Some Pleasant Sequence-Space Arithmetic In Continuous Time

This paper proposes an analytic representation of sequence-space Jacobians in heterogeneous agent models with aggregate shocks in continuous time. Our approach is based on a pen-and-paper perturbation of individual policy functions with respect to price changes, rather than numerical or automatic differentiation. We obtain linear partial differential equations that we solve efficiently on variable time grids. Our continuous time algorithm accelerates computation of impulse responses tenfold relative to discrete time. Continuous time is key to taking the analytic perturbation in the presence of binding borrowing constraints. We illustrate our approach in leading heterogeneous agent models with and without nominal rigidities.