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On the Use of the Helmert Transformation, and its Applications in Panel Data Econometrics

Author

Listed:
  • Kolev Gueorgui I.

    (Tilburg University, Tilburg, Netherlands)

  • Āzacis Helmuts

    (Cardiff Business School, Cardiff University, Cardiff, UK)

Abstract

We revisit the Helmert transformation, and provide a useful and simple derivation of the joint distribution of the sample mean and the sample variance in samples from independently and identically distributed normal random variables. Our derivation is distinguished by concreteness, very little abstractness, and should be appealing to beginning students of statistics, and to both beginning and advanced students of econometrics. We also highlight one fruitful application of the Helmert transformation in panel data econometrics. The Helmert transformation can be used to eliminate the fixed effects in the estimation of fixed effects models, and we briefly review this application of the transformation in the panel data context.

Suggested Citation

  • Kolev Gueorgui I. & Āzacis Helmuts, 2023. "On the Use of the Helmert Transformation, and its Applications in Panel Data Econometrics," Journal of Econometric Methods, De Gruyter, vol. 12(1), pages 131-138, January.
    • Handle: RePEc:bpj:jecome:v:12:y:2023:i:1:p:131-138:n:9
    DOI: 10.1515/jem-2021-0023
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    References listed on IDEAS

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    1. Javier Alvarez & Manuel Arellano, 2003. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Econometrica, Econometric Society, vol. 71(4), pages 1121-1159, July.
    2. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
    3. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    4. Kazuhiko Hayakawa, 2009. "First Difference or Forward Orthogonal Deviation- Which Transformation Should be Used in Dynamic Panel Data Models?: A Simulation Study," Economics Bulletin, AccessEcon, vol. 29(3), pages 2008-2017.
    5. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    6. Hayakawa, Kazuhiko, 2009. "A SIMPLE EFFICIENT INSTRUMENTAL VARIABLE ESTIMATOR FOR PANEL AR(p) MODELS WHEN BOTH N AND T ARE LARGE," Econometric Theory, Cambridge University Press, vol. 25(3), pages 873-890, June.
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    More about this item

    Keywords

    Helmert transformation; sample mean; sample variance; panel data econometrics; fixed effects model;
    All these keywords.

    JEL classification:

    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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