The emergence of chaos in productivity distribution dynamics

The distribution of productivity levels, and its evolution over time, is a research topic of utmost importance in empirical and theoretical economics. On the theory side, simple analytical models, involving intertemporal optimization, typically characterize agents’ investment decisions about ways to upgrade technology and enhance productivity. The prototypical model endogenously splits the productivity distribution in two: the right-hand side of the distribution is populated by innovators; the left-hand side is occupied by agents who follow a strategy of adoption or imitation. Given the assumptions of the model, the productivity of innovators grows at a constant rate (which directly depends on a constant probability of innovation). The evolution of the productivity of adopters may, in turn, implicate complex dynamics. Because the pace of productivity growth for adopters depends on the shape of the productivity distribution, different distributions might induce distinct growth paths, some of them potentially leading to the emergence of nonlinearities, such as limit cycles and chaos. This study investigates the presence of nonlinearities in technology adoption, for different configurations of the productivity distribution. Under reasonable parameterizations, endogenous fluctuations emerge as a plausible long-term equilibrium.