S-shaped curves in economic growth. A theoretical contribution and an application

Although the logistic and Gompertz equations have regularly been used in economics to represent S-shaped phenomena, we argue in this paper that they show certain shortcomings in fitting some empirical features of economic growth. In this paper, we try to overcome these limitations by defining a family of unimodal differential equations that covers practically the whole range of sigmoid curves. We also identify three sub-families of these differential equations that may provide acceptable fits for any S-shaped curve. Drawing upon this formal contribution, we fit a generalized logistic equation to certain series of the US economy, in order to analyse the investment and growth patterns during the period 1967-2003. Our results highlight that the period of decelerating growth in the 1970s, the recovery of the 1980s and the long expansion of the 1990s are clearly distinguishable. The patterns of growth differ widely between sectors, showing much more intensity in activities related with information and communication technologies. Regarding these technologies, our fits reveal a process of gestation during the 1970s and the possible existence of expansionary breaks produced by fundamental innovations during the development process.