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Assessing the Relative Power of Structural Break Tests Using a Framework Based on the Approximate Bahadur Slope

  • Dukpa Kim


  • Pierre Perron


We compare the asymptotic relative efficiency of the Exp, Mean, and Sup functionals of the Wald, LM and LR tests for structural change analyzed by Andrews (1993) and Andrews and Ploberger (1994). We derive the approximate Bahadur slopes of these tests using large deviations techniques. These show that tests based on the Mean functional are inferior to those based on the Sup and Exp when using the same base statistic. Also, for a given functional, the Wald-based test dominates the LR-based test, which dominates the LM-based one. We show that the Sup and Mean type tests satisfy Wieand’s (1976) condition so that their slopes yield the limiting (as the size tends to zero) asymptotic relative Pitman efficiency. Using this measure of efficiency, the Mean type tests are also inferior to the Sup. We also compare tests based on the Wald and LM statistics modified with a HAC estimator. In this case, the inferiority of the LM-based tests is especially pronounced. The relevance of our theoretical results in finite samples is assessed via simulations. Our results are in contrast to those of Andrews and Ploberger (1994) based on a local asymptotic framework and our analysis thereby reveals its potential weaknesses in the context of structural change problems.

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Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2006-063.

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Length: 61 pages
Date of creation: Nov 2006
Date of revision:
Handle: RePEc:bos:wpaper:wp2006-063
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  1. Geweke, John, 1981. "The Approximate Slopes of Econometric Tests," Econometrica, Econometric Society, vol. 49(6), pages 1427-42, November.
  2. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests," Working Papers 05-08, Cornell University, Center for Analytic Economics.
  3. Ai Deng & Pierre Perron, 2007. "A Non-local Perspective on the Power Properties of the CUSUM and CUSUM of Squares Tests for Structural Change," Boston University - Department of Economics - Working Papers Series WP2007-019, Boston University - Department of Economics.
  4. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  5. 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.
  6. Donald W.K. Andrews & Inpyo Lee & Werner Ploberger, 1992. "Optimal Changepoint Tests for Normal Linear Regression," Cowles Foundation Discussion Papers 1016, Cowles Foundation for Research in Economics, Yale University.
  7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  8. Perron, Pierre & Vodounou, Cosme, 2005. "The Variance Ratio Test: An Analysis Of Size And Power Based On A Continuous-Time Asymptotic Framework," Econometric Theory, Cambridge University Press, vol. 21(03), pages 562-592, June.
  9. 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.
  10. Crainiceanu, Ciprian & Vogelsang, Timothy, 2001. "Spectral Density Bandwidth Choice: Source of Nonmonotonic Power for Tests of a Mean Shift in a Time Series," Working Papers 01-14, Cornell University, Center for Analytic Economics.
  11. Donald W.K. Andrews & Werner Ploberger, 1993. "Admissibility of the Likelihood Ratio Test When a Nuisance Parameter Is Present OnlyUnder the Alternative," Cowles Foundation Discussion Papers 1058, Cowles Foundation for Research in Economics, Yale University.
  12. 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.
  13. Estrella, Arturo, 2003. "Critical Values And P Values Of Bessel Process Distributions: Computation And Application To Structural Break Tests," Econometric Theory, Cambridge University Press, vol. 19(06), pages 1128-1143, December.
  14. 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.
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