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Testing multiple inequality hypotheses: a smoothed indicator approach

Author

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  • Le-Yu Chen

    (Institute for Fiscal Studies and Academia Sinica)

  • Jerzy Szroeter

    (Institute for Fiscal Studies)

Abstract

This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby obviated. A simple procedure is enabled using fixed critical values. The test is shown to have correct asymptotic size in the uniform sense that supremum finite-sample rejection probability over null-restricted data distributions tends asymptotically to nominal significance level. This applies under weak assumptions allowing for estimator covariance singularity. The test is unbiased for a wide class of local alternatives. A new theorem establishes directions in which the test is locally most powerful. The proposed procedure is compared with predominant existing tests in structure, theory and simulation. This paper is a revised version of CWP13/09.

Suggested Citation

  • Le-Yu Chen & Jerzy Szroeter, 2012. "Testing multiple inequality hypotheses: a smoothed indicator approach," CeMMAP working papers CWP16/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:16/12
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    References listed on IDEAS

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    Cited by:

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    3. Markus Frölich & Martin Huber, 2017. "Direct and indirect treatment effects–causal chains and mediation analysis with instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1645-1666, November.
    4. Julia Schmieder, 2020. "Fertility as a Driver of Maternal Employment," Discussion Papers of DIW Berlin 1882, DIW Berlin, German Institute for Economic Research.
    5. M. Azhar Hussain & Nikolaj Siersbæk & Lars Peter Østerdal, 2020. "Multidimensional welfare comparisons of EU member states before, during, and after the financial crisis: a dominance approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 645-686, December.
    6. Martin Huber & Giovanni Mellace, 2014. "Testing exclusion restrictions and additive separability in sample selection models," Empirical Economics, Springer, vol. 47(1), pages 75-92, August.
    7. Bolzern, Benjamin & Huber, Martin, 2017. "Testing the validity of the compulsory schooling law instrument," Economics Letters, Elsevier, vol. 159(C), pages 23-27.
    8. Salm, Martin & Siflinger, Bettina & Xie, Mingjia, 2021. "The Effect of Retirement on Mental Health: Indirect Treatment Effects and Causal Mediation," Other publications TiSEM e28efa7f-8219-437c-a26d-2, Tilburg University, School of Economics and Management.
    9. Christina Felfe & Martin Huber, 2017. "Does preschool boost the development of minority children?: the case of Roma children," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(2), pages 475-502, February.
    10. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    11. M. Azhar Hussain & Nikolaj Siersbæk & Lars Peter Østerdal, 0. "Multidimensional welfare comparisons of EU member states before, during, and after the financial crisis: a dominance approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 0, pages 1-42.
    12. Fiorini, Mario & Katrien Stevens, 2014. "Assessing the Monotonicity Assumption in IV and fuzzy RD designs," Working Papers 2014-13, University of Sydney, School of Economics.

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    More about this item

    Keywords

    Test; Multiple inequalities; One-sided hypothesis; Composite null; Binding constraints; Asymptotic exactness; Covariance singularity; Indicator smoothing;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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