Mean growth and stochastic stability in endogenous growth models

Raouf Boucekkine (1) , Patrick Pintus (1) , Benteng Zou (2)

1 AMSE - Aix-Marseille Sciences Economiques
2 CREA - Center for Research in Economic Analysis

Under uncertainty, mean growth of, say, wealth is often defined as the growth rate of average wealth, but it can alternatively be defined as the average growth rate of wealth. We argue that stochastic stability points to the latter notion of mean growth as the theoretically relevant one. Our discussion is cast within the class of continuous-time AK-type models subject to geometric Brownian motions. First, stability concepts related to stochastic linear homogeneous differential equations are introduced and applied to the canonical AK model. It is readily shown that exponential balanced-growth paths are not robust to uncertainty. In a second application, we evaluate the quantitative implications of adopting the stochastic-stability-related concept of mean growth for the comparative statics of global diversification in the seminal model due to Obstfeld (1994).

Keywords: Global diversification; Stochastic stability; Mean growth; Endogenous stochastic growth; AK model

Domains: Economics and Finance; Quantitative Finance [q-fin]

Raouf Boucekkine, Patrick Pintus, Benteng Zou. Mean growth and stochastic stability in endogenous growth models. Economics Letters, 2018, 166 (C), pp.18 - 24. ⟨10.1016/j.econlet.2018.02.014⟩. ⟨hal-01793166⟩