Low Real Interest Rates and the Zero Lower Bound

How do low real interest rates constrain monetary policy? Is the zero lower bound optimal if the real interest rate is sufficiently low? What is the role of forward guidance? A model is constructed that can in- corporate sticky price frictions, collateral constraints, and conventional monetary distortions. The model has neo-Fisherian properties. Forward guidance in a liquidity trap works through the promise of higher future inflation, generated by a higher future nominal interest rate. With very tight collateral constraints, the real interest rate can be very low, but the zero lower bound need not be optimal.