A Micro-Distributional Theory of the Aggregate Labor Share:Firm Size Distribution and Technological Heterogeneity

TL;DR

This paper develops a micro-distributional theory linking firm size distributions to macro labor shares by deriving a Cobb-Douglas aggregate from a Pareto output distribution and scale-dependent technology. It formalizes a weighting effect: when large firms are more capital-intensive ($ heta$) than small firms ($eta$), a shift toward superstar firms lowers the aggregate labor share via output-weighted averaging, with the effect further modulated by industry-level technological heterogeneity through $ ext{δ}$. Empirically, using Chinese manufacturing data (1998–2015), it verifies capital deepening ($ar{eta}>eta$), negative size-labor share relationships ($ ext{δ}<0$), and a conditional weighting effect that is stronger in capital-intensive industries; a counterfactual decomposition shows that size-distribution changes explain about 129% of the labor-share decline. Robustness tests, including IV, substitution-elasticity sensitivity, placebo tests, and alternative measures, support the central mechanism and suggest that market structure effects operate alongside traditional channels in determining macro labor shares, with important policy implications for antitrust and distributional policy in a world of superstar firms.

Abstract

The global decline in the labor income share has challenged the classical Kaldor facts; however, the macroeconomic aggregation mechanism -- namely, how aggregate factor shares emerge from firm-level heterogeneity -- remains underexplored. This paper bridges this gap by constructing a theoretical framework that links firm size distribution to aggregate factor shares. We extend Houthakker's aggregation theory and formalize the \textit{weighting effect}: when large firms are systematically more capital-intensive than small firms, a shift in market structure toward larger firms mechanically reduces the aggregate labor share. Using comprehensive firm-level data from Chinese manufacturing (2001--2015), we empirically validate this mechanism. First, we estimate production function parameters and confirm that capital elasticity significantly exceeds labor elasticity, implying a negative relationship between firm size and labor share. Second, we find that the negative effect of firm size on labor share is significant only in industries with high technological heterogeneity. Counterfactual decomposition reveals that the shift in the size distribution toward ``superstar firms'' during 2001--2015 constitutes the primary driver of the labor share decline. Our findings provide a technical micro-foundation for the ``superstar firm'' hypothesis and highlight the distributional consequences of ``winner-take-all'' market structures.