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On the fixed-effects vector decomposition


  • Breusch, Trevor
  • Ward, Michael B
  • Nguyen, Hoa
  • Kompas, Tom


This paper analyses the properties of the fixed-effects vector decomposition estimator, an emerging and popular technique for estimating time-invariant variables in panel data models with unit effects. This estimator was initially motivated on heuristic grounds, and advocated on the strength of favorable Monte Carlo results, but with no formal analysis. We show that the three-stage procedure of this decomposition is equivalent to a standard instrumental variables approach, for a specific set of instruments. The instrumental variables representation facilitates the present formal analysis which finds: (1) The estimator reproduces exactly classical fixed-effects estimates for time-varying variables. (2) The standard errors recommended for this estimator are too small for both time-varying and time-invariant variables. (3) The estimator is inconsistent when the time-invariant variables are endogenous. (4) The reported sampling properties in the original Monte Carlo evidence are incorrect. (5) We recommend an alternative shrinkage estimator that has superior risk properties to the decomposition estimator, unless the endogeneity problem is known to be small or no relevant instruments exist.

Suggested Citation

  • Breusch, Trevor & Ward, Michael B & Nguyen, Hoa & Kompas, Tom, 2010. "On the fixed-effects vector decomposition," MPRA Paper 21452, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:21452

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    References listed on IDEAS

    1. Kazimi, Camilla & Brownstone, David, 1999. "Bootstrap confidence bands for shrinkage estimators," Journal of Econometrics, Elsevier, vol. 90(1), pages 99-127, May.
    2. Hausman, Jerry A & Taylor, William E, 1981. "Panel Data and Unobservable Individual Effects," Econometrica, Econometric Society, vol. 49(6), pages 1377-1398, November.
    3. Ansgar Belke & Julia Spies, 2008. "Enlarging the EMU to the east: what effects on trade?," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 35(4), pages 369-389, September.
    4. Han, Chirok & Schmidt, Peter, 2001. "The asymptotic distribution of the instrumental variable estimators when the instruments are not correlated with the regressors," Economics Letters, Elsevier, vol. 74(1), pages 61-66, December.
    5. Guglielmo Caporale & Christophe Rault & Robert Sova & Anamaria Sova, 2009. "On the bilateral trade effects of free trade agreements between the EU-15 and the CEEC-4 countries," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 145(2), pages 189-206, July.
    6. Signe Krogstrup & Sébastien Wälti, 2008. "Do fiscal rules cause budgetary outcomes?," Public Choice, Springer, vol. 136(1), pages 123-138, July.
    7. Wong, Ka-fu, 1997. "Effects on inference of pretesting the exogeneity of a regressor," Economics Letters, Elsevier, vol. 56(3), pages 267-271, November.
    8. Baltagi, Badi H. & Bresson, Georges & Pirotte, Alain, 2003. "Fixed effects, random effects or Hausman-Taylor?: A pretest estimator," Economics Letters, Elsevier, vol. 79(3), pages 361-369, June.
    9. Mittelhammer, Ron C. & Judge, George G., 2005. "Combining estimators to improve structural model estimation and inference under quadratic loss," Journal of Econometrics, Elsevier, vol. 128(1), pages 1-29, September.
    10. Plümper, Thomas & Troeger, Vera E., 2007. "Efficient Estimation of Time-Invariant and Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects," Political Analysis, Cambridge University Press, vol. 15(02), pages 124-139, March.
    11. Mitze, Timo, 2009. "Endogeneity in Panel Data Models with Time-Varying and Time-Fixed Regressors: To IV or not IV?," Ruhr Economic Papers 83, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    12. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    13. 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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    More about this item


    panel data models; fixed-effects vector decomposition; instrumental variables; inconsistent estimator; incorrect standard errors; improved shrinkage estimator;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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