Our contributions 1 we characterize the general solutions of linear rational expectations model with exogenous markovswitching of the parameters. The literature on markovswitching linear rational expectations mslre models has been an active field in empirical macroeconomics leeper and zha 2003, blake and zampolli 2006, svensson and. Statespace models with markovswitching abstract in this paper we use a statespace model with markovswitching to detect speculative bubbles in stockprice data. Optimal discretionary policy in rational expectations. Understanding markov switching rational expectations models. We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forwardlooking markovswitching rational expectations models and we develop an algorithm to. The longrun taylor principle revisited final wp version. The general conclusions about the forecasting ability of the segmented trends model was not affected by the choice of estimation period, but the model estimated on quarterly data does. Boundedly rational agents form expectations using a simple univariate model. In other words, researchers consider linear rational 2.
In a general class of markov switching rational expectations models, this study derives necessary and sufficient conditions for determinacy, indeterminacy and the case of no stable solution. Rise is an objectoriented matlab toolbox for solving and estimating nonlinear regime switching dynamic stochastic general equilibrium rsdsge models. Section 2 of this article describes the rational expectations models of exchange. Markovswitching rational expectations models 2 2006, 2007, and farmer, waggoner, and zha 2008a. The mslre approach introduces an important nonlinearity into the standard linear rational expectations models. Because the markov chain enters the model multiplicatively, the model is inherently nonlinear. This alternative question is important because, ultimately, an equilibrium we select ought to explain the observed data. Waggoner, and tao zha working paper 200823a september 2010 abstract. The literature on markovswitching linear rational expectations mslre models has been an active eld in empirical macroeconomics leeper and zha 2003, blake and zampolli 2006, svensson and williams 2007, davig and leeper 2007, and farmer et al. This procedure enables us to estimate a tworegime markov.
Classification of the models into these three mutually disjoint and exhaustive subsets is completely characterized by the most stable solution in the mean. Markovswitching models, rational expectations and the. For markov switching rational expectations models themselves, however, a more relevant question is based on the likelihood principle. We use three examples, based on the new keynesian model of monetary policy, to illustrate our technique. Regimeswitching rational expectations models, in which the parameters of the model evolve according to a. Characterizing markovswitching rational expectation. Issues that are well understood in linear contexts, such as equilibrium determinacy and stability under adaptive learning, reemerge in this new context.
There are two main shortcomings with the mslre approach. Optimal discretionary policy in rational expectations models. Waggoner, and tao zha working paper 20095 march 2009 abstract. Understanding markov switching rational expectations models roger e. If s t is postulated as the indicator variable 1 f t cgsuch that s t 0 or 1 depending on whether the value of t is greater than the cuto threshold value c, 2. Expectational stability in regimeswitching rational. Methods for measuring expectations and uncertainty in markovswitching models.
We develop a new method for deri ving minimal state variable msv equilibria of a general class of markovswitching rational expectations models and a new algorithm for computing these equilibria. Su cient conditions for determinacy in a class of markov. We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forwardlooking markov switching rational expectations models, and we develop an algorithm to check these conditions in practice. Linear rational expectations models with changes in regime. Determinacy and classification of markovswitching rational. More importantly, we innovate by introducing statedependent probability distributions. Stochastic consistent expectations equilibria in a regime switching. I extend a simple new keynesian model with the markovswitchingtype taylor rule introduced by davig and leeper 2007 by incorporating the constraint of the zero lower bound zlb, using the concept and algorithms of the stochastic rational expectations equilibrium proposed by billi 20. So, the models were also estimated on monthly data. Markovswitching rational expectations model lead to a determinate equilibrium see farmer et al.
As an illustration, we apply our method to determine the optimal monetary policy solution in the presence of structural changes in intrinsic output persistence, within a hybrid new. Understanding markovswitching rational expectations. We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forwardlooking markovswitching rational expectations. The literature on markov switching linear rational expectations mslre models has been an active eld in empirical macroeconomics leeper and zha 2003, blake and zampolli 2006, svensson and williams 2007, davig and leeper 2007, and farmer, waggoner. These models are very general and flexible tools for modelling model uncertainty. Characterizing markovswitching rational expectation models. Understanding markovswitching rational expectations models, nber working papers 14710, national bureau of economic research, inc. Identification of speculative bubbles using statespace. Perturbation methods for markovswitching dynamic stochastic. This note identifies a restriction on the solution under which the condition is sufficient as well as necessary. A classical belief is that under rational expectations and rational behaviour of economic agents any asset price should be in line with its market fundamental value. The literature on markovswitching linear rational expectations mslre models has been an active. Estimating macroeconomic models of financial crises.
