DOES NEARâ€ RATIONALITY MATTER IN FIRSTâ€ ORDER APPROXIMATE SOLUTIONS? A PERTURBATION APPROACH
Frank Hespeler and
Marco Sorge ()
Bulletin of Economic Research, 2018, vol. 70, issue 1, E97-E113
This paper studies firstâ€ order approximate solutions to nearâ€ rational dynamic equilibrium models. Under nearâ€ 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 decisionâ€ makers â€“ e.g., ambiguityâ€ averse households or policyâ€ makers with a concern for robustness â€“ 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 firstâ€ order decision rules, nearâ€ rationality may also induce failure of the certainty equivalence principle. Moreover, the martingale representation of distorted beliefs might prove nonâ€ unique, pointing to a subtle form of equilibrium indeterminacy.
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