The Rise of the Machines: Automation, Horizontal Innovation and Income Inequality

We construct an endogenous growth model of directed technical change with automation (the introduction of machines which replace low-skill labor and complement high-skill labor) and horizontal innovation (the introduction of new products, which increases demand for both types of labor). For general processes of technical change, we demonstrate that although low-skill wages can drop during periods of increasing automation intensity, the asymptotic growth rate is weakly positive --- though lower than that of the economy. We then endogenize the evolution of technology and show that the transitional path follows three distinct phases. First, wages are low, such that few machines are used and low-skill wages keep pace with the growth rate of the economy. Then, as wages grow, the share of automated products increases and the economy substitutes towards the use of machines -- depressing the growth rate of low-skill wages (potentially to negative). Finally, as the economy reaches steady state, the share of automated products is constant and the relative growth rate of low-skill wages recovers somewhat, yet remains lower than that of the economy overall. Allowing workers to endogenously transition from low-skill to high-skill alleviates the growth in income inequality, but does not alter the structure of the model. We extend the model to include middle-skill workers and demonstrate that the model endogenously captures the defining characteristics of the U.S. income distribution over the past 50 years: initially a monotone dispersion of the income distribution, and thereafter a wage growth polarization in which middle-skill workers experience the lowest wage growth. Finally, in an extension we allow machines to be produced with a different technology than the consumption good. This allows for faster productivity growth for machines potentially leading to permanently negative growth of low-skill wages.