Not a Typical Firm: The Joint Dynamics of Firms, Labor Shares, and Capital–Labor Substitution

While the US labor share has declined, especially in manufacturing and retail, the labor share of a typical firm in these sectors has risen. This paper introduces a model where firms incur fixed costs to automate tasks. In response to lower capital prices, the model reproduces the labor share patterns observed in the data: large firms automate more tasks, reducing the aggregate labor share; while the median firm continues to operate a labor-intensive technology with a rising labor share. Using our model, we decompose the labor share decline and the rise in sales concentration in each sector into a part driven by lower capital prices and a part driven by reallocation to higher-markup firms. Reallocation played a minor role in explaining the labor share decline in manufacturing and some role in retail and other sectors during 1982-2012.