We derive new results on the asymptotic behavior of the estimated parameters of a linear asset pricing model and their associated t-statistics in the presence of a factor that is independent of the returns. The inclusion of this "useless" factor in the model leads to a violation of the full rank (identification) condition and renders the inference nonstandard. We show that the estimated parameter associated with the useless factor diverges with the sample size but the misspecification-robust t-statistic is still well-behaved and has a standard normal limiting distribution. The asymptotic distributions of the estimates of the remaining parameters and the model specification test are also affected by the presence of a useless factor and are nonstandard. We propose a robust and easy-to-implement model selection procedure that restores the standard inference on the parameters of interest by identifying and removing the factors that do not contribute to improved pricing. The finite-sample properties of our asymptotic approximations and the practical relevance of our results are illustrated using simulations and an empirical application.
JEL classification: G12, C13, C32
Key words: asset pricing models, Hansen-Jagannathan distance, model selection, model misspecification
Gospodinov gratefully acknowledges financial support from Fonds de recherche sur la société et la culture (FQRSC), Institut de Finance Mathematique de Montreal (IFM2), 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. They also thank seminar participants at the Federal Reserve Bank of Atlanta, Singapore Management University, the University of Georgia, and participants at the third annual CIRPEE Applied Financial Time Series Workshop at HEC (Montreal) and Mathematical Finance Days 2012 for helpful comments. 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, Department of Economics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec H3G 1M8, Canada, and CIREQ, 514-848-2424, 514-848-4536 (fax), firstname.lastname@example.org; Raymond Kan, Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario M5S 3E6, Canada, email@example.com; or Cesare Robotti, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street N.E., Atlanta, GA 30309, and EDHEC Risk Institute, firstname.lastname@example.org.
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