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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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Author Info
Qian Chen (School of Public Finance and Public Policy, Central University of Finance & Economics)
David E. Giles () (Department of Economics, University of Victoria)

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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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Publisher 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
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Handle: RePEc:vic:vicewp:0703

Note: ISSN 1485-6441
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Postal: PO Box 1700, STN CSC, Victoria, BC, Canada, V8W 2Y2
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Related research
Keywords: Saddlepoint approximation half-life estimator PPP puzzle

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
F31 - International Economics - - International Finance - - - Foreign Exchange
F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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  1. Diebold, Francis X & Husted, Steven & Rush, Mark, 1991. "Real Exchange Rates under the Gold Standard," Journal of Political Economy, University of Chicago Press, vol. 99(6), pages 1252-71, December. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
  3. Lutz Kilian & Tao Zha, 1999. "Quantifying the half-life of deviations from PPP: The role of economic priors," Working Paper 99-21, Federal Reserve Bank of Atlanta. [Downloadable!]
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  4. 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, vol. 1(1), pages 1-4, January. [Downloadable!] (restricted)
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  5. Cheung, Yin-Wong & Lai, Kon S. & Bergman, Michael, 2004. "Dissecting the PPP puzzle: the unconventional roles of nominal exchange rate and price adjustments," Journal of International Economics, Elsevier, vol. 64(1), pages 135-150, October. [Downloadable!] (restricted)
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  6. 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, vol. 20(03), pages 597-625, June. [Downloadable!]
  7. 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. [Downloadable!]
  8. Edison, Hali J. & Fisher, Eric O'N, 1991. "A long-run view of the European monetary system," Journal of International Money and Finance, Elsevier, vol. 10(1), pages 53-70, March. [Downloadable!] (restricted)
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  9. 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. [Downloadable!] (restricted)
  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, Department of Economics. [Downloadable!]
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  11. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
  13. repec:cup:etheor:v:13:y:1997:i:1:p:52-78 is not listed on IDEAS
  14. 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. [Downloadable!] (restricted)
  15. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July. [Downloadable!] (restricted)
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  16. Paul Cashin & C. John McDermott, 2003. "An Unbiased Appraisal of Purchasing Power Parity," IMF Staff Papers, Palgrave Macmillan Journals, vol. 50(3), pages 1. [Downloadable!] (restricted)
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  17. 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. [Downloadable!] (restricted)
  18. repec:fth:michin:450 is not listed on IDEAS
  19. Taylor, Mark P. & Sarno, Lucio, 1998. "The behavior of real exchange rates during the post-Bretton Woods period," Journal of International Economics, Elsevier, vol. 46(2), pages 281-312, December. [Downloadable!] (restricted)
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  20. 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. [Downloadable!] (restricted)
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  21. Meese, Richard A & Rogoff, Kenneth, 1988. " Was It Real? The Exchange Rate-Interest Differential Relation over the Modern Floating-Rate Period," Journal of Finance, American Finance Association, vol. 43(4), pages 933-48, September. [Downloadable!] (restricted)
    Other versions:
  22. 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. [Downloadable!]
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  23. Claude Lopez & Christian J. Murray & David H. Papell, 2003. "More Powerful Unit Root Tests and the PPP Puzzle," University of Cincinnati, Economics Working Papers Series 2003-07, University of Cincinnati, Department of Economics, revised Sep 2006. [Downloadable!]
  24. 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, vol. 42(4), pages 1015-42, November.
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  25. 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. [Downloadable!] (restricted)
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  26. 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. [Downloadable!] (restricted)
  27. 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. [Downloadable!] (restricted)
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  28. 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 11/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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  29. 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. [Downloadable!] (restricted)
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