Factor shares, the price markup, and the elasticity of substitution between capital and labor

In a Walrasian labor market, the labor income share is constant under the assumptions of a Cobb–Douglas production function and perfect competition. Given the observed decline of the labor share in recent decades, this paper relaxes these assumptions, proposes a time-series calculation of the aggregate price mark-up reflecting the degree of imperfect competition in the product market, and provides estimates of the elasticity of substitution under such product market imperfections. We focus on Spain and the US and show that the elasticity of substitution is above one in Spain and below one in the US. We also show that the price markup drives the elasticity of substitution away from one, upwards in Spain, downwards in the US. These results are used to explain the declining path of the labor income share, common to both economies, and their contrasted patterns in terms of capital deepening.