We present an incomplete markets model to understand the costs and benefits of increasing government debt in a low interest rate environment. Higher risk increases the demand for safe assets, lowering the natural rate of interest below zero, constraining monetary policy at the zero lower bound,...

We provide a simple rational bubble model demonstrating that a concentration of income is necessary and sufficient for the existence of equilibria with risky speculative bubbles. Income concentration among top earners leads to excess savings and depressed interest rates, which facilitate the...

We develop a simple model of defaultable debt and rational bubbles in the price of an asset, which can be pledged as collateral in a competitive credit pool. When the asset pledgeability is low, the down payment is high, and bubble investment is unleveraged, as in a standard rational bubble...