Eigenvalue Ratio Test for the Number of Factors


  • Seung C. Ahn,

    1. Dept. of Economics, Arizona State University, Tempe, AZ 85287, U.S.A. and Dept. of Economics, Sogang University, 35 Beakbeom-ro, Mapo-gu, Seoul 121-742, South Korea; miniahn@asu.edu
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  • Alex R. Horenstein

    1. Dept. of Economics, University of Miami, Coral Gables, FL 33124, U.S.A. and Dept. of Business, Instituto Tecnológico Autónomo de México, México, 01080; horenstein@bus.miami.edu
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    • We thank the editor and three anonymous referees for their numerous comments and suggestions that helped us improve the quality of the paper substantially. We also thank Jushan Bai, Alexei Onatski, Marcos Perez, Crocker Liu, Federico Nardari, Manuel Santos, Stephan Dieckmann, Na Wang, and Matteo Barigozzi for their helpful comments and/or sharing codes and data with us. The paper was presented in the econometrics seminars at Tokyo University, Kyoto University, Hitotsubashi University, the Korea Econometric Society Summer Meeting, Korea University, Wilfrid Laurier University, University of Southern California, Texas A&M University, Sam Houston State University, Bar Ilan University, Norwegian School of Economics and Business Administration, University of Alberta, Instituto Tecnológico Autónomo de México, and Seoul National University. We would like to thank the participants in the seminars. All remaining errors are, of course, our own.


This paper proposes two new estimators for determining the number of factors (r) in static approximate factor models. We exploit the well-known fact that the r largest eigenvalues of the variance matrix of N response variables grow unboundedly as N increases, while the other eigenvalues remain bounded. The new estimators are obtained simply by maximizing the ratio of two adjacent eigenvalues. Our simulation results provide promising evidence for the two estimators.