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The Limit Distribution of the Estimates in Cointegrated Regression Models with Multiple Structural Changes

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  • Mohitosh Kejriwal

    ()
    (Boston University, Department of Economics)

  • Pierre Perron

    ()
    (Boston University, Department of Economics)

Abstract

This paper studies the problem of estimation and inference in cointegrated regression models with multiple structural changes. Our framework is general enough to incorporate both stationary and integrated regressors. Both pure and partial structural change models are analyzed. We derive the consistency, rate of convergence and the limit distribution of the estimated break fractions. Our conditions are considerably less restrictive than those in Bai, Lumsdaine and Stock (1998) who considered the single break case in a multi-equations system, and permit a wide class of practically relevant models. We show that if the coefficients of the integrated regressors are allowed to change, the estimated break fractions are asymptotically dependent so that confidence intervals need to be constructed jointly. Methods to construct such confidence intervals are discussed. If, however, only the intercept and/or the coefficients of the stationary regressors are allowed to change, the estimates of the break dates are asymptotically independent as in the stationary framework analyzed by Bai and Perron (1998). We also show that our results remain valid, under very weak conditions, when the potential endogeneity of the nonstationary regressors is accounted for via an increasing sequence of leads and lags of their first-differences as additional regressors. Simulation evidence is presented to assess the adequacy of the asymptotic approximations in finite samples.

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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 WP2006-064.

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Length: 36 pages
Date of creation: Dec 2006
Date of revision:
Handle: RePEc:bos:wpaper:wp2006-064

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Keywords: Change-point; Break Dates; Unit Roots; Cointegration; Confidence Intervals.;

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References

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  1. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  2. Hansen, Bruce E, 1992. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 321-35, July.
  3. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July.
  4. Kejriwal, Mohitosh & Perron, Pierre, 2010. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 503-522.
  5. 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.
  6. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477444.
  7. Mohitosh Kejriwal & Pierre Perron, 2007. "Data Dependent Rules for the Selection of the Number of Leads and Lags in the Dynamic OLS Cointegrating Regression," Boston University - Department of Economics - Working Papers Series WP2007-018, Boston University - Department of Economics.
  8. 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.
  9. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
  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, 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.
  12. Ng, S. & Perron, P., 1995. "Estimation and Inference in Nearly Unbalanced, Nearly Cointegrated Systems," Cahiers de recherche 9534, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  13. Zhongjun Qu & Pierre Perron, 2005. "Estimating and testing structural changes in multivariate regressions," Boston University - Department of Economics - Working Papers Series WP2005-012, Boston University - Department of Economics.
  14. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626.
  15. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477451.
  16. Altissimo, Filippo & Corradi, Valentina, 2003. "Strong rules for detecting the number of breaks in a time series," Journal of Econometrics, Elsevier, vol. 117(2), pages 207-244, December.
  17. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 14(02), pages 222-259, April.
  18. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521405515.
  19. 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.
  20. 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.
  21. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
  22. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
  23. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
  24. 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.
  25. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
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