**The Role Of Superstars**

Our calibration of the persistence of the superstar shock is guided by the Gini index for wealth we want to match. However, we cannot estimate this persistence from standard data sets. This is not the case for the process governing regular households’ shocks, which is very close to the idiosyncratic component of the earnings process estimated by Storesletten, Telmer, and Yaron 2004) using data from the PSID. What is the contribution of superstars in shaping the overall level

of wealth inequality? To answer this question, we eliminate the superstar shock and recalibrate all economies so that they still produce the same aggregates. The results are shown in Table 5. The Gini index for wealth falls to 0.645, whereas in the benchmark economy with superstars the Gini index for regular households is 0.75 (its counterpart in the data is 0.77, see Table 1). Importantly, wealth inequality is slightly lower in the benchmark economy than in the one-asset economy and the diﬀerence in the Gini indices is about the same magnitude as in the speciﬁcation with superstars. Thus, adding the superstars not only helps us bring the overall Gini coeﬃcient for wealth closer to that of the data, but it also helps us obtain the implied level of wealth inequality for households outside the top 1 percent of the earnings distribution. Eliminating superstars, however, does not change our main result: the existence of illiquid assets and credit frictions mitigate somewhat the eﬀect of uninsurable idiosyncratic labor risk on wealth inequality resulting in slightly lower inequality.

**The Role Of the Persistence Of the Earnings Process**

Our benchmark model with illiquid assets and credit frictions delivers just slightly lower wealth inequality than the standard one-asset economy used in the literature. This result is obtained using an earnings process with very high persistence (consistent with the empirical evidence). To determine if our result is robust to this speciﬁcation, we simulate our model economy using a diﬀerent transition matrix for the earnings process holding the earnings shocks and the stationary distribution constant. In particular, we keep the probability of becoming a superstar unchanged but assume the probability of being one of the six regular types is the same for all types. The transition matrix is shown in Table 6. We recalibrate the relevant parameters so that aggregate statistics remain the same (the parameter values are in the notes to Table 7). We call this economy

the volatile benchmark economy. With lower persistence in the earnings process, wealth inequality is much lower than before (the Gini index is 0.635 in the volatile bechmark case). Houses are more equally distributed (the Gini coeﬃcient is 0.256) and ﬁnancial assets are less concentrated (the Gini coeﬃcient is 0.863). Housing wealth as a fraction of total wealth decreases in all quintiles – since earnings shocks are not persistent, households accumulate proportionally more liquid assets. As with the persistent earnings

process, housing wealth as a fraction of total wealth decreases with wealth but the diﬀerences across quintiles are less extreme. In the one-asset economy, wealth is also less concentrated (the Gini index is 0.676). Importantly, inequality is still higher in the volatile one-asset economy than in the volatile benchmark economy. Moreover, the diﬀerence is now more pronounced. In order to understand why this is the case, it is useful to construct a measure of permanent earnings in our model. Since we abstract from aggregate uncertainty, for any household whose earnings shock in period t is e, we can write permanent earnings, e, as the sum of current and future earnings: The (normalized) permanent earnings shocks with the volatile process and the original process are: {1.00, 1.01, 1.01, 1.02, 1.04, 1.09, 7.38} and {1.00, 1.22, 1.49, 1.84, 2.32, 3.04, 13.07}, respectively. Regular households are much more similar with the more volatile earnings process, they save less, which leads to lower inequality. For the same reason, houses are more similar across households, which results in less diﬀerences in wealth composition across quintiles. Furthermore, with less savings, more households are likely to be aﬀected by the frictions of our model, which explains the larger diﬀerence in inequality between the benchmark economy and the one-asset economy in this case. However, the diﬀerence in wealth inequality across models is still modest in magnitude.

This calibration allows us to illustrate further the predictions of our model regarding the distribution of houses. Table 8 presents key distributional statistics for homeowners in the data (ﬁrst panel) and in the model with both persistent and volatile earnings (second panel and third panels respectively). With persistent earnings, the Gini index for earnings is lower in the model than in

the data (0.408 vs. 0.479 in the data). This implies lower levels of inequality for any dimension of wealth but, nevertheless, the model with persistent earnings captures the remarkable similarity of the distributions of earnings and houses observed in the data. This feature of the data is not speciﬁc to 1998 as shown in Table 9 (although houses are becoming slightly more concentrated than earnings in the recent years). In our model, houses cannot be more unequally distributed than earnings for homeowners because the return to owner occupied housing falls with the size of the house. Note that with volatile earnings, the Gini coeﬃcient for houses is less than half the coef-ﬁcient for earnings (0.179 vs. 0.449).14 What causes this diﬀerence? The distributions of earnings and houses are quite close with persistent earnings in our model because permanent earnings and current earnings are highly correlated and households acquire houses according to their permanent income.15 While permanent income still guides house purchases with volatile earnings, current earnings in this case are not highly correlated with permanent income and the distributions are not

alike. In summary, high persistence is necessary to obtain a Gini index for wealth close to the one observed in the data. Nevertheless, earnings persistence cannot be estimated directly using the Survey of Consumer Finances.16 Our analysis in this section suggests that the distribution of houses might be used to discriminate among earnings processes that diﬀer in their persistence. That is, the distribution of houses gives us indirect evidence of the persistence of the earnings process. Changes in the down payment and the adjustment cost Over the last few decades, there has been a signiﬁcant reduction in the down payment required by

