Asymmetric Influence of Employees and Trading Partners on Company's Sales and its Dynamical Origin

Abstract: Growth of business firms or companies has been a subject of intensive research over a century. However, there still remains controversy about the basic mechanisms of their growth. Inspired by previous work on scaling laws in other systems, here we extend the notion of size of firms from a scalar to a vector in order to characterize in more detail the mechanisms of growth and decay of firms. Based on a large scale dataset of Japanese firms covering over two million firms for two decades (1994-2015), we compile the dataset of vectors of three components, namely, annual sales, number of employee and number of trading partners. We find that the number of employees is more influential in determining firm sales compared to the number of trading partners. This asymmetry is validated by regressions of sales against these parameters and the analysis of growth rate correlations. We then explore multi-variate dynamics of firms by elaborating an evolutionary flow diagram of the averaged motion in the three-dimensional vector space. The flow diagram indicates that firms which deviate from the balanced scaling relation tend to return to this relation. We also find that firms with a chance of large sales growth suffer the risk of high disappearance rate. These results could serve for prediction and modeling of firms, and are relevant for theoretical understanding of the general principles governing complex systems.