Stochastic stability of endogenous growth: The AK case

This note studies the stochastic stability of the standard AK growth model un- der uncertain output technology. Capital accumulation follows a stochastic lin- ear homogenous differential equation. It’s shown that exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncertainty. Precisely, it’s demonstrated that the economy almost surely col- lapses at exponential speed even though productivity is initially arbitrarily high.