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.
Highlights
It is well-known that in structural models with occasionally binding constraints, equilibria may not exist or there may be multiple equilibria
To the best of our knowledge, there are no general results about the conditions for existence and uniqueness of equilibria in dynamic forward-looking models with rational expectations when some variables are subject to occasionally binding constraints
We propose a method for checking the coherency and completeness (CC) condition, that is, 13The support of the distribution of the shock t has been carefully chosen to avoid incoherency
Summary
It is well-known that in structural models with occasionally binding constraints, equilibria may not exist (incoherency) or there may be multiple equilibria (incompleteness). We derive our main result first in a simple model that consists of an active Taylor rule with a ZLB constraint and a nonlinear Fisher equation with a single discount factor (AD) shock that can take two values This setup has been used, amongst others, by Eggertsson and Woodford (2003) and Aruoba et al (2018), and it suffices to study the problem analytically and convey the main intuition. A more straightforward approach is to assume that UMP can relax the ZLB constraint sufficiently to restore the generic coherency of the model without support restrictions This underscores another potentially important role of UMP not emphasized in the literature so far: UMP does help take the economy out of a liquidity trap, but it is useful in ensuring the economy does not collapse in the sense that there is no bounded equilibrium.
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