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A Saddlepoint Approximation to the Distribution of the Half-Life Estimator in an Autoregressive Model: New Insights Into the PPP Puzzle

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Abstract

We derive saddlepoint approximations for the density and distribution functions of the half-life estimated by OLS from an AR(1) or AR(p) model. Our analytic results are used to prove that none of the integer-order moments of these half-life estimators exist. This provides an explanation for the unreasonably large estimates of persistency associated with the purchasing power parity “puzzle”, and it also explains the excessively wide confidence intervals reported in the empirical PPP literature.

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Bibliographic Info

Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0703.

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Length: 23 pages
Date of creation: 28 May 2007
Date of revision:
Handle: RePEc:vic:vicewp:0703

Note: ISSN 1485-6441
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Keywords: Saddlepoint approximation; half-life estimator; PPP puzzle;

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References

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  1. Cheung, Yin-Wong & Lai, Kon S., 1998. "Parity reversion in real exchange rates during the post-Bretton Woods period," Journal of International Money and Finance, Elsevier, Elsevier, vol. 17(4), pages 597-614, August.
  2. Glen, Jack D., 1992. "Real exchange rates in the short, medium, and long run," Journal of International Economics, Elsevier, Elsevier, vol. 33(1-2), pages 147-166, August.
  3. Abuaf, Niso & Jorion, Philippe, 1990. " Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, American Finance Association, vol. 45(1), pages 157-74, March.
  4. Jae Kim & Param Silvapulle & Rob J. Hyndman, 2006. "Half-Life Estimation based on the Bias-Corrected Bootstrap: A Highest Density Region Approach," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 11/06, Monash University, Department of Econometrics and Business Statistics.
  5. David E. A. Giles, 2000. "A Saddlepoint Approximation to the Distribution Function of the Anderson-Darling Test Statistic," Econometrics Working Papers, Department of Economics, University of Victoria 0005, Department of Economics, University of Victoria.
  6. Georgios Chortareas & George Kapetanios, 2013. "How Puzzling Is The Ppp Puzzle? An Alternative Half‐Life Measure Of Convergence To Ppp," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(3), pages 435-457, 04.
  7. Taylor, Mark P & Peel, David A & Sarno, Lucio, 2001. "Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution to the Purchasing Power Parity Puzzles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1015-42, November.
  8. Charles Engel & James C. Morley, 2001. "The Adjustment of Prices and the Adjustment of the Exchange Rate," NBER Working Papers 8550, National Bureau of Economic Research, Inc.
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  12. Papell, David H. & Theodoridis, Hristos, 1998. "Increasing evidence of purchasing power parity over the current float," Journal of International Money and Finance, Elsevier, Elsevier, vol. 17(1), pages 41-50, February.
  13. Lieberman, Offer, 1997. "The Effect of Nonnormality," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 13(01), pages 52-78, February.
  14. Yin-wong Cheung & Kon S. Lai & Michael Bergman, 2003. "Dissecting the PPP Puzzle: The Unconventional Roles of Nominal Exchange Rate and Price Adjustments," Working Papers 102003, Hong Kong Institute for Monetary Research.
  15. Cheung, Yin-Wong & Lai, Kon S., 1994. "Mean reversion in real exchange rates," Economics Letters, Elsevier, Elsevier, vol. 46(3), pages 251-256, November.
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  17. Hali J. Edison & Eric Fisher, 1989. "A long-run view of the european monetary system," International Finance Discussion Papers, Board of Governors of the Federal Reserve System (U.S.) 339, Board of Governors of the Federal Reserve System (U.S.).
  18. Choi, Chi-Young & Mark, Nelson C. & Sul, Donggyu, 2006. "Unbiased Estimation of the Half-Life to PPP Convergence in Panel Data," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 38(4), pages 921-938, June.
  19. Guglielmo Maria Caporale & Mario Cerrato & Nicola Spagnolo, 2005. "Measuring half-lives: using a non-parametric bootstrap approach," Applied Financial Economics Letters, Taylor and Francis Journals, Taylor and Francis Journals, vol. 1(1), pages 1-4, January.
  20. El-Gamal, Mahmoud A. & Ryu, Deockhyun, 2006. "Short-memory and the PPP hypothesis," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 30(3), pages 361-391, March.
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  22. Pedroni, Peter, 2004. "Panel Cointegration: Asymptotic And Finite Sample Properties Of Pooled Time Series Tests With An Application To The Ppp Hypothesis," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 20(03), pages 597-625, June.
  23. 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.
  24. Lothian, James R & Taylor, Mark P, 1996. "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 104(3), pages 488-509, June.
  25. Baum, Christopher F. & Barkoulas, John T. & Caglayan, Mustafa, 2001. "Nonlinear adjustment to purchasing power parity in the post-Bretton Woods era," Journal of International Money and Finance, Elsevier, Elsevier, vol. 20(3), pages 379-399, June.
  26. Meese, R. & Rogoff, K., 1988. "Was It Real? The Exchange Rate-Interest Differential Ralation Over The Modern Floating-Rate Period," Working papers, Wisconsin Madison - Social Systems 368, Wisconsin Madison - Social Systems.
  27. C. John McDermott & Paul Cashin, 2001. "An Unbiased Appraisal of Purchasing Power Parity," IMF Working Papers 01/196, International Monetary Fund.
  28. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
  29. Grilli, Vittorio & Kaminsky, Graciela, 1991. "Nominal exchange rate regimes and the real exchange rate : Evidence from the United States and Great Britain, 1885-1986," Journal of Monetary Economics, Elsevier, Elsevier, vol. 27(2), pages 191-212, April.
  30. Murray, Christian J. & Papell, David H., 2005. "Do Panels Help Solve the Purchasing Power Parity Puzzle?," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 23, pages 410-415, October.
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Cited by:
  1. Hwa-Taek Lee & Gawon Yoon, 2013. "Does purchasing power parity hold sometimes? Regime switching in real exchange rates," Applied Economics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 45(16), pages 2279-2294, June.

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