On the probability distribution of long-term changes in the growth rate of the global economy: an outside view

Abstract

A scan of the history of gross world product (GWP) at multi-millennium timescale generates fundamental questions about the human past and prospect. What is the probability distribution for negative shocks ranging from mild recessions to the pandemics? Were the agricultural and industrial revolutions one-offs or did they manifest dynamics still ongoing? Is the pattern of growth best seen as exponential, if with occasional step changes in the rate, or as superexponential? If the latter, how do we interpret the typical corollary, that output will become infinite in finite time? In a modest step toward answering such ambitious questions, this paper introduces the first internally consistent statistical model of world economic history. Using the stochastic calculus, it casts a GWP series as a sample path in a diffusion, whose specification is rooted in a functional form from neoclassical growth theory. After fitting to historical data, the model fits growth history since 10,000 BCE well enough that most empirical observations lie between the 40th and 60th percentiles of modeled distributions. But the model is surprised by the 19th-century growth surge (two-tailed ?? ≈ 0.1) and the stable growth of recent decades. Multivariate stochastic modeling might better replicate such developments. The univariate fit implies that, conditional on the 2019 GWP, explosion is essentially inevitable, at a median year of 2047. This implausibility does not prima facie invalidate the modeling approach. Infinities are avoided if natural resources are endogenized too. Then, explosion can lead to implosion. The propensity to explosion thus suggests that the world economic system over the long term tends not to the steady growth seen in industrial countries in the last century or so, but to instability. The credible range of future paths seems wide.