR representation via the Sylvester equation is straightforward to implement, efficient, and can be handled easily with standard matrix algebra. An application to the workhorse New Keynesian model with accompanying Matlab codes is provided to illustrate the implementation of the procedure in practice.

Bootstrapping DSGE Models

This paper explores the potential of bootstrap methods in the empirical evaluation of dynamic stochastic general equilibrium (DSGE) models and, more generally, in linear rational expectations models featuring unobservable (latent) components. We consider two dimensions. First, we provide mild regularity conditions that su¢ ce for the bootstrap Quasi-Maximum Likelihood (QML) estimator of the structural parameters to mimic the asymptotic distribution of the QML estimator. Consistency of the bootstrap allows to keep the probability of false rejections of the cross-equation restrictions under control. Second, we show that the realizations of the bootstrap estimator of the structural parameters can be constructively used to build novel, computationally straightforward tests for model misspecification, including the case of weak identification. In particular, we show that under strong identification and bootstrap consistency, a test statistic based on a set of realizations of the bootstrap QML estimator approximates the Gaussian distribution. Instead, when the regularity conditions for inference do not hold as e.g. it happens when (part of) the structural parameters are weakly identified, the above result is no longer valid. Therefore, we can evaluate how close or distant is the estimated model from the case of strong identification. Our Monte Carlo experimentations suggest that the bootstrap plays an important role along both dimensions and represents a promising evaluation tool of the cross-equation restrictions and, under certain conditions, of the strength of identification. An empirical illustration based on a small-scale DSGE model estimated on U.S. quarterly observations shows the practical usefulness of our approach.

Solving Re Models with Discontinuous Policy Rules: An Application to Minimum Wage Setting in Germany

The legal regulations require the minimum wage in Germany to be adjusted biennially which gives rise to a policy discontinuity. From the perspective of rational expectations models, such policy features render standard local approximation techniques infeasible. The paper presents a stylised model in which negotiated wages and corporate profits are the outcome of an optimisation problem, while changes to the minimum wage are modelled by a discontinuous policy rule. Using the simple example of minimum wage setting in Germany, the paper illustrates how such models can be solved using the method of undetermined coefficients and presents selected simulation results.

Analysis on the Decision Making of the Hanwoo Breeding Farms under Expectation Theories

The number Hanwoo is determined by the behavior of female breeding farms. The behavior is decided by the expected farm prices. This paper analyzes the behavior of Hanwoo female breeding farms. We use four expectation theories: naive expectation, adaptive expectation, partial adjustment, and rational expectation. We compare the estimation results of these four models to see which model fits well the actual data. We estimate female slaughter function and calf supply function. The results show that the behavior of the breeding farms can be explained by the naive expectation model and rational expectation model rather than the complicated adaptive expectation model and partial adjustment model. The result of the rational expectation model shows the best goodness of fit.

Financial Markets and Limited Investor Attention

I consider a rational expectations model in which individual investors become informed by allocating limited attention to stocks. A single informed individual provides no measurable effects. However, individuals' equilibrium attention allocations are identical. Consequently, there exists an informed herd that crowds out institutions in some stocks. Recent empirical work indicates that some individual traders are informed, their actions are measurable, and their trades appear coordinated. My model explains the data and provides new cross sectional and time series predictions regarding investor clienteles and attentiveness. The model challenges the standard assumption that the actions of informed individuals are subsumed by institutions.

Can Economists Forecast Exchange Rates? The Debate Re‐Visited: The Case of the USD/GBP Market

In the debate on forecasting exchange rates, critics claimed that traditional macroeconomic models could not outperform a random walk in post‐sample forecasts. Perceived deficiencies include inadequate allowance for simultaneity, and expectations hypotheses inconsistent with the structure of models employed. This paper re‐visits the debate, first to address critics' major concerns, and second because in the view of the present authors, the debate closed on an unduly pessimistic note.This paper develops a simultaneous, rational expectations model of the USD/GBP market, with functional relationships for hedgers, speculators and a spot rate equation. The model is estimated with data contemporaneous to the debate, including a period during which the US Commodity Futures Trading Commission did not collect data on traders' open positions. Using the results of post‐debate research on tests for stationarity with missing observations, the model, using only public information, outperforms a random walk in post‐sample forecasts of the spot rate. Recent microstructure models of the exchange rate based on order flow have re‐kindled the forecasting debate. The model developed here, however, is differentiated from these microstructure models, first because order flow utilises both public and private information, and second because the microstructure models do not directly address critics' concerns.

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.

Yield curve responses to market sentiments and monetary policy

Central banks recently started to target longer term interest rates. The empirical failure of the rational expectations theory of the yield curve, however, limits its applicability to monetary policy analysis. The success of agent-based behavioral asset pricing models and behavioral macroeconomic models in replicating statistical regularities of empirical data series motivates to apply them to yield curve modeling. This paper analyses how the interaction of monetary policy and market sentiments shape the yield curve in a behavioral model with heterogeneous and bounded-rational agents. One result is that the behavioral model replicates empirical facts of term structure data. Moreover, it overcomes one major deficiency of rational expectations models of the yield curve in explaining the empirically observed uncertain responses of longer term yields to changes in the central bank rate. These are explained by the behavioral model’s ability to generate different responses of market sentiments to shocks at different times which lead to a variety of interest rate responses. Further results of this paper can be used as policy advice on how central banks can target the level, slope and curvature of the yield curve by targeting market sentiments about inflation and the business cycle.

