The unbearable lightness of equilibria in a low interest rate environment

TL;DR

This paper examines the coherence of structural economic models with low interest rates, showing that models with multiple shocks or binding constraints often require restrictive assumptions that lead to incompleteness and multiple solutions.

Contribution

It demonstrates that models with occasionally binding constraints and multiple shocks are generally incoherent unless specific support restrictions are imposed, highlighting limitations in current modeling approaches.

Findings

Models with binding constraints are often incoherent without restrictions.

Support restrictions on shocks are necessary for model coherence.

Such restrictions lead to multiple solutions and model incompleteness.

Abstract

Structural models with no solution are incoherent, and those with multiple solutions are incomplete. We show that models with occasionally binding constraints are not generically coherent. Coherency requires restrictions on the parameters or on the support of the distribution of the shocks. In presence of multiple shocks, the support restrictions cannot be independent from each other, so the assumption of orthogonality of structural shocks is incompatible with coherency. Models whose coherency is based on support restrictions are generically incomplete, admitting a very large number of minimum state variable solutions.