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Correlated Random Effects Models with Endogenous Explanatory Variables and Unbalanced Panels

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  • Riju Joshi
  • Jeffrey M. Wooldridge

Abstract

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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    File URL: https://www.jstor.org/stable/10.15609/annaeconstat2009.134.0243
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    Keywords

    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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