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Spurious Inference in Reduced‐Rank Asset‐Pricing Models

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  • Nikolay Gospodinov
  • Raymond Kan
  • Cesare Robotti

Abstract

This note studies some seemingly anomalous results that arise in possibly misspecified, reduced‐rank linear asset‐pricing models estimated by the continuously updated generalized method of moments. When a spurious factor (that is, a factor that is uncorrelated with the returns on the test assets) is present, the test for correct model specification has asymptotic power that is equal to the nominal size. In other words, applied researchers will erroneously conclude that the model is correctly specified even when the degree of misspecification is arbitrarily large. The rejection probability of the test for overidentifying restrictions typically decreases further in underidentified models where the dimension of the null space is larger than 1.

Suggested Citation

  • Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2017. "Spurious Inference in Reduced‐Rank Asset‐Pricing Models," Econometrica, Econometric Society, vol. 85, pages 1613-1628, September.
    • Handle: RePEc:wly:emetrp:v:85:y:2017:i::p:1613-1628
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    Cited by:

    1. 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.
    2. Zhang, Xiang & Liu, Yangyi & Wu, Kun & Maillet, Bertrand, 2021. "Tradable or nontradable factors—what does the Hansen–Jagannathan distance tell us?," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 853-879.
    3. Frank Windmeijer, 2018. "Testing Over- and Underidentification in Linear Models, with Applications to Dynamic Panel Data and Asset-Pricing Models," Bristol Economics Discussion Papers 18/696, School of Economics, University of Bristol, UK.
    4. Anatolyev, Stanislav & Mikusheva, Anna, 2022. "Factor models with many assets: Strong factors, weak factors, and the two-pass procedure," Journal of Econometrics, Elsevier, vol. 229(1), pages 103-126.
    5. Manresa, Elena & Peñaranda, Francisco & Sentana, Enrique, 2023. "Empirical evaluation of overspecified asset pricing models," Journal of Financial Economics, Elsevier, vol. 147(2), pages 338-351.
    6. 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.
    7. Lingwei Kong, 2023. "Weak (Proxy) Factors Robust Hansen-Jagannathan Distance For Linear Asset Pricing Models," Papers 2307.14499, arXiv.org.
    8. Borup, Daniel, 2019. "Asset pricing model uncertainty," Journal of Empirical Finance, Elsevier, vol. 54(C), pages 166-189.
    9. Gospodinov, Nikolay & Robotti, Cesare, 2021. "Common pricing across asset classes: Empirical evidence revisited," Journal of Financial Economics, Elsevier, vol. 140(1), pages 292-324.
    10. Yinchu Zhu, 2019. "How well can we learn large factor models without assuming strong factors?," Papers 1910.10382, arXiv.org, revised Nov 2019.
    11. Lioui, Abraham & Tarelli, Andrea, 2020. "Factor Investing for the Long Run," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).
    12. Sun, Yang & Zhang, Xuan & Zhang, Zhekai, 2022. "The reduced-rank beta in linear stochastic discount factor models," International Review of Financial Analysis, Elsevier, vol. 84(C).
    13. Bretscher, Lorenzo & Hsu, Alex & Tamoni, Andrea, 2020. "Fiscal policy driven bond risk premia," Journal of Financial Economics, Elsevier, vol. 138(1), pages 53-73.
    14. Gospodinov, Nikolay & Maasoumi, Esfandiar, 2021. "Generalized aggregation of misspecified models: With an application to asset pricing," Journal of Econometrics, Elsevier, vol. 222(1), pages 451-467.

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