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.     

Forecasting South African macroeconomic variables with a Markov-switching small open-economy dynamic stochastic general equilibrium model

This paper seeks to identify evidence of regime-switching behaviour in the monetary policy response function and the variance of the shocks. It makes use of various specifications of a small open-economy Markov-switching dynamic stochastic general equilibrium model that is applied to South African data from 1989 to 2014. While the in-sample statistics suggest that some of the regime-switching models may provide superior results, the out-of-sample statistics suggest that the inclusion of various forms of regime-switching does not significantly improve upon the forecasting performance of the model. The results also suggest that the central bank response function has been consistently applied over the sample period.     

A Nonlinear Approach for Modeling and Forecasting US Business Cycles

The purpose of this paper is to provide a complete evaluation of four regime-switching models by checking their performance in detecting US business cycle turning points, in replicating US business cycle features and in forecasting US GDP growth rate. Both individual and combined forecasts are considered. Results indicate that while the Markov-switching model succeeded in replicating all the NBER peak and trough dates without an extra-cycle detection, it seems to be outperformed by the Bounce-back model in term of the delay time to a correct alarm. Concerning business cycle features characterization, none of the competing models dominates over all the features. The performance of the Markov-switching and bounce back models in detecting turning points was not translated into an improved business cycle feature characterization since they are outperformed by the Floor and Ceiling model. The forecast performance of the considered models varies across regimes and across forecast horizons. That is, the model performing best in an expansion period is not necessarily the same in a recession period and similarly for the forecast horizons. Finally, combining such individual forecasts generally leads to increased forecast accuracy especially for h=1.     

The non-linear impact of high and growing government external debt on economic growth: A Markov Regime-switching approach

Today, the major reason for external debt is to finance high public deficits. This study aims to examine the relationship between external indebtedness and growth variables. In this context, Markov-switching model is used because it allows the examination of unobservable variables in an observable model and provides steady algorithm to achieve robust optimization by iterations in a dynamic system, and is more flexible than prior models. This paper concentrates on the analysis of Turkey and utilizes the data set for the period of 1974 to 2009. Throughout the analyses, the relationship between growth and external borrowing is examined in terms of public and private external borrowing. Paper yields that, according to results of multivariate dynamic Markov-switching model, the main growth variables such as investment and human capital have positive impact on growth as expected. Findings can be summarized as follows; firstly, public and/or private external borrowing has negative impact on growth both in regime at zero and regime at one. Secondly, the negative impact of public borrowing on economic growth and development is higher than that of private borrowing on economic growth and development. Eventually, the conclusion reveals that the economic development and borrowing variables do not follow a linear path.     

The stability of the Turkish Phillips curve and alternative regime shifting models

This article, presents empirical evidence supporting instability of the Phillips curve in Turkey. We employ the multiple structural break models and the Markov-switching models and then evaluate the performance of the two models. The data pertain to the monthly inflation rate in Turkey for the period of 1987 to 2004. The results show that the Turkish Phillips curve is not linear. There exists no evidence on the asymmetry in the inflation response to output gap. The persistence of inflation is found to be much lower than in linear models. After 2001, slight decline in persistence of inflation is observed. There exits weaker support for the Phillips curve for the periods where the policymakers attempt to take the advantage of the tradeoff between output and inflation relationship.     

Mixed-frequency VAR models with Markov-switching dynamics

This paper extends the Markov-switching vector autoregressive models to accommodate both the typical lack of synchronicity that characterizes the real-time daily flow of macroeconomic information and economic indicators sampled at different frequencies. The results of the empirical application suggest that the model is able to capture the features of the NBER business cycle chronology very accurately.     

New directions in business cycle research and financial analysis

This paper serves as a partial introduction to and survey of the literature on Markov-switching models. We review the history of this class of models, describe their mathematical structure, and exposit the basic ideas behind estimation and inference. The paper also describes how the approach can be extended in a variety of directions, such as non-Gaussian distributions, time-varying transition probabilities, vector processes, state-space and GARCH models, and surveys recent methodological advances. The contributions of the other papers in this volume are reviewed. A final section offers conclusions and implications for policy. First Version Received: August 2001/Final Version Received: October 2001     

A Bayesian Approach To Testing for Markov-Switching in Univariate and Dynamic Factor Models

Though Hamilton's (1989) Markov-switching model has been widely estimated in various contexts, formal testing for Markov-switching is not straightforward. Univariate tests in the classical framework by Hansen (1992) and Garcia (1998) do not reject the linear model for GDP. We present Bayesian tests for Markov-switching in both univariate and multivariate settings based on sensitivity of the posterior probability to the prior. We find that evidence for Markov-switching, and thus the business cycle asymmetry, is stronger in a switching version of the dynamic factor model of Stock and Watson (1991) than it is for GDP by itself.     

