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Spurious Inference in Unidentified Asset-Pricing Models

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Abstract

This paper studies some seemingly anomalous results that arise in possibly misspecified and unidentified linear asset-pricing models estimated by maximum likelihood and one-step generalized method of moments (GMM). Strikingly, when useless factors (that is, factors that are independent of the returns on the test assets) are present, the models exhibit perfect fit, as measured by the squared correlation between the model's fitted expected returns and the average realized returns, and the tests for correct model specification have 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. We also derive the highly nonstandard limiting behavior of these invariant estimators and their t-tests in the presence of identification failure. These results reveal the spurious nature of inference as useless factors are selected with high probability, while useful factors are driven out from the model. The practical relevance of our findings is demonstrated using simulations and an empirical application.

Suggested Citation

  • Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2014. "Spurious Inference in Unidentified Asset-Pricing Models," FRB Atlanta Working Paper 2014-12, Federal Reserve Bank of Atlanta.
    • Handle: RePEc:fip:fedawp:2014-12
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    Citations

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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. 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.
    3. Stefano Giglio & Dacheng Xiu, 2017. "Inference on Risk Premia in the Presence of Omitted Factors," NBER Working Papers 23527, National Bureau of Economic Research, Inc.
    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. Craig Burnside, 2016. "Identification and Inference in Linear Stochastic Discount Factor Models with Excess Returns," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 295-330.
    6. 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.
    7. 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.
    8. Nikolay Gospodinov & Esfandiar Maasoumi, 2017. "General Aggregation of Misspecified Asset Pricing Models," FRB Atlanta Working Paper 2017-10, Federal Reserve Bank of Atlanta.
    9. Yinchu Zhu, 2019. "How well can we learn large factor models without assuming strong factors?," Papers 1910.10382, arXiv.org, revised Nov 2019.
    10. He, Zhongzhi (Lawrence) & Zhu, Jie & Zhu, Xiaoneng, 2015. "Dynamic factors and asset pricing: International and further U.S. evidence," Pacific-Basin Finance Journal, Elsevier, vol. 32(C), pages 21-39.
    11. Shang, Hua & Yuan, Ping & Huang, Lin, 2016. "Macroeconomic factors and the cross-section of commodity futures returns," International Review of Economics & Finance, Elsevier, vol. 45(C), pages 316-332.

    More about this item

    Keywords

    asset pricing; irrelevant risk factors; unidentified models; model misspecification; continuously updated GMM; maximum likelihood; rank test; test for overidentifying restrictions;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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