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Time Invariant Variables and Panel Data Models : A Generalised Frisch-Vaugh Theorem and its Implications

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  • Jaya Krishnakumar

Abstract

Mundlak (1978) showed that when individual effects are correlated with the explanatory variables in an error component (EC) model, the GLS estimator is given by the within. In this paper we bring out some additional interesting properties of the within estimator in Mundlak’s model and go on to show that the within estimator remains valid in an extended EC model with time invariant variables and correlated specific effects. Adding an auxiliary regression to take account of possible correlation between the explanatory variables and the individual effects, we find that not only the elegant results obtained by Mundlak but also the above mentioned special features carry over to the extended case with interesting interpretations. We obtain these results using a generalised version of the Frisch-Waugh theorem, stated and proved in the paper. Finally, for both the EC models with and without time invariant variables we have shown that the estimates of the coefficients of the auxiliary variables can also be arrived at by following a two-step procedure.

Suggested Citation

  • Jaya Krishnakumar, 2003. "Time Invariant Variables and Panel Data Models : A Generalised Frisch-Vaugh Theorem and its Implications," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2004.01, Institut d'Economie et Econométrie, Université de Genève.
  • Handle: RePEc:gen:geneem:2004.01
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    References listed on IDEAS

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    1. Cornwell, Christopher & Schmidt, Peter & Wyhowski, Donald, 1992. "Simultaneous equations and panel data," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 151-181.
    2. Baltagi, Badi H., 1981. "Simultaneous equations with error components," Journal of Econometrics, Elsevier, vol. 17(2), pages 189-200, November.
    3. Baltagi, Badi H. & Krämer, Walter, 1995. "A Mixed-Error Component Model," Econometric Theory, Cambridge University Press, vol. 11(01), pages 192-193, February.
    4. Hausman, Jerry A & Taylor, William E, 1983. "Identification in Linear Simultaneous Equations Models with Covariance Restrictions: An Instrumental Variables Interpretation," Econometrica, Econometric Society, vol. 51(5), pages 1527-1549, September.
    5. Breusch, Trevor S & Mizon, Grayham E & Schmidt, Peter, 1989. "Efficient Estimation Using Panel Data," Econometrica, Econometric Society, vol. 57(3), pages 695-700, May.
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    Cited by:

    1. Jonathan Kaminski & Alban Thomas, 2011. "Land Use, Production Growth, and the Institutional Environment of Smallholders: Evidence from Burkinabè Cotton Farmers," Land Economics, University of Wisconsin Press, vol. 87(1), pages 160-182.
    2. Jean-Bernard Chatelain & Kirsten Ralf, 2010. "Inference on Time-Invariant Variables using Panel Data: A Pre-Test Estimator with an Application to the Returns to Schooling," Working Papers hal-00492039, HAL.
    3. Jean-Bernard Chatelain & Kirsten Ralf, 2010. "Inference on Time-Invariant Variables using Panel Data: A Pre-Test Estimator with an Application to the Returns to Schooling," PSE Working Papers hal-00492039, HAL.
    4. Bache, Stefan Holst Milton & Kristensen, Troels, 2013. "A simple but efficient approach to the analysis of multilevel data," COHERE Working Paper 2013:6, University of Southern Denmark, COHERE - Centre of Health Economics Research.

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    Keywords

    panel data; error components; correlated effects; within estimator.;

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