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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

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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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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Web page: http://web.uvic.ca/econ

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  1. C. John McDermott & Paul Cashin, 2001. "An Unbiased Appraisal of Purchasing Power Parity," IMF Working Papers 01/196, International Monetary Fund.
  2. 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, vol. 27(2), pages 191-212, April.
  3. Francis X. Diebold & Steven Husted & Mark Rush, 1990. "Real exchange rates under the gold standard," Discussion Paper / Institute for Empirical Macroeconomics 32, Federal Reserve Bank of Minneapolis.
  4. Cheung, Yin-Wong & Lai, Kon S., 1994. "Mean reversion in real exchange rates," Economics Letters, Elsevier, vol. 46(3), pages 251-256, November.
  5. 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, vol. 17(4), pages 597-614, August.
  6. Charles Engel & James Morley, 2000. "The Adjustment of Prices and the Adjustment of the Exchange Rate," Discussion Papers in Economics at the University of Washington 0009, Department of Economics at the University of Washington.
  7. Christopher F. Baum & Mustafa Caglayan & John Barkoulas, 1998. "Nonlinear Adjustment to Purchasing Power Parity in the post-Bretton Woods Era," Boston College Working Papers in Economics 404., Boston College Department of Economics, revised 16 Nov 1999.
  8. Chi-Young Choi & Nelson Mark & Donggyu Sul, 2004. "Unbiased Estimation of the Half-Life to PPP Convergence in Panel Data," NBER Working Papers 10614, National Bureau of Economic Research, Inc.
  9. Sarno, Lucio & Taylor, Mark P, 1997. "The Behaviour of Real Exchange Rates During the Post-Bretton Woods Period," CEPR Discussion Papers 1730, C.E.P.R. Discussion Papers.
  10. Georgios Chortareas & George Kapetanios, 2004. "How Puzzling is the PPP Puzzle? An Alternative Half-Life Measure of Convergence to PPP," Working Papers 522, Queen Mary University of London, School of Economics and Finance.
  11. Peter Pedroni, 2004. "Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis," Department of Economics Working Papers 2004-15, Department of Economics, Williams College.
  12. Peel, David & Sarno, Lucio & Taylor, Mark P, 2001. "Nonlinear Mean-Reversion in Real Exchange Rates: Towards a Solution to the Purchasing Power Parity Puzzles," CEPR Discussion Papers 2658, C.E.P.R. Discussion Papers.
  13. David E. A. Giles, 2000. "A Saddlepoint Approximation to the Distribution Function of the Anderson-Darling Test Statistic," Econometrics Working Papers 0005, Department of Economics, University of Victoria.
  14. Guglielmo Maria Caporale & Mario Cerrato & Nicola Spagnolo, 2004. "Measuring Half-Lives Using A Non-Parametric Bootstrap Approach," Economics and Finance Discussion Papers 04-13, Economics and Finance Section, School of Social Sciences, Brunel University.
  15. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
  16. Meese, R. & Rogoff, K., 1988. "Was It Real? The Exchange Rate-Interest Differential Ralation Over The Modern Floating-Rate Period," Working papers 368, Wisconsin Madison - Social Systems.
  17. 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.
  18. Hali J. Edison & Eric Fisher, 1989. "A long-run view of the european monetary system," International Finance Discussion Papers 339, Board of Governors of the Federal Reserve System (U.S.).
  19. Kim, Jae H. & Silvapulle, Param & Hyndman, Rob J., 2007. "Half-life estimation based on the bias-corrected bootstrap: A highest density region approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3418-3432, April.
  20. Christian J. Murray & David H. Papell, 2000. "The Purchasing Power Parity Persistence Paradigm," Econometric Society World Congress 2000 Contributed Papers 0017, Econometric Society.
  21. Lothian, James R., 1997. "Multi-country evidence on the behavior of purchasing power parity under the current float," Journal of International Money and Finance, Elsevier, vol. 16(1), pages 19-35, February.
  22. Papell, David H. & Theodoridis, Hristos, 1998. "Increasing evidence of purchasing power parity over the current float," Journal of International Money and Finance, Elsevier, vol. 17(1), pages 41-50, February.
  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. Glen, Jack D., 1992. "Real exchange rates in the short, medium, and long run," Journal of International Economics, Elsevier, vol. 33(1-2), pages 147-166, August.
  25. Lieberman, Offer, 1997. "The Effect of Nonnormality," Econometric Theory, Cambridge University Press, vol. 13(01), pages 52-78, February.
  26. Abuaf, Niso & Jorion, Philippe, 1990. " Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, vol. 45(1), pages 157-74, March.
  27. 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, vol. 104(3), pages 488-509, June.
  28. Wu, Yangru, 1996. "Are Real Exchange Rates Nonstationary? Evidence from a Panel-Data Test," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(1), pages 54-63, February.
  29. Murray, Christian J. & Papell, David H., 2005. "Do Panels Help Solve the Purchasing Power Parity Puzzle?," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 410-415, October.
  30. El-Gamal, Mahmoud A. & Ryu, Deockhyun, 2006. "Short-memory and the PPP hypothesis," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 361-391, March.
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