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

  • Ruxandra Prodan

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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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 90.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:90
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  1. 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.
  2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  3. 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.
  4. 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.
  5. 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.
  6. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  7. Diebold & Senhadji, . "Deterministic vs. Stochastic Trend in U.S. GNP, Yet Again," Home Pages _054, University of Pennsylvania.
  8. Jeremy Berkowitz & Lutz Kilian, 1996. "Recent developments in bootstrapping time series," Finance and Economics Discussion Series 96-45, Board of Governors of the Federal Reserve System (U.S.).
  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. 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.
  11. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
  12. Claude Lopez & Christian J. Murray & David H. Papell, 2003. "State of the Art Unit Root Tests and the PPP Puzzle," Macroeconomics 0310009, EconWPA.
  13. 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.
  14. Atsushi Inoue & Lutz Kilian, 2000. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometric Society World Congress 2000 Contributed Papers 0401, Econometric Society.
  15. Rudebusch, Glenn D, 1993. "The Uncertain Unit Root in Real GNP," American Economic Review, American Economic Association, vol. 83(1), pages 264-72, March.
  16. 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.
  17. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
  18. Alan M. Taylor, 2000. "A Century of Purchasing-Power Parity," NBER Working Papers 8012, National Bureau of Economic Research, Inc.
  19. 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.
  20. Samuelson, Paul A, 1994. "Facets of Balassa-Samuelson Thirty Years Later," Review of International Economics, Wiley Blackwell, vol. 2(3), pages 201-26, October.
  21. Diebold, Francis X. & Chen, Celia, 1996. "Testing structural stability with endogenous breakpoint A size comparison of analytic and bootstrap procedures," Journal of Econometrics, Elsevier, vol. 70(1), pages 221-241, January.
  22. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
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  24. repec:cup:etheor:v:13:y:1997:i:6:p:818-49 is not listed on IDEAS
  25. 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.
  26. Vogelsang, T.I. & Perron, P., 1991. "Nonstationary and Level Shifts With An Application To Purchasing Power Parity," Papers 359, Princeton, Department of Economics - Econometric Research Program.
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