Risk-Taking, Global Diversification and Growth: Comment

In a seminal article, Obstfeld (1994) showed that growth and welfare gains from international risk-sharing arise in a continuous-time stochastic AK model. More precisely, he proved that a portfolio shift from safe and low-return capital to riskier and high-return capital triggers an unambiguous increase in growth. In this note I stress necessary and sufficient conditions ensuring stochastic stability of the exponential balanced-growth path, an issue that has not been addressed by Obstfeld. Not surprisingly, stability requires the average of the wealth growth rate to be positive, which makes clear how mean growth should be defined. Differently, Obstfeld defines mean growth as the growth rate of average wealth, which is smaller than the mean growth rate of wealth under the maintained assumption that wealth is log-normally distributed, because the latter growth concept is risk-adjusted. The two notions of mean growth have very different comparative statics properties both for economies that hold some risk-free capital and for economies that fully specialize in risky capital. Different from Obstfeld's results, international financial integration increases the stability-related mean growth rate for both complete and incomplete specialization, if risk aversion takes on moderate values and provided that the intertemporal substitution elasticity is smaller than one. Although the welfare computations presented by Obstfeld are preserved, because they ultimately depend on parameter values, this note shows that stochastic stability sheds new light on the mechanisms that trigger growth changes under financial integration and underlines the intuition behind them.