This paper proposes a hierarchical modeling approach to perform stochastic model specification in Markov switching vector error correction models. We assume that a common distribution gives rise to the regime-specific regression coefficients. The mean as well as the variances of this distribution are treated as fully stochastic and suitable shrinkage priors are used. These shrinkage priors enable to assess which coefficients differ across regimes in a flexible manner. In the case of similar coefficients, our model pushes the respective regions of the parameter space towards the common distribution. This allows for selecting a parsimonious model while still maintaining sufficient flexibility to control for sudden shifts in the parameters, if necessary. We apply our modeling approach to real-time Euro area data and assume transition probabilities between expansionary and recessionary regimes to be driven by the cointegration errors. The results suggest that the regime allocation is governed by a subset of short-run adjustment coefficients and regime-specific variance-covariance matrices. These findings are complemented by an out-of-sample forecast exercise, illustrating the advantages of the model for predicting Euro area inflation in real time.
Albert, J. H., and S. Chib. 1993. “Bayesian Analysis of Binary and Polychotomous Response Data.” Journal of the American Statistical Association 88 (422): 669–679.
Amisano, G., and G. Fagan. 2013. “Money Growth and Inflation: A Regime Switching Approach.” Journal of International Money and Finance 33 (3): 118–145.
Ang, A., G. Bekaert, and M. Wei. 2007. “Do Macro Variables, Asset Markets, or Surveys Forecast Inflation Better?” Journal of Monetary Economics 54 (4): 1163–1212.
Atkeson, A., and L. E. Ohanian. 2001. “Are Phillips Curves Useful for Forecasting Inflation?” Federal Reserve Bank of Minneapolis Quarterly Review 25 (1): 2–11.
Bańbura, M., D. Giannone, and L. Reichlin. 2010. “Large Bayesian Vector Auto Regressions.” Journal of Applied Econometrics 25 (1): 71–92.
Bec, F., and A. Rahbek. 2004. “Vector Equilibrium Correction Models with Nonlinear Discontinuous Adjustments.” The Econometrics Journal 7 (2): 628–651.
Bessec, M., and O. Bouabdallah. 2005. “What Causes the Forecasting Failure of Markov-Switching Models? A Monte Carlo Study.” Studies in Nonlinear Dynamics & Econometrics 9: (2): Article 6.
Bidarkota, P. V. 2001. “Alternative Regime Switching Models for Forecasting Inflation.” Journal of Forecasting 20 (1): 21–35.
Billio, M., R. Casarin, F. Ravazzolo, and H. K. van Dijk. 2016. “Interconnections between Eurozone and US Booms and Busts Using a Bayesian Panel Markov-Switching VAR Model.” Journal of Applied Econometrics 31 (7): 1352–1370.
Bognanni, M., and E. Herbst. 2018. “A Sequential Monte Carlo Approach to Inference in Multiple-Equation Markov-Switching Models.” Journal of Applied Econometrics 33 (1): 126–140.
Burns, A. F., and W. C. Mitchell. 1946. Measuring Business Cycles. NBER Book Series Studies in Business Cycles. Cambridge, MA: National Bureau of Economic Research.
Carriero, A., T. E. Clark, and M. Marcellino. 2015. “Bayesian VARs: Specification Choices and Forecast Accuracy.” Journal of Applied Econometrics 30 (1): 46–73.
Castelnuovo, E., and P. Surico. 2010. “Monetary Policy, Inflation Expectations and The Price Puzzle.” The Economic Journal 120 (549): 1262–1283.
Chib, S. 1996. “Calculating Posterior Distributions and Modal Estimates in Markov Mixture Models.” Journal of Econometrics 75 (1): 79–97.
Clark, T. E. 2011. “Real-Time Density Forecasts from Bayesian Vector Autoregressions with Stochastic Volatility.” Journal of Business & Economic Statistics 29 (3): 327–341.
Doan, T., R. Litterman, and C. Sims. 1984. “Forecasting and Conditional Projection Using Realistic Prior Distributions.” Econometric Reviews 3 (1): 1–100.
Droumaguet, M., A. Warne, and T. Wozniak. 2017. “Granger Causality and Regime Inference in Markov Switching VAR Models with Bayesian Methods.” Journal of Applied Econometrics 32 (4): 802–818.
Filardo, A. J. 1994. “Business-Cycle Phases and Their Transitional Dynamics.” Journal of Business & Economic Statistics 12 (3): 299–308.
Frühwirth-Schnatter, S. 2006. Finite Mixture and Markov Switching Models. Berlin: Springer.
Geweke, J., and G. Amisano. 2010. “Comparing and Evaluating Bayesian Predictive Distributions of Asset Returns.” International Journal of Forecasting 26 (2): 216–230.
Giannone, D., J. Henry, M. Lalik, and M. Modugno. 2012. “An Area-Wide Real-Time Database for the Euro Area.” Review of Economics and Statistics 94 (4): 1000–1013.
Goldfeld, S. M., and R. E. Quandt. 1973. “A Markov Model for Switching Regressions.” Journal of Econometrics 1 (1): 3–15.
Griffin, J. E., and P. J. Brown. 2010. “‘Inference with Normal-Gamma Prior Distributions in Regression Problems.” Bayesian Analysis 5 (1): 171–188.
