Clearing Up the Effective Lower Bound Morass

TL;DR

This paper resolves ambiguities in the New Keynesian model at the Effective Lower Bound by employing a truncated Markov chain, demonstrating unique equilibria and clarifying the effects of government spending.

Contribution

It introduces a truncated Markov chain approach to analyze the model, proving the non-existence of the expectations-driven trap and establishing equilibrium uniqueness.

Findings

Expectations-driven trap does not occur as an equilibrium.

Equilibrium under truncated Markov chain is unique.

Government spending positively affects consumption without sign reversal.

Abstract

Depending on the persistence of the underlying Markov chain shock, the standard New Keynesian model predicts starkly different conclusions at the Effective Lower Bound. We clear up this morass by using a truncated Markov chain. We prove that the expectations-driven trap \`a la Mertens & Ravn (2014) doesn't arise as an equilibrium outcome. In addition, the equilibrium under a truncated Markov chain is guaranteed to be unique, the effect of government spending is positive on consumption and does not switch signs but may grow unbounded \textemdash a puzzle.