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Testing for Structural Change in Conditional Models

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  • Bruce E. Hansen

    ()
    (Boston College)

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

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 310..

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Length: 26 pages
Date of creation: Apr 1998
Date of revision:
Handle: RePEc:boc:bocoec:310

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Keywords: structural change;

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  1. 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.
  2. Engle, Robert F & Hendry, David F & Richard, Jean-Francois, 1983. "Exogeneity," Econometrica, Econometric Society, vol. 51(2), pages 277-304, March.
  3. 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).
  4. James H. Stock & Mark W. Watson, 1994. "Evidence on Structural Instability in Macroeconomic Time Series Relations," NBER Technical Working Papers 0164, National Bureau of Economic Research, Inc.
  5. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
  6. 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.
  7. 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.
  8. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  9. 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.
  10. 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.
  11. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, September.
  12. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  13. 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.
  14. repec:cup:etheor:v:7:y:1991:i:1:p:1-21 is not listed on IDEAS
  15. 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.
  16. 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.
  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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