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

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New-Keynesian (NK) models of the business cycle are still the workhorse models in the study of aggregate fluctuations and in the design of monetary and fiscal policies. In the aftermath of the financial crisis, with an prolonged zero-interest rate policy (ZIRP) period, the theory has fallen on hard times and has been criticized on both the theoretical and empirical ends (Cochrane, 2017a). In contrast to alternative doctrines (e.g., Old-Keynesian models and the monetarist view) the NK models predict that quantitative easing operations are irrelevant for inflation, but at the same time they predict counterfactual dynamics and policy paradoxes. In this project we approach this criticism and try to develop potential solutions to the problems. In a recent contribution we show that the ability to explain the facts, including a ZIRP with an active Taylor rule, crucially depends on the way we interpret and solve the model (Posch, 2018). A joint view of monetary and fiscal policy, in particular implementing the ideas from the fiscal theory of the price level (FTPL), allows us to select different equilibria and thus potentially gives alternative explanations. Including financial frictions, without which unconventional monetary policies in the form of large scale asset purchases – also known as “Quantitative Easing” operations – would be irrelevant, will enable us to model the important channels and it provides insights for a comprehensive understanding of the recent episodes. Our goal is to develop new (joint) strategies for monetary and fiscal policy to cope with future financial crises, or even circumvent them (Brunnermeier and Sannikov, 2016).