New Monetarism in Continuous Time: Methods and Applications

We develop a New Monetarist model in continuous time where agents trade continuously in competitive markets and infrequently in pairwise meetings. Agents can produce and consume both in flows over time intervals and in discrete quantities at points in time. We detail the methodology to solve individual optimisation problems and characterise the full set of perfect foresight equilibria. We illustrate the role of continuous time and the tractability of our approach with three applications related to monetary policy: (i) forward guidance with policy announcements; (ii) aggregate demand management and firm entry; (iii) open market operations with partially liquid assets.