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Correlated Random Effects Models with Endogenous Explanatory Variables and Unbalanced Panels


  • Riju Joshi
  • Jeffrey M. Wooldridge


This paper shows how the correlated random effects approach can be extended to linear panel data models when instrumental variables are needed and the panel is unbalanced. We obtain the algebraic equivalence between the fixed effects two stage least squares (FE2SLS) estimator and a pooled 2SLS (P2SLS) estimator on a transformed equation. This equivalence allows us to obtain fully robust Hausman tests comparing random effects 2SLS (RE2SLS) and FE2SLS. In addition, we obtain an equivalence result for control function estimates and FE2SLS estimates in an unbalanced panel. We use this result to obtain a robust variable addition Hausman test that effectively compares the FE and FE2SLS estimates. We illustrate the tests using an unbalanced panel on student performance and spending at the school level.

Suggested Citation

  • Riju Joshi & Jeffrey M. Wooldridge, 2019. "Correlated Random Effects Models with Endogenous Explanatory Variables and Unbalanced Panels," Annals of Economics and Statistics, GENES, issue 134, pages 243-268.
  • Handle: RePEc:adr:anecst:y:2019:i:134:p:243-268
    DOI: 10.15609/annaeconstat2009.134.0243

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    Cited by:

    1. Hans Lööf & Ingrid Viklund‐Ros, 2020. "Board of directors and export spillovers: What is the impact on extensive margins of trade?," The World Economy, Wiley Blackwell, vol. 43(5), pages 1188-1215, May.
    2. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 0. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 0, pages 1-33.
    3. Trong‐Anh Trinh & Alberto Posso & Simon Feeny, 2020. "Child Labor and Rainfall Deviation: Panel Data Evidence from Rural Vietnam," The Developing Economies, Institute of Developing Economies, vol. 58(1), pages 63-76, March.
    4. Bělín, Matěj, 2020. "Time-invariant regressors under fixed effects: Simple identification via a proxy variable," Economics Letters, Elsevier, vol. 186(C).
    5. Kölling, Arnd & Schnabel, Claus, 2019. "Owners, external managers, and industrial relations in German establishments," Discussion Papers 110, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Labour and Regional Economics.
    6. F Baum, Christopher & Lööf, Hans & Stephan, Andreas & Viklund-Ros, Ingrid, 2019. "The impact of board directors on the innovation of new ventures," Working Paper Series in Economics and Institutions of Innovation 483, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    7. Man Jin & Shunan Zhao & Subal C. Kumbhakar, 2020. "Information asymmetry and leverage adjustments: a semiparametric varying‐coefficient approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 581-605, February.

    More about this item


    Unbalanced Panel Data; Variable Addition Hausman Test; Fixed Effects; Correlated Random Effects; Control Function; Specification Tests;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation


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