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 com-plement high-skill labor) and horizontal innovation (the introduction of new prod-ucts, which increases demand for both types of labor). Such an economy endoge-nously follows three phases. First, low-skill wages are low, which induces little automation, such that income inequality and labor’s share of GDP are constant. Second, as low-skill wages increase, investment in automation is stimulated, which depresses the future growth rate of low-skill wages (potentially to negative), and reduces the total labor share. Finally, the share of automated products stabilizes and the economy moves toward an asymptotic steady state, where low-skill wages grow but at a lower rate than high-skill wages. This model therefore delivers per-sistently increasing wage inequality and stagnating real wages for low skill workers for an extended period of time, features of modern labor markets which have been difficult to reconcile with the theoretical literature on economic growth. We fur-ther include middle-skill workers, which allows the model to generate a phase o