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Testing for Multiple Structural Changes in Cointegrated Regression Models

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  • Mohitosh Kejriwal

    ()

  • Pierre Perron

    ()

Abstract

This paper considers issues related to testing for multiple structural changes in cointegrated systems. We derive the limiting distribution of the Sup-Wald test under mild conditions on the errors and regressors for a variety of testing problems. Our asymptotic results show that as long as the intercept is allowed to change across regimes, inference is possible even if we allow stationary variables in the regression. We also find that including stationary regressors whose coefficients are not allowed to change does not affect the limiting distribution of the tests under the null hypothesis. We propose a procedure that allows one to test the null hypothesis of, say, changes, versus the alternative hypothesis of changes. This sequential procedure is useful in that it permits consistent estimation of the number of breaks present. When the regression is spurious, we show that the procedure tends to select the maximum number of breaks allowed. This feature helps distinguish a cointegrated model from a purely spurious one. Our simulation experiments show that in the presence of serial correlation in the errors, the commonly used LM tests suffer from the important problem of nonmonotonic power in finite samples. In fact, in certain cases, power can go to zero as the magnitude of the break(s) increase. We propose a modified Wald test based on a new estimator of the long run variance which uses information under both the null and alternative hypotheses. The proposed test is able to mitigate size distortions associated with the usual Wald test while maintaining monotonic power.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2006-051.

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Length: 63 pages
Date of creation: Sep 2006
Date of revision:
Handle: RePEc:bos:wpaper:wp2006-051

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Keywords: Change-point; Sequential procedure; Wald tests; Unit Roots; Cointegration.;

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References

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  1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
  2. Zhongjun Qu, 2007. "Searching for cointegration in a dynamic system," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 580-604, November.
  3. Kejriwal, Mohitosh, 2009. "Tests for a mean shift with good size and monotonic power," Economics Letters, Elsevier, vol. 102(2), pages 78-82, February.
  4. Kuo, Biing-Shen, 1998. "Test for partial parameter instability in regressions with I(1) processes," Journal of Econometrics, Elsevier, vol. 86(2), pages 337-368, June.
  5. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, 03.
  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. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  9. Peter Reinhard Hansen, 2000. "Structural Changes in the Cointegrated Vector Autoregressive Model," Working Papers 2000-20, Brown University, Department of Economics.
  10. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
  11. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
  12. Ng, S. & Perron, P., 1995. "Estimation and Inference in Nearly Unbalanced, Nearly Cointegrated Systems," Cahiers de recherche 9534, Universite de Montreal, Departement de sciences economiques.
  13. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 14(02), pages 222-259, April.
  14. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  15. Hao, K., 1996. "Testing for Structural Change in Cointegrated Regression Models: Some Comparisons and Generalizations," Monash Econometrics and Business Statistics Working Papers 3/96, Monash University, Department of Econometrics and Business Statistics.
  16. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
  17. 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.
  18. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2006. "Testing the Null of Cointegration with Structural Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(5), pages 623-646, October.
  19. Bai, Jushan & Lumsdaine, Robin L & Stock, James H, 1998. "Testing for and Dating Common Breaks in Multivariate Time Series," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 395-432, July.
  20. Kejriwal, Mohitosh & Perron, Pierre, 2008. "The limit distribution of the estimates in cointegrated regression models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 146(1), pages 59-73, September.
  21. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July.
  22. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
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Citations

