“Superexponential [Modeling the Human Trajectory]”, 2020-07-30 (; backlinks; similar):
A scan of the history of gross world product (GWP) over millennia raises fundamental questions about the human past and prospect. What is the distribution of shocks ranging from recession to pandemic? Were the agricultural and industrial revolutions one-offs or did they manifest ongoing dynamics? Is growth exponential, if with occasional step changes in the rate, or is it superexponential? If the latter, how do we interpret the implication that output will become infinite in finite time?
This paper introduces the first coherent statistical model of GWP history. It casts a GWP series as a sample path in a stochastic diffusion, one whose specification is novel yet rooted in neoclassical growth theory.
After maximum likelihood fitting to GWP back to 10,000 BC, most observations fall between the 40th and 60th percentiles of predicted distributions. The fit implies that GWP explosion is all but inevitable, in a median year of 2047.
This projection cuts against the steadiness of growth in income per person seen in the last two centuries in countries at the economic frontier. And it essentially contradicts the laws of physics. But neither tension justifies immediate dismissal of the explosive projection. Accelerating economic growth is better explained by theory than constant growth. And if physical limits are articulated in a neoclassical-type model by endogenizing natural resources, explosion leads to implosion, formally avoiding infinities. The quality of the superexponential fit to the past suggests not so much that growth is destined to ascend as that the human system is unstable.
[Keywords: endogenous growth, macroeconomic history, gross world product, stochastic differential equations]