The state space representation and estimation of a time-varying parameter VAR with stochastic volatility
AbstractTo capture the evolving relationship between multiple economic variables, time variation in either coefficients or volatility is often incorporated into vector autoregressions (VARs). However, allowing time variation in coefficients or volatility without restrictions on their dynamic behavior can increase the number of parameters too much, making the estimation of such a model practically infeasible. For this reason, researchers typically assume that time-varying coefficients or volatility are not directly observed but follow random processes which can be characterized by a few parameters. The state space representation that links the transition of possibly unobserved state variables with observed variables is a useful tool to estimate VARs with time-varying coefficients or stochastic volatility. ; In this paper, we discuss how to estimate VARs with time-varying coefficients or stochastic volatility using the state space representation. We focus on Bayesian estimation methods which have become popular in the literature. As an illustration of the estimation methodology, we estimate a time-varying parameter VAR with stochastic volatility with the three U.S. macroeconomic variables including inflation, unemployment, and the long-term interest rate. Our empirical analysis suggests that the recession of 2007-2009 was driven by a particularly bad shock to the unemployment rate which increased its trend and volatility substantially. In contrast, the impacts of the recession on the trend and volatility of nominal variables such as the core PCE inflation rate and the ten-year Treasury bond yield are less noticeable.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Federal Reserve Bank of Kansas City in its series Research Working Paper with number RWP 12-04.
Date of creation: 2012
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-08-23 (All new papers)
- NEP-ECM-2012-08-23 (Econometrics)
- NEP-ETS-2012-08-23 (Econometric Time Series)
- NEP-MAC-2012-08-23 (Macroeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gary Koop & Dimitris Korobilis, 2009.
"Bayesian Multivariate Time Series Methods for Empirical Macroeconomics,"
Working Paper Series
47_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
- Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
- Koop, Gary & Korobilis, Dimitris, 2009. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," MPRA Paper 20125, University Library of Munich, Germany.
- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-17, October.
- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002.
"Bayesian Analysis of Stochastic Volatility Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 20(1), pages 69-87, January.
- Fabio Canova & Luca Gambetti, 2003.
"Structural changes in the US economy: is there a role for monetary policy?,"
Economics Working Papers
918, Department of Economics and Business, Universitat Pompeu Fabra, revised Apr 2008.
- Canova, Fabio & Gambetti, Luca, 2009. "Structural changes in the US economy: Is there a role for monetary policy?," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 477-490, February.
- Clark, Todd E., 2011. "Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 327-341.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lu Dayrit).
If references are entirely missing, you can add them using this form.