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A Bayesian evaluation of alternative models of trend inflation

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  • Todd E.Clark
  • Taeyoung Doh

Abstract

The concept of trend inflation is important in making accurate inflation forecasts. However, there is little consensus on how the trend in inflation should be modeled. While some studies suggest a survey-based measure of long-run inflation expectations as a good empirical proxy for trend inflation, others have argued for a statistical exercise of decomposing inflation data into trend and cycle components. In this paper, we assess alternative models of trend inflation based on the accuracy of medium-term inflation forecasts. To incorporate recent evidence on the time-varying macroeconomic volatility, we consider models with both constant volatility and time-varying volatility. For all the models, we compare not only point predictions but also density forecasts, such as deflation probability. Our analysis yields two broad results. First, models with time-varying volatility consistently dominate those with constant volatility. Second, once time-varying volatility is incorporated, it is difficult to say that one model of trend inflation is better. Simply averaging forecasts with time-varying volatility is as good as forecasts from the best-fitting model. In addition, the relative performance of each model varies greatly over time. Overall, our results suggest that it is important to consider predictions from a range of models with time-varying volatility.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Kansas City in its series Research Working Paper with number RWP 11-16.

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Date of creation: 2011
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Handle: RePEc:fip:fedkrw:rwp11-16

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Keywords: Bayesian statistical decision theory ; Inflation (Finance) ; Forecasting;

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References

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  1. Todd E. Clark & Michael W. McCracken, 2009. "Nested forecast model comparisons: a new approach to testing equal accuracy," Working Papers 2009-050, Federal Reserve Bank of St. Louis.
  2. Luc Bauwens & Gary Koop & Dimitris Korobilis & Jeroen Rombouts, 2011. "A Comparison of Forecasting Procedures For Macroeconomic Series: The Contribution of Structural Break Models," CIRANO Working Papers 2011s-13, CIRANO.
  3. Koop, Gary & Korobilis, Dimitris, 2009. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," MPRA Paper 20125, University Library of Munich, Germany.
  4. Kadiyala, K. Rao & Karlsson, Sune, 1994. "Numerical Aspects of Bayesian VAR-modeling," Working Paper Series in Economics and Finance 12, Stockholm School of Economics.
  5. Geweke, John & Amisano, Gianni, 2008. "Comparing and evaluating Bayesian predictive distributions of assets returns," Working Paper Series 0969, European Central Bank.
  6. Peter N. Ireland, 2005. "Changes in the Federal Reserve’s Inflation Target: Causes and Consequences," Boston College Working Papers in Economics 607, Boston College Department of Economics.
  7. Todd E. Clark & Michael W. McCracken, 2010. "Testing for unconditional predictive ability," Working Papers 2010-031, Federal Reserve Bank of St. Louis.
  8. Timothy Cogley & Giorgio E. Primiceri & Thomas J. Sargent, 2010. "Inflation-Gap Persistence in the US," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(1), pages 43-69, January.
  9. Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
  10. Cogley, Timothy W. & Morozov, Sergei & Sargent, Thomas J., 2003. "Bayesian fan charts for UK inflation: Forecasting and sources of uncertainty in an evolving monetary system," CFS Working Paper Series 2003/44, Center for Financial Studies (CFS).
  11. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
  12. Todd E. Clark & Michael W. McCracken, 2010. "Averaging forecasts from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 5-29.
  13. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
  14. Michael T. Kiley, 2008. "Monetary policy actions and long-run inflation expectations," Finance and Economics Discussion Series 2008-03, Board of Governors of the Federal Reserve System (U.S.).
  15. Elmar Mertens, 2011. "Measuring the level and uncertainty of trend inflation," Finance and Economics Discussion Series 2011-42, Board of Governors of the Federal Reserve System (U.S.).
  16. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
  17. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
  18. Todd E. Clark & Michael W. McCracken, 2011. "Advances in forecast evaluation," Working Papers 2011-025, Federal Reserve Bank of St. Louis.
  19. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  20. James Morley & Jeremy Piger, 2012. "The Asymmetric Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 208-221, February.
  21. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  22. Todd E. Clark & Troy Davig, 2009. "Decomposing the declining volatility of long-term inflation expectations," Research Working Paper RWP 09-05, Federal Reserve Bank of Kansas City.
  23. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
  24. Robert J. Gordon, 1998. "Foundations of the Goldilocks Economy: Supply Shocks and the Time-Varying NAIRU," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 29(2), pages 297-346.
  25. Michael Dotsey & Shigeru Fujita & Tom Stark, 2011. "Do Phillips curves conditionally help to forecast inflation?," Working Papers 11-40, Federal Reserve Bank of Philadelphia.
  26. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
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Citations

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Cited by:
  1. Gefang, Deborah & Koop, Gary & Potter, Simon M., 2008. "The Dynamics of UK and US Inflation Expectations," SIRE Discussion Papers 2008-59, Scottish Institute for Research in Economics (SIRE).
  2. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
  3. Chan, Joshua & Koop, Gary & Potter, Simon, 2012. "A New Model Of Trend Inflation," SIRE Discussion Papers 2012-12, Scottish Institute for Research in Economics (SIRE).
  4. Davide Delle Monache & Ivan Petrella, 2014. "Adaptive Models and Heavy Tails," Working Papers 720, Queen Mary, University of London, School of Economics and Finance.
  5. Taeyoung Doh, 2011. "Is unemployment helpful in understanding inflation?," Economic Review, Federal Reserve Bank of Kansas City, issue Q IV, pages 5-26.

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