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Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime STAR Model

Author

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  • Frédérique Bec
  • Mélika Ben Salem
  • Marine Carrasco

Abstract

Recent studies on general equilibrium models with transaction costs show that the dynamics of the real exchange rate are necessarily nonlinear. Our contribution to the literature on nonlinear price adjustment mechanisms is treefold. First, we model the real exchange rate by a Multi-Regime Logistic Smooth Transition AutoRegression (MR-LSTAR), allowing for both ESTAR-type and SETAR-type dynmaics. This choice is motivated by the fact that even the theoretical models, which predict a smooth behavior for the real exchange rate, do not rule out the possibility of a discontinuous adjustment as a limit case. Second, we propose two classes of unit-root tests against this MR-LSTAR alternative, based respectively on the likelihood and on a auxiliary model. Their asymptotic distributions are derived analytically. Third, when applied to 28 bilateral real exchange rates, our tests reject the null hypothesis of a unit root for eleven series bringing evidence in favor of the purchasing power parity. Des études récentes sur les modèles d'équilibre général prenant en considération les coûts des transactions démontrent que la dynamique du taux de change réel est nécessairement non linéaire. Notre contribution à la littérature portant sur les mécanismes d'ajustement non linéaire des prix comporte trois volets. Premièrement, nous modélisons le taux de change réel en recourant à une autorégression de type MR-LSTAR (Multi-Regime Logistic Smooth Transition AutoRegression), qui permet d'observer la dynamique des modèles ESTAR (Exponential Smooth TAR) et SETAR (Self-Exciting Treshold Autoregressive). Notre choix est motivé par le fait que même les modèles théoriques, qui prédisent un comportement lisse du taux de change réel, n'excluent pas la possibilité d'un ajustement discontinu à la limite. Deuxièmement, nous proposons deux catégories de tests de racine unitaire, dans le cadre de l'option MR-LSTAR, fondées respectivement sur la vraisemblance et sur un modèle auxiliaire. Leurs distributions asymptotiques résultent d'un processus analytique. Troisièmement, lorsque nos tests sont appliqués à 28 taux de change réels bilatéraux, ils rejettent l'hypothèse nulle d'une racine unitaire dans le cas de onze séries, faisant ainsi la preuve de la parité du pouvoir d'achat.

Suggested Citation

  • Frédérique Bec & Mélika Ben Salem & Marine Carrasco, 2009. "Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime STAR Model," CIRANO Working Papers 2009s-18, CIRANO.
    • Handle: RePEc:cir:cirwor:2009s-18
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    File URL: https://cirano.qc.ca/files/publications/2009s-18.pdf
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    1. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
    2. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    3. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
    4. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    5. Kilian, Lutz & Taylor, Mark P., 2003. "Why is it so difficult to beat the random walk forecast of exchange rates?," Journal of International Economics, Elsevier, vol. 60(1), pages 85-107, May.
    6. Obstfeld, Maurice & Taylor, Alan M., 1997. "Nonlinear Aspects of Goods-Market Arbitrage and Adjustment: Heckscher's Commodity Points Revisited," Journal of the Japanese and International Economies, Elsevier, vol. 11(4), pages 441-479, December.
    7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    8. Sarno,Lucio & Taylor,Mark P., 2003. "The Economics of Exchange Rates," Cambridge Books, Cambridge University Press, number 9780521485845.
    9. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    10. George Kapetanios, 2000. "Testing for a Unit Root against Nonlinear STAR Models," National Institute of Economic and Social Research (NIESR) Discussion Papers 164, National Institute of Economic and Social Research.
    11. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
    12. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    13. 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.
    14. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-879, August.
    15. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    16. Lo, Ming Chien & Zivot, Eric, 2001. "Threshold Cointegration And Nonlinear Adjustment To The Law Of One Price," Macroeconomic Dynamics, Cambridge University Press, vol. 5(4), pages 533-576, September.
    17. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    18. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    19. Bec, Frederique & Guay, Alain & Guerre, Emmanuel, 2008. "Adaptive consistent unit-root tests based on autoregressive threshold model," Journal of Econometrics, Elsevier, vol. 142(1), pages 94-133, January.
    20. Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-311, July.
    21. 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.
    22. Mark P. Taylor, 2003. "Purchasing Power Parity," Review of International Economics, Wiley Blackwell, vol. 11(3), pages 436-452, August.
    23. Berka, Martin, 2005. "General Equilibrium Model of Arbitrage Trade and Real Exchange Rate Persistence," MPRA Paper 234, University Library of Munich, Germany.
    24. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
    25. Taylor, Alan M, 2001. "Potential Pitfalls for the Purchasing-Power-Parity Puzzle? Sampling and Specification Biases in Mean-Reversion Tests of the Law of One Price," Econometrica, Econometric Society, vol. 69(2), pages 473-498, March.
    26. Papell, David H., 1997. "Searching for stationarity: Purchasing power parity under the current float," Journal of International Economics, Elsevier, vol. 43(3-4), pages 313-332, November.
    27. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    28. Joon Y. Park & Mototsugu Shintani, 2005. "Testing for a Unit Root against Transitional Autoregressive Models," Vanderbilt University Department of Economics Working Papers 05010, Vanderbilt University Department of Economics.
    29. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    30. O'Connell, Paul G. J. & Wei, Shang-Jin, 2002. ""The bigger they are, the harder they fall": Retail price differences across U.S. cities," Journal of International Economics, Elsevier, vol. 56(1), pages 21-53, January.
    31. Lothian, James R. & Taylor, Mark P., 2000. "Purchasing power parity over two centuries: strengthening the case for real exchange rate stability: A reply to Cuddington and Liang," Journal of International Money and Finance, Elsevier, vol. 19(5), pages 759-764, October.
    32. Sercu, Piet & Uppal, Raman & Van Hulle, Cynthia, 1995. "The Exchange Rate in the Presence of Transaction Costs: Implications for Tests of Purchasing Power Parity," Journal of Finance, American Finance Association, vol. 50(4), pages 1309-1319, September.
    33. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    34. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-180.
    35. repec:cup:macdyn:v:5:y:2001:i:4:p:533-76 is not listed on IDEAS
    36. Michael Pippenger & Gregory Goering, 2000. "Additional results on the power of unit root and cointegration tests under threshold processes," Applied Economics Letters, Taylor & Francis Journals, vol. 7(10), pages 641-644.
    37. Uppal, Raman, 1993. "A General Equilibrium Model of International Portfolio Choice," Journal of Finance, American Finance Association, vol. 48(2), pages 529-553, June.
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    More about this item

    Keywords

    Half-life; purchasing power parity; mixing conditions; smooth transition autoregressive model; unit-root test; real exchange rate; Demi-vie; parité du pouvoir d'achat; conditions de mélange; modèle autorégressif à transition lisse; test d'unité racinaire; taux de change réel;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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

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