A Schumpetreian growth model with random quality improvements

A common assumption in the Schumpeterian growth literature is that the innovation size is constant and identical across industries. This is in contrast with the empirical evidence which shows that: (1) innovation size is not identical across industries and (2) the size distribution of profit returns from innovation is highly skewed toward the low value side, with a long tail on the high value side. In the present paper, we develop a Schumpeterian growth model that is consistent with this evidence. In particular, we assume that when a firm innovates, the size of its quality improvement is the result of a random draw from a Pareto distribution. This enables us to extend the class of quality-ladder growth models to encompass firm heterogeneity. We study the policy implications of this new setup numerically and find that it is optimal to heavily subsidize R&D for plausible parameter values. Although it is optimal to tax R&D for some parameter values, this case only occurs when the steady-state rate of economic growth is very low.