Toward a Theory of the Labor Share’s Fall: A Dynamic Model of the “Superstar†Firm

In the last few years, there have been a growing number of studies pointing to a decline in the labor share, and this new fact has been clearly confirmed by Autor et al. and Karabarbounis and Neiman, among others. One of their key findings is that the decline in the labor share is primarily driven by reallocation among firms, rather than the decline in the weighted average labor share within firms (between-firm effect). On the other hand, at the industry level, the aggregate macro labor share is mainly affected by within-industry effects (the movement of the labor share in each industry). To explain these facts simultaneously, Autor et al. propose the “superstar†firm theory. That is, the aggregate labor share of an industry tends to decline as the most productive firms with the lowest labor share, called “superstar†firms, increasingly dominate the industry. Their theory is analyzed completely within the framework of statics, even though it clearly has many dynamical aspects. In this study, we propose a multiple-firm optimal growth model as a benchmark model that provides a solid theoretical foundation for the superstar firm theory. The multi-firm optimal growth model was intensively investigated by J. Scheinkman and L. McKenzie, under the title "Turnpike theory for multisector optimal growth model." The focus here is on the dynamic theory of superstar firms, but as the causes of the declining labor income share are as diverse as those reported in the McKinsey Discussion Paper, the policies that address them must also be diverse.