Research
Reverse Calculus and Nested Optimization (2020, with A. Clausen)
Nested optimization problems arise when an agent must take into account the effect of their decisions on their own future behavior, or the behavior of others. In these problems, calculating marginal costs and benefits involves differentiating the solutions to nested problems. But are these solutions differentiable functions? We develop a tool called Reverse Calculus, and establish first-order conditions for (i) a Stackelberg leader considering the follower's best response function, (ii) a sovereign borrower considering its own future default policy, and (iii) non-convex dynamic programming problems.
Old draft (circulated as A General and Intuitive Envelope Theorem)
Older draft (circulated as A General and Intuitive Envelope Theorem)
Even older draft (circulated as Envelope Theorems for Non-Smooth and Non-Concave Optimization)
Money Cycles (2016, with A. Clausen)
Operating overheads are widespread and lead to concentrated bursts of activity. To transfer resources between active and idle spells, agents demand financial assets. Futures contracts and lotteries are unsuitable, as they have substantial overheads of their own. We show that money – under efficient monetary policy – is a liquid asset that leads to efficient allocations.
Under all other policies, agents follow inefficient “money cycle” patterns of saving, activity, and inactivity. Agents spend their money too quickly – a “hot potato effect of inflation”. We show that inflation can stimulate inefficiently high aggregate output.
Central Bank Design with Heterogeneous Agents (2009, with A. Berentsen)
We study alternative institutional arrangements for the determination of monetary policy in a general equilibrium model with heterogeneous agents, where monetary policy has redistributive effects. Inflation is determined by a policy board using either simple-majority voting, supermajority voting, or bargaining. We compare the equilibrium inflation rates to the first-best allocation.
Grundzüge der analytischen Makroökonomie (2004, mit T. Hens)
Die Themen der Makroökonomie (Wachstum, Konjunktur, Beschäftigung, Inflation, Wechselkurse, Aktienkurse usw.) sind diejenigen der Ökonomie, die am meisten allgegenwärtig sind. Die Zusammenhänge dieser Fragen zu verstehen, ist die Hauptmotivation von Studienanfängern der Wirtschaftswissenschaften. Dieses Buch möchte die Studierenden an das analytische Werkzeug heranführen, das die Wirtschaftswissenschaften zum Verständnis dieser Fragen liefert.
Es wird ein umfassendes makroökonomisches Modell entwickelt, das den Arbeits-, den Güter-, den Kapital-, den Geld- und sogar den Aktienmarkt beinhaltet. Das didaktische Konzept dieses Buches ist der sukzessive Aufbau eines komplexen makroökonomischen Modells, das mikroökonomisch fundiert ist. Dabei wird jeder Schritt intuitiv und analytisch dargestellt und anhand von Fallstudien illustriert. Die Hauptthese des Buches: die Methoden der Mikroökonomik sind ideal für die Analyse der Fragestellungen der Makroökonomik.