ﬁnancial institutions as well as a proliferation of home equity loans. In our model, a decrease in the parameter θ captures these ﬁnancial changes (although we cannot disentangle one from the other). We analyze the eﬀects of ﬁnancial liberalization on aggregate ratios and on the wealth distribution by simulating our model economy for diﬀerent values of the down payment requirement (keeping all other parameters constant). A decrease in the down payment requirement relaxes the borrowing constraint. Thus, fewer households are constrained and their purchases of houses increase. Therefore, inequality in houses should decrease (see Table 10). However, because a decrease in θ implies higher borrowing in the economy, ﬁnancial assets become more concentrated and overall, wealth inequality worsens. In general, the observed eﬀects tend to be small. This is because changes in the down payment aﬀect mainly liquidity constrained households, who are concentrated at the bottom of the wealth distribution.

Since their asset holdings amount to a very small fraction of aggregate wealth, the eﬀect of changing the down payment on total wealth is not large. For instance, the Gini of wealth with no down payment is 0.81, while with a 20 percent down payment it is 0.801. When the down payment is 100 percent, the Gini coeﬃcient for wealth is substantially lower, 0.736. Table 10 demonstrates that the distribution of ﬁnancial assets across quintiles is signiﬁcantly more concentrated for lower down payments. The counterpart to this result is in Table 11, where we show that the portfolio of poor households becomes substantially more illiquid as down payments fall. Table 11 also indicates that with lower down payments, the housing stock increases, the capital stock decreases and the interest rate rises (from 3.473 for a 100 percent down payment to 3.996 for no down payment).

With a rental market, as down payments decrease, homeownership increases (results not tabulated for brevity). For example, with a down payment of 50 percent, homeownership is only 49 percent, while with a 5 percent down payment the rate is 83 percent. As a result, inequality in housing decreases considerably more than without a rental market (the corresponding Gini coeﬃcients for housing for a 50 percent and a 5 percent down payment are 0.68 and 0.55 respectively). As before, because there is more borrowing, ﬁnancial assets become more concentrated with lower down payments. The eﬀect on overall inequality is even smaller in this case and can be non-monotonic in the down payment. For example, going from a 50 percent to a 20 percent down payment leads to less inequality (the Gini index for wealth goes from 0.8116 to 0.809), while going from a 20 percent to a 5 percent down payment increases inequality slightly (the Gini index increases from 0.809 to 0.8121). However, with or without a rental market, when down payments decrease the housing stock increases, the capital stock decreases and the interest rate rises (the equilibrium interest rate in the choice economy with a 50 percent down payment is 3.87 percent while the interest rate is 3.95 percent with a 5 percent down payment).

We also investigate the eﬀect of changes in the degree of illiquidity of houses. In Table 10, we report aggregates with a higher adjustment cost, with no adjustment costs and for an economy with liquid houses and no down payments (ρ = 0, θ = 0). As before, all remaining parameters are kept at their benchmark values. For a given down payment, lowering ρ makes the durable more attractive for households of all wealth levels, which leads to an important increase in the housing stock. Thus, the change in aggregate wealth composition seems more dramatic than the eﬀect of lowering down payments. Since the housing stock increases, the capital stock decreases and the interest rate sharply rises (from 3.71 to 4.25 when going from 10 percent to 0 percent in transaction costs). However, the eﬀect on the wealth distribution is negligible. In terms of wealth composition (see Table 11), decreasing the degree of illiquidity increases the housing wealth to total wealth ratio substantially for the lower quintiles.

**Final Comments**

In this paper, we explicitly model the existence of illiquid houses that serve as collateral for loans in the context of a heterogenous agents model with uninsurable earnings risk. Our goal is to asses whether the availability of houses mitigates the eﬀect of uninsurable idiosyncratic labor risk on wealth inequality. In our model, households can save in the form of a liquid asset and in the form

of illiquid houses that can be purchased on credit (minus a down payment). Our economy delivers slightly less wealth inequality than the one-asset economy analyzed in the literature. We show that the standard model is indeed equivalent to an economy with liquid houses, a zero down payment and a perfect rental market. The diﬀerence in terms of wealth inequality between both economies is small because the frictions of our model (required down payments and adjustment costs) mainly aﬀect the poor who only account for a small fraction of aggregate wealth. Importantly, our two-asset economy has one main advantage over the standard one-asset framework:it allows us to study wealth composition issues. Our model is able to reproduce all main patterns of the U.S. distribution: (1) wealth is more concentrated than earnings, (2) ﬁnancial assets are more concentrated than wealth, (3) households’ portfolios become more liquid as wealth increases, and (4) the distribution of houses and earnings for homeowners are very similar. A fairly persistent earnings process is necessary to obtain the latter result. We also show that the easing of collateral credit has an important eﬀect on the portfolios of the relatively poor.In this study, we abstract from some important issues that remain topics for future research. The most obvious and potentially important one, is the omission of life-cycle eﬀects. In the data,a household’s portfolio composition varies with age and it would be interesting to analyze whether or not the model can account for the life-cycle patterns of wealth holding and wealth composition. Also, some of the aggregate eﬀects discussed in this paper may be ampliﬁed when including life cycle considerations. An further extension could deal with the interaction between collateral credit and earnings ability. For example, access to collateral credit could increase the probability of becoming a superstar.

## No comments:

## Post a Comment