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

Stefano Nasini, Rabia Nessah and Bertrand Wigniolle ()
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Stefano Nasini: IESEG - UCL - Université catholique de Lille, LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique
Rabia Nessah: IESEG - UCL - Université catholique de Lille, LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique
Bertrand Wigniolle: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris

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Abstract: 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.

Keywords: Maximum a-posteriori estimation; Returns to scale; Incomplete information; Multi-sector general equilibrium model; Learning dynamics (search for similar items in EconPapers)
Date: 2026-02
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Published in Journal of Mathematical Economics, 2026, 122, ⟨10.1016/j.jmateco.2025.103212⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-05650472

DOI: 10.1016/j.jmateco.2025.103212

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