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.     

Terminal conditions as a means of ensuring unique solutions for rational expectations models with forward expectations

Terminal conditions are imposed on rational expectations models as a means of finding a unique solution among a continuum of potential solutions. It is argued that using terminal conditions is superior to invoking stability. The method can be applied to non-linear as well as linear systems.     

An improved single equation estimation procedure for rational expectations models

This paper introduces a new readily programmable single-equation errors in variables estimation procedure for rational expectations models. For the illustrative example provided, this new estimator outperforms the currently available estimators.     

Approximate equilibria in microeconomic rational expectations models

For general equilibrium models in which prices transmit information among asymmetrically informed traders, strict rational expectations approximate equilibria are defined. A state-dependent price function is an ε-equilibrium if, when agents use their own information and that conveyed by prices, aggregate excess demand (in each state of the world) does not exceed ε. For any positive ε, existence requires only very mild assumptions—continuity and compact support. Moreover, there are revealing ε-equilibria for all smooth economies satisfying a dimensionality condition. In an open neighborhood of this case, existence of maximally revealing ε-equilibria holds.     

Disequilibrium models with rational expectations: An application to the UK labour market

This paper develops and estimates an explicit switching model for the U.K. labour market which includes expectations terms in the labour demand function. These expectations terms are dealt with by using the rational expectations hypothesis.     

Backward looking and forward looking solutions to monetary models of inflation with rational expectations

We show that an indeterminacy problem, noted by Blanchard, concerning monetary models of inflation with rational expectations may be resolved by requiring solutions for real variables in such models to be invariant to the choice of accounting unit.     

The government behavioural constraint in rational expectations models

Models with rational expectations typically include state variables whose values are controlled by the government. Hence, the need to specify behavioural rules for the authorities. Our purpose is to show, in the context of a well-known Cagan type model of the demand for money, that the assumption of rational expectations imposes the hitherto neglected requirement of rationality of the postulated behaviour of government. In particular the occurance of non-unique solutions highlights the need for a rational choice between these on grounds other than mathematical convenience or ad hoc economic assumptions of minimum variance, terminal conditions etc.     

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.     

Multiple equilibria in dynamic rational expectations models: A critical review

Multiple equilibria are a ubiquitous feature of dynamic rational expectations models. Researchers have been divided on the implications of this phenomenon. Some have viewed this as a reflection of reality and a possible explanation of a wide range of economic phenomena. Others have suggested various selection criteria for choosing one among the many equilibria. This paper reviews the major selection criteria that have been proposed, and through application to three well-known models shows under what circumstances one might expect them to choose the same or different equilibria. In addition, this paper proposes a new criteria based on the limit of finite-horizon equilibria and investigates its relation to the other criteria.     

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.     

On the derivation of reduced forms of rational expectations models

This paper introduces a more intuitive and straightforward method to obtain the reduced forms of linear models containing expectations of the current endogenous variables formed rationally in various previous periods, besides the two proposed by Lucas and Aoki and Canzoneri. This method is then used, with the aid of some examples, to derive the conditions for complete (i.e., in mean and variance) policy ineffectiveness in this kind of models.     

Rational expectations in microeconomic models: An overview

This paper is an expository introduction to several topics of current research in the general equilibrium theory of rational expectations. More specifically, we discuss the existence of exact and approximate rational expectations equilibria, the implementation of equilibria, the behavior of learning and smoothing processes by which traders construct expectations from repeated observations of the market, and the lagged use of the information revealed by prices in an intertemporal sequence of markets. The purpose of this discussion is to introduce papers on these topics appearing in the Journal of Economic Theory Symposium on Rational Expectations in Microeconomic Models.     

A note on Wiener-Kolmogorov prediction formulas for rational expectations models

A prediction formula for geometrically declining sums of future forcing variables is derived for models in which the forcing variables are generated by a vector autoregressive-moving average process. This formula is useful in deducing and characterizing cross-equation restrictions implied by linear rational expectations models.     

On linear models with rational expectations which admit a unique solution

Based on a generalization of Doob's theorem, the method used in this paper is applied to derive the unique reduced form a general linear model containing rational expectations of the current endogenous variables made in several previous periods. In this procedure there is no need for assumptions on the structure of the policy instruments.     

Cobweb versus rational expectations models: Lessons from the market for public school teachers

A cobweb model of occupational choice is found to fit the data almost as well as a rational expectations model, even though there are large forecastable changes in demand. Striking differences, however, are revealed when we simulate the two models.     

Markov-switching models,rational expectations and the term structure of interest rates

In order to evaluate the efficiency of the monetary transmission mechanism, we develop the formulas for testing rational expectations theory in the term structure of interest rates with VAR models of stochastically switching regimes in which all the parameters are regime dependent. These formulas are obtained for the strict version of rational expectations as well as for the case where measurement errors are assumed in the expectations relationship. They are extensible to other contexts that involve variables linked by rational-expectations behaviours. The testing procedure is implemented on interest rates of the Spanish inter-bank money market. Measurement errors must be assumed to find signs favourable to the theory.     

Complete systems methods of estimating models with rational and adaptive expectations: A case study

This paper examines the use of complete fully efficient systems methods to compare model estimates under rational and adaptive schemes of expectations generation. To do this we employ a small well-known model designed to distinguish monetarist from Keynesian macroeconomic structures.