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Contributions to the Theory of Optimal Tests

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  • Moreira, Humberto Ataíde
  • Moreira, Marcelo J.

Abstract

This paper considers tests which maximize the weighted average power (WAP). The focus is on determining WAP tests subject to an uncountable number of equalities and/or inequalities. The unifying theory allows us to obtain tests with correct size, similar tests, and unbiased tests, among others. A WAP test may be randomized and its characterization is not always possible. We show how to approximate the power of the optimal test by sequences of nonrandomized tests. Two alternative approximations are considered. The rst approach considers a sequence of similar tests for an increasing number of boundary conditions. This discretization allows us to implement the WAP tests in practice. The second method nds a sequence of tests which approximate the WAP test uniformly. This approximation allows us to show that WAP similar tests are admissible. The theoretical framework is readily applicable to several econometric models, including the important class of the curved-exponential family. In this paper, we consider the instrumental variable model with heteroskedastic and autocorrelated errors (HAC-IV) and the nearly integrated regressor model. In both models, we nd WAP similar and (locally) unbiased tests which dominate other available tests.

Suggested Citation

  • Moreira, Humberto Ataíde & Moreira, Marcelo J., 2013. "Contributions to the Theory of Optimal Tests," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 747, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    • Handle: RePEc:fgv:epgewp:747
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    References listed on IDEAS

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    1. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages 2-18, September.
    2. Donald W.K. Andrews, 2011. "Similar-on-the-Boundary Tests for Moment Inequalities Exist, But Have Poor Power," Cowles Foundation Discussion Papers 1815, Cowles Foundation for Research in Economics, Yale University.
    3. Müller, Ulrich K. & Watson, Mark W., 2013. "Low-frequency robust cointegration testing," Journal of Econometrics, Elsevier, vol. 174(2), pages 66-81.
    4. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    5. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    6. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Admissible Invariant Similar Tests For Instrumental Variables Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 806-818, June.
    7. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    8. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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    Cited by:

    1. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
    2. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    3. Philipp Ketz & Adam McCloskey, 2021. "Short and Simple Confidence Intervals when the Directions of Some Effects are Known," Papers 2109.08222, arXiv.org.
    4. Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978, Cowles Foundation for Research in Economics, Yale University.
    5. David M. Kaplan, 2015. "Bayesian and frequentist tests of sign equality and other nonlinear inequalities," Working Papers 1516, Department of Economics, University of Missouri.
    6. Donald W.K. Andrews, 2011. "Similar-on-the-Boundary Tests for Moment Inequalities Exist, But Have Poor Power," Cowles Foundation Discussion Papers 1815R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2012.
    7. Marcelo Moreira & Rafael Mourão & Humberto Moreira, 2016. "A critical value function approach, with an application to persistent time-series," CeMMAP working papers CWP24/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Ketz, Philipp, 2018. "Subvector inference when the true parameter vector may be near or at the boundary," Journal of Econometrics, Elsevier, vol. 207(2), pages 285-306.
    9. Mills, Benjamin & Moreira, Marcelo J. & Vilela, Lucas P., 2014. "Tests based on t-statistics for IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 182(2), pages 351-363.

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