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.

We consider the estimation methods for the rank of a beta matrix corresponding to a multifactor model and study which method would be appropriate for data with a large number of assets. Our simulation results indicate that a restricted version of Cragg and Donald’s (1997) Bayesian information criterion estimator is quite reliable for such data. We use this estimator to analyze some selected asset pricing models with U.S. stock returns. Our results indicate that the beta matrix from many models fails to have full column rank, suggesting that risk premiums in these models are underidentified.