Endogenous sigma-augmenting technological change: An R&D-based approach

There is now increasing evidence that for the U.S. economy, the elasticity of substitution between capital and labor, "sigma", is rising over time. To account for this, we propose a microfounded model, where the evolution of "sigma", and, hence, the shape of the aggregate production function occur endogenously. We develop a Schumpeterian growth model in which firms can undertake R&D activities that stochastically lead to the discovery of production technologies characterized by a higher elasticity of substitution between capital and labor. Improved possibilities for factor substitution mitigate the diminishment of the marginal product of capital and spur capital accumulation. Due to successful innovations, the steady state of the economy entails higher levels of the capital stock and the output good. Moreover, our numerical simulations show that the timing of innovations is important: two economies with the same steady-state elasticity of substitution between capital and labor can differ in terms of their steady-state levels of the capital stock and the output good.