Optimal monetary policy in markov switching models with rational expectations agents staff working papers set out research in progress by our staff, with the aim of encouraging comments and debate. Economic fluctuations and growth program, monetary economics program we develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forwardlooking markovswitching. Closedform solution of dsges and assetpricing implications lucas tree model with crra utility. Rational expectations in a var with markov switching diva.
Davig and doh2008 re fer towoodford2003 to linearise a nonlinear new keynesian model with markov switching. For markovswitching rational expectations models themselves, however, a more relevant question is based on the likelihood principle. The literature on markovswitching linear rational expectations mslre is now well established e. Monetary policy regime shifts under the zero lower. We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forwardlooking markov switching rational expectations models and we develop an algorithm to. The literature on markov switching linear rational expectations mslre is now well established e.
We develop a new method for deri ving minimal state variable msv equilibria of a general class of markov switching rational expectations models and a new algorithm for computing these equilibria. When the response of long rates to short rates is restricted to be this rationalexpectations forecast, the residuals have a standard deviation of only 0. This paper describes a method for solving a class of forwardlooking markov switching rational expectations models under noisy measurement, by specifying the unobservable expectations component as a generalmeasurable function of the observable states of the system, to be determined optimally via stochastic control and filtering theory. Understanding markovswitching rational expectations models. Online appendix to sufficient conditions for determinacy. That is, p 00 and p 11 arenot identi edunder the null, and they arenuisance parameters. Markovswitching rational expectations msre models can bring out fresh insights beyond what linear rational expectations re models have done for macroeconomics as davig and leeper 2007 and. Characterizing markovswitching rational expectations models by. Understanding markovswitching rational expectations models, frb atlanta working paper 200905, federal reserve bank of atlanta. Var, markov chain, regime switching, rational expectations, expectations hypothesis. Equilibria scee in linear markov regime switching mrs models.
Perturbation methods for markovswitching dsge models. Request pdf markovswitching models, rational expectations and the term structure of interest rates in order to evaluate the efficiency of the monetary transmission mechanism, we develop the. In particular, a rational expectations equilibrium is any uniformly bounded solution to. Building on standard linear rational expectations models, the mslre approach allows pa. When there are unidenti ed nuisance parameters under the null, the.
Under the null, the markov switching model reduces to an ark model, and the likelihood value isnota ected by p 00 and p 11. First, most of the analyzed models do not begin from rst principles. It is known that the former is merely a necessary condition. Markov switching rational expectations models 2 2006, 2007, and farmer, waggoner, and zha 2008a. Rationality in switching environments rise toolbox. A technical guide seonghoon cho january 26, 2015 abstract cho 2014 proposes a solution method and derives su cient conditions for determinacy and indeterminacy in the meansquare stability sense in the class of general markov switching rational expectations msre models.
Markovswitching dsge models and applications description. Monetary policy regime shifts under the zero lower bound. Transition probabilities, exogenous markov switching, infinite hidden markov model, endogenous markov switching, markov process, finite mixture model, changepoint model, nonhomogeneous markov switching, time series analysis, business cycle analysis. Statedependent probability distributions in non linear.
Regime switching rational expectations models, in which the parameters of the model evolve according to a. Rational expectations in a var with markov switching. Msre models are more complicated than linear rational expectations models since the agents of the model must be allowed to take account of the possibility of future regime changes when formingexpectations. Regime switching rational expectations models, in which the parameters of the model evolve according to a finite state markov process, have properties that differentiate them from linear models. Essays on markovswitching dynamic stochastic general. R package for estimation, simulation and forecasting of a univariate markov switching model. Why use markovswitching models in exchange rate prediction. We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forwardlooking markovswitching rational expectations models, and we develop an algorithm to check these conditions in practice. On the solution of markovswitching rational expectations models. In a general class of markovswitching rational expectations models, this study derives necessary and sufficient conditions for determinacy, indeterminacy and the case of no stable solution. Minimal state variable solutions to markov switching rational expectations models frb of atlanta working paper no.
