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Implicit Alternatives and the Local Power of Test Statistics

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Author Info
Davidson, Russell
MacKinnon, James G

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Abstract

The local power of test statistics is analyzed by considering sequences of data-generating processes (DGPs) that approach the null hypothesis without necessarily satisfying the alternative. The three classical test statistics-LR, Wald, and LM-are shown to tend asymptot ically to the same random variable under all such sequences. The powe r of these statistics depends on the null, the alternative, and the sequence of DGPs in a geometrically intuitive way. This implies that, for any statistic that is asymptotically chi-squared under the null, there exists an "implicit alternative hypothesis" against which that statistic will have highest power. Copyright 1987 by The Econometric Society.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 55 (1987)
Issue (Month): 6 (November)
Pages: 1305-29
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Handle: RePEc:ecm:emetrp:v:55:y:1987:i:6:p:1305-29

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  1. Russell Davidson & James G. MacKinnon, 1987. "Testing for Consistency using Artificial Regressions," Working Papers 687, Queen's University, Department of Economics. [Downloadable!]
  2. Russell Davidson & James G. MacKinnon, 2004. "The Power of Bootstrap and Asymptotic Tests," Working Papers 1035, Queen's University, Department of Economics. [Downloadable!]
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  3. Anil K. Bera & Walter Sosa Escudero & Mann Yoon, 2000. "Tests for the Error Component Model in the Presence of Local Misspecification," Econometric Society World Congress 2000 Contributed Papers 1888, Econometric Society. [Downloadable!]
    Other versions:
  4. Russell Davidson & James G. MacKinnon, 1988. "Specification Tests Based on Artificial Regressions," Working Papers 707, Queen's University, Department of Economics. [Downloadable!]
  5. Russell Davidson & James G. MacKinnon, 1996. "The Size and Power of Bootstrap Tests," Working Papers 932, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
  6. Dastoor, Naorayex, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics. [Downloadable!]
  7. E. Fe-Rodríguez & C. Orme, 2006. "On the sensitivity of Kernel-based Conditional Moment Tests to Unconsidered Local Alternatives," The School of Economics Discussion Paper Series 0606, Economics, The University of Manchester. [Downloadable!]
  8. Eduardo Fé-Rodríguez & Chris D. Orme, 2009. "On the Sensitivity of Kernel-based Tests of Conditional Moment Restrictions," The School of Economics Discussion Paper Series 0912, Economics, The University of Manchester. [Downloadable!]
  9. Marine Carrasco, 2004. "Chi-square Tests for Parameter Stability," RCER Working Papers 508, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
  10. Emmanuel Flachaire, 1999. "A better way to bootstrap pairs," Post-Print halshs-00175892_v1, HAL. [Downloadable!]
    Other versions:
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