Learning paths to multi-sector equilibrium: Belief dynamics under uncertain returns to scale

This paper explores the dynamics of learning in a multi-sector general equilibrium model where firms operate under incomplete information about their production returns to scale. Firms iteratively update their beliefs using maximum a-posteriori estimation, derived from observed production outcomes, to refine their knowledge of their returns to scale. The implications of these learning dynamics for market equilibrium and the conditions under which firms can effectively learn their true returns to scale are the key objects of this study. Our results shed light on how idiosyncratic shocks influence the learning process and demonstrate that input decisions encode all pertinent information for belief updates. Additionally, we show that a long-memory (path-dependent) learning which keeps track of all past estimations ends up having a worse performance than a short-memory (path-independent) approach.