By Matteo Iacoviello and Marina Pavan
We present an equilibrium life-cycle model of housing where nonconvex adjustment costs lead households to adjust their housing choice infrequently and by large amounts when they do so. In the cross-sectional dimension, the model matches the wealth distribution, the age profiles of consumption, homeownership, and mortgage debt, and data on the frequency of housing adjustment. In the time-series dimension, the model accounts for the procyclicality and volatility of housing investment, and for the procyclical behavior of household debt. We use a calibrated version of our model to ask the following question: what are the consequences for aggregate volatility of an increase in household income risk and a decrease in downpayment requirements? We distinguish between an early period, the 1950s through the 1970s, when household income risk was relatively small and loan-to-value ratios were low, and a late period, the 1980s through today, with high household income risk and high loan-to-value ratios. In the early period, precautionary saving is small, wealth-poor people are close to their maximum borrowing limit, and housing investment, homeownership and household debt closely track aggregate productivity. In the late period, precautionary saving is larger, wealth-poor people borrow less than the maximum and become more cautious in response to aggregate shocks. As a consequence, the correlation between debt and economic activity on the one hand, and the sensitivity of housing investment to aggregate shocks on the other, are lower, as is found the data. Quantitatively, our model can explain: (one) 45 percent of the reduction in the volatility of household investment; (two) the decline in the correlation between household debt and economic activity; (three) about 10 percent of the reduction in the volatility of GDP.
This is an innovative model that tries to address issues that go beyond the the housing market: how can innovation in the financing of housing explain the evolution of the volatility of GDP, the volatility of housing investment and the relationship of household debt and economic activity? These issues have previously only been addressed with models where households invest and borrow some generic asset. Housing is different, because of its life-cycle aspect and its lumpiness, and this appears to matter.