Linear rational expectations models with changes in regime ast e yt 1 t,st,st 1. A technical guide seonghoon cho january 26, 2015 abstract cho 2014 proposes a solution method and derives su cient conditions for determinacy and indeterminacy in the meansquare stability sense in the class of general markovswitching rational expectations msre models. Markovswitching rational expectations msre models can yield fresh insights beyond what linear rational expectations lre models have done for macroeconomics. Characterizing markovswitching rational expectations models. Cross validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
Testing for switching parameters the null hypothesis is 1 0. Can the markov switching model forecast exchange rates. One is the longrun taylor principle of davig and leeper 2007 and the other is by farmer, waggoner, and zha 2009. We develop a set of necessary and sufficient conditions for equilibria to be determinate in a. Minimal state variable solutions to markovswitching rational. Request pdf characterizing markovswitching rational expectation models markovswitching rational expectations msre models can. Minimal state variable solutions to markovswitching.
Markovswitching full information rational expectations models see bianchi 20, for example o. In markov switching models, a subset of parameters change over time, and agents are aware of the probability of changes and their optimizing behavior re. Pdf expectational stability in regimeswitching rational. Rise is an objectoriented matlab toolbox for solving and estimating nonlinear regimeswitching dynamic. I extend a simple new keynesian model with the markov switching type taylor rule introduced by davig and leeper 2007 by incorporating the constraint of the zero lower bound zlb, using the concept and algorithms of the stochastic rational expectations equilibrium proposed by billi 20. An algorithm is devised to compute the solution of a linear rational expectations model with random parameters or regime shifts.
However, most of the literature on solving rational expectations. Markov switching process on quarterly data, and vice versa. To this end we express a presentvalue stockprice model in statespace form which we estimate using the kalman. It is quite common to choose a lagged dependent variable say, z. The literature on markov switching linear rational expectations mslre models has been an active eld in empirical macroeconomics leeper and zha 2003, blake and zampolli 2006, svensson and williams 2007, davig and leeper 2007, and farmer et al. In section 5 we discuss some results from the engineering literature and explain the dif ferences between alternative stability concepts that are equivalent in linear. This paper is also closely related to the growing literature on solving linear exogenous markov switching models. See examples for simple ways of using the package and also check the pdf document for advanced. The literature on markov switching linear rational expectations mslre models has been an active field in empirical macroeconomics leeper and zha 2003, blake and zampolli 2006, svensson and. Optimal monetary policy in markovswitching models with. Minimal state variable solutions to markovswitching rational expectations models frb of atlanta working paper no. Welcome to rise for any issue, suggestion or bug report, please send an email to junior.
Understanding markovswitching rational expectations models roger e. The current work adds to the literature by using markov switching rules in the context of a rational expectations model on turkey and by analyzing whether the conditions were present for monetary policy to stabilize prices without the e ect of scal shocks for the pre and post2001 period. Weinbach markov switchmg model is useful of the potential it offers for. The regime shift model used falls into the general framework of hamilton 1990, but differs to the centered model actually implemented by hamilton and others. This package has designed the estimation, simulation and forecasting of markov switching models. Which equilibrium should be selected conditional on the data we observe. This paper shows how a well known class of rational expectations hypothesis using linear vector autoregressions var. Markov switching rational expectations msre models can bring out fresh insights beyond what linear rational expectations re models have done for macroeconomics as davig and leeper 2007 and. Building on standard linear rational expectations mod. Pt price of stock dt dividend coefficient of relative risk aversion pt dt k 1 ke tdt k 1. In this paper we consider the optimal control problem of models with markov regime shifts and forwardlooking agents. For instance, davig and leeper 2007 consider a regimeswitching monetary policy in an otherwise canonical newkeynesian model and. We extend an algorithm of backus and driffill for optimal discretionary policy in rational expectations models to the case with markov switching in model parameters.
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