Dynamic Macroeconomics with Multiple Regimes

TL;DR

This paper introduces a new framework for macroeconomic modeling that incorporates multiple regimes with distinct propagation operators, challenging the traditional single-law assumption and affecting stability and policy analysis.

Contribution

It develops the Dynamic Macroeconomics with Multiple Regimes (DMR) framework, revealing fundamental structural differences from single-regime models.

Findings

Invariant-law and regime-dependent systems are not topologically equivalent.

Regime dependence cannot be removed by any injective transformation.

Non-commuting regime operators prevent a single map from reproducing all trajectories.

Abstract

Macroeconomic dynamics is typically modeled under the assumption that the economy evolves according to a single invariant law of motion. This paper shows that this assumption imposes a structural restriction. We develop Dynamic Macroeconomics with Multiple Regimes (DMR), a framework in which economic evolution is governed by multiple regime-specific propagation operators. As a result, trajectories arise from ordered compositions of heterogeneous operators rather than from the iteration of a single mapping. We establish three structural results. First, invariant-law and regime-dependent systems are not topologically equivalent. Second, regime dependence is dynamically irreducible: it cannot be eliminated through any injective transformation of the state space. Third, whenever regime operators fail to commute, there exists no map $F:\mathbb{R}^n\to\mathbb{R}^n$ whose iterates reproduce all regime-admissible trajectories. These results establish a structural separation between invariant-law macroeconomics and regime-dependent dynamics, implying that stability, policy evaluation, and structural characterization must be conducted at the level of interacting propagation operators rather than within a single invariant mapping.