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Pseudo-Gaussian and rank-based optimal tests for random individual effects in large n small T panels

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  • Bennala, Nezar
  • Hallin, Marc
  • Paindaveine, Davy

Abstract

We consider the problem of detecting unobserved heterogeneity, that is, the problem of testing the absence of random individual effects in an n×T panel. We establish a local asymptotic normality property–with respect to intercept, regression coefficient, the scale parameter σ of the error, and the scale parameter σu of individual effects (which is the parameter of interest)–for given (scaled) density f1 of the error terms, when n tends to infinity and T is fixed. This result allows, via the Hájek representation theorem, for developing asymptotically optimal rank-based tests for the null hypothesis σu=0 (absence of individual effects). These tests are locally asymptotically optimal at correctly specified innovation densities f1, but remain valid irrespective of the actual underlying density. The limiting distribution of our test statistics is obtained both under the null and under sequences of contiguous alternatives. A local asymptotic linearity property is established in order to control for the effect of substituting estimators for nuisance parameters. The asymptotic relative efficiencies of the proposed procedures with respect to the corresponding pseudo-Gaussian parametric tests are derived. In particular, the van der Waerden version of our rank-based tests uniformly dominates, from the point of view of Pitman efficiency, the classical Honda test. Small-sample performances are investigated via a Monte-Carlo study, and confirm theoretical findings.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 170 (2012)
Issue (Month): 1 ()
Pages: 50-67

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Handle: RePEc:eee:econom:v:170:y:2012:i:1:p:50-67

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Random effects; Panel data; Rank tests; Local asymptotic normality;

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  1. Marc Hallin & Jean-François Ingenbleek & Madan L. Puri, 1985. "Linear serial rank tests for randomness against ARMA alternatives," ULB Institutional Repository 2013/2003, ULB -- Universite Libre de Bruxelles.
  2. Hsiao,Cheng, 2003. "Analysis of Panel Data," Cambridge Books, Cambridge University Press, number 9780521522717.
  3. Honda, Yuzo, 1985. "Testing the Error Components Model with Non-normal Disturbances," Review of Economic Studies, Wiley Blackwell, vol. 52(4), pages 681-90, October.
  4. Abdelhadi Akharif & Marc Hallin, 2003. "Efficient detection of random coefficients in autoregressive models," ULB Institutional Repository 2013/127956, ULB -- Universite Libre de Bruxelles.
  5. Breusch, T.S. & Pagan, A.R., . "The Lagrange multiplier test and its applications to model specification in econometrics," CORE Discussion Papers RP -412, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
  7. Marc Nerlove, 1968. "Further Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross-Sections," Cowles Foundation Discussion Papers 257, Cowles Foundation for Research in Economics, Yale University.
  8. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291, September.
  9. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-72, July.
  10. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
  11. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  12. Chris D. Orme & Takashi Yamagata, 2006. "The asymptotic distribution of the F-test statistic for individual effects," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 404-422, November.
  13. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
  14. Moulton, Brent R & Randolph, William C, 1989. "Alternative Tests of the Error Components Model," Econometrica, Econometric Society, vol. 57(3), pages 685-93, May.
  15. Swensen, Anders Rygh, 1985. "The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 54-70, February.
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