Does Near-Rationality Matter in First-Order Approximate Solutions? A Perturbation Approach

This paper studies first‐order approximate solutions to near‐rational dynamic equilibrium models. Under near‐rationality, agents' subjective beliefs are distorted away from rational expectations via a change of measure process which fulfills some regularity conditions. In most applications, the beliefs distortion process is also directly observed by (a subset of) the decision‐makers – e.g., ambiguity‐averse households or policy‐makers with a concern for robustness – and therefore included into their optimization problems. We investigate conditions for existence and local uniqueness of solutions under endogenous distortions, as well as the relation with their rational expectations counterparts. We show that linearly perturbed solutions may well be affected by the presence of distorted beliefs, depending on the underlying model economy. In particular, while directly affecting first‐order decision rules, near‐rationality may also induce failure of the certainty equivalence principle. Moreover, the martingale representation of distorted beliefs might prove non‐unique, pointing to a subtle form of equilibrium indeterminacy.