[Paper Review] Coherence without Rationality at the Zero Lower Bound

Guido Ascari, Sophocles Mavroeidis+1 more|arXiv (Cornell University)|Aug 3, 2022

Economic theories and models4 citations

TL;DR

This paper demonstrates that models with a zero lower bound (ZLB) on interest rates can achieve coherence and completeness even when rational expectations equilibria (REE) fail to exist or are indeterminate. By replacing full-information rational expectations with adaptive learning or bounded rationality, the authors show that self-confirming equilibria—specifically restricted perceptions equilibria (RPE)—can emerge, restoring stability and uniqueness under mild frictions like imperfect information or less forward-looking behavior.

ABSTRACT

Standard rational expectations models with an occasionally binding zero lower bound constraint either admit no solutions (incoherence) or multiple solutions (incompleteness). This paper shows that deviations from full-information rational expectations mitigate concerns about incoherence and incompleteness. Models with no rational expectations equilibria admit self-confirming equilibria involving the use of simple mis-specified forecasting models. Completeness and coherence is restored if expectations are adaptive or if agents are less forward-looking due to some information or behavioral friction. In the case of incompleteness, the E-stability criterion selects an equilibrium.

Motivation & Objective

• To address the incoherence and incompleteness problems in standard rational expectations models with a zero lower bound (ZLB) constraint.
• To investigate whether alternative expectations formation mechanisms—such as adaptive learning or bounded rationality—can restore equilibrium existence and uniqueness when REE fails.
• To analyze the conditions under which restricted perceptions equilibria (RPE) exist and are stable in ZLB models with stochastic shocks.
• To explore the existence of additional non-rational equilibria, such as lagged expectation equilibria (LEE), in models with imperfect information.
• To provide a robust alternative framework for macroeconomic modeling under ZLB conditions where rational expectations fail.

Proposed method

• Analytically derive conditions for the existence of restricted perceptions equilibria (RPE) in a New Keynesian model with an occasionally binding ZLB.
• Use adaptive learning with mis-specified, under-parameterized forecasting models to generate self-confirming equilibria distinct from REE.
• Apply the E-stability criterion to select a unique equilibrium in cases of REE multiplicity.
• Model continuous-time shocks using a two-state Markov process to analyze RPE existence and stability under varying shock variance, persistence, and price flexibility.
• Introduce a lagged expectations equilibrium (LEE) model where agents observe shocks with a lag, allowing for non-rational but self-confirming equilibria.
• Calibrate the model to assess how structural parameters affect RPE existence, using numerical simulations and graphical analysis (e.g., Figure 8).

Experimental results

Research questions

• RQ1 Under what conditions does a restricted perceptions equilibrium (RPE) exist in a ZLB model when a rational expectations equilibrium (REE) does not?
• RQ2 How does adaptive learning with mis-specified models restore coherence and completeness in ZLB models?
• RQ3 What role does the degree of forward-looking behavior play in the existence and stability of non-rational equilibria?
• RQ4 Can non-rational equilibria like lagged expectation equilibria (LEE) exist in models where REE is incoherent?
• RQ5 How do shock variance, persistence, and price flexibility affect the likelihood of RPE existence?

Key findings

• A ZLB model can be incoherent under rational expectations—meaning no REE exists—yet still admit a self-confirming restricted perceptions equilibrium (RPE) when agents use adaptive learning with mis-specified models.
• The RPE exists and is stable when agents are less forward-looking due to information frictions or behavioral constraints, even when REE fails to exist.
• The E-stability criterion successfully selects a unique equilibrium in cases of REE multiplicity, restoring completeness.
• RPE existence is less likely when shock variance or persistence is high, or when prices are more flexible, as shown in Figure 8.
• Lagged expectation equilibria (LEE) exist even when REE does not, and LEE always exists if REE does, but not vice versa, indicating additional non-rational equilibria can emerge under imperfect information.
• The RPE exhibits a deflationary bias similar to that seen in RE models, but arises from bounded rationality rather than rational expectations.