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A note on the application of EC2SLS and EC3SLS estimators in panel data models

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  • Baltagi, Badi H.
  • Liu, Long

Abstract

Baltagi and Li [Baltagi, B.H., Li, Q., 1992. A note on the estimation of simultaneous equations with error components. Econometric Theory 8, 113-119] showed that for estimating a single equation in a simultaneous panel data model, EC2SLS has more instruments than G2SLS. Although these extra instruments are redundant in White's [White, H., 1986. Instrumental variables analogs of generalized least squares estimators. In: Mariano, R.S. (Ed.), Advances in Statistical Analysis and Statistical Computing, vol. 1. JAI Press, New York, pp. 173-277] terminology, they may yield different estimates and standard errors in empirical studies with finite N and T. We illustrate this using the crime data of Cornwell and Trumbull [Cornwell, C., Trumbull, W.N., 1994. Estimating the economic model of crime with panel data. Review of Economics and Statistics 76, 360-366]. We show that the standard errors of EC2SLS are smaller than those of G2SLS for this example. In general, we prove that the asymptotic variance of G2SLS differs from that of EC2SLS by a positive semi-definite matrix. Although this difference tends to zero as the sample size tends to infinity, in small samples, this difference may be different from zero and can lead to gains in small sample efficiency. This proof is extended to the system equations' 3SLS counterparts.

Suggested Citation

  • Baltagi, Badi H. & Liu, Long, 2009. "A note on the application of EC2SLS and EC3SLS estimators in panel data models," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2189-2192, October.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:20:p:2189-2192
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    1. Badi H. Baltagi, 2021. "Simultaneous Equations with Error Components," Springer Texts in Business and Economics, in: Econometric Analysis of Panel Data, edition 6, chapter 0, pages 157-186, Springer.
    2. Cornwell, Christopher & Trumbull, William N, 1994. "Estimating the Economic Model of Crime with Panel Data," The Review of Economics and Statistics, MIT Press, vol. 76(2), pages 360-366, May.
    3. Badi H. Baltagi, 2006. "Estimating an economic model of crime using panel data from North Carolina," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 543-547, May.
    4. Baltagi, Badi H. & Li, Qi, 1992. "A Note on the Estimation of Simultaneous Equations with Error Components," Econometric Theory, Cambridge University Press, vol. 8(1), pages 113-119, March.
    5. Balestra, Pietro & Varadharajan-Krishnakumar, Jayalakshmi, 1987. "Full Information Estimations of a System of Simultaneous Equations with Error Component Structure," Econometric Theory, Cambridge University Press, vol. 3(2), pages 223-246, April.
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    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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