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The Dollar Exchange Rate, Adjustment to the Purchasing Power Parity, and the Interest Rate Differential

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  • Michael Frömmel

    (Department of Economics, Ghent University, Sint Pietersplein 5, 9000 Ghent, Belgium)

  • Darko B. Vukovic

    (Graduate School of Management, Saint Petersburg State University, Volkhovskiy Pereulok 3, 199004 Saint Petersburg, Russia
    Geographical Institute “Jovan Cvijic” SASA, Djure Jaksica 9, 11000 Belgrade, Serbia)

  • Jinyuan Wu

    (Department of Economics, Ghent University, Sint Pietersplein 5, 9000 Ghent, Belgium)

Abstract

This study applies a Markov switching error correction model to describe the single most important real exchange rate (Deutsche mark versus US dollar) over the flexible exchange rates period from 1973 to 2004. We show an alternative way of modelling non-linear adjustment to the purchasing power parity (PPP) besides standard threshold models. The model merges the two possible sources of non-linearity by additionally allowing the probability of a mean-reverting regime to increase with the distance from PPP. The interest rate differential as an additional determinant of real exchange rate behaviour in a Markov switching framework is introduced in the model. The study finds that the real dollar exchange rate during the post-Bretton Woods era is well described by a Markov switching error correction model with (PPP) as long-run equilibrium. There is one mean reversion regime where PPP and the interest parity condition are valid. Contrary, the second regime is characterised by persistent mean aversion, where a regime switch does not become more likely with increasing distance from PPP. The unconditional half-life of shocks is about 1.5 years.

