A Theory of Factor Shares

This paper presents a theory of how factor income shares are determined in an environment with labor market frictions and heterogeneous firms. I assume neither a specific aggregate production function nor competitive factor markets. Instead, I first develop microfoundations for an aggregate production function that incorporates a frictional process of matching workers and firms. Wages are determined by Bertrand style competition between firms whose productivity levels are assumed to be Pareto-distributed. In the limiting case where the unemployment rate goes to zero, the aggregate production function is Cobb-Douglas and factor shares are constant. In general, however, the behavior of factor shares is driven by labor market conditions such as unemployment and workers' reservation wage. I simulate the model and examine its predictions for factor shares in the U.S. during the period 1951-2010. The theory can explain much of the variation in factor shares from 1951 to 2003 but the sharp fall in labor's share in around 2004-2005 remains puzzling.