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Bootstrap Testing in Nonlinear Models


  • Davidson, Russell
  • MacKinnon, James G


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

    1. Dubin, Robin A, 1988. "Estimation of Regression Coefficients in the Presence of Spatially Autocorrelated Error Terms," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 466-474, August.
    2. Mandy, David M & Martins-Filho, Carlos, 1994. "A Unified Approach to Asymptotic Equivalence of Aitken and Feasible Aitken Instrumental Variables Estimators," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(4), pages 957-979, November.
    3. J. Bradford De Long & Lawrence H. Summers, 1991. "Equipment Investment and Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 106(2), pages 445-502.
    4. Heijmans, Risto D. H. & Magnus, Jan R., 1986. "Consistent maximum-likelihood estimation with dependent observations : The general (non-normal) case and the normal case," Journal of Econometrics, Elsevier, vol. 32(2), pages 253-285, July.
    5. Potscher, Benedikt M. & Prucha, Ingmar R., 1986. "A class of partially adaptive one-step m-estimators for the non-linear regression model with dependent observations," Journal of Econometrics, Elsevier, vol. 32(2), pages 219-251, July.
    6. Benedikt M. Pötscher & Ingmar R. Prucha, 1999. "Basic Elements of Asymptotic Theory," Electronic Working Papers 99-001, University of Maryland, Department of Economics.
    7. Anselin, Luc, 1990. "Some robust approaches to testing and estimation in spatial econometrics," Regional Science and Urban Economics, Elsevier, vol. 20(2), pages 141-163, September.
    8. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    9. Potscher, Benedikt M & Prucha, Ingmar R, 1989. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Processes," Econometrica, Econometric Society, vol. 57(3), pages 675-683, May.
    10. Moulton, Brent R, 1990. "An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Unit," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 334-338, May.
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    JEL classification:

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


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