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Consistent and Asymptotically Unbiased MinP Tests of Multiple Inequality Moment Restrictions

  • Christopher J. Bennett

    ()

    (Department of Economics, Vanderbilt University)

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    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.

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    File URL: http://www.accessecon.com/pubs/VUECON/vu09-w08.pdf
    File Function: First version, 2009
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    Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0908.

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    Date of creation: Jul 2009
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    Handle: RePEc:van:wpaper:0908
    Contact details of provider: Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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    1. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    2. Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche 9805, Université Laval - Département d'économique.
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    4. Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-48, September.
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    15. 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.
    16. Fan, Yanqin & Park, Sang Soo, 2010. "Confidence sets for some partially identified parameters," MPRA Paper 37149, University Library of Munich, Germany.
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