Suggested Citation

  • Michael Frömmel & Darko B. Vukovic & Jinyuan Wu, 2022. "The Dollar Exchange Rate, Adjustment to the Purchasing Power Parity, and the Interest Rate Differential," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4504-:d:987478
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    as
    1. Kapetanios, George & Shin, Yongcheol, 2008. "GLS detrending-based unit root tests in nonlinear STAR and SETAR models," Economics Letters, Elsevier, vol. 100(3), pages 377-380, September.
    2. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    3. Caner, M. & Kilian, L., 2001. "Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 639-657, October.
    4. Mohsen Bahmani-Oskooee & Ali M. Kutan & Su Zhou, 2008. "Do Real Exchange Rates Follow a Nonlinear Mean Reverting Process in Developing Countries," Southern Economic Journal, John Wiley & Sons, vol. 74(4), pages 1049-1062, April.
    5. Charles Engel, 1999. "Accounting for U.S. Real Exchange Rate Changes," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 507-538, June.
    6. 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.
    7. Hall, Stephen & Psaradakis, Zacharias & Sola, Martin, 1997. "Switching error-correction models of house prices in the United Kingdom," Economic Modelling, Elsevier, vol. 14(4), pages 517-527, October.
    8. Lucio Sarno & Giorgio Valente & Mark E. Wohar, 2004. "Monetary Fundamentals and Exchange Rate Dynamics under Different Nominal Regimes," Economic Inquiry, Western Economic Association International, vol. 42(2), pages 179-193, April.
    9. 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.
    10. Mukhriz Izraf Azman Aziz & Zaghum Umar & Mariya Gubareva & Tatiana Sokolova & Xuan Vinh Vo, 2022. "ASEAN-5 forex rates and crude oil: Markov regime-switching analysis," Applied Economics, Taylor & Francis Journals, vol. 54(54), pages 6234-6253, November.
    11. Kanas, Angelos & Genius, Margarita, 2005. "Regime (non)stationarity in the US/UK real exchange rate," Economics Letters, Elsevier, vol. 87(3), pages 407-413, June.
    12. Bahmani-Oskooee, Mohsen & Chang, Tsangyao & Lee, Kuei-Chiu, 2016. "Purchasing power parity in emerging markets: A panel stationary test with both sharp and smooth breaks," Economic Systems, Elsevier, vol. 40(3), pages 453-460.
    13. Ivan Paya & David Peel, 2005. "The process followed by PPP data. On the properties of linearity tests," Applied Economics, Taylor & Francis Journals, vol. 37(21), pages 2515-2522.
    14. 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.
    15. Meese, Richard A, 1986. "Testing for Bubbles in Exchange Markets: A Case of Sparkling Rates?," Journal of Political Economy, University of Chicago Press, vol. 94(2), pages 345-373, April.
    16. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
    17. Alan M. Taylor & Mark P. Taylor, 2004. "The Purchasing Power Parity Debate," Journal of Economic Perspectives, American Economic Association, vol. 18(4), pages 135-158, Fall.
    18. Mark P. Taylor & Lucio Sarno, 2001. "Official Intervention in the Foreign Exchange Market: Is It Effective and, If So, How Does It Work?," Journal of Economic Literature, American Economic Association, vol. 39(3), pages 839-868, September.
    19. Cheung, Yin-Wong & Chinn, Menzie D. & Pascual, Antonio Garcia, 2005. "Empirical exchange rate models of the nineties: Are any fit to survive?," Journal of International Money and Finance, Elsevier, vol. 24(7), pages 1150-1175, November.
    20. 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.
    21. Mario Cerrato & Hyunsok Kim & Ronald Macdonald, 2010. "Three‐Regime Asymmetric STAR Modeling and Exchange Rate Reversion," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(7), pages 1447-1467, October.
    22. Kanas, Angelos, 2005. "Regime linkages in the US/UK real exchange rate-real interest differential relation," Journal of International Money and Finance, Elsevier, vol. 24(2), pages 257-274, March.
    23. Frommel, Michael & MacDonald, Ronald & Menkhoff, Lukas, 2005. "Do fundamentals matter for the D-Mark/Euro-Dollar? A regime switching approach," Global Finance Journal, Elsevier, vol. 15(3), pages 321-335, February.
    24. Faruk Mike & Oktay Kızılkaya, 2019. "Testing the theory of PPP for emerging market economies that practice flexible exchange rate regimes," Applied Economics Letters, Taylor & Francis Journals, vol. 26(17), pages 1411-1417, October.
    25. Mohsen Bahmani‐Oskooee & Ali M. Kutan & Su Zhou, 2008. "Do Real Exchange Rates Follow a Nonlinear Mean Reverting Process in Developing Countries?," Southern Economic Journal, John Wiley & Sons, vol. 74(4), pages 1049-1062, April.
    26. 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.
    27. 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.
    28. Kanas, Angelos, 2006. "Purchasing Power Parity and Markov Regime Switching," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(6), pages 1669-1687, September.
