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A Note on R2 in the Instrumental Variables Model

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  • Windmeijer, Frank

Abstract

The properties of two goodness-of-fit measures are analyzed for the instrumental variables model. One measure is based on the two-step approach to IV estimation and is equal to the coefficient of determination in the second stage equation. This measure therefore measures the fit of a transformation of the original model. The other measure is the one proposed by Barten (1987) for the linear model without a constant term. In comparison with the other R2-measure, Barten's measure has as an advantage that it measures the fit of the original model. As a disadvantage, the measure does not have a relation with the chi-squared statistic, testing whether all slope coefficients are equal to zero.

Suggested Citation

  • Windmeijer, Frank, 1995. "A Note on R2 in the Instrumental Variables Model," MPRA Paper 102511, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:102511
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    File URL: https://mpra.ub.uni-muenchen.de/102511/1/MPRA_paper_102511.pdf
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    References listed on IDEAS

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    1. Knight, John L., 1980. "The coefficient of determination and simultaneous equation systems," Journal of Econometrics, Elsevier, vol. 14(2), pages 265-270, October.
    2. McElroy, Marjorie B., 1977. "Goodness of fit for seemingly unrelated regressions : Glahn's R2y.x and Hooper's r2," Journal of Econometrics, Elsevier, vol. 6(3), pages 381-387, November.
    3. BARTEN, Anton P., 1987. "The coefficient of determination for regression without a constant term," LIDAM Reprints CORE 766, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Carter, Richard A. L. & Nagar, Anirudh L., 1977. "Coefficients of correlation for simultaneous equation systems," Journal of Econometrics, Elsevier, vol. 6(1), pages 39-50, July.
    5. H. Neudecker & F.A.G. Windmeijer, 1991. "R2 in Seemingly Unrelated Regression Equations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 45(4), pages 405-411, December.
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    Keywords

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    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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