Dynamic Mode Decompositions and Vector Autoregressions

We establish connections between dynamic mode decompositions (DMDs), vector autoregressions, and linear state‐space models, showing that DMD provides a computationally efficient, SVD‐based estimator of low‐rank first‐order VAR projection coefficients in high‐dimensional settings. When the measurement matrix has full column rank, the recovered nonzero eigenvalues coincide with those of the underlying state transition matrix. We apply DMD to a 100‐household heterogeneous‐agent economy with complete markets and Gorman aggregation. From high‐dimensional household income and consumption panels, DMD recovers latent aggregate dynamics, and cross‐sectional loadings reveal the sharing rule governing redistribution, demonstrating DMD's capacity to extract economically meaningful structure from microeconomic panels.