Statistical Properties of Labor Productivity Distributions

We employed the latest version of the world's largest corporate financial database and identified the following three statistical properties of the physical labor productivity of firms: 1) The probability density function (PDF) of labor productivity follows power-law and log-normal distributions in the large- and mid-scale ranges. 2) Time-reversal symmetry was observed in the correlation of labor productivities in two consecutive years, and the initial-value dependence of the growth-rate distribution has regularity. These two properties accurately derive the above two kinds of PDFs. 3) The dependence of labor productivity distribution is negligible on the number of employees. This indicates a slight difference in the distribution of labor productivity among large-, mid-, and small-sized firms.