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Cited by:
  1. Roeger, Edward & Leibtag, Ephraim S., 2011. "How Retail Beef and Bread Prices Respond to Changes in Ingredient and Input and Costs," Economic Research Report 102757, United States Department of Agriculture, Economic Research Service.
  2. Jing Zhou & Pierre Perron, 2008. "Testing for Breaks in Coefficients and Error Variance: Simulations and Applications," Boston University - Department of Economics - Working Papers Series wp2008-010, Boston University - Department of Economics.
  3. Joscha Beckmann & Ansgar Belke & Michael Kühl, 2011. "Cointegration, structural breaks and monetary fundamentals of the Dollar/Yen Exchange," International Advances in Economic Research, Springer, vol. 17(4), pages 397-412, November.
  4. Mylonidis, Nikolaos & Kollias, Christos, 2010. "Dynamic European stock market convergence: Evidence from rolling cointegration analysis in the first euro-decade," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2056-2064, September.
  5. Pierre Perron & Yohei Yamamoto, 2011. "Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors," Boston University - Department of Economics - Working Papers Series WP2011-053, Boston University - Department of Economics.
  6. Pierre Perron & Yohei Yamamoto, 2008. "Estimating and Testing Multiple Structural Changes in Models with Endogenous Regressors," Boston University - Department of Economics - Working Papers Series wp2008-017, Boston University - Department of Economics.
  7. Joscha Beckmann & Ansgar Belke & Michael Kühl, 2009. "How Stable Are Monetary Models of the Dollar-Euro Exchange Rate?: A Time-Varying Coefficient Approach," Discussion Papers of DIW Berlin 944, DIW Berlin, German Institute for Economic Research.
  8. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," PSE Working Papers halshs-00564897, HAL.
  9. Hernandez-Villafuerte, Karla Vanessa, 2011. "Relationship Between Spatial Price Transmission And Geographical Distance In Brazil," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114545, European Association of Agricultural Economists.
  10. Andreas Beyer & Alfred A. Haug & William G. Dewald, 2009. "Structural Breaks, Cointegration and the Fisher Effect," Working Paper Series 1013, European Central Bank.
  11. Chihwa Kao & Lorenzo Trapani & Giovanni Urga, 2012. "Testing for Breaks in Cointegrated Panels," Center for Policy Research Working Papers 135, Center for Policy Research, Maxwell School, Syracuse University.
  12. Boetel, Brenda L. & Liu, Donald J., 2008. "Incorporating Structural Changes in Agricultural and Food Price Analysis: An Application to the U.S. Beef and Pork Sectors," Working Papers 44076, University of Minnesota, The Food Industry Center.
  13. Mustafa SAATCÝ & Yasemin DUMRUL, 2013. "The Relationship Between Energy Consumption and Economic Growth: Evidence From A Structural Break Analysis For Turkey," International Journal of Energy Economics and Policy, Econjournals, vol. 3(1), pages 20-29.
  14. Pierre Perron & Jing Zhou, 2008. "Testing Jointly for Structural Changes in the Error Variance and Coefficients of a Linear Regression Model," Boston University - Department of Economics - Working Papers Series wp2008-011, Boston University - Department of Economics.
  15. Travaglini, Guido, 2007. "The U.S. Dynamic Taylor Rule With Multiple Breaks, 1984-2001," MPRA Paper 3419, University Library of Munich, Germany, revised 15 Jun 2007.
  16. Vicente Esteve & Manuel Navarro-Ibáñez & María A. Prats, 2013. "The present value model of U.S. stock prices revisited: long-run evidence with structural breaks, 1871-2010," Working Papers 1305, Department of Applied Economics II, Universidad de Valencia.
  17. Roeger, Edward & Leibtag, Ephraim S., 2010. "The Magnitude and Timing of Retail Beef and Bread Price Response to Changes in Input Costs," 2010 Annual Meeting, July 25-27, 2010, Denver, Colorado 61041, Agricultural and Applied Economics Association.
  18. Joscha Beckmann & Ansgar Belke & Michael Kühl, 2011. "The dollar-euro exchange rate and macroeconomic fundamentals: a time-varying coefficient approach," Review of World Economics (Weltwirtschaftliches Archiv), Springer, vol. 147(1), pages 11-40, April.
  19. Marco Taboga, 2013. "What is a prime bank? A Euribor – OIS spread perspective," Temi di discussione (Economic working papers) 895, Bank of Italy, Economic Research and International Relations Area.
  20. Loredana Ureche-Rangau & Franck Speeg, 2011. "A simple method for variance shift detection at unknown time points," Economics Bulletin, AccessEcon, vol. 31(3), pages 2204-2218.
  21. Kejriwal, Mohitosh & Perron, Pierre, 2008. "The limit distribution of the estimates in cointegrated regression models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 146(1), pages 59-73, September.
  22. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," Working Papers halshs-00564897, HAL.
  23. You, Kefei & Sarantis, Nicholas, 2012. "Structural breaks and the equilibrium real effective exchange rate of China: A NATREX approach," China Economic Review, Elsevier, vol. 23(4), pages 1146-1163.

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