On the modeling of size distributions when technologies are complex

Abstract

The study considers a stochastic R&D process where the invented production technologies consist of a large number n of complementary components. The degree of complementarity is captured by the elasticity of substitution of the CES aggregator function. Drawing from the Central Limit Theorem and the Extreme Value Theory we find, under very general assumptions, that the cross-sectional distributions of technological productivity are well-approximated either by the lognormal, Weibull, or a novel “CES/Normal” distribution, depending on the underlying elasticity of substitution between technology components. We find the tail of the “CES/Normal” distribution to be fatter than the Weibull tail but qualitatively thinner than the Pareto (power law) one. We also numerically assess the rate of convergence of the true technological productivity distribution to the theoretical limit with n as fast in the body but slow in the tail.