We show that in misspecified models with useless factors (for example, factors that are independent of the returns on the test assets), the standard inference procedures tend to erroneously conclude, with high probability, that these irrelevant factors are priced and the restrictions of the model hold. Our proposed model selection procedure, which is robust to useless factors and potential model misspecification, restores the standard inference and proves to be effective in eliminating factors that do not improve the model's pricing ability. The practical relevance of our analysis is illustrated using simulations and empirical applications.
JEL classification: G12, C12, C52
Key words: asset pricing models, lack of identification, model misspecification, GMM estimation
The authors thank the editor (Andrew Karolyi), two anonymous referees, Anton Braun, Chu Zhang, Guofu Zhou, and seminar participants at the Federal Reserve Bank of Atlanta, Imperial College London, Queen's University, Singapore Management University, and the University of Georgia. They also thank participants at the third Annual CIRPÉE Applied Financial Time Series Workshop at HEC (Montreal), Mathematical Finance Days 2012, and the 2013 SoFiE Conference for helpful discussions and comments. Gospodinov gratefully acknowledges financial support from Fonds Québécois de recherche sur la société et la culture, Institut de Finance Mathématique de Montréal, and the Social Sciences and Humanities Research Council of Canada. Kan gratefully acknowledges financial support from the Social Sciences and Humanities Research Council of Canada and the National Bank Financial of Canada. 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, Federal Reserve Bank of Atlanta, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street NE, Atlanta, GA 30309-4470, firstname.lastname@example.org; Raymond Kan, University of Toronto, or Cesare Robotti (contact author), Imperial College Business School, Tanaka Building, South Kensington Campus, London SW7 2AZ, United Kingdom, 44 (0)20 7589 5111, email@example.com.
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