Firm size distributions through the lens of functional principal components analysis

Abstract

AbstractWe explore the dynamics of firm size distributions through the lens of Functional Principal Component Analysis as proposed by Kneip and Utikal (2001). Using samples of UK firms from Geroski et al. (2003) we apply the methodology to their balanced panel sample, present in the sample for all 31 years. We extend the analysis to an unbalanced panel sample (minimum and maximum spell of five and 31 years). For the unbalanced panel, we reject the null hypothesis that the densities are the same, while we fail to reject the null hypothesis for the balanced panel. These results suggest that inclusion of young firms that non‐randomly exit will affect the firm size distribution. The difference in the results is due to the presence of survivorship bias. These results highlight the attractiveness of this methodology and its ability to succinctly describe the time dynamics of distributions without the need for explicit parametric specification of the growth and exit processes. Copyright © 2010 John Wiley & Sons, Ltd.