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.

Bayesian Analysis of DSGE Models with Regime Switching

I estimate DSGE models with recurring regime changes in monetary policy (inflation target and reaction coefficients), technology (growth rate and volatility), and/or nominal price rigidities. In the models, agents are assumed to know deep parameter values but make probabilistic inference about prevailing and future regimes based on Bayes’ rule. I develop an estimation method that takes these probabilistic inferences into account when relating state variables to observed data. In an application to postwar U.S. data, I find stronger support for regime switching in monetary policy than in technology or nominal rigidities. In addition, a model with regime switching policy that conforms to the long-run Taylor principle given in Davig and Leeper (2007) is preferred to a determinacy-indeterminacy model motivated by Lubik and Schorfheide (2004). These empirical results indicate that, even though a passive policy regime produced more volatility in the economy from the early 1970s to the mid-1980s, the economy can be explained by determinacy over the entire postwar period, implying no role for sunspot shocks in explaining the changes in volatility

Heterogeneous expectations in the foreign exchange market : evidence from the daily Dollar/DM exchange rate

In this study a regime switching approach is applied to estimate the chartist and fundamentalist (c&f) exchange rate model originally proposed by Frankel and Froot (1986). The c&f model is tested against alternative regime switching specifications applying likelihood ratio tests. Nested atheoretical models like the popular segmented trends model suggested by Engel and Hamilton (1990) are rejected in favour of the multi agent model. Moreover, the c&f regime switching model seems to describe the data much better than a competing regime switching GARCH(1,1) model. Finally, our findings turned out to be relatively robust when estimating the model in subsamples. The empirical results suggest that the model is able to explain daily DM/Dollar forward exchange rate dynamics from 1982 to 1998

On the Solution of Markov-switching Rational Expectations Models

This paper describes a method for solving a class of forward-looking Markov-switching Rational Expectations models under noisy measurement, by specifying the unobservable expectations component as a general-measurable function of the observable states of the system, to be determined optimally via stochastic control and filtering theory. Solution existence is proved by setting this function to the regime-dependent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight autoregressive Markov jump state motion. As the exact expression of the conditional (rational) expectations term is derived both in finite and infinite horizon model formulations, no (asymptotic) stationarity assumptions are needed to solve forward the system, for only initial values knowledge is required. A simple sufficient condition for the mean-square stability of the obtained rational expectations equilibrium is also provided.Rational Expectations, Markov-switching dynamic systems, Dynamic programming, Time-varying Kalman filter

Bayesian Analysis of DSGE Models with Regime Switching

I estimate DSGE models with recurring regime changes in monetary policy (inflation target and reaction coefficients), technology (growth rate and volatility), and/or nominal price rigidities. In the models, agents are assumed to know deep parameter values but make probabilistic inference about prevailing and future regimes based on Bayes’ rule. I develop an estimation method that takes these probabilistic inferences into account when relating state variables to observed data. In an application to postwar U.S. data, I find stronger support for regime switching in monetary policy than in technology or nominal rigidities. In addition, a model with regime switching policy that conforms to the long-run Taylor principle given in Davig and Leeper (2007) is preferred to a determinacy-indeterminacy model motivated by Lubik and Schorfheide (2004). These empirical results indicate that, even though a passive policy regime produced more volatility in the economy from the early 1970s to the mid-1980s, the economy can be explained by determinacy over the entire postwar period, implying no role for sunspot shocks in explaining the changes in volatility.New Keynesian DSGE; Markov-switching; Monetary Policy; Indeterminacy; Long-run Taylor Principle; Bayesian Analysis;

Understanding the New Keynesian model when monetary policy switches regimes

This paper studies a New Keynesian model in which monetary policy may switch between regimes. We derive sufficient conditions for indeterminacy that are easy to implement and we show that the necessary and sufficient condition for determinacy, provided by Davig and Leeper, is necessary but not sufficient. More importantly, we use a two-regime model to show that indeterminacy in a passive regime may spill over to an active regime no matter how active the latter regime is. As a result, a passive monetary policy is more damaging than has been previously thought. Our results imply that the propagation of shocks in an active regime, such as that of the Federal Reserve in the post-1982 period, may be substantially affected by the possibility of a return to a passive regime of the kind that was followed in the 1960s and 1970s.

Realised and Optimal Monetary Policy Rules in an Estimated Markov-Switching DSGE Model of the United Kingdom

This paper conducts a systematic investigation of parameter instability in a small open economy DSGE model of the UK economy over the past thirty-five years. Using Bayesian analysis, we find a number of Markov-switching versions of the model provide a better fit for the UK data than a model with time-invariant parameters. The Markov-switching DSGE model that has two independent Markov-chains - one governing the shifts in UK monetary policy and nominal price rigidity and one governing the standard deviations of shocks - is selected as the best fitting model. The preferred model is then used to evaluate and design monetary policy. For the latter, we use the Markov-Jump-Linear-Quadratic (MJLQ) model, as it incorporates abrupt changes in structural parameters into derivations of the optimal and arbitrary policy rules. It also reveals the entire forecasting distribution of the targeted variables. To our knowledge, this is the first paper that attempts to evaluate and design UK monetary policy based on an estimated open economy Markov-switching DSGE model.DSGE models; Markov-switching; Bayesian analysis

Macroeconomic regimes

A New-Keynesian macro-model is estimated accommodating regime-switching behavior in monetary policy and macro-shocks. A key to our estimation strategy is the use of survey-based expectations for inflation and output. Output and inflation shocks shift to the low volatility regime around 1985 and 1990, respectively. Monetary policy experiences multiple shifts with an important role in shaping macro-volatility. New estimates of the onset and demise of the Great Moderation are provided and the relative role played by macro-shocks and monetary policy is quantified. The estimated rational expectations model exhibits indeterminacy in the mean-square stability sense, mainly due to passive monetary policy

Indeterminacy in a forward-looking regime-switching model

This paper is about the properties of Markov-switching rational expectations (MSRE) models. We discuss possible solution concepts for MSRE models, distinguishing between stationary and bounded equilibria. For the case of models with one variable, we provide a necessary and sufficient condition for uniqueness of a bounded equilibrium, and we relate this condition to an alternative, the generalized Taylor principle suggested by Davig and Leeper. We provide examples of models with multiple bounded and multiple stationary equilibria which suggest that it may be more difficult to rule out nonfundamental equilibria in MSRE models than in the single-regime case where the Taylor principle is known to guarantee local uniqueness.