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Identification-Robust Estimation and Testing of the Zero-Beta CAPM

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  • Marie-Claude Beaulieu
  • Jean-Marie Dufour
  • Lynda Khalaf

Abstract

We propose exact simulation-based procedures for: (i) testing mean-variance efficiency when the zero-beta rate is unknown; (ii) building confidence intervals for the zero-beta rate. On observing that this parameter may be weakly identified, we propose likelihood-ratio-type tests as well as Fieller-type procedures based on a Hotelling-HAC statistic, which are robust to weak identification and allow for non-Gaussian distributions including parametric GARCH structures. The Fieller-Hotelling-HAC procedure also accounts (asymptotically) for general forms of heteroskedasticity and autocorrelation. We propose confidence sets for the zero-beta rate based on "inverting" exact tests for this parameter; for both procedures proposed, these sets can be interpreted as multivariate extensions of the classic Fieller method for inference on ratios. The exact distribution of likelihood-ratio-type statistics for testing efficiency is studied under both the null and the alternative hypotheses. The relevant nuisance parameter structure is established and finite-sample bound procedures are proposed, which extend and improve available Gaussian-specific bounds. Finite-sample distributional invariance results are also demonstrated analytically for the HAC statistic proposed by MacKinlay and Richardson (1991) . We study invariance to portfolio repacking for the tests and confidence sets proposed. The statistical properties of the proposed methods are analysed through a Monte Carlo study and compared with alternative available methods. Empirical results on NYSE returns show that exact confidence sets are very different from asymptotic ones, and allowing for non-Gaussian distributions affects inference results. Simulation and empirical evidence suggests that likelihood-ratio-type statistics--with p-values corrected using the Maximized Monte Carlo test method--are generally preferable to their multivariate Fieller-Hotelling-HAC counterparts from the viewpoints of size control and power. Copyright 2013, Oxford University Press.

Suggested Citation

  • Marie-Claude Beaulieu & Jean-Marie Dufour & Lynda Khalaf, 2013. "Identification-Robust Estimation and Testing of the Zero-Beta CAPM," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(3), pages 892-924.
    • Handle: RePEc:oup:restud:v:80:y:2013:i:3:p:892-924
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    File URL: http://hdl.handle.net/10.1093/restud/rds044
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    Cited by:

    1. Jean-Thomas Bernard & Michael Gavin & Lynda Khalaf & Marcel Voia, 2015. "Environmental Kuznets Curve: Tipping Points, Uncertainty and Weak Identification," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 60(2), pages 285-315, February.
    2. Lütkepohl, Helmut & Milunovich, George & Yang, Minxian, 2020. "Inference in partially identified heteroskedastic simultaneous equations models," Journal of Econometrics, Elsevier, vol. 218(2), pages 317-345.
    3. Geoffrey Poitras & John Heaney, 2015. "Classical Ergodicity and Modern Portfolio Theory," Post-Print hal-03680380, HAL.
    4. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2020. "Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: Invariance and finite-sample distributional theory," Journal of Econometrics, Elsevier, vol. 218(2), pages 390-418.
    5. Lynda Khalaf & Beatriz Peraza López, 2020. "Simultaneous Indirect Inference, Impulse Responses and ARMA Models," Econometrics, MDPI, vol. 8(2), pages 1-26, April.
    6. Bodnar, Taras & Reiß, Markus, 2016. "Exact and asymptotic tests on a factor model in low and large dimensions with applications," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 125-151.
    7. Sriananthakumar, Sivagowry, 2015. "Approximate Non-Similar critical values based tests vs Maximized Monte Carlo tests," Economic Modelling, Elsevier, vol. 49(C), pages 387-394.
    8. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2014. "Exact confidence sets and goodness-of-fit methods for stable distributions," Journal of Econometrics, Elsevier, vol. 181(1), pages 3-14.
    9. Frank Kleibergen & Lingwei Kong, 2023. "Identification Robust Inference for the Risk Premium in Term Structure Models," Papers 2307.12628, arXiv.org.
    10. Jean-Marie Dufour & Emmanuel Flachaire & Lynda Khalaf & Abdallah Zalghout, 2020. "Identification-Robust Inequality Analysis," Cahiers de recherche 03-2020, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    11. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda & Melin, Olena, 2023. "Identification-robust beta pricing, spanning, mimicking portfolios, and the benchmark neutrality of catastrophe bonds," Journal of Econometrics, Elsevier, vol. 236(1).
    12. Bergamelli, Michele & Bianchi, Annamaria & Khalaf, Lynda & Urga, Giovanni, 2019. "Combining p-values to test for multiple structural breaks in cointegrated regressions," Journal of Econometrics, Elsevier, vol. 211(2), pages 461-482.
    13. Khalaf, Lynda & Saunders, Charles J., 2017. "Monte Carlo forecast evaluation with persistent data," International Journal of Forecasting, Elsevier, vol. 33(1), pages 1-10.
    14. Khalaf, Lynda & Saunders, Charles J., 2020. "Monte Carlo two-stage indirect inference (2SIF) for autoregressive panels," Journal of Econometrics, Elsevier, vol. 218(2), pages 419-434.
    15. Sriananthakumar, Sivagowry, 2013. "Testing linear regression model with AR(1) errors against a first-order dynamic linear regression model with white noise errors: A point optimal testing approach," Economic Modelling, Elsevier, vol. 33(C), pages 126-136.
    16. De Moor, Lieven & Dhaene, Geert & Sercu, Piet, 2015. "On comparing zero-alpha tests across multifactor asset pricing models," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 235-240.
    17. 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.
    18. 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.
    19. Tuvaandorj, Purevdorj, 2020. "Regression discontinuity designs, white noise models, and minimax," Journal of Econometrics, Elsevier, vol. 218(2), pages 587-608.
    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.

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