The marginal likelihood of Structural Time Series Models, with application to the euroareaa nd US NAIRU
AbstractWe propose a simple procedure for evaluating the marginal likelihood in univariate Structural Time Series (STS) models. For this we exploit the statistical properties of STS models and the results in Dickey (1968) to obtain the likelihood function marginally to the variance parameters. This strategy applies under normal-inverted gamma-2 prior distributions for the structural shocks and associated variances. For trend plus noise models such as the local level and the local linear trend, it yields the marginal likelihood by simple or double integration over the (0,1)-support. For trend plus cycle models, we show that marginalizing out the variance parameters greatly improves the accuracy of the Laplace method. We apply this ethodology to the analysis of US and euro area NAIRU.
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 The Rimini Centre for Economic Analysis in its series Working Paper Series with number 21-08.
Date of creation: Jan 2008
Date of revision: Jan 2008
Marginal likelihood; Markov Chain Monte Carlo; unobserved components; bridge sampling; Laplace method; NAIRU;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-09-13 (All new papers)
- NEP-ECM-2008-09-13 (Econometrics)
- NEP-ETS-2008-09-13 (Econometric Time Series)
- NEP-ORE-2008-09-13 (Operations Research)
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.:
- James H. Stock & Mark W. Watson, 2006.
"Why Has U.S. Inflation Become Harder to Forecast?,"
NBER Working Papers
12324, National Bureau of Economic Research, Inc.
- Harvey, Andrew C. & Trimbur, Thomas M. & Van Dijk, Herman K., 2007.
"Trends and cycles in economic time series: A Bayesian approach,"
Journal of Econometrics,
Elsevier, vol. 140(2), pages 618-649, October.
- Harvey, A.C. & Trimbur, T.M. & van Dijk, H.K., 2005. "Trends and cycles in economic time series: A Bayesian approach," Econometric Institute Research Papers EI 2005-27, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- BAUWENS, Luc & ROMBOUTS, Jeroen V.K., .
CORE Discussion Papers RP
-1713, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Hansen, Gary D., 1997.
"Technical progress and aggregate fluctuations,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 21(6), pages 1005-1023, June.
- Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
- Harvey, A.C. & Trimbur, T.M., 2001.
"General Model-based Filters for Extracting Cycles and Trends in Economic Time Series,"
Cambridge Working Papers in Economics
0113, Faculty of Economics, University of Cambridge.
- Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
- Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept.
- Richard, J. -F. & Tompa, H., 1980. "On the evaluation of poly-t density functions," Journal of Econometrics, Elsevier, vol. 12(3), pages 335-351, April.
- Christophe Planas & Werner Roeger & Alessandro Rossi, 2004.
"How much has labour taxation contributed to European structural unemployment?,"
- Planas, Christophe & Roeger, Werner & Rossi, Alessandro, 2007. "How much has labour taxation contributed to European structural unemployment?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1359-1375, April.
- Christophe Planas & Werner Roeger & Alessandro Rossi, 2003. "How much has labour taxation contributed to European structural unemployment?," European Economy - Economic Papers 183, Directorate General Economic and Monetary Affairs (DG ECFIN), European Commission.
- Clark, Peter K, 1987. "The Cyclical Component of U.S. Economic Activity," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 797-814, November.
- Robert E. Hall & Frederic S. Mishkin, 1980.
"The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households,"
NBER Working Papers
0505, National Bureau of Economic Research, Inc.
- Hall, Robert E & Mishkin, Frederic S, 1982. "The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households," Econometrica, Econometric Society, vol. 50(2), pages 461-81, March.
- Joseph Stiglitz, 1997. "Reflections on the Natural Rate Hypothesis," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 3-10, Winter.
- Stock, James H & Watson, Mark W, 1988. "Variable Trends in Economic Time Series," Journal of Economic Perspectives, American Economic Association, vol. 2(3), pages 147-74, Summer.
- C�cile Denis & Daniel Grenouilleau & Kieran Mc Morrow & Werner R�ger, 2006. "Calculating potential growth rates and output gaps - A revised production function approach," European Economy - Economic Papers 247, Directorate General Economic and Monetary Affairs (DG ECFIN), European Commission.
- Planas, Christophe & Rossi, Alessandro & Fiorentini, Gabriele, 2008. "Bayesian Analysis of the Output Gap," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 18-32, January.
- Harvey, Andrew, 2006. "Forecasting with Unobserved Components Time Series Models," Handbook of Economic Forecasting, Elsevier.
- Pagan, Adrian R, 1975. "A Note on the Extraction of Components from Time Series," Econometrica, Econometric Society, vol. 43(1), pages 163-68, January.
- Froeb, Luke & Koyak, Robert, 1994. "Measuring and comparing smoothness in time series the production smoothing hypothesis," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 97-122.
- Kuttner, Kenneth N, 1994. "Estimating Potential Output as a Latent Variable," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 361-68, July.
- Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
- Philippe Moës, 2012. "Multivariate models with dual cycles: implications for output gap and potential growth measurement," Empirical Economics, Springer, vol. 42(3), pages 791-818, June.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Roberto Patuelli).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.