Pseudo-Gaussian and rank-based optimal tests for random individual effects in large n small T panels
AbstractWe 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 InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 170 (2012)
Issue (Month): 1 ()
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Random effects; Panel data; Rank tests; Local asymptotic normality;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
- C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Chris D. Orme & Takashi Yamagata, 2006.
"The asymptotic distribution of the F-test statistic for individual effects,"
Royal Economic Society, vol. 9(3), pages 404-422, November.
- C Orme & Y Yamagata, 2006. "The Asymptotic Distribution of the F-Test Statistic for Individual Effects," The School of Economics Discussion Paper Series 0610, Economics, The University of Manchester.
- Nerlove, Marc, 1971.
"Further Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross Sections,"
Econometric Society, vol. 39(2), pages 359-82, March.
- 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.
- Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
- 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.
- 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).
- Breusch, T S & Pagan, A R, 1980. "The Lagrange Multiplier Test and Its Applications to Model Specification in Econometrics," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 239-53, January.
- Marc Hallin & Jean-François Ingenbleek & Madan L. Puri, 1984.
"Linear serial rank tests for randomness against ARMA alternatives,"
ULB Institutional Repository
2013/2167, ULB -- Universite Libre de Bruxelles.
- 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.
- Abdelhadi Akharif & Marc Hallin, 2003. "Efficient detection of random coefficients in autoregressive models," ULB Institutional Repository 2013/127956, ULB -- Universite Libre de Bruxelles.
- Hsiao,Cheng, 2003.
"Analysis of Panel Data,"
Cambridge University Press, number 9780521818551, April.
- Marc Hallin & Bas Werker, 2003.
"Semiparametric efficiency, distribution-freeness, and invariance,"
ULB Institutional Repository
2013/2119, ULB -- Universite Libre de Bruxelles.
- Hallin, M. & Werker, B.J.M., 2003. "Semiparametric efficiency, distribution-freeness and invariance," Open Access publications from Tilburg University urn:nbn:nl:ui:12-117062, Tilburg University.
- Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-72, July.
- Moulton, Brent R & Randolph, William C, 1989. "Alternative Tests of the Error Components Model," Econometrica, Econometric Society, vol. 57(3), pages 685-93, May.
- Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
- repec:cup:cbooks:9780521496032 is not listed on IDEAS
- 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.
- 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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