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Potential Pitfalls in Determining Multiple Structural Changes With an Application to Purchasing Power Parity

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  • Prodan, Ruxandra

Abstract

Tests for structural change play an important role in macroeconomics and international finance. We investigate the empirical performance of the Bai and Perron (1998) multiple structural change tests and show that the use of their critical values may cause severe size distortions in persistent series. To correct these size distortions, we implement the Bai (1999) structural change test, where we calculate bootstrap critical values. While the size is correct, his sequential method lacks power on data that includes breaks of opposite sign. We extend this test in two directions. First, we propose a new procedure to choose the number of breaks. Second, we develop a restricted version that specifically models breaks that imply mean or trend reversion. The simulation results show good power and satisfactory size of the new procedures. Using long-run real exchange rates, we illustrate the practical importance of these results. We investigate contradictory evidence of purchasing power parity from the application of unit root and structural change tests. We argue that the Bai and Perron test is the culprit and instead use the Bai test along with our newly proposed methodologies. Consequently, we reconcile the results of unit root tests with those of tests for structural change when testing for purchasing power parity

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 26 (2008)
Issue (Month): (January)
Pages: 50-65

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Handle: RePEc:bes:jnlbes:v:26:y:2008:p:50-65

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  1. Claude Lopez & Christian J. Murray & David H. Papell, 2004. "State of the Art Unit Root Tests and Purchasing Power Parity," University of Cincinnati, Economics Working Papers Series 2004-04, University of Cincinnati, Department of Economics.
  2. Francis X. Diebold & Abdelhak S. Senhadji, 1996. "Deterministic vs. Stochastic Trend in U.S. GNP, Yet Again," NBER Working Papers 5481, National Bureau of Economic Research, Inc.
  3. Vogelsang, Timothy J., 1997. "Wald-Type Tests for Detecting Breaks in the Trend Function of a Dynamic Time Series," Econometric Theory, Cambridge University Press, vol. 13(06), pages 818-848, December.
  4. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-20, July.
  5. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  6. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
  7. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
  8. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
  9. 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.
  10. Glenn D. Rudebusch, 1992. "The uncertain unit root in real GNP," Finance and Economics Discussion Series 193, Board of Governors of the Federal Reserve System (U.S.).
  11. Jushan Bai & Pierre Perron, 2003. "Critical values for multiple structural change tests," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 72-78, 06.
  12. Alan M. Taylor, 2002. "A Century Of Purchasing-Power Parity," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 139-150, February.
  13. 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.
  14. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  15. 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.
  16. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  17. Cuddington, John T. & Liang, Hong, 2000. "Purchasing power parity over two centuries?," Journal of International Money and Finance, Elsevier, vol. 19(5), pages 753-757, October.
  18. Francis X. Diebold & Celia Chen, 1993. "Testing structural stability with endogenous break point: a size comparison of analytic and bootstrap procedures," Working Papers 93-11, Federal Reserve Bank of Philadelphia.
  19. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  20. Hegwood, Natalie D & Papell, David H, 1998. "Quasi Purchasing Power Parity," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 3(4), pages 279-89, October.
  21. Samuelson, Paul A, 1994. "Facets of Balassa-Samuelson Thirty Years Later," Review of International Economics, Wiley Blackwell, vol. 2(3), pages 201-26, October.
  22. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
  23. West, Kenneth D., 1987. "A note on the power of least squares tests for a unit root," Economics Letters, Elsevier, vol. 24(3), pages 249-252.
  24. 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.
  25. Atsushi Inoue & Lutz Kilian, 2000. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometric Society World Congress 2000 Contributed Papers 0401, Econometric Society.
  26. repec:cup:etheor:v:13:y:1997:i:6:p:818-49 is not listed on IDEAS
  27. Claude Lopez & Christian J. Murray & David H. Papell, 2003. "State of the Art Unit Root Tests and the PPP Puzzle," Macroeconomics 0310009, EconWPA.
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