IDEAS home Printed from https://ideas.repec.org/p/vic/vicewp/0703.html
   My bibliography  Save this paper

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

Author

Listed:

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.

Suggested Citation

  • Qian Chen & David E. Giles, 2007. "A Saddlepoint Approximation to the Distribution of the Half-Life Estimator in an Autoregressive Model: New Insights Into the PPP Puzzle," Econometrics Working Papers 0703, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:0703
    Note: ISSN 1485-6441
    as

    Download full text from publisher

    File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp0703.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    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 1252-1271, December.
    2. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    3. 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.
    4. 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.
    5. 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, April.
    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.
    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, vol. 42(4), pages 1015-1042, November.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Abuaf, Niso & Jorion, Philippe, 1990. " Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, vol. 45(1), pages 157-174, March.
    16. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    17. Paul Cashin & C. John McDermott, 2003. "An Unbiased Appraisal of Purchasing Power Parity," IMF Staff Papers, Palgrave Macmillan, vol. 50(3), pages 1-1.
    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, vol. 38(4), pages 921-938, June.
    19. Lieberman, Offer, 1997. "The Effect of Nonnormality," Econometric Theory, Cambridge University Press, vol. 13(01), pages 52-78, February.
    20. 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.
    21. 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.
    22. 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.
    23. repec:fth:michin:450 is not listed on IDEAS
    24. 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.
    25. 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.
    26. Cheung, Yin-Wong & Lai, Kon S., 1994. "Mean reversion in real exchange rates," Economics Letters, Elsevier, vol. 46(3), pages 251-256, November.
    27. 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 933-948, September.
    28. 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, vol. 20(3), pages 379-399, June.
    29. 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.
    30. Charles Engel & James Morley, 2000. "The Adjustment of Prices and the Adjustment of the Exchange Rate," Working Papers 0009, University of Washington, Department of Economics.
    31. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, vol. 45(16), pages 2279-2294, June.

    More about this item

    Keywords

    Saddlepoint approximation; half-life estimator; PPP puzzle;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vic:vicewp:0703. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Graham Voss). General contact details of provider: http://edirc.repec.org/data/devicca.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.