A Dynamic Model of the Racial Wealth Gap

Over the past three decades, the wealth gap between Black and White Americans has widened. The fact that it remains much larger than the income gap implies that saving rates and portfolio returns play decisive roles in its existence. The importance of portfolios can be illustrated by comparing the historical evolution of the racial wealth gap with a counterfactual in which Black households had invested their wealth in stocks and housing in the same proportions as White households. Figure 1 shows that, in such a counterfactual, the wealth gap would have narrowed substantially from 1989 to 2022. A comparable convergence would have occurred had equity returns not outpaced house prices over this period (Derenoncourt et al. 2023).

In this paper, we study whether economic factors can explain differences in the portfolio decisions and consumption choices of Black and White households and, consequently, why the racial wealth gap greatly exceeds the income gap. To this end, we analyze the implications of various racial disparities through the lens of a life-cycle model. Besides the earnings gap, we consider disparities in economic factors such as income risk, intergenerational transfers, household structure, medical spending, mortality, borrowing costs, and asset returns. We also model the system of taxes and transfers, including progressive government programs providing retirement income, health insurance, and protection against poverty. The focus of our analysis is what we call the excess racial wealth gap: the portion of wealth inequality that cannot be mechanically accounted for by the earnings gap.

In the model, disparities in economic factors are exogenous and calibrated to match data and estimates from the literature. However, their effect on wealth accumulation is not limited to their direct monetary cost, but also depends on the endogenous response of households, who optimally and dynamically adjust their portfolios and consumption behaviors in response to their circumstances. In principle, these endogenous responses can either amplify or mitigate the effects of racial disparities on wealth accumulation. Modeling these responses allows us to quantify the multiple mechanisms through which any single economic factor shapes wealth accumulation and its net overall effect.

The first takeaway of our study is that economic factors explain well why Black and White households hold different portfolios. The second takeaway is that, for many economic factors, the net effect on wealth accumulation is smaller than one would expect. On the one hand, adverse economic conditions can make it difficult to build wealth; but on the other hand, in the face of such adversity, households can respond by adjusting their savings. These competing forces make it harder for any one factor to explain a significant share of the racial wealth gap. When we consider all channels jointly, we find that the dozen economic disparities in our model together explain roughly half of the excess racial wealth gap.¹ Among these, the earnings gap, the gap in intergenerational transfers, differences in expected returns to wealth, and health expenditures are the most important, but each of these factors accounts for only about 11–13% of the total.

The earnings gap contributes to differences in wealth-to-earnings ratios because lower incomes limit access to asset markets—particularly homeownership—and because progressive social programs create a positive relationship between income and optimal saving rates. Differences in expected returns to wealth also matter: higher returns could, in principle, induce White households to consume more, since the return gap makes them effectively richer (an income effect). However, this offsetting force is balanced by a stronger incentive to save when returns are higher (a substitution effect). Finally, disparities in health expenditures widen the wealth gap because White households face higher out-of-pocket medical costs later in life, which raises their optimal saving rate earlier in life.

Our findings show that the impact of any single economic disparity on the racial wealth gap is difficult to assess. A natural approach for empirical researchers would be to estimate its effect based on its lifetime monetary cost, but our results demonstrate that such static calculations can be misleading. In a dynamic setting, households adjust their consumption and saving behavior in response to economic conditions, which can substantially offset the direct effects of these disparities. As a result, the excess wealth gap represents a deeper puzzle than such calculation would suggest. We illustrate this point quantitatively: in our model, the economic factors explaining differences in portfolio returns have limited effects on the wealth gap, because the resulting loss in returns is offset by changes in consumption behaviors.

To understand the intuition behind this result, consider as an example the role of stock market returns over the past forty years. As Figure 1 shows, Black households invested less in equities, and thus earned lower portfolio returns. We find that a primary explanation for the gap in equity investment is that Black workers are more likely to lose their jobs during recessions, and therefore should invest less in stocks (Catherine 2022; Derenoncourt et al. 2024). This slows wealth accumulation by lowering returns. But at the same time, higher income risk increases precautionary savings (Zeldes 1989). Because portfolio and consumption responses move wealth in opposite directions, matching the equity investment gap only explains a small fraction of the wealth gap.

The inheritance gap offers a second example. White families are far more likely to receive sizable bequests. This advantage unambiguously increases the racial gap in lifetime income. However, if intergenerational transfers are even partly anticipated, White families should choose to save less for retirement. This reduction in White savings rates reduces the incidence of bequests on the racial wealth gap. The inheritance gap therefore amplifies wealth inequality only to the extent that the timing and size of bequests are uncertain, preventing households from fully smoothing consumption in anticipation of future transfers.

For some economic disparities, adjustments in consumption and portfolio choices can also amplify the incidence on wealth. An important example is differences in rates of return on the same asset class. A lower rate of return not only slows down the growth of a given portfolio, but it can also discourage households from saving and from building higher-risk, higher-return portfolios. For instance, higher mortgage rates (Ghent et al. 2014) and higher property taxes (Avenancio-León and Troup 2022) reduce the optimal homeownership rate and leverage of Black households, further reducing their accumulation of wealth. Conversely, the lower price-to-rent ratios in Black neighborhoods (Diamond and Diamond 2023) make homeownership more affordable and more profitable, increasing Black wealth and even dominating these effects quantitatively.

We also consider the role of progressive social programs, which can act as substitutes to private wealth and play a greater role in the lower part of the income distribution. We explicitly model Social Security, Medicare, Medicaid, and various parts of the social safety net. With the exception of Medicare, the benefit formulas of these programs favor low-income and/or low-wealth families, and therefore reduce their need to save for retirement, unexpected income losses, or medical expenditures. They therefore reduce savings rates in the lower part of the income distribution, amplifying the effect of the racial income gap on the wealth gap. Using counterfactual policy experiments, we find that the progressive design of these programs can explain only a small share of the wealth gap in excess of the earnings gap.

Of course, our study does not explore the entire set of potential causes of the racial wealth gap. However, our findings shed light on an important distinction between measuring the monetary and welfare costs of economic disparities to Black Americans and explaining the racial wealth gap. We argue that, despite the extensive list of documented disparities, the racial wealth gap is hard to explain within the framework of a life-cycle model. By contrast, we find that differences in the composition of wealth between Black and White Americans can be rationalized using a standard portfolio choice model. Importantly, the fact that an economic factor has a limited effect on the racial wealth gap does not mean that its welfare cost is also small. A second contribution of our paper is to quantify these welfare costs and show that they are unambiguously substantial.

Related literature

Our paper contributes to the large literature on racial wealth inequality in the United States. In a recent study, (Derenoncourt et al. 2023) find that the racial gap in market wealth has widened over the past four decades, a trend that they attribute to differences in the composition of Black and White portfolios. Inspired by their findings, one goal of our paper is to explain these portfolio differences. In doing so, we bridge the gap between studies on racial wealth inequality and the household finance literature on portfolio choices. In particular, we show that models with countercyclical income risk (Storesletten et al. 2007; Lynch and Tan 2011; Catherine 2022) can explain why Black workers invest relatively less in stocks. In the data, higher income risk has been associated with lower equity investment (d’Astous and Shore 2024; Betermier et al. 2012; Bonaparte et al. 2014; Fagereng et al. 2018). In particular, workers facing more tail risk during economic downturns—like Black workers—invest less in stocks (Catherine, Sodini, et al. 2024).

In a contemporaneous study, (Derenoncourt et al. 2024) also argue that unemployment risk can explain the equity investment gap. Unlike these authors, we find the overall effect on the wealth gap to be small because higher income risk also increases precautionary savings.² Our emphasis on endogenous consumption responses links the literature on racial wealth inequality to theoretical (Zeldes 1989; Aiyagari 1994; Carroll 1997; Gourinchas and Parker 2002) and empirical studies (Carroll and Samwick 1998; Banks et al. 2001; Bertola et al. 2005; Fagereng et al. 2017) on precautionary savings in the presence of uninsurable risk. We argue that findings from this literature make the racial wealth gap harder to explain. As existing papers have shown, low precautionary savings among Black households make it more difficult for them to smooth consumption (Ganong et al. 2023) and take advantage of retirement savings incentives (Choukhmane et al. 2024).³

Our analysis also points to the important but conflicting roles of heterogeneous returns on wealth. Recent studies have underlined the importance of the positive relationship between wealth and returns in the evolution of wealth inequality in recent decades (Bach et al. 2020; Greenwald et al. 2021; Fagereng et al. 2021; Catherine et al. 2023). We show that portfolio rebalancing can amplify the effect of disparities in rates of returns. Black Americans may earn lower returns on wealth due to higher mortgage rates (Ghent et al. 2014), higher property taxes (Avenancio-León and Troup 2022) and discounts when selling properties in distress (Kermani and Wong 2024). On the other hand, (Diamond and Diamond 2023) find that Black Americans benefit from higher total returns on housing thanks to higher implicit rental yields. Their ability to become homeowners and capture these returns may, however, be hindered by higher financial constraints and lower access to credit (Charles and Hurst 2002; Gupta et al. 2024). Beliefs regarding returns can also play an important role: (Boerma and Karabarbounis 2023) find that a lack of knowledge regarding returns to entrepreneurship could explain the racial gap in private business ownership.

