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Efficient Estimation: The Rao-Zyskind Condition, Kruskal's Theorem and Ordinary Least Squares

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  • McAleer, Michael

Abstract

This paper emphasizes the practicability and accessibility of the necessary and sufficient condition for ordinary least squares to yield best linear unbiased estimators in several problems that are available in econometrics. Two convenient equivalent alternative forms of the condition are presented. It is shown that the condition is useful for analyzing different problems and is especially relevant for pedagogical purposes. Several practical economic examples are presented. Copyright 1992 by The Economic Society of Australia.

Suggested Citation

  • McAleer, Michael, 1992. "Efficient Estimation: The Rao-Zyskind Condition, Kruskal's Theorem and Ordinary Least Squares," The Economic Record, The Economic Society of Australia, vol. 68(200), pages 65-72, March.
    • Handle: RePEc:bla:ecorec:v:68:y:1992:i:200:p:65-72
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    Cited by:

    1. Chang, C-L. & McAleer, M.J. & Franses, Ph.H.B.F., 2010. "Combining Non-Replicable Forecasts," Econometric Institute Research Papers EI 2010-44, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Chia-Lin Chang & Michael McAleer & Chien-Hsun Wang, 2017. "An Econometric Analysis of ETF and ETF Futures in Financial and Energy Markets Using Generated Regressors," IJFS, MDPI, vol. 6(1), pages 1-24, December.
    3. Chang, Chia-Lin & Franses, Philip Hans & McAleer, Michael, 2013. "Are forecast updates progressive?," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 9-18.
    4. Franses, Ph.H.B.F. & McAleer, M.J. & Legerstee, R., 2010. "Evaluating Macroeconomic Forecast: A Review of Some Recent Developments," Econometric Institute Research Papers EI 2010-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Alan J. Rogers, 2013. "Concentration Ellipsoids, Their Planes of Support, and the Linear Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 32(2), pages 220-243, February.
    6. Chang, Chia-Lin & Franses, Philip Hans & McAleer, Michael, 2011. "How accurate are government forecasts of economic fundamentals? The case of Taiwan," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1066-1075, October.
    7. Philip Hans Franses & Michael McAleer & Rianne Legerstee, 2014. "Evaluating Macroeconomic Forecasts: A Concise Review Of Some Recent Developments," Journal of Economic Surveys, Wiley Blackwell, vol. 28(2), pages 195-208, April.
    8. Franses, Ph.H.B.F. & McAleer, M.J. & Legerstee, R., 2008. "Does the ROMC have expertise, and can it forecast?," Econometric Institute Research Papers EI 2008-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Alessandra Luati & Tommaso Proietti, 2011. "On the equivalence of the weighted least squares and the generalised least squares estimators, with applications to kernel smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 851-871, August.
    10. Philip Hans Franses & Michael McAleer & Rianne Legerstee, 2009. "Expert opinion versus expertise in forecasting," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(3), pages 334-346, August.
    11. Lu, Cuicui & Schmidt, Peter, 2012. "Conditions for the numerical equality of the OLS, GLS and Amemiya–Cragg estimators," Economics Letters, Elsevier, vol. 116(3), pages 538-540.
    12. Chia-Lin Chang & Michael McAleer, 2019. "Modeling Latent Carbon Emission Prices for Japan: Theory and Practice," Energies, MDPI, vol. 12(21), pages 1-21, November.
    13. Fisher, Gordon, 2004. "Une condition d’invariance du modèle de régression à coefficients aléatoires," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 405-419, Juin-Sept.
    14. Chang, C-L. & Franses, Ph.H.B.F. & McAleer, M.J., 2009. "How Accurate are Government Forecast of Economic Fundamentals?," Econometric Institute Research Papers EI 2009-09, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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