Capacity-Constrained Stability in Macroeconomic Systems: An Operator-Theoretic Approach

Abstract Macroeconomic systems are traditionally modeled using equilibrium-based frameworks that characterize stability via spectral properties and asymptotic behavior. However, such approaches do not control finite-time responses in non-normal systems, where substantial transient amplification may occur despite spectral stability. This work develops a capacity-constrained operator-theoretic framework for macroeconomic dynamics modeled by non-normal linear operators. A dimensionless instability functional is introduced, linking transient amplification, perturbation magnitude, and system capacity. A finite-time instability criterion is established: instability occurs when the amplified perturbation exceeds system capacity, independently of eigenvalue stability. Lower bounds on transient growth are derived using resolvent estimates, and numerical examples demonstrate that spectrally stable systems may exhibit large amplification leading to operational instability. The framework provides a consistent extension of classical stability analysis by incorporating structural amplification and capacity limits.