Expectation formation in an overlapping generation model with production

In this paper, we investigate the dynamic properties of an overlapping generations' model with capital accumulation, in which agents work in both periods of life. We compare three different expectation mechanisms: Perfect foresight, myopic foresight, and adaptive expectations, focusing, in particular, on this last one. We show that the steady state is the same under each mechanism, and we prove its global stability for perfectly foresighted agents. After investigating local stability conditions under myopic expectations, we study in detail the case of adaptive expectations. We show that, under both reduced rationality mechanisms, if the share of time devoted to labor in the second period of life is large enough, periodic and complex dynamics can occur. Moreover, deepening the investigation through numerical simulations, we study the global stability behavior under adaptive expectations. Such complex scenarios also include the coexistence between the stable steady state and a periodic or chaotic attractor, giving rise to multistability, which does not arise under myopic expectations. Finally, we provide some considerations about the possibility for the agents to improve their forecasts by observing the forecasting error time series.