Financial crises and dynamic linkages across international stock and currency markets

This paper investigates contagion across stock and currency markets of China, Eurozone, India, Japan and US during global financial crisis and Eurozone crisis. The crisis periods are selected using Markov-switching models for US and Eurozone markets. We, then, utilize the DCC-GARCH model to estimate conditional correlation among the assets and test for contagion/flight to quality effects during the crises. The results show significant contagion as well as flight to quality effects both across and within asset classes. We examine the impact of financial stress index on the correlation across markets and find that portfolio diversification benefits for equity markets may be non-existent.     

Evaluating currency crises: A Bayesian Markov switching approach

In this paper we examine the nature of a currency crisis. We do so by employing an out-of-sample forecasting exercise to analyse the Mexican crisis in 1994. Forecast evaluation was based on modern econometric techniques concerning the shape of forecaster’s loss function. We also extend the empirical framework suggested by Jeanne and Masson [Jeanne, O., Masson, P., 2000. Currency crises and Markov-switching regimes. Journal of International Economics 50, 327–350] to test for the hypothesis that the currency crisis was driven by sunspots. To this end we contribute to the existing literature by comparing Markov regime switching model with a time-varying transition probabilities with two alternative models. The first is a Markov regime switching model with constant transition probabilities. The second is a linear benchmark model. Empirical results show that the proxy for the probability of devaluation is an important factor explaining the nature of currency crisis. More concretely, when the expectation market pressure was used as a proxy of probability of devaluation, forecast evaluation supports the view that currency crisis was driven by market expectation unrelated to fundamentals. Alternatively, when interest rate differential is used as a proxy for probability of devaluation, currency crisis was due to predictable deterioration of fundamentals.     

Estimation and testing of alternative production function models

The paper deals with four different decision models for a firm operating with a constant elasticity of substitution production function. The assumptions underlying the different models and their consequences for estimation are carefully specified. Maximum likelihood estimates of the parameters are obtained of the full four-equation models, using data pertaining to the Dutch manufacturing sector. Finally likelihood ratio test procedures are developed in order to determine whether one or more of the decision models can be rejected on the basis of this data.     

A Markov–switching vector equilibrium correction model of the UK labour market

There is a wide literature on the dynamic adjustment of employment and its relationship with the business cycle. In this paper we present a statistical model that offers a congruent representation of part of the UK labour market since the mid 1960s. We use a cointegrated vector autoregressive Markov-switching model in which some parameters change according to the phase of the business cycle. Output, employment, labour supply and real earnings are found to have a common cyclical component. The long run dynamics are characterized by one cointegrating vector relating unemployment to trend-adjusted real wages and output. Despite there having been many changes affecting this sector of the UK economy, the Markov-switching vector-equilibrium-correction model with three regimes (representing recession, normal growth, and high growth) provides a good characterization of the sample data, and performs well relative to alternative linear and non-linear models. The results of an impulse-response analysis highlight the dangers of using VARs when the constancy of the estimated coefficients has not been established, and demonstrate the advantages of generating regime dependent responses. First Version Received: December 2000/Final Version Received: August 2001     

Forecasting Brazilian inflation by its aggregate and disaggregated data: a test of predictive power by forecast horizon

This work aims to compare the forecast efficiency of different types of methodologies applied to Brazilian consumer inflation (Índice de Preços ao Consumidor Amplo; IPCA). We will compare forecasting models using disaggregated and aggregated data from IPCA over 12 months ahead. We used IPCA in a monthly basis, over the period between January 1996 and March 2012. Out-of-sample analysis will be made through the period of January 2008 to March 2012. The disaggregated models were estimated by Seasonal Autoregressive Integrated Moving Average (SARIMA) and will have different levels of disaggregation from IPCA as groups and items, as well as disaggregation with more economic sense used by Brazilian Central Bank as: (1) services, monitored prices, food and industrials and (2) durables, non-durables, semi-durables, services and monitored prices. Aggregated models will be estimated by time series techniques as SARIMA, state-space structural models and Markov-switching. The forecasting accuracy among models will be made by the selection model procedure known as Model Confidence Set developed by Peter Hansen, Asger Lunde and James Nason. We were able to find evidence of forecast accuracy gains in models using more disaggregated rather than aggregate data.     

Financial crises and time-varying risk premia in a small open economy: a Markov-switching DSGE model for Estonia

Under a currency board, the central bank relinquishes control over its monetary policy and domestic interest rates converge towards the foreign rates. Nevertheless, a spread between both usually remains. This spread can be persistently positive due to elevated risk in the economy. This paper models that feature by building a DSGE model with a currency board, where the domestic interest rate is endogenously derived as a function of the foreign rate, the external debt position and an exogenous risk premium component. Time variation in the volatility of the risk premium component is then modelled via a Markov-switching component. Estimating the model with Bayesian methods and Estonian data shows that the economy does not react much to shocks to domestic interest rates in quiet times but is much more sensitive during crises, and matches the financial and banking crises, which cannot be captured by the standard DSGE model.     

