Growth, automation, and the long-run share of labor

We study the long run implications of workplace automation induced by capital accumulation. We describe a minimal set of sufficient conditions for sustained growth, along with a declining labor share of income in the long run: (i) a basic asymmetry between physical and human capital; (ii) the technical possibility of automation in each sector; (ii) a self-replication condition on the production function for robot services; (iv) asymptotic homotheticity (more generally neutrality) of demand, and (v) a minimal degree of patience or intergenerational altruism among a fraction of households. However, the displacement of human labor is gradual, and absolute real wages could rise indefinitely. The results obtain in the absence of any technical progress; they extend to endogenous technical progress even if such progress is not biased ex ante in favor of automation