Roadmap

The remainder of this paper is organized as follows. Section 1 describes our life-cycle model and Section 2.1 discusses our data. In Section 2, we calibrate the model and, in particular, economic disparities between Black and White households. We estimate preference parameters and assess the model’s ability to match the data in Section 3. In Section 4, we conduct counterfactual experiments to assess the effect of each economic factor on the balance sheet of Black Americans and the wealth gap. We consider potential model extensions in Section 5. Section 6 concludes.

Model

This section lays out the assumptions of our life-cycle model. Households are indexed by \(i\) and differ in demographic characteristics including age \(a\in\{1,\dots,a_{\rm max}\}\), race \(j\in\{B,W\}\), number of adults \(n_A\in\{1,2\}\), number of earners \(k\in\{1,2\}\), number of children \(n_{Ct}\), and household size \(N_{it} = n_A+n_{Ct}\). Let \(\omega_j\) denote the percentage of the population in racial group \(j\).

Asset returns

Riskfree bond

Households can invest in a riskless one-period bond. The gross return on this bond, denoted \(R_{fj}\), is constant and depends on race \(j\). As expected returns on all assets (bonds, stocks, and housing) depend on the riskfree return, any difference between \(R_{fB}\) and \(R_{fW}\) applies to all asset classes.

Stock market

The stock market delivers risky return \(R_{St}\). The log return is the sum of two components: \[ r_{Sjt} = r_{fj} + s_{1t} + s_{2t}. \] The term \(s_{2t}\) represents i.i.d. normal noise with variance \(\sigma_{s_2}^2\). The term \(s_{1t}\) represents the cyclical component of returns, which is correlated with the condition of the labor market. With probability \(p_s\), \(s_1\) is likely to be low, representing a stock-market crash. Mathematically, this is summarized by the normal mixture distribution \[ s_{1t} = \left\{ \begin{array}{lll} s^-_{1t} \sim \mathcal{N}(\mu_s^-,\sigma_{s_1}^2) & with probability & p_s, \\ s^+_{1t} \sim \mathcal{N}(\mu_s^+,\sigma_{s_1}^2) & with probability & 1-p_s, \\ \end{array} \right. \] where \(\mu_s^-\) is the average excess return in a crash and, of course, \(\mu_s^+>\mu_s^-\).

House prices

Households face stochastic local house prices and choose whether to own or rent. One unit of housing has local market price \(P_t\), implying gross return \(R_{Ht}=P_t/P_{t-1}\). Log housing returns (price changes) follow \[ r_{Hjt} = p_{jt}-p_{j,t-1}= r_{fj} + \mu_p + \varepsilon_{pt}, \] where \(\varepsilon_{pt}\) is i.i.d. normally distributed with variance \(\sigma_p^2\). Because the correlation between housing and equity returns is almost zero in the data (Flavin and Yamashita 2002), we assume that shocks to these asset prices are uncorrelated.

Labor income

Before retirement, household \(i\) receives labor income \(L_{it}=L_{1t}\cdot L_{2it}\), the product of the national wage index \(L_{1t}\) and an idiosyncratic income component \(L_{2it}\).

Aggregate labor income

As in the data, the growth in the national wage index \(L_1\) is correlated with both stock-market and housing returns. Specifically, we assume that its log growth rate is \[ l_{1t}-l_{1,t-1}= \mu_l + \lambda_{ls} s_{1t} + \lambda_{lp} \varepsilon_{pt} + \varepsilon_{lt}, \] where \(\varepsilon_{lt}\) are normally distributed shocks with variance \(\sigma_l^2\); \(\mu_l\) is the growth rate of aggregate income; and \(\lambda_{ls}\) and \(\lambda_{lp}\) govern the sensitivity of income growth to stock-market crashes and house-price shocks, respectively.

Idiosyncratic labor income

The idiosyncratic component \(L_{2it}\) is the product of a deterministic trend \(f_{it}\), a persistent component \(z_{it}\), and a transitory component \(\eta_{it}\): \[ L_{2it} = \exp\{f_{it} + z_{it} + \eta_{it}\}. \] The deterministic component \(f_{it}\) is a function of the household’s age \(a_t\), race \(j\), and structure \(\{n_A,k\}\) — that is, \(f_{it}=f(a_t,j,n_A,k)\).

The persistent component \(z_{it}\) captures the fact that workers face long-lived shocks to their labor income from negative events, like job loss, and positive events, like promotions. We assume \(z_i\) evolves as an AR(1) with cyclical skewness, \[ z_{it} = \rho_{z,k}z_{it-1} + \zeta_{it}, \] where shocks arrive according to a mixture of normals: \[ \zeta_{it} = \left\{ \begin{array}{lll} \zeta^-_{it} \sim \mathcal{N}\left(\mu^{-}_{z,jkt},\sigma^{-^2}_{z,k}\right) & with probability & p_{z,k}, \\ \zeta^+_{it} \sim \mathcal{N}\left(\mu^{+}_{z,jkt},\sigma^{+^2}_{z,k}\right) & with probability & 1-p_{z,k}. \\ \end{array} \right. \] With probability \(p_{z,k}<0.5\), the average household of demographic \(\{j,k\}\) experiences a persistent permanent-income shock \(\mu^{-}_{z,jkt}\). Unconditional cross-sectional skewness is negative, so these shocks tend to be negative. Bad shocks tend to be more negatively skewed in bad macroeconomic states, so we assume that \(\mu^{-}_{z,jkt}\) is lower when aggregate income falls, including during stock-market crashes. The sensitivity of \(\mu^{-}_{z,jkt}\) to aggregate income depends on the number of earners \(k\), because multiple incomes diversify risk, and on race \(j\), because Black and White individuals have different labor-income cyclicality. These conditions are captured by letting the mean negative income shock be an affine function of wage-index growth: \[ \mu^{-}_{z,jkt} = \overline{\mu^{-}_{z,k}} + (\alpha_j -1)(l_{1t}-l_{1,t-1}) + \lambda_{zl,k}\alpha_j(l_{1t}-l_{1,t-1}). \] The coefficients \(\alpha_j\) are “racial income betas" and govern the excess cyclical skewness of each racial group—their population-weighted average is \(\sum_j\omega_j\alpha_j=1\). The more negative is \(\mu^{-}_{z,jkt}\), the more skewed is the cross-sectional distribution; the larger is \(\alpha_j\), the more cyclical is this skewness for racial group \(j\). To ensure that idiosyncratic shocks \(\zeta_{it}\) are mean-zero in the population of households, we impose the condition that \(\mu^{+}_{z,jkt}\) satisfies \[ p_{z,k} \mu^{-}_{z,jkt} + (1-p_{z,k}) \mu^{+}_{z,jkt}= (\alpha_j-1)(l_{1t}-l_{1,t-1}) \] for each \(j\) and \(k\).⁴ Finally, we assume \(\sigma^{-}_{z,k}\gg \sigma^{+}_{z,k}\) such that “big events" like unemployment and promotions occur principally in the \(\zeta^-_{it}\) state.

The final component of idiosyncratic income is the transitory shock \(\eta_{it}\), which represents short-lived noise in income. It is also drawn from a mixture of normals: \[ \eta_{it} = \left\{ \begin{array}{lll} \eta^-_{it} \sim \mathcal{N}\left(0,\sigma^{-^2}_{\eta,k}\right) & if & \zeta_{it}=\zeta^-_{it}, \\ \eta^+_{it} \sim \mathcal{N}\left(0,\sigma^{+^2}_{\eta,k}\right) & if & \zeta_{it}=\zeta^+_{it}. \end{array} \right. \] The occurrence of each state coincides with the occurrence of the persistent income shock, capturing the idea that large persistent and transitory shocks may happen at the same time.

Health expenditures and benefits

In addition to income risk, households face exogenous shocks to their health that require medical expenditures \[ M_{it} = \exp\{g_{it} + \delta_{it}\}L_{1t}, \] where \(g_{it}=g(a_t,j,n_A)\) is a deterministic function and \(\delta_{it}\) is a stochastic component following \[ \delta_{it} = \rho_\delta(j,n_A)\delta_{i,t-1} + \sigma_\delta(j,n_A)\epsilon_{\delta it}, \] where \(\epsilon_{\delta it}\sim N(0,1)\).

Households are partially insured against these medical expenses either privately or through government programs. Let \(M_{it}^{\rm OOP}\) denote the portion of \(M_{it}\) not covered by insurance or transfers, i.e. the out-of-pocket expenditure.

Before retirement, households are covered by Medicaid if eligible or insured by private insurance. Private insurance requires an annual premium of \(\Phi_{Mt}=0.1L_{1t}\)⁵ and covers most medical expenses, leaving an out-of-pocket payment \[M_{it}^{\rm OOP}=\min\{0.3M_{it},0.15L_{1t}\}.\]

In retirement, households are covered by Medicare and, if eligible, Medicaid. Appendix 8.2 provides the details regarding the computation of these benefits, which we only summarize here. We assume retirees pay an annual premium \(\Phi_{Mt}=0.03n_AL_{1t}\) for Medicare Plan B, which covers 66% of their medical expenses as in (De Nardi et al. 2016).

Households can be eligible for Medicaid through two pathways: “categorically needy” or “medically needy.” First, households with income below 138% of the federal poverty line \(\varrho(N)\) during working period or with eligibility for Supplemental Security Income (SSI) benefits during retirement qualify for Medicaid under “categorically needy.” They thus receive benefits equal to total medical expenditure \(B_{it}^{\rm M}=M_{it}\). Second, households can be eligible based on the “medically needy” rule if their medical expenses (net of Medicare payments if in retirement) exceed a combined fraction of their income and non-housing wealth. In this case, households pay out-of-pocket expenses until they cross the eligibility threshold. The remainder of their expenses is then covered by Medicaid.

