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Unexplained factors and their effects on second pass R-squared’s

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  • Frank Kleibergen
  • Zhaoguo Zhan

    (Tsinghua University)

Abstract

We construct the large sample distributions of the OLS and GLS R^2’s of the second pass regression of the Fama-MacBeth (1973) two pass procedure when the observed proxy factors are minorly correlated with the true unobserved factors. This implies an unexplained factor structure in the first pass residuals and, consequently, a large estimation error in the estimated beta’s which is spanned by the beta’s of the unexplained true factors. The average portfolio returns and the estimation error of the estimated beta’s are then both linear in the beta’s of the unobserved true factors which leads to possibly large values of the OLS R2 of the second pass regression. These large values of the OLS R2 are not indicative of the strength of the relationship. Our results question many empirical findings that concern the relationship between expected portfolio returns and (macro-)economic factors.

Suggested Citation

  • Frank Kleibergen & Zhaoguo Zhan, 2014. "Unexplained factors and their effects on second pass R-squared’s," UvA-Econometrics Working Papers 14-05, Universiteit van Amsterdam, Dept. of Econometrics.
  • Handle: RePEc:ame:wpaper:1405
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    Cited by:

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    2. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2015. "Regression-based estimation of dynamic asset pricing models," Journal of Financial Economics, Elsevier, vol. 118(2), pages 211-244.
    3. Matias D. Cattaneo & Richard K. Crump & Max H. Farrell & Ernst Schaumburg, 2020. "Characteristic-Sorted Portfolios: Estimation and Inference," The Review of Economics and Statistics, MIT Press, vol. 102(3), pages 531-551, July.
    4. Marie-Claude Beaulieu & Jean-Marie Dufour & Lynda Khalaf, 2020. "Arbitrage Pricing, Weak Beta, Strong Beta: Identification-Robust and Simultaneous Inference," CIRANO Working Papers 2020s-30, CIRANO.
    5. Atsushi Inoue & Barbara Rossi, 2015. "Tests for the validity of portfolio or group choice in financial and panel regressions," Economics Working Papers 1523, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Sainan Jin & Liangjun Su & Yonghui Zhang, 2015. "Nonparametric testing for anomaly effects in empirical asset pricing models," Empirical Economics, Springer, vol. 48(1), pages 9-36, February.
    7. Antoine A. Djogbenou, 2021. "Model selection in factor-augmented regressions with estimated factors," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 470-503, April.
    8. Adrian, Tobias & Friedman, Evan & Muir, Tyler, 2015. "The Cost of Capital of the Financial Sector," CEPR Discussion Papers 11031, C.E.P.R. Discussion Papers.
    9. Joachim Freyberger & Andreas Neuhierl & Michael Weber, 2020. "Dissecting Characteristics Nonparametrically," Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2326-2377.
    10. Díaz Antonia & Puch Luis A., 2019. "Investment, technological progress and energy efficiency," The B.E. Journal of Macroeconomics, De Gruyter, vol. 19(2), pages 1-28, June.
    11. Anatolyev, Stanislav & Mikusheva, Anna, 2021. "Limit Theorems For Factor Models," Econometric Theory, Cambridge University Press, vol. 37(5), pages 1034-1074, October.
    12. Marie-Claude Beaulieu & Jean-Marie Dufour & Lynda Khalaf, 2020. "Arbitrage Pricing, Weak Beta, Strong Beta: Identification-Robust and Simultaneous Inference," Cahiers de recherche 15-2020, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    13. Khalaf, Lynda & Schaller, Huntley, 2016. "Identification and inference in two-pass asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 165-177.
    14. Laurinaityte, Nora & Meinerding, Christoph & Schlag, Christian & Thimme, Julian, 2020. "GMM weighting matrices incross-sectional asset pricing tests," Discussion Papers 62/2020, Deutsche Bundesbank.
    15. Baltzer, Markus & Koehl, Alexandra & Reitz, Stefan, 2020. "Procyclical leverage in Europe and its role in asset pricing," Journal of International Money and Finance, Elsevier, vol. 107(C).
    16. Gospodinov, Nikolay & Robotti, Cesare, 2021. "Common pricing across asset classes: Empirical evidence revisited," Journal of Financial Economics, Elsevier, vol. 140(1), pages 292-324.
    17. Gospodinov, Nikolay & Kan, Raymond & Robotti, Cesare, 2019. "Too good to be true? Fallacies in evaluating risk factor models," Journal of Financial Economics, Elsevier, vol. 132(2), pages 451-471.
    18. M. Hashem Pesaran & Ron P. Smith, 2021. "Factor Strengths, Pricing Errors, and Estimation of Risk Premia," CESifo Working Paper Series 8947, CESifo.
    19. Beaulieu, Marie-Claude & Gagnon, Marie-Hélène & Khalaf, Lynda, 2016. "Less is more: Testing financial integration using identification-robust asset pricing models," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 45(C), pages 171-190.
    20. Seung C. Ahn & Alex R. Horenstein, 2017. "Asset Pricing and Excess Returns over the Market Return," Working Papers 2017-12, University of Miami, Department of Economics.
    21. Lin, Qi, 2021. "The q5 model and its consistency with the intertemporal CAPM," Journal of Banking & Finance, Elsevier, vol. 127(C).
    22. Gregory Connor & Robert A. Korajczyk, 2019. "Semi-strong factors in asset returns," Economics Department Working Paper Series n294-19.pdf, Department of Economics, National University of Ireland - Maynooth.

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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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