A nonparametric analysis of firm size, leverage and labour productivity distribution dynamics

This paper investigates the evolution of firm distributions for entrant manufacturing firms in Canada using nonparametric methods. These nonparametric methods use functional principal components to describe these densities over time. This method is applied to a novel administrative firm-level database from Statistics Canada to investigate the evolution of the 1985 and 1989 cohorts of new entrants. We find that firm leverage (debt-to-asset ratio) distributions have persistent deviations from the initial distributions. Bootstrap test statistics suggest that the distributions are different across all time periods. Firm size and labour productivity have transitory deviations and some of the distributions are the same across all time periods. Univariate finite mixture and stochastic dominance tests are used to conduct pairwise comparisons as robustness measures. We find that these static pairwise comparisons confirm the dynamic evolution of these densities. This method illustrates the efficacy of functional principal components to analyse firm distributions.