Taxes, benefits, and inheritances

To account for the effects of taxes and transfers in the U.S., we model the Social Security system, the largest social safety net programs, and taxes.

Social Security

Before retirement, households pay \(12.4\%\) of their earnings towards the Social Security system, up to the maximum taxable earnings cap, which represents 2.5 times the wage index \(L_{1t}\) per earner. Thus payroll tax expenses are: \[ T_{it}^{\rm SS}=0.124 \min \left\{L_{it}, (2.5 k) L_{1t} \right\} \]

Households retire at a full-retirement age \(a_{\rm ret}\). Social Security benefits are a function of lifetime income, summarized by the average indexed yearly earnings (AIYE) at age 60. The AIYE is the average of past taxable earnings, adjusted for growth in the wage index. Mathematically, it is defined as: \[ \textrm{AIYE}_{it} = \frac{1}{t-t_0}\sum_{s=t_0}^t \min\left\{L_{is}, (2.5 k) L_{1s} \right\}\frac{L_{1t_{60}}}{L_{1s}}, \] where \(t_{60}\) denotes the year the household reaches age 60.

Benefits are a concave, piece-wise linear function of the AIYE and indexed to inflation. The concavity of the benefit function offers higher replacement rates to workers with lower lifetime earnings. Specifically, a single-adult household receives benefits \[ B_{it}^{\rm SS} = \left\{ \begin{array}{ll} 0.9 \textrm{AIYE}_{it_{60}} & if \textrm{AIYE}_{it_{60}}/L_{1t_{\rm ret}} < 0.2, \\ 0.116L_{1t_{\rm ret}} + 0.32 \textrm{AIYE}_{it_{60}} & if 0.2 \leq \textrm{AIYE}_{it_{60}}/L_{1t_{\rm ret}} < 1.25, \\ 0.286L_{1t_{\rm ret}} + 0.15 \textrm{AIYE}_{it_{60}} & if \textrm{AIYE}_{it_{60}}/L_{1t_{\rm ret}}\geq 1.25. \\ \end{array} \right. \] where \(t_{\rm ret}\) denotes the retirement year.

For a double-income household, the formula () needs to apply to the first and second earner separately because (i) the benefits of the higher earner are capped at \(2.5\) times the average wage and (ii) the lower earner is guaranteed a minimum benefit equal to one-half of the higher earner’s benefit (the “spousal benefit"). Thus, if the higher earner accounts for a fraction \(w_1\) of total household income, then that earner’s benefits \(B_{i_1t}^{\rm SS}\) are calculated from () using \(\min\{w_1\textrm{AIYE}_{it_{60}},2.5L_{1t_{\rm ret}}\}\) instead of just \(\textrm{AIYE}_{it_{60}}\). The lower earner’s benefits \(B_{i_2t}^{\rm SS}\) are then the maximum of \(0.5B_{i_1t}^{\rm SS}\) and the benefit calculated from () using \((1-w_1)\textrm{AIYE}_{it_{60}}\).

Social safety net

Poorer households receive additional support through two government welfare programs: the Supplemental Nutrition Assistance Program (SNAP, or food stamps) during working life, and the Supplemental Security Income (SSI) program during retirement.

Households are eligible for SNAP benefits if they meet two criteria, laid out in full in Appendix 8.1. The gross income test, stipulates that “gross income”—defined as \(L_{it}^{\rm g}\equiv L_{it}/0.85\)—must fall below 130% of the poverty threshold \(\varrho(N)L_{1t}\) for a household of size \(N\).⁶ The net income test, requires that “net income” remain below the poverty line. Net income equals gross income minus a standard deduction (which depends on family size), an earned-income deduction, and a shelter-cost deduction (accounting for rent, property taxes, or mortgage payments). Households meeting both criteria receive SNAP benefits equal to a fraction \(b^{\rm SN}(N)\) of the wage index minus 30% of net income.

SSI benefits support retirees with very low Social Security benefits. Eligible one-adult households receive a supplement ensuring that total retirement income reaches at least 17.74% of the wage index in that year, provided that their wealth remains below approximately 3% of the wage index. For two-adult households, the wealth threshold rises to 4.17%, and SSI guarantees total retirement income of at least 26.62% of the wage index.

In summary, welfare benefits from the social safety net are \[ B_{it}^{\rm SN} = \left\{ \begin{array}{ll} \left(b^{\rm SN}(N_{it})L_{1t}-0.3 L_{it}^{\rm n} \right)^+ & if L_{it}^{\rm g} \leq 1.3\varrho(N_{it})L_{1t}, L_{it}^{\rm n} \leq \varrho(N_{it})L_{1t}, \text{ and } t < t_{\rm ret},\\ \left(0.1774 L_{1t}-B_{it}^{\rm SS}\right)^+ & if W_{it} < 0.0314 L_{1t}, t \geq t_{\rm ret}, \text{ and } n_A=1,\\ \left(0.2662 L_{1t}-B_{it}^{\rm SS}\right)^+ & if W_{it} < 0.047 L_{1t}, t \geq t_{\rm ret}, \text{ and } n_A=2.\\ \end{array} \right. \]

Income taxes and tax credits

Households pay income taxes on labor income and Social Security benefits. The U.S. has a progressive income tax system: marginal tax rates increase in taxable income. Let \(T_{it}^{\rm inc}\) denote the total income tax payments. We also model the earned income tax credit (EITC), a program through which households earning low labor income receive a gradual benefit. We denote this benefit as \(B_{it}^{\rm EITC}\). Finally, Medicare is funded by a tax on labor income \(T^M_{it}\). The computations of income taxes and tax credits are detailed in Appendix 8.3.

Disposable income

Disposable income \(Y_{it}\) is the sum of its labor income \(L\) and non-medical benefits \(B=B^{\rm SS}+B^{\rm SN}+B^{\rm EITC}\) net of taxes \(T=T^{\rm SS}+T^{\rm inc} + T^{\rm M}\): \[ Y_{it}=L_{it} + B_{it}- T_{it}. \] Households also pay out-of-pocket medical expenses \(M_{it}^{\rm OOP}\) (i.e., net of payments by private insurance, Medicare, and Medicaid) and medical premiums \(\Phi_{Mt}\).

Inheritance

Households receive inheritances over the life cycle. The arrival rate and size of inheritance are functions of age \(a_t\), race \(j\), and income \(\hat{y}_{it}\) (which equals the permanent income shock \(\zeta_{it}\) in working life or Social Security benefits \(B_{it}^{\rm SS}\) in retirement). In summary, inheritance is distributed according to \[ I_{it}=\begin{cases} I_{it}^+ \sim \textrm{lognormal}(\mu_I(a_t,j,\hat{y}_{it}),\sigma_I(j)^2) &\textrm{with prob. }p_I(a_t,j,\hat{y}_{it}), \\ 0 &\textrm{otherwise}. \end{cases} \] The probability \(p_I(a_t,j,\hat{y}_{it})\) and mean \(\mu_I(a_t,j,\hat{y}_{it})\) are race-dependent polynomials of age and income and the variance \(\sigma_I(j)^2\) is a race-dependent constant. In making this assumption, we capture the fact that inheritances are both more frequent and conditionally larger for White and high-income households in the data.

Housing market

Households can either rent or own a house. Let \(H_{it}\) denote the size of the house they choose to occupy and \(P_tH_{it}\) its value. Renters must pay \(P_{t}H_{it}/\Upsilon_j\) to occupy a house of size \(H_{it}\), whereas homeowners must pay property taxes \(P_{t}H_{it} \tau^H_j\). The cost of occupying a house is therefore: \[ X_{it} = \left\{ \begin{array}{ll} P_{t}H_{it}/\Upsilon_j & if renter,\\ P_{t}H_{it} \tau^H_j & if homeowner,\\ \end{array} \right. \] where \(\Upsilon_j\) is the price-to-rent ratio, \(\tau^H_j\) is the property tax rate, and both depend on race.

When purchasing a property, households are subject to two constraints. First, the property price must be above a minimum value as in (Cocco 2005), which represents a multiple \(\kappa_{\rm min}\) of the wage index. Second, the purchase can be financed by a one-year renegotiable mortgage, but borrowers are subject to a downpayment constraint, such that the property cannot be worth more than a multiple \(\kappa_{\rm max}\) of their net worth. Overall, the house value must respect the condition:

\[ \underbrace{\kappa_{\rm min}L_{1t}}_{\textrm{minimum house value}} \leq P_tH_{it} \leq \underbrace{\kappa_{\rm max}W_{it}}_{\textrm{downpayment constraint}}. \]

Borrowers must pay a spread between the mortgage rate \(r_{Mit}\) and the riskfree interest rate \(r_{fj}\). This spread depends on household’s disposable income, leverage (debt-to-value ratio), and race. Because of leverage, wealth can become negative when a of large negative house price shock occurs. In this case, the agent defaults, gives up all assets, and starts the next period with zero wealth, housing, and debt.

