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

  • Jaya Krishnakumar

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.

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Paper provided by Institut d'Economie et Econométrie, Université de Genève in its series Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva with number 2004.01.

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Length: 17 pages
Date of creation: Dec 2003
Date of revision:
Handle: RePEc:gen:geneem:2004.01
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  1. 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 1527-49, September.
  2. Breusch, Trevor S & Mizon, Grayham E & Schmidt, Peter, 1989. "Efficient Estimation Using Panel Data," Econometrica, Econometric Society, vol. 57(3), pages 695-700, May.
  3. Baltagi, Badi H., 1981. "Simultaneous equations with error components," Journal of Econometrics, Elsevier, vol. 17(2), pages 189-200, November.
  4. Baltagi, Badi H. & Krämer, Walter, 1995. "A Mixed-Error Component Model," Econometric Theory, Cambridge University Press, vol. 11(01), pages 192-193, February.
  5. Cornwell, Christopher & Schmidt, Peter & Wyhowski, Donald, 1992. "Simultaneous equations and panel data," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 151-181.
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