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Testing for structural change in conditional models

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  • Hansen, Bruce E.

Abstract

In the past decade, we have seen the development of a new set of tests for structural change of unknown timing in regression models, most notably the SupF statistic of Andrews (1993), the ExpF and AveF statistics of Andrews-Ploberger (1994), and the L statistic of Nyblom (1989). The distribution theory used for these tests is primarily asymptotic, and has been derived under the maintained assumption that the regressors are stationary. This excludes structural change in the marginal distribution of the regressors. As a result, these tests technically cannot discriminate between structural change in the conditional and marginal distributions. This paper attempts to remedy this deficiency by deriving the large sample distributions of the test statistics allowing for structural change in the marginal distribution of the regressors. We find that the asymptotic distributions of the SupF, ExpF, AveF and L statistics are not invariant to structural change in the regressors. To solve the size problem, we introduce a 'fixed regressor bootstrap' which achieves the first-order asymptotic distribution, and appears to possess reasonable size properties in small samples. Our bootstrap theory allows for arbitrary structural change in the regressors, including structural shifts, polynomial trends, and exogenous stochastic trends. It allows for lagged dependent variables and heteroskedastic error processes.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 97 (2000)
Issue (Month): 1 (July)
Pages: 93-115

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Handle: RePEc:eee:econom:v:97:y:2000:i:1:p:93-115

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
  2. Peter C.B. Phillips & Mico Loretan, 1989. "Estimating Long Run Economic Equilibria," Cowles Foundation Discussion Papers 928, Cowles Foundation for Research in Economics, Yale University.
  3. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  4. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
  5. Ploberger, Werner & Kramer, Walter, 1996. "A trend-resistant test for structural change based on OLS residuals," Journal of Econometrics, Elsevier, vol. 70(1), pages 175-185, January.
  6. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  7. Hansen, Bruce E, 1997. "Approximate Asymptotic P Values for Structural-Change Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 60-67, January.
  8. Hendry, David F, 1988. "The Encompassing Implications of Feedback versus Feedforward Mechanisms in Econometrics," Oxford Economic Papers, Oxford University Press, vol. 40(1), pages 132-49, March.
  9. 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.
  10. Engle, Robert F & Hendry, David F & Richard, Jean-Francois, 1979. "Exogeneity," The Warwick Economics Research Paper Series (TWERPS) 162, University of Warwick, Department of Economics.
    • Engle, Robert F & Hendry, David F & Richard, Jean-Francois, 1983. "Exogeneity," Econometrica, Econometric Society, vol. 51(2), pages 277-304, March.
    • ENGLE, Robert F. & HENDRY, David F. & RICHARD, Jean-François, . "Exogeneity," CORE Discussion Papers RP -516, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. 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.
  12. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  13. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
  14. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
  15. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  16. repec:cup:etheor:v:7:y:1991:i:1:p:1-21 is not listed on IDEAS
  17. Engle, R. & Hendry, D., 1990. "Testing Super Exogeneity And Invariance In Regression Models," Economics Series Working Papers 99100, University of Oxford, Department of Economics.
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