When selling a property, households incur proportional transaction costs equal to a percentage \(c_H\) of the property value. In addition, households selling in distress sell at a discount \(\theta_j > 0\). We define a distress sale as any transaction occurring in the large-income-shock state (\(\zeta_{it}=\zeta_{it}^-\)). The overall transaction cost is: \[ \Phi_{Hit} = \left\{ \begin{array}{ll} c_HP_{t}H_{it} + \theta_j\mathbb{I}_{\zeta_{it}=\zeta_{it}^-}P_{t}H_{it-1} & if selling\\ 0 & otherwise.\\ \end{array} \right. \]

Other frictions

Liquidity constraint in large-income-shock state

In the large-income-shock state (\(\zeta_{it}=\zeta_{it}^-\)), a household can only finance its consumption against income and the liquid part of its wealth, which we assume to be a fraction \(\varpi\) of \(W_{it}\). This amounts to the constraint \[ (Y_{it} + \varpi W_{it} - C_{it})\mathbb{I}_{\zeta_{it}=\zeta_{it}^-} \geq 0, \] where \(Y_{it}\) is disposable (i.e., post-transfer) income, defined below. Homeowners can fully liquidate their wealth by selling their house but are then subject to the distress sale discount.

Stock market participation costs and short-sale constraint

Participation in the stock market results in two forms of cost. The first is a fixed cost that grows in proportion to the aggregate wage: \[ \Phi_{\pi it} = \left\{ \begin{array}{ll} c_\pi L_{1t} & if \pi_{it} > 0\\ 0 & otherwise.\\ \end{array} \right. \] The second is a proportionate cost of capital-gains taxation. To account for these taxes, we will consider post-tax equity returns in the data. A household cannot short-sell or borrow against future earnings.

Households

Evolution of wealth

Wealth \(W_{it}\) is defined as the sum of asset holdings before receipt of income and before expenditures on consumption, housing, medical costs, and participation costs. Hence, wealth evolves as follows: \[ W_{it+1} = \left( W_{it}+Y_{it} + I_{it} -C_{it} -X_{it} - M_{it}^{\rm OOP} - \Phi_{Mit} - \Phi_{Hit} - \Phi_{\pi it} \right)R_{Wi,t+1}, \] where the gross return on wealth equals \[ R_{Wi,t+1} = R_{fj}+ \pi_{it}(R_{Sj,t+1}-R_{fj})+h_{it}(R_{Hj,t+1}-R_{fj}) - (h_{it}-1)^+(R_{Mit}-R_{fj}). \] In this wealth-return expression, \(\pi_{it}\) is the equity share and \(h_{it}\) is the housing share. The term \((h_{it}-1)^+(R_{Mit}-R_{fj})\) represents the fact that, if \(h_{it}>1\), the household requires a mortgage and must pay the premium on it.

Preferences and objective

Household have constant relative risk aversion preference and choose goods consumption \(C_{it}\), housing consumption \(H_{it}\), equity share \(\pi_{it}\), and homeownership status \(\mathbb{I}_{{\rm own},it}\) to maximize expected lifetime utility: \[ V_{it} = \max_{\{C,H,\pi,\mathbb{I}_{\rm own}\}} \left\lbrace \frac{1}{1-\gamma}\left(\frac{C_{it}^{1-\nu} H_{it}^{\nu}}{\sqrt{N_{it}}}\right)^{1-\gamma} + (1-m_{it}) \beta \mathbb{E}_{t} V_{it+1} \right\rbrace \] where \(\gamma\) is the coefficient of relative risk aversion, \(\nu\) captures the preference weight on housing relative to goods, \(\beta\) is the subjective discount factor, and \(m_{it}=m(a_t,j,n_A)\) is the period mortality rate that depend on age, race, and household composition. Total household consumption is divided by \(\sqrt{N_{it}}\) to account for synergies within the family.⁷

We abstract from modeling bequest motives explicitly. Introducing such motives would add flexibility to match the wealth accumulation profile over the life cycle. However, differences in estimated bequest motives and discount factors between Black and White households can both be interpreted as differences in their effective preference for the present. We therefore summarize this heterogeneity using a single structural parameter, which offers a more parsimonious and transparent interpretation of the unexplained component of the racial wealth gap. Importantly, even without bequest motives, the model accurately reproduces the wealth trajectory of Black households during retirement, the population for which we conduct all our counterfactual analyses.

Model calibration

This section reviews the ways in which the economic conditions faced by Black and White households differ, and how these differences are reflected in the model calibration.

Data

Our calibration and estimation rely mainly on three public data sources. First, we use the Survey of Consumer Finances (SCF) to analyze the empirical composition of balance sheets. Second, we use the Current Population Survey (CPS) to study the dynamics of wage earnings over the life cycle and over the business cycle. Lastly, we use the Medical Expenditure Panel Survey (MEPS) to calibrate the medical expenditure process.

Survey of Consumer Finances

For household portfolio data, we use the Survey of Consumer Finances (SCF), a repeated cross-section of household finances in the United States. We use waves from 2016 to 2022 to calculate the moments of wealth and portfolios. We apply the SCF survey weights to adjust for the oversampling of high-wealth households. Because the SCF does not provide the genders of both the reference person and the spouse, we define the race of the household by its reference person alone. We also restrict the sample to households who are not business owners and are between 22 and 85 years old.

We define wealth using the SCF net worth variable (networth), which is the value of financial and non-financial assets, net of all debts.⁸ Equity holdings (equity) are defined as the value of publicly traded stock, held either directly or through mutual funds, retirement accounts, trusts, or managed portfolios. Housing (houses) is defined as the value of the primary residence. The equity and housing shares are then defined as the shares of these variables in wealth, for households with positive wealth. The equity participation rate is the percentage of households with positive equity holdings. The conditional equity share is equity divided by net worth among only those households with positive equity holdings.

Current Population Survey

To compare income profiles between Black and White households, we use the Current Population Survey (CPS). The CPS contains repeated cross-sections of labor force statistics in the U.S., including income and demographic information. We use the CPS waves from 1978 to 2021. We restrict our sample so that observations belong to the household’s main family unit (famunit=1), the head of the family is between 22 and 65 years old, and the race is Black or White. The households must have at least one adult (the head). Wage income (incwage) is aggregated at the household level and scaled by the Social Security wage index (SSWI).

Medical Expenditure Panel Survey

For medical expenditures, we use the Medical Expenditure Panel Survey (MEPS). The MEPS is a nationally representative survey that provides detailed information on medical expenditure, insurance coverage, and other health-related questions. Participants of MEPS are interviewed in five rounds over the course of two full calendar years. The longitudinal design allows us to examine the persistence of health shocks. We use waves from 1996 to 2022 and restrict our sample to adults aged 22 to 85. The main variable of interest is exptot, which captures the total medical expenditure incurred during the year.

Macroeconomic environment

Eleven parameters summarize the dynamics of stock-market returns, aggregate income shocks, and house prices. The estimation process and results follow from (Catherine 2022).

Table 1 reports the result of the estimation. The house price growth rate (\(\mu_p\)) is estimated using the 1977–2013 Case-Shiller indices, and the volatility (\(\sigma_p\)) is set to 14%, following (Flavin and Yamashita 2002). The stock-market dynamics are characterized by the crash probability \(p_s\), the expected returns during crashes and normal times (\(\mu_s^-\) and \(\mu_s^+\)), and the standard deviations in cyclical and noise components of returns (\(\sigma_{s_1}\) and \(\sigma_{s_2}\)). Aggregate income parameters include the growth rate \(\mu_l\), the sensitivity to stock and housing markets (\(\lambda_{ls}\) and \(\lambda_{lp}\)), and the standard deviation \(\sigma_l\). These moments and correlation coefficients are estimated by SMM from yearly S&P 500 returns (1900–2015) and from average wage growth time series (1978–2010).

The table reports estimates for our return and aggregate-income processes. The S&P 500 log return in year \(t\) is \(r_{st}=r_f+s_{1t}+s_{2t}\), where \(s_{2,t} \sim \mathcal{N}(0,\sigma^2_{s_2})\). With probability \(p_s\), the stock market crashes in year \(t\) and \(s_{1,t}=s^-_{1,t} \sim \mathcal{N}(\mu_s^-,\sigma^2_{s_1})\). With probability \(1-p_s\), \(s_{1,t}=s^+_{1,t} \sim \mathcal{N}(\mu_s^+,\sigma^2_{s_1})\). The log growth rate of aggregate wage index is \(l_{1t}-l_{1,t-1}=\mu_l+\lambda_{ls}s_{1t}+\lambda_{lp}\epsilon_{pt}+\epsilon_{lt}\), where \(\epsilon_{lt} \sim \mathcal(0,\sigma_l^2)\). The estimation uses SMM and is detailed in (Catherine 2022).

Differences in business-cycle exposure

We use income data from the CPS to measure the extent to which Black and White Americans experience differences in countercyclical income risk.

Panel A of Figure 2 plots average three-year income growth for each racial group. Average Black income is much more cyclical than White income, falling by more in recessions and rising by more in moderations. This suggests that, within the cross-section of Black households, income growth is more cyclically skewed.⁹ These differences in the cyclicality of income arise largely from differences in unemployment rates, as illustrated by Panel B. The Black unemployment rate is not only persistently higher than the White unemployment rate, but also more countercyclical. It tends to rise by more (in percentage points) in recessions and fall by more in moderations. To showcase the consequence of these differential labor-income dynamics for equity investing and wealth returns, Panel C plots annual returns on the stock market over the same period. Evidently, returns are cyclical, falling when average income falls and unemployment rises.

