Wealth Distribution and Durable Goods

In the United States, wealth is significantly more unequally distributed than earnings. Models with uninsurable idiosyncratic labor risk have been used widely to study the determinants of wealth inequality across households and to try to understand this fact. In these models, wealth inequality arises because a market to insure specific earnings risks does not exist and households self-insure by accumulating an asset (assumed to be perfectly liquid) that is used to smooth consumption over time. Our contribution is to quantitatively study the determinants of wealth inequality in economies where households not only accumulate liquid financial assets, but can also save in the form of illiquid assets such as a house. In reality, houses also provide collateral for loans. The question that we address is whether the inclusion of illiquid assets that serve as collateral amplifies or mitigates the effect of uninsurable idiosyncratic labor risk on wealth

inequality. 

This project is motivated by the fact that houses comprise almost 40 percent of the total wealth held by households in the U.S. economy. Moreover, according to the Survey of Consumer Finances, 92 percent of all available credit to consumers is collateral credit. Collateral debt accounts for 15.5 percent of aggregate household net worth and the average ratio of collateral credit to total debt across households is roughly 79 percent.In this post, we build a general equilibrium model economy of ex-ante identical households who face uninsurable idiosyncratic shocks to their labor endowments. Households have two means of

saving: liquid financial assets and illiquid houses. We model houses as assets that can be adjusted to any level at a given non-convex cost. Furthermore, houses can be financed (minus a down payment) and can be used as collateral for home equity loans. For simplicity, we allow no other form of credit. In our model, households derive utility from consumption of a nondurable good and durable goods from housing services. We assume there is no rental market for houses so households obtain housing services by purchasing residential stock. We calibrate the model economy so that its steady state statistics match selected aggregate statistics of the U.S. economy and data on the earnings distribution. In particular, we construct an earnings process that is a mixture of a process estimated directly from the data plus an extra shock that allows us to jointly match the observed level of earnings and wealth inequality. We assume there are two types of households, regular households and superstars.

The process that governs the earnings of regular households is calibrated using data for households outside the top 1 percent of the earnings distribution of households with positive earnings in the 1998 Survey of Consumer Finances (SCF-98), and is very similar to the idiosyncratic component of the earnings process estimated by Storesletten, Telmer, and Yaron (2004) using the Panel Study

of Income Dynamics (PSID). We calibrate the superstar shock level and its persistence so that the overall Gini index for earnings and wealth match those observed in the data. Our goal is to assess the role of illiquid assets in explaining the wealth distribution. To this end, we must compare our benchmark economy to the standard economy without illiquid assets considered in the literature. This comparison is not straightforward. We show that, in fact, Aiyagari’s (1994) economy is equivalent to an economy with liquid houses, no down payments, home equity loans with a loan-to-value ratio of 1, and a perfect rental market. We call this economy the one-asset economy. Using the same earnings process, we calibrate the one-asset economy to produce the same aggregates as our benchmark economy. We find that with illiquid assets and limited collateral loans wealth inequality is just slightly lower than in the one-asset economy. Wealth inequality is lower because the credit restriction implies that all households must hold some wealth in the form of the required down payment (this is not the case in the one-asset economy). The difference is small because the frictions of our model (required down payments and adjustment costs) mainly affect poor households that only account for a small fraction of aggregate wealth. Eliminating the superstars, introducing a rental market, or imposing a minimum size for the houses that households can purchase does not change our conclusions. However, when we lower the persistence of the earnings process, the frictions of our model have a larger effect because more households are affected by them.

 

In summary, the standard one-asset economy analyzed in the literature implicitly allows for collateral loans and the fact that one asset is illiquid does not have much of an effect over the wealth distribution. Nevertheless, our richer model allows us to study other dimensions of wealth inequality. For example, financial assets are more concentrated than total wealth, while residential assets are less concentrated than total wealth. Our model can replicate and explain these facts easily. Furthermore, we document that the earnings and the housing distributions are remarkably similar in the United States. Our model can account for this fact as long as the earnings process is fairly persistent. Finally, we can use our framework to analyze how changes in down payment requirements and the availability of home equity loans affect the economy. We find that as collateral credit expands, total wealth decreases, the interest rate increases and wealth inequality—measured by the Gini index—may worsen (more details are given throughout the paper). Furthermore, the easing of credit has a significant effect on the portfolios of poor households.