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Bootstrap Testing in Nonlinear Models

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  • Davidson, Russell
  • MacKinnon, James G

Abstract

Bootstrap testing of nonlinear models normally requires at least one nonlinear estimation for every bootstrap sample. We show how to reduce computational costs by performing only a fixed, small number of Newton or quasi-Newton steps for each bootstrap sample. The number of steps is smaller for likelihood ratio tests than for other types of classical tests and smaller for Newton's method than for quasi-Newton methods. The suggested procedures are applied to tests of slope coefficients in the Tobit model and to tests of common factor restrictions. In both cases, bootstrap tests work well, and very few steps are needed. Copyright 1999 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • Davidson, Russell & MacKinnon, James G, 1999. "Bootstrap Testing in Nonlinear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 487-508, May.
  • Handle: RePEc:ier:iecrev:v:40:y:1999:i:2:p:487-508
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    References listed on IDEAS

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    1. Gregory, Allan W & Veall, Michael R, 1987. "Formulating Wald Tests of the Restrictions Implied by the Rational Expectations Hypothesis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 2(1), pages 61-68, January.
    2. Orme, Chris, 1995. "On the Use of Artificial Regressions in Certain Microeconometric Models," Econometric Theory, Cambridge University Press, vol. 11(02), pages 290-305, February.
    3. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    4. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    5. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
    6. Olsen, Randall J, 1978. "Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model," Econometrica, Econometric Society, vol. 46(5), pages 1211-1215, September.
    7. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-1468, November.
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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