In our benchmark economy, houses have a very similar distribution to that of earnings. In the data, however, houses are much more concentrated. In the model, the Gini indices for earnings and houses are 0.499 and 0.483, respectively, whereas in the data they are 0.497 and 0.649. This discrepancy may be explained by the fact that we are abstracting from a housing rental market. Thus, the question we address here is whether the existence of a rental market has an impact on the level of wealth inequality.
To investigate this possibility, we consider an alternative economy with an explicit rental market. Households can obtain housing services either by purchasing them in the market or by buying housing stock. We proceed as in Gervais (2002) and assume there is a ﬁnancial intermediary that buys housing stock and sells housing services in the market. Our main simpliﬁcation is that the ﬁnancial intermediary is not subject to adjustment costs when transacting the housing stock. As commonly used in the tenure choice literature (see Henderson and Ioannides 1983), we assume rental units depreciate at a higher rate than owner-occupied units to capture possible moral hazard problems in the rental market. We have labeled this economy the choice economy (we provide a more detailed description, as well as an equilibrium concept in Appendix B). Importantly, the economy is calibrated so that it produces the same aggregates as both the one-asset and the benchmark economy (parameters shown in Table 3). When calibrating the model we have one extra target, the homeownership rate (roughly 69 percent in the U.S.) and one more parameter, the additional depreciation of rental units, δf . An incremental depreciation of 0.6 percent allows us to obtain our target. The bottom panel of Table 4 presents the comparable wealth distribution measures.
The role of the housing rental market
Without a rental market, all households must buy some housing stock. Therefore, they are forced to keep some savings in the form of the required down payment. However, this wealth is illiquid. Since poor households face more ﬂuctuations in their income than relatively rich households (uncertain earnings are a higher proportion of total income for them), they feel more compelled to build a buﬀer stock of liquid assets to smooth their nondurable consumption. With a rental market, poor households can rent instead instead of owning a house and they do not need to accumulate extra savings, and as a result, wealth inequality is slightly higher than in the one-asset economy (the Gini index for total wealth increases from 0.801 to 0.809). The eﬀect on total wealth inequality is small because the introduction of the rental market aﬀects mainly the poor who account for just a small fraction of total wealth. However, the eﬀect on the distribution of houses is signiﬁcant.
The Gini coeﬃcient for houses rises from 0.483 to 0.585, closer to the number in the data, 0.649. In summary, inequality in houses substantially increases when a rental market is introduced but the overall level of wealth inequality rises just slightly.
The role of the minimum house size
In our computation strategy so far, we have not imposed any minimum house size available to consumers. Households can buy or rent whatever size house they desire. In absence of a rental market, imposing a minimum size for the houses individuals can purchase would produce a lower wealth inequality than in the benchmark economy. Without a rental market, households are forced to save more to accumulate the down payment if the house they must purchase is bigger. Poor households, who are most likely aﬀected, have to increase their savings proportionally more than wealthier ones. Also, by increasing the minimum size we are compressing the variance of the housing distribution. As a result, wealth inequality must be lower.
In the choice economy, however, the result would be the opposite. The larger the smallest house available, the higher the earnings of the household who is indiﬀerent between renting and buying, and the higher the fraction of households who rent. Therefore, the fraction of households whose portfolio return is equal to the interest rate is higher, and wealth inequality must be larger the larger the house minimum size. Nevertheless, inequality is never larger than in the one-asset economy, the case in which all households get the same portfolio return. The reason is the following. Consider the extreme case in which the minimum house size is so large that all households rent (and the economy is calibrated to produce the same aggregates). Further, assume that there is no moral hazard problems (i.e., the depreciation rate of owner occupied units and rental units is the same). In this economy, housing services are produced by a ﬁnancial intermediary nd households only hold liquid ﬁnancial assets. The ﬁnancial intermediary decides what proportion of ﬁnancial assets is rented out to the ﬁrm as capital and what proportion is sold to household as housing services (in equilibrium both returns are the same). In the one-asset economy, a household’s wealth is composed of ﬁnancial assets and houses but both are equally liquid so the two economies are equivalent. This can be seen by comparing the second and fourth panels in below: the one-asset economy and the high minimum size economy just described produce identical distributions.