Multiplicity and Nonexistence at the Zero Lower Bound in a Piecewise-Linear HANK Model: Complete Solution Sets for the Sequence-Space Complementarity Problem
Year: 2026
Type: preprint
Abstract: In sequence space the zero lower bound is usually imposed by conjecturing the dates at which it binds and verifying the conjecture, which cannot establish that no other equilibrium exists. This paper instead characterizes the complete set of perfect-foresight equilibria of a piecewise-linear heterogeneous-agent New Keynesian model with an occasionally binding lower bound over a finite horizon. Writing the problem as a linear complementarity problem makes its entire solution set computable, with completeness certified by a mixed-integer formulation that carries no big-$\bar M$ constant. At the benchmark shock the model has exactly two equilibria, with five- and nine-period spells, and no other set of binding periods solves the problem. A matched representative-agent counterpart has an upper triangular complementarity matrix, hence a P-matrix with a unique equilibrium for every shock; in the heterogeneous-agent model that triangularity fails, because policy wedges propagate forward through the wealth distribution. The two heterogeneous-agent solutions carry local indices $+1$ and $-1$, so the matrix has degree zero. Subject to a nondegeneracy condition, the number of equilibria is therefore even, and never exactly one, at every nondegenerate shock; over the shock processes examined it is two or none. Multiplicity and nonexistence are two realizations of a single integer. The second equilibrium survives even at zero shock amplitude, but is always large.
Authors: Koichi Yano, Tae Okada, Chenchen Zhao
Language: English
Topic: Economic theories and models
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7169587349