Quantitative easing and the loan to collateral value ratio

We study optimal monetary policy in a New Keynesian model at the zero bound interest rate where households use cash alongside house equity borrowing to conduct transactions. The amount of borrowing is limited by a collateral constraint. When either the loan to value ratio declines or house prices fall, we observe a decrease in the money multiplier. We argue that the central bank should respond to the fall in the money multiplier and therefore to the reduction in house prices or the loan to collateral value ratio. We also find that optimal monetary policy generates a large and persistent fall in the money multiplier in response to the drop in the loan to collateral value ratio.