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Testing for structural change in conditional models

  • Hansen, Bruce E.

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. 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).
  2. 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.
  3. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  4. repec:cup:etheor:v:7:y:1991:i:1:p:1-21 is not listed on IDEAS
  5. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  6. Bruce E. Hansen, 1995. "Approximate Asymptotic P-Values for Structural Change Tests," Boston College Working Papers in Economics 297., Boston College Department of Economics.
  7. 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).
  8. 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.
  9. 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.
  10. 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.
  11. Engle, Robert F. & Hendry, David F., 1993. "Testing superexogeneity and invariance in regression models," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 119-139, March.
  12. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  13. Phillips, Peter C B & Loretan, Mico, 1991. "Estimating Long-run Economic Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 407-36, May.
  14. 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.
  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. 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.
  17. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, March.
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