DFG-Project

"Continuous-Time Modeling of Dynamic, Stochastic Equilibrium Models – Theory and Applications"

The German research foundation (DFG) is funding the project "Continuous-Time Modeling of Dynamic, Stochastic Equilibrium Models – Theory and Applications“ for 3 years. This project is intended to develop a benchmark New-Keynesian model in continuous time together with the required numerical solution methods in order to provide new insights on the effects of different monetary interventions and fiscal measures, and their effects on financial markets and the real economy.

New Keynesian (NK) models of the business cycle have become a fundamental tool, being the workhorse models in the study of aggregate fluctuations and in the design of monetary and fiscal policies. They are extensively used by central banks around the world to assess the effects of different monetary interventions and/or fiscal measures on financial markets and the real economy.
Nearly all of this extensive literature has worked with a formulation of the model in discrete time. This was in part because of the familiarity of macroeconomist with previous models of the business cycle, as the discrete-time real business cycle model, and in part because of the natural mapping of discrete-time models with empirical data, which come by construction in discrete observations. Motivated by the advantages of a powerful set of mathematical tools (numerical and analytical) and recent advances in empirical analysis (using mixed-frequency data) in comparison to existing approaches, we want to set up and provide methods to solve a NK-model in continuous time. This new formulation of the NK-model should serve as a benchmark to answer empirical relevant questions, at the same time retain a flexible and user-friendly implementation. This project provides new insights to the following questions: What are the effects of increased uncertainty on economic decisions? What are the effects of different monetary interventions and fiscal measures in times when the standard policy instrument, i.e., the nominal interest rate, is no longer available to the central bank because of the presence of a zero-lower-bound (ZLB)? What are the effects of rare, but periodically occurring events such as financial crises on the design of monetary and fiscal policies? With this project we built on the previous literature. In particular, we set up and solve a continuous-time NK-model in which firms can only change prices following a Calvo’s pricing rule. We illustrate the advantages of the continuous-time formulation in three applications.