Solving generalized multivariate linear rational expectations models

We generalize the linear rational expectations solution method of Whiteman (1983) to the multivariate case. This facilitates the use of a generic exogenous driving process that must only satisfy covariance stationarity. Multivariate cross-equation restrictions linking the Wold representation of the exogenous process to the endogenous variables of the rational expectations model are obtained. We argue that this approach offers important insights into rational expectations models. We give two examples in the paper—an asset pricing model with incomplete information and a monetary model with observationally equivalent monetary-fiscal policy interactions. We relate our solution methodology to other popular approaches to solving multivariate linear rational expectations models, and provide user-friendly code that executes our approach.

Estimating the effects of forward guidance in rational expectations models

Simulations of forward guidance in rational expectations models should be assessed using the “modest policy interventions” framework introduced by Eric Leeper and Tao Zha. That is, the estimated effects of a policy intervention should be considered reliable only if that intervention is unlikely to trigger a revision in private sector beliefs about the way that monetary policy will be conducted. I show how to constrain simulations of forward guidance to ensure that they are regarded as modest policy interventions and illustrate the technique using a medium-scale DSGE model estimated on US data. I find that many experiments that generate the large responses of macroeconomic variables deemed implausible by many economists – the so-called “forward guidance puzzle” – are not modest policy interventions. Those experiments should therefore be treated with caution, since they may prompt agents to believe that there has been a change in the monetary policy regime that is not accounted for within the model. More reliable results can be obtained by constraining the experiment to be a modest policy intervention. In the cases I study, the quantitative effects on macroeconomic variables are more plausible when this constraint is imposed.

Delegated trade and the pricing of public and private information

We extend a standard, rational expectation model of trade to incorporate the possibility of individual investors delegating their trades to an informed financial intermediary. In the presence of delegated trade, we show that a firm׳s risk premium is a function of both the firm׳s exposure to a common risk factor and idiosyncratic characteristics of the firm׳s information environment. We show that even in a large economy, priced risks can manifest in the form of both idiosyncratic firm characteristics and common risk factors; as a consequence, factor-based asset pricing tests cannot rule out that a particular risk is priced.

Can the Learnability Criterion Ensure Determinacy in New Keynesian Models?

Forward-looking rational expectation (RE) models such as the popular New Keynesian (NK) model do not provide a unique prediction about how the model economy behaves. We need some mechanism that ensures determinacy. McCallum (2012) says it is not needed because models are learnable only with the determinate solution and so the NK model, once learnt in this way, will be determinate. We agree the only learnable solution that has agents converge on the true NK model is the bubble-free one. But once they have converged, they must then understand the model and its full solution therefore including the bubble. Hence, the learnability criterion still fails to pick a unique RE solution in NK models. JEL Classifications: C62, D84

Using Survey Data of Inflation Expectations in the Estimation of Learning and Rational Expectations Models

Does survey data contain useful information for estimating macroeconomic models? We address this question by using survey data of inflation expectations to estimate the New Keynesian model by Smets and Wouters () and compare its performance under rational expectations and adaptive learning. The survey information serves as an additional moment restriction and helps us to determine the learning agents' forecasting model for inflation. Adaptive learning fares similarly to rational expectations in fitting macro data, but clearly outperforms rational expectations in fitting macro and survey data simultaneously. In other words, survey data contain additional information that is not present in the macro data alone.

Permanent Income and Subjective Well-Being

We provide a new explanation for the stronger relationship between income and subjective well-being (SWB) found in cross-sectional versus panel studies based on the predictions of a rational expectations model of utility maximization with permanent and transitory income shocks. The model predicts that SWB is affected by unanticipated rather than anticipated income, and is more influenced by permanent rather than transitory income shocks. We hypothesize that share of cross-sectional income variation accounted for by permanent income is greater than the share of changes in income over time accounted for by unanticipated shocks to permanent income. We test our predictions using a unique panel dataset from rural China which includes subjective expectations of future income and actual income in each wave, enabling us to separately identify the effects of unanticipated permanent and transitory income shocks. The results confirm the predictions, providing support for the importance of permanent income in explaining SWB.

Learning About Noise

This paper studies how acquisition of non-fundamental information (learning about noise) affects financial markets. We develop a rational expectations model with investors who are endowed with fundamental information of heterogeneous quality and who optimally allocate learning capacity between fundamentals and noise. We demonstrate that learning about noise increases price informativeness, and the price can be the most informative when the majority of investors acquire non-fundamental information. We also find that i) investors endowed with high (low) quality information about fundamentals learn only about fundamentals (noise) and ii) learning about fundamentals (noise) increases (decreases) the heterogeneity of information quality across investors.

On Existence and Uniqueness of Equilibrium in a Class of Noisy Rational Expectations Models: Figure 1

I study a general class of noisy rational expectations models that nests the standard Grossman and Stiglitz (1980) and Hellwig (1980) models, but relaxes the usual assumption of joint normality of asset pay-offs and supply, and allows for more general signal structures. I provide a constructive proof of existence of equilibrium, characterize the price function, and provide sufficient conditions for uniqueness within the class of equilibria with continuous price functions, which are met by both the Grossman and Stiglitz (1980) models and the Hellwig (1980) models with a continuum of investors. My solution approach does not rely on the typical “conjecture and verify” method, and I exhibit a number of non-normal examples in which asset prices can be characterized explicitly and in a closed form. The results presented here open up a broad class of models for applied work. To illustrate the usefulness of generalizing the standard model, I show that in settings with non-normally distributed pay-offs, shocks to fundamentals may be amplified purely due to learning effects, price drifts can arise naturally, and the disagreement–return relation depends in a novel way on return skewness.