Asymptotic Variance Approximations for Invariant Estimators in Uncertain Asset-Pricing Models

Nikolay Gospodinov, Raymond Kan, and Cesare Robotti

Working Paper 2015-9
October 2015

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This paper derives explicit expressions for the asymptotic variances of the maximum likelihood and continuously updated GMM estimators under potentially misspecified models. 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. Although 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, which arise from explicitly incorporating model misspecification in the analysis, are illustrated using simulations and an empirical application.

JEL classification: C12; C13; G12

Key words: asset pricing, model misspecification, continuously updated GMM, maximum likelihood, asymptotic approximation, misspecification-robust tests


The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.
Please address questions regarding content to Nikolay Gospodinov (corresponding author), Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street N.E., Atlanta, GA 30309, nikolay.gospodinov@atl.frb.org; Raymond Kan, Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6, kan@chass.utoronto.ca; or Cesare Robotti, Imperial College Business School, South Kensington Campus, London, SW7 2AZ, United Kingdom, c.robotti@imperial.ac.uk.
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