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

In recent years, several studies have pointed out a decline in the labor shareLabor share, a trend supported by researchers like Autor et al. and, Karabarbounis and Neiman. One[aut]Karabarbounis, L. key finding[aut]Neiman, B. from their research is that this decline primarily stems from reallocation among firms, rather than a decrease in the weighted average labor shareLabor share within individual firms (referred to as the between-firm effectBetween-firm effect). At the industry level, the overall macro labor share is mainly influenced by within-industry effectsWithin-industry effect, which capture the movement of the labor share within each industry. To address these simultaneous facts, Autor et al. propose the theory of “superstar” firms. According to this theory, the aggregate labor shareAggregate labor share within an industry tends to decrease as the most productive firms, known as “superstar” firms, gradually dominate the industry, even though their labor share is relatively low. While their theory has been primarily analyzed within a static framework, it inherently possesses dynamic aspects. In this chapter, I introduce a multi-firm optimal growth model, which provides a solid theoretical foundation for understanding the dynamics of superstar firmsSuperstar firms. The multi-firm optimal growth model was extensively studied[aut]Scheinkman, J. by J. Scheinkman and L. McKenzie under the title “Turnpike theoryTurnpike theory for multisector optimal growth modelMultisector optimal growth model.”