Stable Noisy K-state Markov Sunspots

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.

Characterizing Markov-Switching Rational Expectations Models

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.

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.

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.

The business cycle analysis of Arthur F. Burns and Wesley C. Mitchell and the National Bureau of Economic Research presumed that aggregate economic variables evolve on a time scale defined by business cycle turning points rather than by months or quarters. Do macroeconomic variables appear to evolve on an economic rather than a calendar time scale? Evidence presented here suggests that they do. However, the estimated economic time scales are only weakly related to business cycle time scales, providing evidence against the view underlying traditional business cycle analysis. Copyright 1987 by University of Chicago Press.

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.

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

Equilibrium beliefs in linear rational expectations models

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

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.

Reflectance data and relative chlorophyll content for Phyllostachys violascens at leaf scale were measured during the growth period from April, 5th to June, 18th using a portable Analytical Spectral Devices （ASD） field spectrometer and a hand-held Chlorophyll Content Meter （CCM）-200. Correlation analyses were conducted between hyper-spectral vegetation indices and chlorophyll content based on the data. Then individual univariate linear inversion models were developed for chlorophyll content and hyper-spectral vegetation indices, such as red edge indexes GM, Vog3, double difference index DD, modified normalized differential vegetation index mND705, modified simple ratio mSR705, and Red-edge positions （REP）. Also multivariate linear models for selected hyper-spectral vegetation indices and chlorophyll content were tested. Multivariate linear models are designed in two methods, strategy A is based on the 20 Phyllostachys violascens samples, and each data for the sample is the average for all the 14 times. On the contrary, strategy B is based on the data of 14 times, which average the 20 samples for each time. Results over the entire growth period showed （1） significant （P＜0.01） correlations between chlorophyll content and hyper-spectral vegetation indices, GM （r = 0.866 3）, Vog3 （r = 0.927 4 ）, DD （r = 0.880 6）, mND705 （r = 0.917 9）, mSR705 （r = 0.924 9）, and REP （r =0.895 4）. At the end of the growth period, all vegetation indices had a favorable relationship with chlorophyll content, showing as the high correlation coefficients, although some indexes perform bad in most other time periods；（2） Using the univariate linear model, correlation for hyper-spectral vegetation indices and chlorophyll content showed r ＞ 0.85. The multivariate linear models of the six hyper-spectral vegetation indices listed above and chlorophyll content using two strategies, both accurately predicted chlorophyll content of Phyllostachys violascens ［with correlation coefficients between predicted values and measured values that were all above r = 0.89］. The multivariate linear models can be used to predicte chlorophyll content in the leaf of Phyllostachys violascens. Considering the calculate method, strategy B is more fit for the dynamic change of chlorophyll content for Phyllostachys violascens at leaf scale. ［Ch, 4 fig. 2 tab. 45 ref.］

The objective of this study was to estimate and compare variance components and sire breeding values for disease resistance to vibriosis in Atlantic cod (Gadus morhua L.) using 3 statistical approaches. A total of 3,576 individually tagged juvenile cod from 50 full-sib families were infected with Vibrio anguillarum, which causes vibriosis, a frequently reported disease in cod aquaculture. The experimental fish were progeny of captured wild cod from populations of southern coastal cod (POP1), and northern coastal cod and northeast Arctic cod (combined as POP2 in the genetic analyses). Fish were randomly assigned to 1 of 3 test tanks, and daily mortality was recorded until the termination of the experiment at d 31 postinfection. Variance components were estimated separately for the 2 populations using a Cox regression model, univariate linear model, and a linear model that accounted for censoring. With all approaches, the additive genetic sire variance estimated from POP1 was greater than for POP2. Heritability estimates across populations varied from 0.08 to 0.17 depending on the method used. The Cox regression model and univariate linear model resulted in greater heritability estimates for POP1 (0.10 and 0.16) than for POP2 (0.08 and 0.13), whereas the contrary was true with a linear model that accounted for censoring (0.17 vs. 0.14). The predicted breeding values for the sires from the 3 approaches were highly correlated (0.97 to 0.99). This is likely due to the fact that censoring only occurred at the end of the test; i.e., observations of the most resistant fish were censored. The considerable genetic variation found in this study suggests that vibriosis resistance may be improved through selective breeding. The univariate linear model, even without censoring of the data, was robust for the estimation of breeding values using the present data. Therefore, inclusion of vibriosis resistance in the multivariate linear estimation of breeding values for the traits of economic importance in Atlantic cod seems appropriate.

Exchange rate behavior is analyzed in the context of a stochastic rational expectations model in which there are random shocks to the price setting mechanism and in which the authorities choose to impose either nominal or real exchange rate bands. Results are compared to those which emerge from a simple monetary model subject to velocity shocks. The effects of a realignment of the Band, and of fiscal policy used in conjunction with monetary policy to defend the band, are also examined.