Bell-Shaped Curve for Productivity Growth: An Explanation

A recent analysis of the productivity growth data shows, somewhat surprisingly, that the dependence of the 20-century productivity growth on time can be reasonably well described by a Gaussian formula. In this paper, we provide a possible theoretical explanation for this observation. 1 Formulation of the Problem An empirical fact. A recent book [2] shows that, when averaged over decades, the productivity growth n(t) in the US from 1900 until now follows a bell-shaped Gaussian curve n(t) = c0 · exp(−k0 · (t− t0)), for appropriate values c0, k0, and t0 (see also [1]). This fact is somewhat surprising. Such curves normally describe how the probability of a certain value x depend on this value. It is somewhat surprising to find a similar curve in the description of how productivity growth depends on time. What we do in this paper. In this paper, we provide a possible explanation for this surprising phenomenon.