Idiosyncratic income risk

We use eight parameters to describe the distribution of idiosyncratic labor-income shocks: \(p_{z}\), \(\rho_z\), \(\overline{\mu^-_z}\), \(\lambda_{zl}\), \(\sigma^-_z\), \(\sigma^+_z\), \(\sigma^-_{\eta}\), and \(\sigma^+_{\eta}\). Table 2 reports the estimated parameters for both single- and double-earner processes.

The labor-income process for single earners follows from (Catherine 2022), which employs SMM to estimate parameters. This estimation targets the empirical moments of individual earnings growth from 1978 to 2010 using Social Security Administration data from (Guvenen et al. 2014). Targeting the cross-sectional mean, variance, and skewness at 1-, 3-, and 5-year horizons allows for disentangling between transitory and persistent shocks. To address the overestimation of income persistence, potentially due to different life-cycle income profiles that workers face ex ante (Guvenen 2009), parameters \(\sigma_{\alpha}\) and \(\sigma_{\varphi}\) are introduced to capture heterogeneity in levels and trends.

For the double-earner income process, we first generate simulated data for couples using the single-earner process by randomly pairing two earners. We then recompute the target moments as the sum of both incomes, taking into account that the highest earner typically earns \(70\%\) of the combined salaries. Using SMM, we estimate the double-earner income process by targeting moments specific to double earners, analogous to the method used for single earners. The values of targeted and simulated moments are detailed in Appendix 9.2.

Within a double-earner household, the probability of experiencing a significant career shock increases to \(p_{z} = 0.188\), compared to \(p_{z} = 0.136\) in a single-earner household. Since every earner is subject to this labor income shock, it is intuitive that it is more likely for households to experience this shock if there are two earners. However, due to diversification, the standard deviation of this shock for a double-earner household is nearly halved (\(\sigma^-_z=0.290\)) compared to single earners (\(\sigma^-_z=0.562\)). Similarly, the magnitude of a transitory shock under a large career shock also decreases from \(\sigma^-_{\eta} = 0.895\) to \(0.588\). Additionally, diversification provides several benefits. First, it reduces the negative skewness of income shocks at the household level: \(\overline{\mu^-_z}\) decreases from \(-0.086\) to \(-0.031\). Second, it reduces cyclicality, with \(\lambda_{zl}\) decreasing from \(4.291\) to \(3.146\).

This table reports parameter estimates for the idiosyncratic income process, conditional on the group-level aggregate shock. The single-earner process is estimated as in (Catherine 2022) by targeting the time-series of cross-sectional moments of individual income log growth rates in the SSA administrative data from (Guvenen et al. 2014). To estimate the double-earner process, we first simulate data for couples using the single-earner process and recompute the target moments using the sum of two incomes. We assume a 30% gap between the highest and lowest earner and no assortative matching. Appendix 9.2 provides details regarding our estimation and reports the values of targeted and simulated moments.

Life-cycle income profiles

We estimate the deterministic income profiles \(f_{it}\) as a cubic polynomial of age, which we calibrate to match the observed mean income path of each race\(\times\)family type in the CPS. We report the coefficients for each group in Appendix . Figure 3 plots the fit of income profile using stochastic returns across age for six types of households.

Health expenditures

We estimate the deterministic and stochastic components of health expenditures, () and (), using the MEPS data. For each combination of race \(j\) and number of adults \(n_A\), the deterministic component is a polynomial function of age. The persistence \(\rho_\delta(j,n_A)\) and volatility \(\sigma_\delta(j,n_A)\) of the autoregressive component are then inferred from the residuals. Persistence is similar between Black and White households, but volatility is higher for Black households, implying more uncertain and larger health expenditures.¹⁰ Appendix 9.3 reports coefficient estimates and gives details about the procedure.

Housing market

Preference for housing

We calibrate preference for housing \(\nu\) to be 0.3, following (Catherine 2022).

Mortgage rate

The mortgage rate \(R_{Mit}\) depends on a household’s income, debt-to-value ratio, and race. Appendix 9.4 provides details on this relationship. In SCF data, Black households pay on average 44 basis points more. Controlling for income and debt-to-value, Black borrowers still pay 23.7 basis points more than similar White households. Our estimate is close to the 29 basis-point estimate of (Ghent et al. 2014).

Distress sales

(Kermani and Wong 2024) document that, during a distressed sale, Black and White homeowners sell their houses at a discount \(\theta_j\) of \(36.9\%\) and \(26.4\%\), respectively. Following (Catherine et al. 2020), we set the liquid wealth share that households can access without selling their house to \(\varpi = 0.024\).

Property tax

We set property taxes to be 1.4\(\%\) for White households, the median tax rate reported in (Avenancio-León and Troup 2022), and 1.582\(\%\) for Black households, reflecting their finding that Black households pay a 13\(\%\) higher tax.

Other parameters

We set the price-to-rent ratio \(\chi_j\) at 24 for White homeowners and 16.9 for Black homeowners, to match that minority homeowners earn a \(1.3\%\) higher rental yield on housing (Diamond and Diamond 2023).¹¹ Similar to (Catherine 2022), the transaction cost \(c_H\) is \(10\%\), the minimum house size coefficient \(\kappa_{\rm min}\) is 1.75, and the maximum house size coefficient \(\kappa_{\rm max}\) is 10 (a 10% down payment).

Demographic parameters

Family structures

In a comparison limited to Black and White households, Black families represent \(17\%\) of the overall population. Table 3 categorizes households into six types of family structures and reports the proportions within each racial group.

This table reports the within-race population share of three family types. We obtain this table using 2016 to 2022 SCF surveys and limit to individuals aged 30 to 50.

Family size

We model family size \(N_{it}\) as a cubic polynomial of household head’s age. Appendix 9.6 details the coefficients and the fit.

Mortality

We use the National Vital Statistics Reports published by the Centers for Disease Control and Prevention (CDC) as our source of mortality rate by racial group and gender.

Other calibrated parameters

Inheritance

The probability and conditional expected value of receiving an inheritance over the life cycle are estimated from regressions on age, race, and income using the SCF. Figure 4 plots the fitted values for both the average probability of inheritance receipt \(p_I(a_t,j,\hat{y}_{it})\) and the average log inheritance size \(\mu_I(a_t,j,\hat{y}_{it})\), normalized by the wage index, across age and race. Inheritances are both more frequent and, on average, larger for White households throughout most of the life cycle. We also find that the variance of log inheritance, \(\sigma_I(j)^2\), is higher for White than for Black households. By Jensen’s inequality, this greater variance further increases the expected inheritance in levels.¹² Full details of this calibration are provided in Appendix 9.5.

Financial market

We set the riskfree rate \(r_{f\mathrm{W}}\) to \(1\%\) for White households. For Black households, we use the estimate of (Petach and Tavani 2021) that \(R_{f\mathrm{B}}=R_{f\mathrm{W}}-0.0055\), implying \(r_{f\mathrm{B}}\approx0.45\%\). The combination of fees and capital income taxes totals to \(2\%\).

Estimation and validation

This section presents the results of our structural estimation of the model. We validate the model by comparing non-targeted moments from the data to their simulated counterparts.

Estimation

We structurally estimate three parameters using the most recent three waves (2016, 2019, and 2022) of the SCF. The three parameters are the subjective discount factor \(\beta\), the coefficient of relative risk aversion \(\gamma\), and the participation cost \(c_\pi\) of entering the stock market. Three moment conditions identify these parameters:

1. Mean wealth – Average wealth identifies the discount factor \(\beta\). As households become more patient, they save at higher rates and accumulate more wealth.

2. Equity share of wealth – The allocation of wealth to stocks is falling in risk aversion, identifying \(\gamma\).

3. Stock-market participation rate – A higher stock-market participation cost \(c_\pi\) reduces the number of households willing to enter the stock market.

Table 5 reports the results of this estimation under two different approaches. The “Pooled" condition assumes that Black and White households have identical preferences and participation costs; accordingly, these estimates target pooled data moments. The pooled parameter estimates fall in a reasonable range: \(\beta = 0.96\) and \(\gamma = 6.0\). They agree with the estimates of (Catherine 2022), for instance. Alternatively, the “White" and “Black" conditions separately estimate the three parameters for each racial group using race-specific data moments. Compared to White households, Black households have lower \(\beta\) and \(\gamma\). Since, in the model, Black households have more precautionary savings (for instance, in response to countercyclical labor-income risks), we need a lower discount factor \(\beta\) to match the data. Panel B confirms that all three sets of estimates explain the data well.

This table reports all estimated parameters and their identifying moments. Panel A presents the three structurally estimated parameters and their standard errors for Black and White households. Panel B lists the identifying moment conditions and compares the model-produced moments with the 2016–2022 SCF moments. The “Pooled” specification assumes the same parameters for Black and White households and targets moments from the joint population of Black and White households. Parameters are estimated using the algorithm of (Catherine, Ebrahimian, et al. 2024).

Model fit

We validate the model by comparing additional dimensions of portfolio differences between Black and White households. First, we compare the model predictions for the composition of balance sheets by category of households and race. Second, we report the life-cycle profiles of wealth, stock holdings, homeownership rates, and housing shares for Black Americans in the model and in the data.

Balance sheet by race and household type

Table  reports average portfolio decisions in the data within the two racial groups using SCF waves from 2016 to 2022. We disaggregate these statistics by single-earner, double-earner, and retired households, and by homeowners and renters. Table is the model-implied counterpart.

