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Using mean reversion as a measure of persistence

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  • Robalo Marques, Carlos
  • Dias, Daniel

Abstract

This paper elaborates on the alternative measure of persistence recently suggested in Marques (2004), which is based on the idea of mean reversion. A formal distinction between the "unconditional probability of a given process not crossing its mean in period t" and its estimator, is made clear and the relationship between this new measure and the widely used "sum of the autoregressive coefficients", as alternative measures of persistence, is investigated. Using the law of large numbers and the central limit theorem, properties for the estimator of the new measure of persistence are established, which allow tests of hypotheses to be performed, under very general conditions. Finally, some Monte Carlo experiments are conducted in order to compare the finite sample properties of the estimator for the "unconditional probability of a given process not crossing its mean in period t" and the OLS estimator for the "sum of the autoregressive coefficients". JEL Classification: E31, C22, E52

Suggested Citation

  • Robalo Marques, Carlos & Dias, Daniel, 2005. "Using mean reversion as a measure of persistence," Working Paper Series 450, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:2005450
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    1. Cheung, Yin-Wong & Lai, Kon S., 2000. "On the purchasing power parity puzzle," Journal of International Economics, Elsevier, vol. 52(2), pages 321-330, December.
    2. Altissimo, Filippo & Corradi, Valentina, 2003. "Strong rules for detecting the number of breaks in a time series," Journal of Econometrics, Elsevier, vol. 117(2), pages 207-244, December.
    3. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    4. Filippo Altissimo & Michael Ehrmann & Frank Smets, 2006. "Inflation persistence and price-setting behaviour in the euro area – a summary of the IPN evidence," Occasional Paper Series 46, European Central Bank.
    5. Frankel, Jeffrey A. & Rose, Andrew K., 1996. "A panel project on purchasing power parity: Mean reversion within and between countries," Journal of International Economics, Elsevier, vol. 40(1-2), pages 209-224, February.
    6. Lee, Junsoo, 1996. "On the power of stationarity tests using optimal bandwidth estimates," Economics Letters, Elsevier, vol. 51(2), pages 131-137, May.
    7. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    8. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    9. Burdekin, Richard C K & Siklos, Pierre L, 1999. "Exchange Rate Regimes and Shifts in Inflation Persistence: Does Nothing Else Matter?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(2), pages 235-247, May.
    10. García, Ana & Sansó, Andreu, 2006. "A Generalization Of The Burridge–Guerre Nonparametric Unit Root Test," Econometric Theory, Cambridge University Press, vol. 22(4), pages 756-761, August.
    11. Caner, M. & Kilian, L., 2001. "Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 639-657, October.
    12. Jeff Fuhrer & George Moore, 1995. "Inflation Persistence," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 127-159.
    13. Gerard O'Reilly & Karl Whelan, 2005. "Has Euro-Area Inflation Persistence Changed Over Time?," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 709-720, November.
    14. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
    15. Andrew T. Levin & Jeremy M. Piger, 2003. "Is inflation persistence intrinsic in industrial economies?," Working Papers 2002-023, Federal Reserve Bank of St. Louis.
    16. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
    17. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    18. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    19. Fuhrer, Jeffrey C., 2010. "Inflation Persistence," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 9, pages 423-486, Elsevier.
    20. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1350-1366, December.
    21. Buiter, Willem H & Jewitt, Ian, 1981. "Staggered Wage Setting with Real Wage Relativities: Variations on a Theme of Taylor," The Manchester School of Economic & Social Studies, University of Manchester, vol. 49(3), pages 211-228, September.
    22. Pivetta, Frederic & Reis, Ricardo, 2007. "The persistence of inflation in the United States," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1326-1358, April.
    23. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    24. Burridge, Peter & Guerre, Emmanuel, 1996. "The Limit Distribution of level Crossings of a Random Walk, and a Simple Unit Root Test," Econometric Theory, Cambridge University Press, vol. 12(4), pages 705-723, October.
    25. 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.
    26. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    27. Luca Benati, 2008. "Investigating Inflation Persistence Across Monetary Regimes," The Quarterly Journal of Economics, Oxford University Press, vol. 123(3), pages 1005-1060.
    28. Corvoisier, Sandrine & Mojon, Benoît, 2005. "Breaks in the mean of inflation: how they happen and what to do with them," Working Paper Series 451, European Central Bank.
    29. Ignazio Angeloni & Luc Aucremanne & Matteo Ciccarelli, 2006. "Price setting and inflation persistence: did EMU matter? [‘One market, one money, one price? Price dispersion in the European Union’]," Economic Policy, CEPR;CES;MSH, vol. 21(46), pages 354-387.
    30. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(3), pages 315-352, June.
    31. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
    32. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    33. Jeffrey C. Fuhrer, 1995. "The persistence of inflation and the cost of disinflation," New England Economic Review, Federal Reserve Bank of Boston, issue Jan, pages 3-16.
    34. Lucas, Andre, 1995. "An outlier robust unit root test with an application to the extended Nelson-Plosser data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 153-173.
    35. Gadzinski, Gregory & Orlandi, Fabrice, 2004. "Inflation persistence in the European Union, the euro area, and the United States," Working Paper Series 414, European Central Bank.
    36. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
    37. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    38. Jaeger, Albert & Kunst, Robert M, 1990. "Seasonal Adjustment and Measuring Persistence in Output," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(1), pages 47-58, January-M.
    39. Edwards, Sebastian, 1998. "Two Crises: Inflationary Inertia and Credibility," Economic Journal, Royal Economic Society, vol. 108(448), pages 680-702, May.
    40. Murray, Christian J. & Papell, David H., 2002. "The purchasing power parity persistence paradigm," Journal of International Economics, Elsevier, vol. 56(1), pages 1-19, January.
    41. Alogoskoufis, George S & Smith, Ron, 1991. "The Phillips Curve, the Persistence of Inflation, and the Lucas Critique: Evidence from Exchange-Rate Regimes," American Economic Review, American Economic Association, vol. 81(5), pages 1254-1275, December.
    42. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
    43. Fagan, Gabriel & Henry, Jérôme & Mestre, Ricardo, 2001. "An area-wide model (AWM) for the euro area," Working Paper Series 42, European Central Bank.
    44. Jonathan L. Willis, 2003. "Implications of structural changes in the U.S. economy for pricing behavior and inflation dynamics," Economic Review, Federal Reserve Bank of Kansas City, vol. 88(Q I), pages 5-27.
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    More about this item

    Keywords

    inflation persistence; mean reversion; non-parametric estimator;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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