THE SPECTRAL APPROACH TO LINEAR RATIONAL EXPECTATIONS MODELS

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.

Event Abstract Back to Event 2nd level modelling in fMRI analysis with a clinically depressed sample - Comparisons between classical and Bayesian methods Peter Goodin1, 2*, Joseph Ciorciari1, Susan Rossell1, 2, Matt Hughes1 and Richard Nibbs1 1 Swinburne University, BPsyC, Australia 2 Monash Alfred Psychiatric Research Centre, Australia The use of the Frequentist statistics in fMRI analysis has been the mainstay of the field for the last 25 years. Several other methods have been developed as alternatives, including those based on Bayesian statistics. Bayesian analysis methods have the benefit of allowing interrelation of data through effect size and confidence thresholds, can be more robust to outlier data and may negate the need for stringent multiple comparison correction. When examining functional differences in those with a mental illness , this can lead to detection of more subtle activation that may be of importance. Depression is a disorder that despite a common theme of symptoms is also characterised by functional heterogeneities between individuals, making inferences using Frequentist methods sometimes difficult. Utilising both Frequentist and Bayesian 2nd level analysis methods offered by SPM8 , we examined differences in activation between a healthy control sample and those with major depressive disorder during a novel emotional processing n-back task. Activation using classical methods showed small differences in more posterior visual regions however this was only detectable with liberal thresholding (p = .001 uncorrected, k = 0). In contrast Bayesian analysis (y = 0, 95% confidence) uncovered widespread differences (including overlap with those areas found with the Frequentist method) in multiple regions implicated with the disorder. This suggests that using Bayesian methods in fMRI analysis with a clinical population could be extremely useful in detecting responses that may otherwise go unnoticed or under-represented in more traditional methods, however determination of effect size importance is paramount. Keywords: Depression, fMRI, working memory, Bayesian, Frequentist Conference: XII International Conference on Cognitive Neuroscience (ICON-XII), Brisbane, Queensland, Australia, 27 Jul - 31 Jul, 2014. Presentation Type: Poster Topic: Methods Development Citation: Goodin P, Ciorciari J, Rossell S, Hughes M and Nibbs R (2015). 2nd level modelling in fMRI analysis with a clinically depressed sample - Comparisons between classical and Bayesian methods. Conference Abstract: XII International Conference on Cognitive Neuroscience (ICON-XII). doi: 10.3389/conf.fnhum.2015.217.00203 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 19 Feb 2015; Published Online: 24 Apr 2015. * Correspondence: Mr. Peter Goodin, Swinburne University, BPsyC, Hawthorn, Australia, peter@hitiq.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Peter Goodin Joseph Ciorciari Susan Rossell Matt Hughes Richard Nibbs Google Peter Goodin Joseph Ciorciari Susan Rossell Matt Hughes Richard Nibbs Google Scholar Peter Goodin Joseph Ciorciari Susan Rossell Matt Hughes Richard Nibbs PubMed Peter Goodin Joseph Ciorciari Susan Rossell Matt Hughes Richard Nibbs Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

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.

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

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.

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

Stable Noisy K-state Markov Sunspots

Background:Non-nutritive suck (NNS) is used to promote ororhythmic patterning and assess oral feeding readiness in preterm infants in the neonatal intensive care unit (NICU). While time domain measures of NNS are available in real time at cribside, our understanding of suck pattern generation in the frequency domain is limited. The aim of this study is to model the development of NNS in the frequency domain using Fourier and machine learning (ML) techniques in extremely preterm infants (EPIs).Methods:A total of 117 EPIs were randomized to a pulsed or sham orocutaneous intervention during tube feedings 3 times/day for 4 weeks, beginning at 30 weeks post-menstrual age (PMA). Infants were assessed 3 times/week for NNS dynamics until they attained 100% oral feeding or NICU discharge. Digitized NNS signals were processed in the frequency domain using two transforms, including the Welch power spectral density (PSD) method, and the Yule-Walker PSD method. Data analysis proceeded in two stages. Stage 1: ML longitudinal cluster analysis was conducted to identify groups (classes) of infants, each showing a unique pattern of change in Welch and Yule-Walker calculations during the interventions. Stage 2: linear mixed modeling (LMM) was performed for the Welch and Yule-Walker dependent variables to examine the effects of gestationally-aged (GA), PMA, sex (male, female), patient type [respiratory distress syndrome (RDS), bronchopulmonary dysplasia (BPD)], treatment (NTrainer, Sham), intervention phase [1, 2, 3], cluster class, and phase-by-class interaction.Results:ML of Welch PSD method and Yule-Walker PSD method measures revealed three membership classes of NNS growth patterns. The dependent measures peak_Hz, PSD amplitude, and area under the curve (AUC) are highly dependent on PMA, but show little relation to respiratory status (RDS, BPD) or somatosensory intervention. Thus, neural regulation of NNS in the frequency domain is significantly different for each identified cluster (classes A, B, C) during this developmental period.Conclusions:Efforts to increase our knowledge of the evolution of the suck central pattern generator (sCPG) in preterm infants, including NNS rhythmogenesis will help us better understand the observed phenotypes of NNS production in both the frequency and time domains. Knowledge of those features of the NNS which are relatively invariant vs. other features which are modifiable by experience will likewise inform more effective treatment strategies in this fragile population.

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