Functional Principal Component Analysis of Density Families With Categorical and Continuous Data on Canadian Entrant Manufacturing Firms
This article investigates the evolution of firm distributions for entrant manufacturing firms in Canada using functional principal components analysis. This methodology describes the dynamics of firms by examining production variables, size, and labor productivity, and a financial variable, leverage (debt-to-asset ratio). We adapt the canonical functional principal components analysis to allow for the inclusion of qualitative information in the form of discrete variables, industry, and region, to capture market structure differences, which is shown to change the dynamics of firm size and labor productivity distributions only. We also perform various tests with the null hypothesis that the distributions are equal across time. When accounting for industry and regional categories, there is a substantial fall in the number of rejections of the null hypothesis of equality for size and labor productivity, which is not the case for leverage. These results show the importance of including qualitative information to account for potential heterogeneity when applying functional principal component analysis to firm-level data. Finally, the methodology finds a correlation between the evolution of variable distributions and macroeconomic factors. This article has supplementary material online.