    29. Engel, Charles, 1994. "Can the Markov switching model forecast exchange rates?," Journal of International Economics, Elsevier, vol. 36(1-2), pages 151-165, February.
    30. Psaradakis, Zacharias & Sola, Martin, 1998. "Finite-sample properties of the maximum likelihood estimator in autoregressive models with Markov switching," Journal of Econometrics, Elsevier, vol. 86(2), pages 369-386, June.
    31. Michael Frömmel, 2010. "Volatility Regimes in Central and Eastern European Countries’ Exchange Rates," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 60(1), pages 2-21, February.
    32. Lucio Sarno & Mark P. Taylor, 2002. "Purchasing Power Parity and the Real Exchange Rate," IMF Staff Papers, Palgrave Macmillan, vol. 49(1), pages 1-5.
    33. Frankel, Jeffrey A. & Rose, Andrew K., 1996. "A panel project on purchasing power parity: Mean reversion within and between countries," Journal of International Economics, Elsevier, vol. 40(1-2), pages 209-224, February.
    34. Philippe Bacchetta & Eric Van Wincoop, 2004. "A Scapegoat Model of Exchange-Rate Fluctuations," American Economic Review, American Economic Association, vol. 94(2), pages 114-118, May.
    35. Zacharias Psaradakis & Martin Sola & Fabio Spagnolo, 2004. "On Markov error-correction models, with an application to stock prices and dividends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(1), pages 69-88.
    36. Efthymios G. Pavlidis & Ivan Paya & David A. Peel, 2012. "Forecast Evaluation of Nonlinear Models: The Case of Long‐Span Real Exchange Rates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 31(7), pages 580-595, November.
    37. 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.
    38. Copeland, Laurence & Heravi, Saeed, 2006. "Structural Breaks in the Real Exchange Rate Adjustment Mechanism," Cardiff Economics Working Papers E2006/21, Cardiff University, Cardiff Business School, Economics Section.
    39. Chortareas, Georgios E. & Kapetanios, George & Shin, Yongcheol, 2002. "Nonlinear mean reversion in real exchange rates," Economics Letters, Elsevier, vol. 77(3), pages 411-417, November.
    40. Dinçer Afat & Michael Frömmel, 2021. "A Panel Data Analysis of Uncovered Interest Parity and Time-Varying Risk Premium," Open Economies Review, Springer, vol. 32(3), pages 507-526, July.
    41. Chambers, Marcus J., 2005. "The purchasing power parity puzzle, temporal aggregation, and half-life estimation," Economics Letters, Elsevier, vol. 86(2), pages 193-198, February.
    42. Frommel, Michael & MacDonald, Ronald & Menkhoff, Lukas, 2005. "Markov switching regimes in a monetary exchange rate model," Economic Modelling, Elsevier, vol. 22(3), pages 485-502, May.
    43. Robinson Kruse, 2011. "A new unit root test against ESTAR based on a class of modified statistics," Statistical Papers, Springer, vol. 52(1), pages 71-85, February.
    44. Alan M. Taylor & Mark P. Taylor, 2004. "The Purchasing Power Parity Debate," Journal of Economic Perspectives, American Economic Association, vol. 18(4), pages 135-158, Fall.
    45. Menkhoff, L., 1998. "The noise trading approach -- questionnaire evidence from foreign exchange," Journal of International Money and Finance, Elsevier, vol. 17(3), pages 547-564, June.
    46. Cheung, Yin-Wong & Lai, Kon S., 1993. "Long-run purchasing power parity during the recent float," Journal of International Economics, Elsevier, vol. 34(1-2), pages 181-192, February.
    47. MacDonald, Ronald, 1999. "Exchange Rate Behaviour: Are Fundamentals Important?," Economic Journal, Royal Economic Society, vol. 109(459), pages 673-691, November.
    48. Sarantis, Nicholas, 1999. "Modeling non-linearities in real effective exchange rates," Journal of International Money and Finance, Elsevier, vol. 18(1), pages 27-45, January.
    49. Caporale, Guglielmo Maria & Pittis, Nikitas & Sakellis, Panayiotis, 2003. "Testing for PPP: the erratic behaviour of unit root tests," Economics Letters, Elsevier, vol. 80(2), pages 277-284, August.
    50. Mark, Nelson C., 1990. "Real and nominal exchange rates in the long run: An empirical investigation," Journal of International Economics, Elsevier, vol. 28(1-2), pages 115-136, February.
    51. Mohsen Bahmani-Oskooee & Tsangyao Chang & Tsung-Pao Wu, 2015. "Purchasing Power Parity in Transition Countries: Panel Stationary Test with Smooth and Sharp Breaks," IJFS, MDPI, vol. 3(2), pages 1-9, May.
    52. 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.
    53. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    54. Ivan Paya & David A. Peel, 2003. "Purchasing Power Parity Adjustment Speeds in High Frequency Data when the Equilibrium Real Exchange Rate is Proxied by a Deterministic Trend," Manchester School, University of Manchester, vol. 71(s1), pages 39-53, September.
    55. Joscha Beckmann & Dionysius Glycopantis & Keith Pilbeam, 2018. "The dollar–euro exchange rate and monetary fundamentals," Empirical Economics, Springer, vol. 54(4), pages 1389-1410, June.
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