Determining the Number of Factors from Empirical Distribution of Eigenvalues

Abstract

We develop a new consistent and simple to compute estimator of the number of factors in the approximate factor models of Chamberlain and Rothchild (1983). Our setting requires both time series and cross-sectional dimensions of the data to be large. The main theoretical advantage of our estimator relative to the previously proposed ones is that it works well even in the situation when the portion of the observed variance attributed to the factors is small relative to the variance due to the idiosyncratic term. This advantage arises because the estimator is based on a Law-of-Large- Numbers type regularity for the idiosyncratic components of the data, as opposed to the estimators based on the assumption that a significant portion of the variance is explained by the systematic part. Extensive Monte Carlo analysis shows that our estimator outperforms the recently proposed Bai and Ng (2002) estimators in finite samples when the "signal-to-noise" ratio is relatively small. We apply the new estimation procedure to determine the number of pervasive factors driving stock returns for the companies traded on NYSE, AMEX, and NASDAQ in the period from 1983 to 2003. Our estimate is equal to 8.