We develop a dynamic general equilibrium model to analyze the eects of central bank purchases of government bonds by investigating the following three questions: Under what conditions are these purchases socially desirable, what incentive problems do they mitigate, and how large are these eects? We show that by purchasing government bonds, central banks induce agents to increase their demand for money, which increases the value of money and thereby improves the allocation and welfare. We then analyze the post-crisis period and show that implementing the zero lower bound was optimal and worth 0:014 percent of total consumption.