Fractal attractors in economic growth models with random pollution externalities

We analyze a discrete time two-sector economic growth model where the production technologies in the final and human capital sectors are affected by random shocks both directly (via productivity and factor shares) and indirectly (via a pollution externality). We determine the optimal dynamics in the decentralized economy and show how these dynamics can be described in terms of a twodimensional affine iterated function system with probability. This allows us to identify a suitable parameter configuration capable of generating exactly the classical Barnsley’s fern as the attractor of the log-linearized optimal dynamical system. In this paper, we build a two-sector growth model that, thanks to pollution externalities randomly affecting output and human capital production, allows for a suitable parameterization that generates the Classical Barnsley’s fern as the unique attractor of the economy.