An analysis of regime shifts in the Turkish economy

We use a time-varying dynamic factor model with regime switching to construct and estimate the leading indicators of the currency crises in Turkey. After that, we analyze the business cycles of the Turkish economy, by using a three-state univariate Markov-switching model. Both models capture the observed dynamics of the Turkish economy over the period 1987–2002.     

Forecasting electricity spot prices using time-series models with a double temporal segmentation

The French wholesale market is set to expand in the next few years under European pressure and national decisions. In this article, we assess the forecasting ability of several classes of time-series models for electricity wholesale spot prices at a day-ahead horizon in France. Electricity spot prices display a strong seasonal pattern, particularly in France, given the high share of electric heating in housing during winter time. To deal with this pattern, we implement a double temporal segmentation of the data. For each trading period and season, we use a large number of specifications based on market fundamentals: linear regressions, Markov-switching (MS) models and threshold models with a smooth transition. An extensive evaluation on French data shows that modelling each season independently leads to better results. Among nonlinear models, MS models designed to capture the sudden and fast-reverting spikes in the price dynamics yield more accurate forecasts. Finally, pooling forecasts give more reliable results.     

Estimating Central Banks’ preferences from a time-varying empirical reaction function

We estimate monetary policy reaction functions for the United States, the United Kingdom, and Germany, using a Markov-switching model that allows for shifts in the coefficients of the central bank's reaction function as well as for independent shifts in the residual variance. The results indicate that central bank policy can be characterized as falling into a low- and a high-inflation regime. Over time all central banks have assigned changing weights to inflation and the output gap. Switching in the residual variance turns out to be important for the fit of the model. As a reaction function is a reduced form, coefficients embody preference parameters as well as parameters characterizing the structure of the economy. To recover the central banks’ preferences, we estimate the preference parameters jointly with a small model of the economy. The results show that the Bundesbank has placed a relatively higher weight on inflation than the Fed. Moreover, for the Bundesbank and the Fed the differences between both regimes seem to originate mainly from a changing preference for interest rate smoothing.     

Portfolio flows and the US dollar–yen exchange rate

This paper investigates the effects of portfolio flows on the US dollar–Japanese yen exchange rate changes over the period 1988:01–2011:04. Using a time-varying transition probability Markov-switching framework, the results suggest that the impact of portfolio flows on the dollar–yen exchange rate changes is state-dependent. In particular, the results show that portfolio inflows from Japan toward the US, more than monetary variables, strengthen the probability of remaining in the dollar–yen appreciation (low volatility) state. Therefore, credit controls on the flows can be used as a policy tool to pursue economic and financial stability.     

Volatility in asset prices and long-run wealth effect estimates

We argue that the equation commonly used in the estimation of the wealth effect on consumption might be unsuitable for that purpose. In particular, if the usual assumptions are employed, the derivation of the equation implies that the wealth effect is indeterminate. Furthermore, it implies that the estimate of the wealth effect should decrease when asset wealth volatility increases. Estimation of a Markov-switching model of the usual long-run aggregate consumption equation provides evidence favourable to the indeterminacy hypothesis.     

Score-driven Markov-switching EGARCH models: an application to systematic risk analysis

We introduce new Markov-switching (MS) dynamic conditional score (DCS) exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models, to be used by practitioners for forecasting value-at-risk (VaR) and expected shortfall (ES) in systematic risk analysis. We use daily log-return data from the Standard & Poor’s 500 (S&P 500) index for the period 1950–2016. The analysis of the S&P 500 is useful, for example, for investors of (i) well-diversified US equity portfolios; (ii) S&P 500 futures and options traded at Chicago Mercantile Exchange Globex; (iii) exchange traded funds (ETFs) related to the S&P 500. The new MS DCS-EGARCH models are alternatives to of the recent MS Beta-t-EGARCH model that uses the symmetric Student’s t distribution for the error term. For the new models, we use more flexible asymmetric probability distributions for the error term: Skew-Gen-t (skewed generalized t), EGB2 (exponential generalized beta of the second kind) and NIG (normal-inverse Gaussian) distributions. For all MS DCS-EGARCH models, we identify high- and low-volatility periods for the S&P 500. We find that the statistical performance of the new MS DCS-EGARCH models is superior to that of the MS Beta-t-EGARCH model. As a practical application, we perform systematic risk analysis by forecasting VaR and ES.

Abbreviation Single regime (SR); Markov-switching (MS); dynamic conditional score (DCS); exponential generalized autoregressive conditional heteroscedasticity (EGARCH); value-at-risk (VaR); expected shortfall (ES); Standard & Poor's 500 (S&P 500); exchange traded funds (ETFs); Skew-Gen-t (skewed generalized t); EGB2 (exponential generalized beta of the second kind); NIG (normal-inverse Gaussian); log-likelihood (LL); standard deviation (SD); partial autocorrelation function (PACF); likelihood-ratio (LR); ordinary least squares (OLS); heteroscedasticity and autocorrelation consistent (HAC); Akaike information criterion (AIC); Bayesian information criterion (BIC); Hannan-Quinn criterion (HQC).