Despite targeting only three aggregated moments for each racial group, the model does remarkably well at explaining wealth and portfolio differences in the disaggregated data. Broadly, the model captures the fact that equity shares, housing shares, and wealth tend to be lower among single-earner households than among double-earner households, not only within racial groups but also within the subsets of renters and homeowners. While the model slightly underestimates the overall level of homeownership for both Black and White households, it correctly captures that White households are 55% more likely to be homeowners. The model also matches the fact that renters invest less in equity, which (Catherine 2022) shows is difficult to explain without countercyclical labor-income risk. The model generates differences in wealth and portfolio choices between narrow subsets of Black and White households (e.g., double-earner homeowners). The model slightly underestimates the wealth of retirees, but this could be explained by the inclusion of a bequest motive without much consequence for the overall population or our main results.

The model slightly underestimates stock-market participation among renters. However, this discrepancy has limited quantitative implications for wealth accumulation. When renter equity shares are adjusted to match the data, lifetime wealth rises by less than 1% for both Black and White households. The effect is small because renters hold much less wealth than homeowners, and many eventually transition into homeownership, making the underestimation of renter equity shares only a temporary distortion over the life cycle.

The model also matches homeownership decisions within sub-groups, which is especially important for our objective of quantifying the relevance of housing-market differences. Black families are less likely to be homeowners than White families, and, within each racial group, double-earner households are less likely to rent. Conditional housing shares of the Black homeowner population are also very close, at 189% in the model and 181% in the data. The higher leverage of Black homeowners increases expected returns to wealth since returns to housing are higher than mortgage interest rates.

Finally, we report Social Security wealth—defined as the net present value of expected benefits net of future payroll taxes—in both the model and the data. Our computations follow (Catherine et al. 2025). The presence of Social Security reduces workers’ optimal saving rates, so it is important to model the program realistically in order to capture saving incentives accurately. We find similar net present values in the data and in the model.

This table decomposes the balance sheets of Black and White households in the 2016–2022 SCF waves. We categorize each racial groups into single earners, double earners, and retirees. Wealth is scaled by the average wage index in the economy in the survey year. Social Security wealth is obtained from (Catherine et al. 2025).

This table reports the average model-implied balance sheets of Black and White households in different subgroups. The data are generated using the separate “Black" and “White" estimated parameters from Table 5. Social Security wealth is the net present value using the same discounting method as in (Catherine et al. 2025) but with a discount rate of 1%. It is a model counterpart to Table .

Balance sheets of Black Americans over the life cycle

As a second way of validating the model, we consider the life-cycle profiles of Black wealth and holdings of different assets. Figure 5 plots these profiles for four key outcomes in the model and SCF data: wealth, equity share, homeownership rate, and conditional housing share. For all four series, the model generates quantitatively realistic life-cycle patterns.

We obtain the empirical life-cycle profiles of Black wealth and portfolios using SCF surveys from 1989 to 2022. We estimate life-cycle profiles after correcting for year and cohort effects using the methodology of (Deaton and Paxson 1994), as detailed in (Catherine 2022).¹³

We find that our model matches the evolution of wealth very well. Both in the model and in the data, wealth peaks around retirement and then decreases. Although our model does not specifically target housing moments, it also matches the life-cycle pattern of homeownership rates and conditional housing share well. Both in the data and in the model, the value of the equity share increases with age until retirement, similar to (Catherine 2022), and decreases afterwards.

Discussion

Interpretation of heterogeneous discount factors

To fully account for the wealth differences between Black and White households, the estimated model requires a lower subjective discount factor \(\beta\) for Black households. This finding can be interpreted in several complementary ways.

The first interpretation takes the structural estimation at face value: Black households have a higher intrinsic preference for the present. In Appendix 13.3, we use survey data from the Health and Retirement Study (HRS) and the Understanding America Survey (UAS) to assess this hypothesis. These surveys ask respondents about their willingness to trade today’s money for future money at various interest rates, allowing us to infer their implied discount rates. Consistent with earlier evidence from (Huffman et al. 2019), we find that Black respondents report having a greater preference for present cash flows. Importantly, these differences in effective subjective discount rates may reflect not only intrinsic time preferences but also the economic and social circumstances respondents face at the time of the survey.

A second interpretation is that this difference reflects not intrinsic impatience, but distinct social norms around consumption. For instance, (Charles et al. 2009) document that minorities devote larger shares of their budgets to status goods. In a status-signaling model, households from lower-income reference groups must spend more on such goods to convey the same social standing. In this view, the lower estimated \(\beta\) captures behavioral patterns driven by social context rather than pure time preference.

A third possibility is that lower \(\beta\) arises from cognitive discounting of the future, stemming from disparities in financial literacy or advice and confidence in making financial decisions. A large literature on economic decision-making shows that inattention to future states of the world leads to cognitive discounting, which in turn manifests as a lower effective discount factor (see, e.g., (Gabaix 2014)). In our context, this inattention would arise naturally if households are either lacking in financial education and advice, in which case it may be more difficult to plan for future states; or if households feel discomfort making financial decisions, in which case they will choose to spend less time attending to future-oriented decisions. In Appendix 13.2, we show empirically that Black households tend to report significantly less confidence making day-to-day financial decisions than White households of the same age, composition, and income, supporting this channel.

Finally, the estimated \(\beta\) differential may simply act as a residual term capturing omitted mechanisms that depress Black savings rates. To the extent that our model does not include all relevant economic or institutional frictions, these omitted channels will be absorbed into the estimated discount factor.

One final question that arises from heterogeneous discount factors is how much of the wealth gap is being explained by these differences in preferences versus the economic disparities we feed into the model. Figure 6 plots the average wealth of Black and White households under different values of \(\beta\).¹⁴ Along with these wealth curves, the figure plots the average levels of wealth in the data and the hypothetical level of Black wealth under the assumption that Black households have White discount factors. Two facts become clear from this comparative static. First, even when Black and White households have identical discount factors, economic disparities explain most of the wealth gap: the White-Black gap is \(2.52\times\) with identical \(\beta\) compared to the full gap of \(3.24\times\). The economic factors we consider therefore explain about \((2.52-1)/(3.24-1) = 68\%\) of the total wealth gap under identical preferences. Second, Black wealth is not very sensitive to the value of \(\beta\): as we decrease \(\beta\) to values lower than the White estimate, Black wealth decreases relatively slowly. This is why the Black \(\beta\) must ultimately be non-negligibly lower.

Decomposing the sources of balance-sheet differences

We use the life-cycle model to decompose racial differences in portfolio composition and wealth into distinct economic channels, including the earnings gaps, income risk, distressed home sales, house prices, mortgage rates, property taxes, inheritances, race-specific returns, health expenditures, mortality, family structure, and preferences.

In the CPS data, the average Black household earns 51.7% of the income of the average White household. We are particularly interested in the portion of the wealth gap that cannot be attributed to this earnings disparity. To quantify it, we define the excess wealth gap as the difference in wealth-to-earnings ratios between White and Black households: \[ \chi = \frac{\overline{W}_{\rm W}}{\overline{L}_{\rm W}} - \frac{\overline{W}_{\rm B}}{\overline{L}_{\rm B}}, \] where \(\overline{W}_j\) and \(\overline{L}_j\) are the average wealth and average earnings of racial group \(j\).

To evaluate how much of the excess wealth gap is explained by a given economic factor \(F\), we conduct a counterfactual experiment. Starting from the Black calibration (\(F=F_{\rm B}\)), we “turn off” factor \(F\) by setting its parameters to the White calibration \((F=F_{\rm W}\)), while keeping all other parameters fixed at their Black values. We define this counterfactual excess wealth gap as \(\chi(F;{\rm B})\), where the first argument denotes the calibration of factor \(F\) (either \(F_{\rm B}\) or \(F_{\rm W}\)) and the second argument indicates which group’s calibration applies to all other parameters (\({\rm B}\) for Black, \({\rm W}\) for White). The contribution of factor \(F\) is then measured as the change in the wealth-to-earnings ratio relative to the excess wealth gap: \[\begin{align} \Delta \chi (F;{\rm B}) = \frac{\chi(F_{\rm B};{\rm B}) - \chi(F_{\rm W};{\rm B})}{\chi}. \end{align}\] In words, \(\Delta \chi(F;{\rm B})\) isolates the marginal effect of \(F\) on Black households, holding constant all other disparities.

We also compute the reverse experiment, in which we start from the White calibration and switch factor \(F\) to its Black value: \[\begin{align} \Delta \chi (F;{\rm W}) = \frac{\chi(F_{\rm B};{\rm W}) - \chi(F_{\rm W};{\rm W})}{\chi}. \end{align}\] The difference between \(\Delta \chi(F;{\rm W})\) and \(\Delta \chi(F;{\rm B})\) captures the interaction effects of factor \(F\) with all other economic differences between the two groups.

Table 6 details the results of these experiments. Column (0) reports the total differences in portfolio composition and wealth between Black and White households. Each subsequent column turns off one channel at a time to quantify its individual contribution to Black households’ portfolio choices, wealth, and expected lifetime utility. The last three rows report the aggregate interaction terms, with the final row reporting \(\Delta \chi(F;{\rm W})\) and \(\Delta \chi(F;{\rm B})\), as discussed above.

