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 and technological heterogeneity to the decline in the aggregate labor share, supported by empirical analysis of Chinese manufacturing data.

Contribution

It extends Houthakker's aggregation theory to explain how larger, more capital-intensive firms reduce the labor share, providing a micro-foundation for the superstar firm hypothesis.

Findings

Larger firms are more capital-intensive than smaller firms.

The negative impact of firm size on labor share is significant in technologically heterogeneous industries.

The shift towards superstar firms explains most of the labor share decline from 2001 to 2015.

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.