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Consistent and Asymptotically Unbiased MinP Tests of Multiple Inequality Moment Restrictions

Author

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  • Christopher J. Bennett

    () (Department of Economics, Vanderbilt University)

Abstract

This paper considers the general problem of testing multiple inequality moment restrictions against an unrestricted alternative. We first introduce a test based on a maximum statistic and show how, via a partially recentered bootstrap scheme, we may obtain a testing procedure that delivers, at least asymptotically, an exact alpha-level test for any configuration of the parameters on the boundary of the null hypothesis. We prove that this bootstrap test is asymptotically unbiased and that it weakly dominates analogous testing procedures based on the canonical (fully centered) bootstrap. Building on these results we introduce a computationally inexpensive minimum p-value test. The minimum p-value test enjoys the asymptotic unbiasedness property of the underlying partially recentered bootstrap test. Additionally, the minimum $p$-value test delivers balance of power among the individual moment inequalities under test without studentization, and also allows users to gauge the strength of the evidence against the individual moment inequalities. To illustrate the use of our proposed testing procedure we examine the distributional effects of Vietnam veteran status on earnings. In particular, the results from our procedure when applied to testing for stochastic dominance and normalized stochastic dominance demonstrate that there is unambiguously greater poverty and greater relative inequality in earnings for veterans.

Suggested Citation

  • Christopher J. Bennett, 2009. "Consistent and Asymptotically Unbiased MinP Tests of Multiple Inequality Moment Restrictions," Vanderbilt University Department of Economics Working Papers 0908, Vanderbilt University Department of Economics.
  • Handle: RePEc:van:wpaper:0908
    as

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    File URL: http://www.accessecon.com/pubs/VUECON/vu09-w08.pdf
    File Function: First version, 2009
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    References listed on IDEAS

    as
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    3. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-355, March.
    4. Christopher J. Bennett, 2009. "p-Value Adjustments for Asymptotic Control of the Generalized Familywise Error Rate," Vanderbilt University Department of Economics Working Papers 0905, Vanderbilt University Department of Economics.
    5. Leslie G. Godfrey, 2005. "Controlling the Overall Significance Level of a Battery of Least Squares Diagnostic Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(2), pages 263-279, April.
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    More about this item

    Keywords

    Bootstrap; moment inequalities; asymptotic bias; stochastic dominance;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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