Earnings gap

Column (1) quantifies the effect of the earnings gap—the fact that Black workers earn substantially less labor income on average. Lower income directly limits wealth accumulation and indirectly reduces participation in asset markets. In our model, the earnings gap lowers the Black stock-market participation rate by 9.01 pp and the homeownership rate by 7.67 pp. These effects arise because fixed costs—such as the stock-market participation cost and the minimum house size—restrict access to these markets when income is low. We find that the earnings gap explains roughly 13% of the excess wealth gap. Because the excess wealth gap is defined relative to earnings, this result indicates that wealth grows proportionally more than earnings. This is explained in part by the fact that social programs benefit lower-income Americans more. If Black households earned the same as their White counterparts, they would need higher savings rates to prepare for retirement and self-insure against out-of-pocket medical expenditures and income fluctuations. Additionally, higher earnings raise excess wealth by increasing access to high-return asset markets (i.e., stocks and housing).

One potential mechanism not captured in our analysis is a non-homothetic bequest motive. If the willingness to leave bequests increases with income and wealth, closing the earnings gap could have an even larger impact on the excess wealth gap (Aliprantis et al. 2025).

Income risk

Black workers face greater countercyclical income risk than White workers, and this affects the racial wealth gap through two opposing channels. On the one hand, because equity returns are procyclical, higher income risk discourages stock-market participation and reduces equity exposure. In the model, these effects lower stock-market participation by 4.25 percentage points and equity shares by 3.81 percentage points. Since equities outperformed other assets over the sample period, the smaller allocation to stocks widened the wealth gap. On the other hand, greater income volatility strengthens the precautionary saving motive, leading Black households to accumulate more wealth and thereby narrowing the gap. On net, the first channel dominates, so that higher income risk increases the (excess) racial wealth gap. However, this conclusion depends on the fact that recent equity returns were higher than the longer historical average.¹⁵

Income risk also interacts strongly with other economic factors. Its impact on wealth is amplified when Black households have higher wealth levels, for two reasons. First, the fixed cost of stock-market participation becomes less likely to bind, allowing for greater adjustments in portfolio choice. Second, reductions in equity shares then apply to larger portfolios. These amplification effects are again stronger in periods when equity returns exceed expectations, as they did over the past thirty years.

Distress sales

(Kermani and Wong 2024) document that Black households face a higher probability of distressed home sales and lower selling prices during distressed sales. While this channel intuitively reduces Black homeownership rates and housing shares, we find that it has a small effect on life-cycle portfolio choices and wealth accumulation. The reason is that, in the population, distressed sales are exceedingly rare. In a given year, they affect only the subset of households who get hit with an unemployment shock, currently own a home, and cannot wait to sell due to financial constraints. To be clear, our findings do not invalidate the empirical evidence presented in (Kermani and Wong 2024). Rather, our model shows that explaining why households end up in situations in which they must sell their house in distress at a deep discount is difficult in a rational, dynamic setting.

House prices

(Diamond and Diamond 2023) document that Black households earn rental yields (rent-to-price ratios) that are 1.3 percentage points higher than those of White households. Because owning is relatively more affordable for them, Black households are more likely to purchase homes. In our model, this higher affordability raises Black homeownership rates by 21.48 percentage points and conditional housing shares by 40.17 percentage points, implying that Black homeowners choose larger dwellings on average. Higher rental yields and housing shares also translate into substantially higher expected returns to wealth—by 2.02 percentage points.¹⁶ This response to lower price-to-rent ratios increases average Black wealth by roughly $12,000 per adult (in 2022 dollars). As a result, lower house prices narrow the racial wealth gap, accounting for a sizable and negative share (\(-\)14.66%) of the existing excess wealth gap.

The interaction effect with other channels, however, is large and of opposite sign. If Black households were closer to their White counterparts in income and wealth, housing affordability would play a smaller role in enabling homeownership.

Mortgage rate and property taxes

Columns (5) and (6) report the effect of higher mortgage rates and property taxes on Black households. Not surprisingly, these housing frictions reduce Black housing shares. These two frictions together lower the expected return on wealth by about one-third of a percentage point; their combined effect is even larger, about 1 pp. These frictions explain 0.8% and 2.2% of the excess wealth gap, respectively.

Inheritance

On average, White Americans receive $88,000 per person in inheritance over their lifetime, almost five times as much as their Black counterparts. This inheritance gap explains roughly 15% of the racial wealth gap in excess of the earnings gap. If we model inheritance deterministically rather than stochastically, meaning that people know exactly when and how much they will receive, then the effect of the inheritance gap on the wealth gap is significantly muted. This is because individuals can adjust their savings in anticipation of the inheritance and will choose to save less for retirement when they know they will receive it later in life.

Race-dependent return

(Petach and Tavani 2021) estimate that Black households earn a 0.55 percentage points lower return on assets on average. This further reduces wealth returns because slower wealth accumulation makes it harder for Black households to enter high-return asset markets. The return difference decreases the Black homeownership rate by 5.76 percentage points and the housing share by 15.41 percentage points.

Health expenditures and mortality rates

White households face higher health expenditures later in life and therefore have stronger incentives to save earlier in the life cycle. If Black households faced the same expected health costs, they would save slightly more, reducing the excess wealth gap by 5.6%. Health expenditures also exhibit sizable interaction effects with other economic factors, explaining an additional 7.5% of the gap. This occurs because changes in income, wealth, or other characteristics reduce eligibility for Medicaid and thereby increase the need to self-insure against medical expenses in retirement.

Finally, differences in mortality rates also contribute to the gap. If Black households had the same survival probabilities, they would save somewhat more to finance longer expected retirements, accounting for 2.9% of the excess wealth gap.

Family structure

Differences in family structure—namely, the fact that more Black households tend to be single and/or have only one earner—reduce Black equity and housing shares. A primary reason for this is that a double income raises household wealth and makes entry into these markets more likely. Equity allocations are also lower for Black households because a single income is more exposed to countercyclical risk than two incomes, which are partially diversified against such shocks. The consequence of this is a 0.91% lower expected wealth return for Black households. To compute the share of the excess wealth gap explained by family structure, we make an adjustment to income when we shut off this channel to reflect the fact that creating more two-income Black households will mechanically increase income without necessarily leading to higher rates of wealth accumulation per person. Specifically, we adjust the wage so that the average wage per person remains the same after changing the family structure.

Preferences and overall effect of economic factors

In the model, preferences account for 43% of the excess wealth gap and interact with other factors to generate an additional 11.7% of the gap. This implies that the remaining factors, taken together, explain 100% – 43% – 11.7% = 45.3% of the gap on their own. If we attribute half of the interaction effect to each side, preferences contribute about 49% in total, while the combined contribution of the other economic factors rises to roughly 51%.

This table decomposes the effect of each economic factor on Black households’ portfolio composition, wealth, and welfare in the model. Column (0) reports the total difference between Black and White households; negative values indicate that the variable is lower for Black households. Columns (1) through (12) report the difference between a Black household and a counterfactual Black household in which the parameters associated with one economic factor are set to their White values. For example, column (1) compares Black households to otherwise identical Black households with the same earnings level as White households. Wealth is expressed in units of the national wage index. The expected return to wealth is the portfolio-weighted sum of returns on bonds, equities, housing, and mortgage costs. Housing returns can be further decomposed into changes in house prices, implicit rental yields, distress-sale costs, and property taxes. Welfare measures the change in lifetime consumption (in percentage points) associated with exposure to each factor; a negative welfare change indicates that the factor lowers equivalent lifetime consumption. Welfare gains are computed under the stochastic return specification (rather than actual historical returns).

The standalone wealth effects are obtained by turning off each economic factor while keeping all other model parameters at their calibration for Black households. The interaction with other channels is defined as the difference between the effect of an economic factor when all other parameters are calibrated for White households and the standalone effect. In column (2), the income risk channel is adjusted so that the expected wage remains constant when varying the volatility of log earnings.

General-equilibrium spillovers

Importantly, Table 6 reports the effect of economic factors in partial equilibrium. In general equilibrium, changing mortgage rates and property taxes, for instance, may affect house prices for all households. Insofar as these spillovers exist, our decomposition will not capture them directly.¹⁷ That said, these equilibrium effects are unlikely to be large, since we are taking a relatively small subset of the population (Black households) and making their conditions more like the majority (White households). In equilibrium, such changes are unlikely to substantially affect the majority group, and thus the aggregate economy, even if the effect is substantial within the smaller group.

Decomposing effects on wealth

Because households adjust their consumption and portfolios, economic disparities can have smaller effects on wealth than their direct cash flow effects would suggest. To illustrate this point, Table 7 decomposes the effect of selected economic channels into four parts: first, its (i) direct and (ii) indirect (i.e., post-transfer) cash flow effects, and then its effect induced by changes in (iii) portfolios and (iv) consumption choices.

To disentangle these channels, we compare simulated data from our baseline and counterfactual models. We reconstruct the evolution of each household’s wealth, taking into account, in order, direct cash flow effects, changes in taxes and benefits, changes in portfolios, and changes in consumption. Specifically, we iterate over equation () and progressively replace baseline simulated variables with their counterfactual values. To establish general results, we conduct this exercise using stochastic returns (as opposed to historical ones as in Table 7).¹⁸

The direct cash flow effects measure how much returning the direct monetary cost of each disparity to Black households increases their mean wealth. It is computed by adding this cost to the baseline level of income and iterating over equation (), holding other variables at their baseline values. For example, in column (1), we increase Black workers’ earnings to eliminate the racial wage gap. In columns (6) and (7), we adjust interest payments and property tax payments to what Black households would have paid on the same houses if there were no difference in loan terms or property tax rates. These direct cash flow effects compound over time based on baseline rates of return to wealth.