Huber, F., and M. M. Fischer. 2018. “A Markov Switching Factor-Augmented VAR Model for Analyzing us Business Cycles and Monetary Policy.” Oxford Bulletin of Economics and Statistics 80 (3): 575–604.
Huber, F., and T. O. Zörner. 2019. “Threshold Cointegration in International Exchange Rates: A Bayesian Approach.” International Journal of Forecasting 35 (2): 458–473.
Hubrich, K., and R. J. Tetlow. 2015. “Financial Stress and Economic Dynamics: The Transmission of Crises.” Journal of Monetary Economics 70: 100–115.
Jarociński, M., and M. Lenza. 2018. “An Inflation-Predicting Measure of the Output Gap in the Euro Area.” Journal of Money, Credit and Banking 50 (6): 1189–1224.
Jochmann, M., and G. Koop. 2015. “Regime-Switching Cointegration.” Studies in Nonlinear Dynamics & Econometrics 19 (1): 35–48.
Kaufmann, S. 2000. “Measuring Business Cycles with a Dynamic Markov Switching Factor Model: An Assessment Using Bayesian Simulation Methods.” Econometrics Journal 3 (1): 39–65.
Kaufmann, S. 2015. “K-State Switching Models with Time-Varying Transition Distributions–Does Loan Growth Signal Stronger Effects of Variables on Inflation?” Journal of Econometrics 187 (1): 82–94.
Kim, C.-J., and C. R. Nelson. 1998. “Business Cycle Turning Points, a New Coincident Index, and Tests of Duration Dependence based on a Dynamic Factor Model with Regime Switching.” Review of Economics and Statistics 80 (2): 188–201.
Kim, C.-J., and C. R. Nelson. 1999. State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. Cambridge, MA and London, England: MIT Press.
Koop, G., R. León-González, and R. W. Strachan. 2009. “Efficient Posterior Simulation for Cointegrated Models with Priors on the Cointegration Space.” Econometric Reviews 29 (2): 224–242.
Koop, G., R. Leon-Gonzalez, and R. W. Strachan. 2011. “Bayesian Inference in a Time Varying Cointegration Model.” Journal of Econometrics 165 (2): 210–220.
Koop, G., and L. Onorante. 2012. “Estimating Phillips Curves in Turbulent Times Using the ECB’s Survey of Professional Forecasters.” ECB Working Paper No. 1422.
Litterman, R. 1986. “Forecasting with Bayesian Vector Autoregressions – Five Years of Experience.” Journal of Business & Economic Statistics 4 (1): 25–38.
Malsiner-Walli, G., S. Frühwirth-Schnatter, and B. Grün. 2016. “Model-Based Clustering Based on Sparse Finite Gaussian Mixtures.” Statistics and Computing 26 (1-2): 303–324.
Martin, G. M. 2000. “Us Deficit Sustainability: A New Approach Based on Multiple Endogenous Breaks.” Journal of Applied Econometrics 15: 83–105.
Paap, R., and H. K. Van Dijk. 2003. “Bayes Estimates of Markov Trends in Possibly Cointegrated Series: An Application to US Consumption and Income.” Journal of Business & Economic Statistics 21 (4): 547–563.
Park, T., and G. Casella. 2008. “The Bayesian Lasso.” Journal of the American Statistical Association 103 (482): 681–686.
Raftery, A. E., and S. Lewis. 1992. “How Many Iterations in the Gibbs Sampler?” In Bayesian Statistics 4, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, 763–773. Oxford: Oxford University Press.
Rubaszek, M., and P. Skrzypczynski. 2008. “On the Forecasting Performance of a Small-Scale DSGE Model.” International Journal of Forecasting 24 (3): 498–512.
Sims, C. A., and T. Zha. 1998. “Bayesian Methods for Dynamic Multivariate Models.” International Economic Review 39: 949–968.
Sims, C. A., and T. Zha. 2006. “Were there Regime Switches in US Monetary Policy?” American Economic Review 96 (1): 54–81.
Sims, C. A., D. F. Waggoner, and T. Zha. 2008. “Methods for Inference in Large Multiple-Equation Markov-Switching Models.” Journal of Econometrics 146 (2): 255–274.
Stock, J. H., and M. W. Watson. 2007. “Why has US Inflation become Harder to Forecast?” Journal of Money, Credit and banking 39: 3–33.
Strachan, R. W. 2003. “Valid Bayesian Estimation of the Cointegrating Error Correction Model.” Journal of Business & Economic Statistics 21 (1): 185–195.
Villani, M. 2001. “Bayesian Prediction with Cointegrated Vector Autoregressions.” International Journal of Forecasting 17 (4): 585–605.
Yau, C., and C. Holmes. 2011. “Hierarchical Bayesian Nonparametric Mixture Models for Clustering with Variable Relevance Determination.” Bayesian Analysis 6 (2): 329.
Zellner, A. 1973. An Introduction to Bayesian Inference in Econometrics. New York: Wiley.
SNDE recognizes that advances in statistics and dynamical systems theory can increase our understanding of economic and financial markets. The journal seeks both theoretical and applied papers that characterize and motivate nonlinear phenomena. Researchers are required to assist replication of empirical results by providing copies of data and programs online. Algorithms and rapid communications are also published.