Precautionary savings and the wealth distribution with illiquid durables

We study the role an illiquid durable consumption good plays in determining the level of precautionary savings and the distribution of wealth in a standard Aiyagari model (i.e. a model with heterogeneous agents, idiosyncratic uncertainty, and borrowing constraints). Transactions costs induce an inaction region over which the durable stock and the associated user cost are not adjusted in response to changes in income, increasing, on average, the volatility of non-durable consumption. The volatility of total consumption is then a function of the share of the durable good in the utility function and the width of the inaction region. We are particularly interested in parameterizations which increase the precautionary motive for saving through an increase in \"committed expenditure risk.\" We find, for an empirically relevant share of durable consumption and for all transaction costs below an upper threshold, that the level of precautionary savings is increasing in the transaction costs. Transaction costs have only a modest impact on the degree of wealth dispersion, as measured by the Gini index, as the associated increase in savings is close to linear in wealth. While we are unable to match the dispersion of wealth in the data, we increase the dispersion over a single asset model (Gini index of .71 for financial assets and .37 for total wealth) and we are able to match the relative dispersion of financial to durable assets, i.e. we find financial assets much more unequal than durable assets. We also match the ratio of housing wealth to total wealth for the median agent. We calibrate the model to data from the PSID, the CES, and the SCF.