Characterizing Markov-Switching Rational Expectations Models

This paper considers the possibility that, in linear rational expectations (RE) models, all determinate (uniquely non-explosive) solutions coincide with the minimum state variable (MSV) solution, which is unique by construction. In univariate specifications of the form y(t) = AE(t)y(t+1) + Cy(t-1) + u(t) that result holds: if a RE solution is unique and non-explosive, then it is the same as the MSV solution. Also, this result holds for multivariate versions if the A and C matrices commute and a certain regularity condition holds. More generally, however, there are models of this form that possess unique non-explosive solutions that differ from their MSV solutions. Examples are provided and a strategy for easily constructing others is outlined.

Indeterminate equilibrium rational expectations (RE) models are ubiquitous in both theoretical and applied work in dynamic macroeconomics. The issue of characterizing the exact dimension of indeterminacy—i.e. of deriving the full set of causal and stable solutions to linear RE models—has only recently been addressed in the context of general and multivariate settings. This paper complements existing results by identifying bounds on the observable dimension of indeterminacy of linear RE models in the presence of arbitrary initial conditions. Implications for the estimation of indeterminate equilibrium RE models are discussed.

We propose a novel approach to deal with the problem of indeterminacy in Linear Rational Expectations models. The method consists of augmenting the original state space with a set of auxiliary exogenous equations to provide the adequate number of explosive roots in presence of indeterminacy. The solution in this expanded state space, if it exists, is always determinate, and is identical to the indeterminate solution of the original model. The proposed approach accommodates determinacy and any degree of indeterminacy, and it can be implemented even when the boundaries of the determinacy region are unknown. Thus, the researcher can estimate the model using standard packages without restricting the estimates to the determinacy region. We apply our method to estimate the New-Keynesian model with rational bubbles by Galí (2017) over the period 1982:Q4 until 2007:Q3. We find that the data support the presence of two degrees of indeterminacy, implying that the central bank was not reacting strongly enough to the bubble component.

Solution of finite-horizon multivariate linear rational expectations models and sparse linear systems

Journal Article A Rational Expectations Approach to Macroeconomics. Testing Policy Ineffectiveness and Efficient-Markets Models Get access A Rational Expectations Approach to Macroeconomics. Testing Policy Ineffectiveness and Efficient-Markets Models. By FREDERIC S. MISHKIN. (Chicago & London: University of Chicago Press for the National Bureau of Economic Research, 1983. Pp. xii+172. £16.00.)Linear Rational Expectations Models. A User's Guide. By CHARLES H. WHITEMAN. (Minneapolis: University of Minnesota Press, 1983. Pp. ix+133. $19.50 hardback, $9.95 paperback.) Denise R. Osborn Denise R. Osborn University of Manchester Search for other works by this author on: Oxford Academic Google Scholar The Economic Journal, Volume 94, Issue 376, 1 December 1984, Pages 978–980, https://doi.org/10.2307/2232321 Published: 01 December 1984

This paper develops a system instrumental variable method to estimate the speed of adjustment coefficient in the long‐run equilibrium of structural error correction models for a class of linear rational expectations models. This method is applied to an exchange rate model with sticky prices, in which the speed of adjustment coefficient governs the half‐life of the real exchange rate. Compared to single equation methods, the system method gives smaller half‐life estimates with sharper standard errors.

This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to be a finite-dimensional affine space in the frequency domain. It is demonstrated that solutions can be discontinuous with respect to the parameters of the models in the context of nonuniqueness, invalidating mainstream frequentist and Bayesian methods. The ill-posedness of the problem motivates regularized solutions with theoretically guaranteed uniqueness, continuity, and even differentiability properties.

In an earlier paper "Granger-causality and Policy Effectiveness" Economica (1984), I showed that for a policy instrument x to Granger-cause some target variable y it is not necessary for x to be useful in controlling y. (The argument that it is not sufficient was already familiar, e.g. from the work of Sargent). Using a linear rational expectations model I showed that x would fail to Granger-cause y (while y did, in some cases, Granger-cause x) if x were set by a variety of optimal, time-consistent or ad hoc policy feedback rules. Yet in all the examples, x was an effective policy instrument. In response to some comments by Professor Granger, I now show that my earlier results are unaffected when the following 3 concessions to "realism" are made: 1. Controllers do not have perfect control of the instruments (this was already allowed for in my earlier paper). 2. Governments may use a different information set to determine instruments from that used by the public. 3. The controller may not have a perfectly specified or estimated model of the economy. The analysis confirms that Granger-causality tests are uninformative about the presence, absence, degree or kind of policy (in)effectiveness.

Equilibrium beliefs in linear rational expectations models

The authors discuss the choice of approximations for unobserved expectations underlying consistent estimators in linear rational expectations models with future expectations. They show how estimators that are more efficient than the commonly used GMM estimators can be obtained if it is assumed that the future expectation depends on a finite number of variables only. Numerical results for a simple model illustrate the related efficiency of various estimators. Copyright 1991 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Many macroeconomic models involving rational expectations give rise to an infinity of solution paths, even when the models are linear in all variables. Some writers have suggested that this non-uniqueness constitutes a serious weakness for the rational expectations hypothesis. One purpose of the present paper is to argue that the non-uniqueness in question is not properly attributable to the rationality hypothesis but, instead, is a general feature of dynamic models involving expectations. It is also argued that there typically exists, in a very wide class of linear rational expectations models, a single solution that excludes "bubbl&' or "bootstrap" effects--ones that occur only because they are arbitrarily expected to occur. A systematic procedure for obtaining solutions free from such effects is introduced and discussed. In addition, this procedure is used to interpret and reconsider several prominent examples with solution multiplicities, including ones developed by Fischer Black and

Stable Noisy K-state Markov Sunspots

Dynamic Monetary and Fiscal Policy Games under Adaptive Learning

Linear rational-expectations models with lagged expectations: A synthetic method

The paper is concerned with the role of monetary policy and argues that activist monetary policy can affect the behavior of real output, rational expectations notwithstanding. A rational expectations model with overlapping labor contracts is constructed, with each labor contract being made for two periods. These contracts inject an element of short-run wage stickiness into the model. Because the money stock is changed by the monetary authority more frequently than labor contracts are renegotiated, and, given the assumed form of the labor contracts, monetary policy has the ability to affect the short-run behavior of output, though it has no effects on long-run output behavior.