We study general dynamic programming problems with continuous and discrete choices and general constraints. The value functions may have kinks arising (1) at indifference points between discrete choices and (2) at constraint boundaries. Nevertheless, we establish a general envelope theorem:...

Classical models of money are typically based on a competitive market without capital or credit. They then impose exogenous timing structures, market participation constraints, or cash-in-advance constraints to make money essential. We present a simple model without credit where money arises...

In monetary models in which agents are subject to trading shocks there is typically an ex-post inefficiency in that some agents are holding idle balances while others are cash constrained. This inefficiency creates a role for financial intermediaries, such as banks, who accept nominal deposits...

An increasing number of central banks implement monetary policy via two standing facilities: a lending facility and a deposit facility. In this paper we show that it is socially optimal to implement a non-zero interest rate spread. We prove this result in a dynamic general equilibrium model...

When agents are liquidity constrained, two options exist - sell assets or borrow. We compare the allocations arising in two economies: in one, agents can sell government (outside) bonds and in the other they can borrow by issuing (inside) bonds. All transactions are voluntary, implying no...

We study the long-run relation between money, measured by inflation or interest rates, and unemployment. We first discuss data, documenting a strong positive relation between the variables at low frequencies. We then develop a framework where both money and unemployment are modeled using...

Inflation and unemployment are central issues in macroeconomics. While progress has been made on these issues recently using models that explicitly incorporate search-type frictions, existing models analyze either unemployment or inflation in isolation. We develop a framework to analyze...

We construct a dynamic stochastic general equilibrium model to study optimal monetary stabilization policy. Prices are fully flexible and money is essential for trade. Our main result is that if the central bank pursues a long-run price path, thereby controlling inflation expectations, it can...

Channel systems for conducting monetary policy are becoming increasingly popular. Despite their popularity, the consequences of implementing policy with a channel system are not well understood. We develop a general equilibrium framework of a channel system and investigate the optimal policy. A...

An increasing number of central banks implement monetary policy via a channel system or a floor system. We construct a general equilibrium model to study the properties of these systems. We find that the optimal framework is a floor system if and only if the target rate satisfies the Friedman...