Indirect cash flow effects account for other changes in disposable income—taxes and benefits. For example, in column (1), if the racial earnings gap disappeared, part of the gains for Black workers would be offset by increases in taxes and losses of social benefits. Hence, in this case, indirect cash flow effects tend to moderate the negative effect of the earnings gap on the wealth gap.

In a third stage, we replace baseline housing choices and financial portfolio weights by their counterfactual values. The incremental change in mean wealth measures how economic factors increase Black households’ wealth through portfolio rebalancing effects. For example, column (2) shows that the greater exposure of Black workers to countercyclical risk reduces their wealth by 0.145\(\times\) average income through that channel. As previously discussed, this is because exposure to the business cycle discourages investment in stocks.

Finally, in the last step, we replace the baseline consumption expenditure by its counterfactual value. For example, if the earnings gap disappeared, Black workers would not save all of their additional income: a large proportion would be consumed, attenuating the impact of the earnings gap on the wealth gap. Combined with the indirect effect, this means that, overall, closing the earnings gap raises Black wealth by roughly 30%, which is close in magnitude to the earnings gap itself. In column (2), we see that higher income risk increases wealth through precautionary savings: due to the increased desire to save a buffer stock, households do not consume the extra (indirect) income. Under stochastic returns, this effect dominates the portfolio effect, so income risk increases Black wealth.¹⁹

Overall, Table 7 demonstrates why studying the racial wealth gap in the context of a household’s full life-cycle problem is important. After considering changes in portfolio and consumption behaviors, the net effect of disparities in economic factors on wealth are quite different, and often smaller, than their direct cash flow effects.

Pairwise interaction effects between economic factors

In the previous sections, we examined the impact of each economic factor both in isolation and in combination with all other factors. Here, we turn to pairwise interactions between mechanisms. Overall, these interactions are limited in magnitude, reinforcing a central insight of our analysis: interactions also generate offsetting effects. We illustrate this intuition with three representative examples, for which we provide further quantitative details in Appendix Table 13.

Consider, for example, the interplay between family structure and income risk. Black families are more likely to rely on a single earner, which increases their exposure to unemployment risk during recessions. This lack of a secondary income source amplifies the adverse effect of countercyclical income risk on equity holdings and thus on returns to wealth. At the same time, it also strengthens the precautionary motive for saving, which works in the opposite direction. As a result, the net impact of this interaction on wealth accumulation is limited.

A second example is the interaction between the earnings gap and health risk. Due to the progressive nature of Medicaid, increasing Black earnings means that a larger share of Black households will no longer be covered by the program. On the one hand, this means that Black households will have higher out-of-pocket medical expenditures, making saving harder. But on the other hand, they will respond to this by increasing precautionary savings. Thus, the interaction is small. This is consistent with what we find in the next subsection.

One exception is when we consider an economic factor that households did not anticipate: for instance, the fact that the stock market performed better than average over the past three decades. We find that, given the actual distribution of returns over the past thirty years, Black workers’ higher exposure to unemployment risk during recession lowered their wealth because the positive effect on precautionary savings was insufficient to fully offset the loss of returns from a lower equity share. However, when we consider more representative paths for stock returns, the net effect on wealth of higher income risk flips sign and the increase in precautionary savings now outweighs the lower return to wealth. In other words, in the model, higher income risk for Black workers increased the racial wealth gap because stock returns were higher than expected over the past thirty years.

Role of Social Security and welfare programs

In previous sections, we decompose the effects on wealth of economic factors that are calibrated differently for Black and White households. Although progressive social programs such as Social Security, EITC, SNAP, and SSI serve Americans regardless of their racial groups, the benefits they offer depend on income and wealth, which themselves differ substantially between Black and White households. In this section, we explore whether the progressivity of Social Security and the existence of the social safety net contribute to the racial wealth gap.

Social Security benefits are concave in lifetime earnings and thus offer higher replacement rates to low earners. In our first experiment, we remove this progressivity by setting benefits at 40% of each individual’s AIYE. As column (2) of Table 8 shows, since Black households typically have lower lifetime earnings and thus gain more from the progressive formula, eliminating it encourages them to save more to offset reduced retirement income, raising their wealth from 2.34 to 2.42 \(\times\) the wage index. Conversely, White households receive higher benefits under the flat rate and, therefore, reduce savings, lowering their wealth from 7.55 to 7.47 \(\times\) the wage index. Overall, Social Security’s progressivity accounts for about 4% of the excess racial wealth gap.

In the second experiment, we cut benefits from safety net programs (SNAP and SSI) and the EITC by 90%. Black wealth rises by 15.3% and White wealth by 7.74%. Column (3) of Table 8 reports our findings. Since safety net programs serve as an insurance for low-income households against negative events such as unemployment, they reduce the need for precautionary savings. Moreover, their means-tested nature discourages low earners from saving so they can remain eligible. Consistent with the finding of (Hubbard et al. 1995) and (Nardi et al. 2010), these effects are stronger for low-income Black households and thus exacerbate the racial wealth gap.

Finally, in column (4) of Table 8, we simultaneously remove Social Security progressivity and cut safety net and EITC benefits by 90%. Together, these changes explain about 4% of the excess racial wealth gap. Since lower-income Black households benefit from these social programs more, the reduction in progressivity and benefit levels encourages Black households to increase savings proportionally more than White households. This partially narrows the racial wealth gap relative to the baseline.

Overall, we conclude that the progressivity of these programs explains only a small part of the racial wealth gap. Importantly, Social Security taxes and replaces earnings only up to 2.5 times the national wage index. This means that, even under a non-progressive benefit formula, workers earning above that threshold must save more privately for retirement. Since these workers are disproportionately White, the existence of Social Security may have a larger effect on the racial wealth gap than what is implied by the progressivity of the benefit formula alone.

Model extensions

We explore three more potential economic factors that could further contribute to the lower wealth accumulation of Black Americans: pessimistic beliefs about stock returns, inertia in mortgage refinancing, and a stronger preference for tangible assets, such as real estate. While these forces are likely present in the data, we omit them from our baseline model because they are difficult to calibrate directly.

Beliefs about returns

We first examine whether differences in subjective expectations of stock returns can explain part of the racial wealth gap. Such differences may arise from disparities in financial literacy or from distinct historical experiences with financial markets. Boerma and Karabarbounis (2023) highlight this mechanism for entrepreneurship, and similar reasoning may apply to stock market participation.

Appendix 14 provides suggestive evidence from the Health and Retirement Study (HRS) consistent with this hypothesis. However, the survey responses imply negative expected returns for both groups, which makes them unsuitable for calibration: if taken literally, no household would invest in equities. Moreover, because households cannot short sell stocks, the heterogeneity of beliefs would also be important to predict the average equity share. For these reasons, our baseline model assumes rational expectations.

To quantify the potential importance of beliefs, we re-solve the model for Black households under alternative expected stock returns, varying the mean of the stock return process (\(\mu_s^+\) and \(\mu_s^-\)) while keeping all other parameters constant. We adjust only the ex-ante expectations under which portfolios are chosen, not the realized distribution of returns. Figure  (a) shows that more pessimistic beliefs about equity returns lower stockholding and, consequently, the rate of return on wealth. A one–percentage-point lower expected stock return increases the racial wealth gap by 6.3%.

Inertia in mortgage refinancing

Gerardi et al. (2023) document that White households are substantially more likely than Black households to refinance or move when interest rates fall. This refinancing inertia implies that Black homeowners pay persistently higher mortgage rates, even after controlling for observable characteristics. To quantify the potential effect of this inertia, we model a higher effective mortgage premium for Black households. Figure  (b) shows that a higher premium reduces wealth accumulation by discouraging homeownership and lowering average returns to housing. A one–percentage-point increase in the mortgage premium widens the racial wealth gap by 3.3%.

Preference for tangible assets

Evidence suggests that households have a preference for “tangible" assets such as housing. Gomes et al. (2021) argue that this preference strengthens when households view financial markets as less trustworthy or efficient. Given historical experiences in the U.S., Black households may plausibly exhibit greater mistrust in financial institutions, translating into a stronger preference for tangible assets.²⁰

In our model, housing is the primary tangible asset. We therefore allow for a utility premium on owner-occupied housing:²¹

\[ u(C,H,N) = \frac{1}{1-\gamma}\left(\frac{C^{1-\nu}\left[(1+\mathbb{I}_{\rm own}\xi)H\right]^\nu}{\sqrt{N}}\right)^{1-\gamma}, \] where \(\mathbb{I}_{\rm own}\) indicates homeownership and \(\xi\geq0\) measures the intensity of the tangibility preference. For example, with \(\xi=0.1\), a homeowner perceives their house as providing 10% more housing services than an equivalent rental unit.

Figure  (c) shows that as \(\xi\) increases, wealth accumulation rises. The main mechanism is that stronger tangibility preferences encourage households to save for and attain homeownership. Higher homeownership and leverage raise average wealth returns, since housing yields exceed mortgage rates. However, greater investment in housing crowds out equity holdings, which partly offsets this effect (Cocco 2005; Yao and Zhang 2005). On balance, the first channel dominates: with \(\xi=0.1\), the racial wealth gap shrinks by 2.8% relative to the baseline.