Hardware and Software over the Course of Long-Run Growth: Theory and Evidence

Abstract

Output is generated through purposefully initiated physical action. Production needs energy and information, provided by respective factors: hardware (“brawn”), including physical labor and physical capital, and software (“brains”), encompassing human cognitive work and pre-programmed software, in particular artificial intelligence (AI). From first principles, hardware and software are essential and complementary in production, whereas their constituent components are mutually substitutable. This framework generalizes the neoclassical model of production with capital and labor, models with capital-skill complementarity and skill-biased technical change, and unified growth theories embracing also the pre-industrial period. Having laid out the theory, we provide an empirical quantification of hardware and software in the US, 1968-2019. We document a rising share of physical capital in hardware (mechanization) and digital software in software (automation); as a whole software has been growing systematically faster than hardware. Accumulation of digital software was a key contributor to US economic growth.