Housing and Debt Over the Life Cycle and Over the Business Cycle

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.

4 Responses to Housing and Debt Over the Life Cycle and Over the Business Cycle

  1. M.H. says:

    The model assumes that some people are patient and some others are not. Models with heterogeneous discount rates are difficult to handle because the asset distribution becomes very skewed. This can be somewhat prevented by the finite lifetimes, and has the positive aspect that it generates large wealth Gini coefficients. Yet, I cannot understand how the authors managed to avoid (near) corner solutions in wealth accumulation.

  2. Matteo says:

    I am not sure what you mean by “near corner solutions in wealth accumulation”. At the individual level, there are obvious corners in wealth accumulation, and wealth-poor people are near these corners most of the time. For the dynamics of aggregate wealth and prices, it is not obvious why these corners should matter that much, because wealth-poor people don’t have much wealth after all. In any event, we do not assume linearity at the individual level, nor do we do at the aggregate level. The behavior of aggregate wealth is different from that of model with homogeneous discount rates, but it can still be characterized by only a few moments.

    P.S. As an aside, my own experience with working with these models (dealing with discussants and seminar participants) is at times funny: (1) some criticize the use of general equilibrium models to address such a question, arguing that one overcomplicates things; (2) some say that considering only a few moments to fit the dynamics of prices and wealth over time is a non-starter in models with large heterogeneity in wealth.

  3. M.H. says:

    Matteo, what I have in mind is the following: suppose there are two classes of people: patient and impatient. There is a market for savings, and the equilibrium interest rate will settle somewhere between the two discount rates. If agents are infinitely lived, the patient ones will keep accumulating, while the impatient ones will borrow more and more. Your economy may not even settle on a steady state.

    In your case, there are limits to this problem: agents are finitely lived, in particular. But your model economy will still suffer from the fact that agents are trending towards these corners during much of their lifetimes.

  4. Matteo says:

    Hi M.H.

    Your argument is correct in principle, but there are two counterarguments.

    First, as you suggest, finite lives mitigate the problem because under or over accumulation cannot continue forever.

    Second, there are borrowing constraints that prevent the impatients from going borrowing more and more: in our paper, it is the housing collateral constraint, but I think that in more general cases the constraint imposed by the natural borrowing limit will stop underaccumulation even in absence of the housing collateral constraint. The existence of these constraints prevents patients’ assets from rising, impatients’ assets from falling indefinitely.


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