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Asymptotic variance approximations for invariant estimators in uncertain asset-pricing models

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  • Nikolay Gospodinov
  • Raymond Kan
  • Cesare Robotti

Abstract

This article derives explicit expressions for the asymptotic variances of the maximum likelihood and continuously-updated GMM estimators in models that may not satisfy the fundamental asset-pricing restrictions in population. The proposed misspecification-robust variance estimators allow the researcher to conduct valid inference on the model parameters even when the model is rejected by the data. While the results for the maximum likelihood estimator are only applicable to linear asset-pricing models, the asymptotic distribution of the continuously-updated GMM estimator is derived for general, possibly nonlinear, models. The large corrections in the asymptotic variances, that arise from explicitly incorporating model misspecification in the analysis, are illustrated using simulations and an empirical application.

Suggested Citation

  • Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2018. "Asymptotic variance approximations for invariant estimators in uncertain asset-pricing models," Econometric Reviews, Taylor & Francis Journals, vol. 37(7), pages 695-718, August.
    • Handle: RePEc:taf:emetrv:v:37:y:2018:i:7:p:695-718
    DOI: 10.1080/07474938.2016.1165945
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    1. Canova, Fabio, 1994. "Statistical Inference in Calibrated Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(S), pages 123-144, Suppl. De.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Watson, Mark W, 1993. "Measures of Fit for Calibrated Models," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1011-1041, December.
    4. Hansen, Lars Peter & Jagannathan, Ravi, 1997. "Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
    5. Gospodinov, Nikolay & Kan, Raymond & Robotti, Cesare, 2013. "Chi-squared tests for evaluation and comparison of asset pricing models," Journal of Econometrics, Elsevier, vol. 173(1), pages 108-125.
    6. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    7. Francisco Peñaranda & Enrique Sentana, 2015. "A Unifying Approach to the Empirical Evaluation of Asset Pricing Models," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 412-435, May.
    8. Shanken, Jay & Zhou, Guofu, 2007. "Estimating and testing beta pricing models: Alternative methods and their performance in simulations," Journal of Financial Economics, Elsevier, vol. 84(1), pages 40-86, April.
    9. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    10. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, September.
    11. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
    12. Raymond Kan & Cesare Robotti & Jay Shanken, 2013. "Pricing Model Performance and the Two‐Pass Cross‐Sectional Regression Methodology," Journal of Finance, American Finance Association, vol. 68(6), pages 2617-2649, December.
    13. Maasoumi, Esfandiar & Phillips, Peter C. B., 1982. "On the behavior of inconsistent instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 183-201, August.
    14. Maasoumi, Esfandiar, 1990. "How to live with misspecification if you must," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 67-86.
    15. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2012. "Robust inference in linear asset pricing models," FRB Atlanta Working Paper 2012-17, Federal Reserve Bank of Atlanta.
    16. Lewellen, Jonathan & Nagel, Stefan & Shanken, Jay, 2010. "A skeptical appraisal of asset pricing tests," Journal of Financial Economics, Elsevier, vol. 96(2), pages 175-194, May.
    17. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2014. "Misspecification-Robust Inference in Linear Asset-Pricing Models with Irrelevant Risk Factors," The Review of Financial Studies, Society for Financial Studies, vol. 27(7), pages 2139-2170.
    18. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1192-1235, December.
    19. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    20. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
    21. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    22. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    23. Raymond Kan & Cesare Robotti, 2009. "Model Comparison Using the Hansen-Jagannathan Distance," The Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3449-3490, September.
    24. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    25. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
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    Cited by:

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    More about this item

    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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