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Bootstrap LM Test for the Box CoxTobit Model


  • David Vincent

    () (Hewlett Packard (UK))


Consistency of the maximum likelihood estimators for the parameters in the standard Tobit model rely heavily on the assumption of a normally distributed error term. The Box Cox transformation presents an obvious attempt to preserve normality when the data make this questionable. This paper sets out an OPG version of an LM test for the null hypotheses of the standard Tobit model, against the alternative of a more general non-linear specification, as determined by the parameter of the Box Cox transformation. Monte Carlo estimates of the rejection probabilities using first order asymptotic and parametric bootstrap critical values are obtained, for sample sizes that are comparable to those used in practice. The results show that the LM-test using bootstrap critical values has practically no size distortion, whereas using asymptotic critical values, the empirical rejection probabilities are significantly larger than the nominal levels. A simple program which carries out this test using bootstrap critical values has also been written and can be run post the official Stata Tobit estimation command.

Suggested Citation

  • David Vincent, 2010. "Bootstrap LM Test for the Box CoxTobit Model," BOS10 Stata Conference 9, Stata Users Group.
  • Handle: RePEc:boc:bost10:9

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    References listed on IDEAS

    1. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2009. "Dealing with limited overlap in estimation of average treatment effects," Biometrika, Biometrika Trust, vol. 96(1), pages 187-199.
    2. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-620, September.
    3. James J. Heckman & Hidehiko Ichimura & Petra E. Todd, 1997. "Matching As An Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 605-654.
    4. Giuseppe Porro & Stefano Maria Iacus, 2009. "Random Recursive Partitioning: a matching method for the estimation of the average treatment effect," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 163-185.
    5. Stefano Iacus & Gary King & Giuseppe Porro, 2008. "Matching for Causal Inference Without Balance Checking," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1073, Universitá degli Studi di Milano.
    6. repec:cup:apsrev:v:95:y:2001:i:01:p:49-69_00 is not listed on IDEAS
    7. Kosuke Imai & Gary King & Elizabeth A. Stuart, 2008. "Misunderstandings between experimentalists and observationalists about causal inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 481-502.
    8. Ho, Daniel E. & Imai, Kosuke & King, Gary & Stuart, Elizabeth A., 2007. "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference," Political Analysis, Cambridge University Press, vol. 15(03), pages 199-236, June.
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    Cited by:

    1. Anagnostopoulos, Achilleas & Siebert, W. Stanley, 2012. "The Impact of Greek Labour Market Regulation on Temporary and Family Employment: Evidence from a New Survey," IZA Discussion Papers 6504, Institute for the Study of Labor (IZA).

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