A Unified Framework for Equilibrium Selection in DSGE Models

TL;DR

This paper introduces a formal, unified framework for understanding equilibrium selection in DSGE models, clarifying how different solution methods and policy choices influence the equilibrium outcome.

Contribution

It formalizes DSGE solution methods as fixed-point selection devices and demonstrates how various selectors can be systematically compared and verified.

Findings

Blanchard-Kahn conditions as a selection operator

Standard solution methods realize this selection operation

Alternative selectors emerge under indeterminacy

Abstract

This paper characterizes DSGE models as fixed-point selection devices for self-referential economic specifications. We formalize this structure as $(S, T, \Pi)$: specification, self-referential operator, and equilibrium selector. The framework applies to any DSGE model through compositional pipelines where specifications are transformed, fixed points computed, and equilibria selected. We provide formal results and computational implementation for linear rational-expectations systems, reinterpreting Blanchard-Kahn conditions as a specific selection operator and verifying that standard solution methods (such as QZ decomposition and OccBin) realize this operation. We show that alternative selectors (minimal-variance, fiscal anchoring) become available under indeterminacy, revealing selection as a policy choice rather than a mathematical necessity. Our framework reveals the formal structure underlying DSGE solution methods, enabling programmatic verification and systematic comparison of selection rules.