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Using Mean Reversion as a Measure of Persistence

  • Daniel Dias
  • Carlos Robalo Marques

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”.

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Paper provided by Banco de Portugal, Economics and Research Department in its series Working Papers with number w200503.

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Date of creation: 2005
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Handle: RePEc:ptu:wpaper:w200503
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  1. Garc a, Ana & Sans , Andreu, 2006. "A Generalization Of The Burridge Guerre Nonparametric Unit Root Test," Econometric Theory, Cambridge University Press, vol. 22(04), pages 756-761, August.
  2. 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.
  3. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  4. Jushan Bai, 1995. "Estimating Multiple Breaks One at a Time," Working papers 95-18, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. 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.
  6. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
  7. 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.
  8. Benati, Luca, 2008. "Investigating inflation persistence across monetary regimes," Working Paper Series 0851, European Central Bank.
  9. Andrew Levin & Jeremy Piger, 2003. "Is Inflation Persistence Intrinsic in Industrial Economies?," Computing in Economics and Finance 2003 298, Society for Computational Economics.
  10. 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.
  11. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  12. 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.
  13. Jeffrey A. Frankel & Andrew K. Rose, 1995. "A Panel Project on Purchasing Power Parity: Mean Reversion Within and Between Countries," NBER Working Papers 5006, National Bureau of Economic Research, Inc.
  14. 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.
  15. 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 235-47, May.
  16. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Universite de Montreal, Departement de sciences economiques.
  17. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1350-1366, December.
  18. Angeloni, Ignazio & Aucremanne, Luc & Ciccarelli, Matteo, 2006. "Price setting and inflation persistence: did EMU matter?," Working Paper Series 0597, European Central Bank.
  19. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  20. Corvoisier, Sandrine & Mojon, Benoît, 2005. "Breaks in the mean of inflation: how they happen and what to do with them," Working Paper Series 0451, European Central Bank.
  21. Timothy Cogley & Giorgio E. Primiceri & Thomas J. Sargent, 2008. "Inflation-Gap Persistence in the U.S," NBER Working Papers 13749, National Bureau of Economic Research, Inc.
  22. Fuhrer, Jeff & Moore, George, 1995. "Inflation Persistence," The Quarterly Journal of Economics, MIT Press, vol. 110(1), pages 127-59, February.
  23. 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.
  24. 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.
  25. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
  26. 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.
  27. 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 1254-75, December.
  28. 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.
  29. 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, 09.
  30. Gadzinski, Gregory & Orlandi, Fabrice, 2004. "Inflation persistence in the European Union, the euro area, and the United States," Working Paper Series 0414, European Central Bank.
  31. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  32. Fagan, Gabriel & Henry, Jérôme & Mestre, Ricardo, 2001. "An area-wide model (AWM) for the euro area," Working Paper Series 0042, European Central Bank.
  33. Edwards, Sebastian, 1998. "Two Crises: Inflationary Inertia and Credibility," Economic Journal, Royal Economic Society, vol. 108(448), pages 680-702, May.
  34. O'Reilly, Gerard & Whelan, Karl, 2004. "Has euro-area inflation persistence changed over time?," Working Paper Series 0335, European Central Bank.
  35. 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 463-85, March.
  36. 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 211-28, September.
  37. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
  38. 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.
  39. 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(04), pages 705-723, October.
  40. Lee, Junsoo, 1996. "On the power of stationarity tests using optimal bandwidth estimates," Economics Letters, Elsevier, vol. 51(2), pages 131-137, May.
  41. 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.
  42. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
  43. 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, issue Q I, pages 5-27.
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