I study the effects of large scale asset purchases in the mortgage market (QE) on aggregate consumption in a continuous-time heterogeneous agent New Keynesian model with lumpy housing and frictional financial intermediation. I find a salient house price channel of QE. In the presence of binding leverage constraints of intermediaries, QE is relevant through decreasing the borrowing spread. Since housing adjustment is lumpy, this lower spread substantially increases housing demand and house prices through accelerating the adjustment threshold. With heterogeneous agents and borrowing constraints, these higher house prices transmit to aggregate consumption through wealth, collateral, and general equilibrium effects.

We study the effects of movements in the loan-to-value (LTV) ratio on inequality in a state-of-the-art New Keynesian model with heterogeneous households and lumpy housing. We find that a loosening of the LTV ratio substantially lowers inequality. We further show that through redistributing resources from households with low marginal propensities to consume (MPCs) to households with high MPCs, movements in the LTV ratio have a sizable impact on macroeconomic aggregates. A loosening of the LTV ratio by 1 pp increases aggregate consumption and output by 0.45% and 1.3%, respectively.

We show that in a New Keynesian model with household heterogeneity, fiscal policy can be a perfect substitute for monetary policy. Three simple conditions for consumption taxes, labor taxes, and the government debt level are sufficient to induce the same consumption and labor supply of each household and, thus, the same allocation as interest rate policies. When monetary policy is constrained by a binding lower bound, a currency union, or an exchange rate peg, fiscal policy can therefore replicate any allocation that hypothetically unconstrained monetary policy would generate.