Rich Heterogeneity in Dynare 7: A Practical Description

Dynare 7 ships a toolkit for solving heterogeneous-agent models: a .mod syntax declaring a heterogeneity dimension alongside the standard aggregate blocks, commands that load or compute the stationary equilibrium, and a first-order solver whose output is the sequence-space Jacobian of the aggregate equilibrium path with respect to the aggregate innovations, the array dr.G. This document is the toolkit’s mathematical companion, and it reads the methods it implements as one object: the state-space treatment of the heterogeneous block due to Bhandari et al. [2023], the sequence-space assembly of Auclert et al. [2021], and the sequence-space determinacy theory of Auclert et al. [2025], recast through the theory of linear time-invariant systems and Toeplitz operators. After stating the class of models, the syntax, and the steady-state algorithms, I develop the first-order theory behind the solver, the backward operator of the heterogeneous block, the transfer operator moving the cross-section, and their assembly into the sequence-space Jacobian, and read the state-space recursion of Bhandari et al. [2023] and the sequence-space Jacobian of Auclert et al. [2021] as two readings of one Fréchet derivative, with the borrowing-constraint atom priced by a weak-derivative and finite-element reading that never forces a derivative onto a Dirac at first order. The same continuous objects carry two extensions the toolkit does not yet ship. The first is existence and determinacy: the criterion of Auclert et al. [2025], established there on the discretized block, is shown to hold for the continuous operators, and the winding-number verdict read off the discretized symbol is certified to be the continuous model’s by a finite-sample bound. The second is a perturbation cascade that carries the second-order heterogeneous construction of Bhandari et al. [2023] to arbitrary order in the sequence space, the one Wiener–Hopf factorization computed at the first order serving every order.