Can income differences explain the racial wealth gap? A quantitative analysis

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Can income differences explain the racial wealth gap? A quantitative analysis ✩ Hero Ashman a , Seth Neumuller b,∗ a b

UC Berkeley, United States Department of Economics, Pendleton East, Wellesley College, 106 Central Street, Wellesley, MA 02481, United States

a r t i c l e

i n f o

Article history: Received 27 November 2018 Received in revised form 8 April 2019 Available online xxxx JEL classification: E21 D15 D31 J15 Keywords: Racial wealth gap Wealth inequality Income differences Bequests

a b s t r a c t We use a quantitative, overlapping-generations, incomplete markets, life-cycle model to explore the extent to which income differences can explain the racial wealth gap. The model features race, education, and family structure-specific stochastic household income processes estimated using data from the PSID, race and education-specific lifespan risk, an income floor, and intergenerational transfers of wealth and labor market ability. A calibrated version of the model fully accounts for the racial wealth gap observed in the data. In addition, it endogenously generates an empirically plausible degree of wealth inequality, both conditional and unconditional on race, and is broadly consistent with observed patterns of wealth accumulation over the life cycle. Simulations of the model suggest that income differences, on their own, can explain 43.0% of the racial wealth gap in levels, while bequest motives and intergenerational transfers of wealth, in the presence of income differences, account for 28.6% and 25.8% of the gap, respectively. We find that the income floor has a negligible impact on the racial wealth gap in levels, but causes the ratio of median wealth (white/black) to more than double as it disproportionately reduces the incentive that low income, low wealth households, the majority of whom are black, have to save. We also find that differences in lifespan risk have only a small impact on the racial wealth gap levels, but lead to a 13.7% increase in the ratio of median wealth. © 2019 Elsevier Inc. All rights reserved.

1. Introduction Differences in the wealth held by black and white households in the U.S. are staggering. According to data from the 1989–2016 waves of the Survey of Consumer Finances (SCF), the median net worth of white households is nearly seven times greater than that of black households.1 Wealth determines a household’s consumption level, ability to withstand labor market fluctuations, and access to quality housing and education services. Wealth is also a source of both political

✩ We thank the editor, Mariacristina De Nardi, the four anonymous referees, Bill Gentry, Kyle Herkenhoff, Felicia Ionescu, Dirk Krueger, David Love, Matthew Luzzetti, Alisdair McKay, Kyung Park, Greg Phelan, Casey Rothschild, Dan Sichel, Akila Weerapana and seminar participants at the Fall 2018 Midwest Macro Meetings, the 14th Annual Conference of Macroeconomists from Liberal Arts Colleges, the 2016 Annual Meetings of the Southern Economics Association, College of the Holy Cross, Wellesley College, and Williams College for helpful comments and suggestions. All remaining errors and omissions are our own. An initial draft of this paper was circulated under the title “Modeling the Racial Wealth Gap” and is available for download here. Corresponding author. E-mail addresses: [email protected] (H. Ashman), [email protected] (S. Neumuller). 1 Based on the 1989–2016 waves of the SCF. See the Online Appendix for details.

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https://doi.org/10.1016/j.red.2019.06.004 1094-2025/© 2019 Elsevier Inc. All rights reserved.

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power and social influence. The racial wealth gap thus serves as a stark reminder of the persistent political and economic racial inequality in the U.S. Racial differences in income, though considerable, are far less pronounced; the median income of white households is less than two times greater than that of black households.2 Whether income differences can explain the wealth gap between black and white households has been the subject of numerous empirical studies.3 Scholz and Levine (2002), in their survey of the literature, conclude that “differences in labor income have a major impact on black-white wealth differentials,” as observed income differences have been found to account for as much as three quarters of the racial wealth gap. What remains unexplained by these empirical findings, however, are the mechanisms by which observed income differences between black and white households result in vast disparities in wealth. We explore the extent to which income differences can explain the racial wealth gap and evaluate potential amplification mechanisms through the lens of a quantitative, overlapping-generations, incomplete markets, life-cycle model.4 Our model builds upon the framework developed by De Nardi (2004), itself an extension of Huggett (1996). The key features of the model are race, education, and family structure-specific stochastic household income processes estimated using data from the Panel Study of Income Dynamics (PSID), race and education-specific lifespan risk, an income floor, and intergenerational transfers of wealth and labor market ability.5 A calibrated version of the model fully accounts for the racial wealth gap observed in the data. In addition, it endogenously generates an empirically plausible degree of wealth inequality, both conditional and unconditional on race, and is broadly consistent with observed patterns of wealth accumulation over the life cycle. We use the model to isolate the effect of income on wealth by considering the case in which the income floor and bequest motives are shut-down, accidental bequests are equally distributed across recipient households, and life expectancy is independent of race. In this counter-factual scenario, the model slightly over-predicts the wealth held by the median white household ($166,050 in the model vs. $146,790 in the data), but severely over-predicts the wealth held by the median black household ($109,089 in the model vs. $21,866 in the data). The model-implied racial wealth gap in levels (white–black) is thus $56,961, which suggests that income differences, on their own, explain 43.0% of racial differences in median wealth. The model-implied ratio of median wealth (white/black), however, is just 1.52 versus a value of 6.71 in the data. Reintroducing bequest motives and direct intergenerational transfers of wealth between family members causes the ratio of median wealth to nearly double, rising from 1.52 to 3.00, and allows the model to fully account for the observed racial wealth gap in levels, with bequest motives accounting for 28.6% of the gap and unequal bequests accounting for 25.8% of the gap. The ratio of median wealth then more than doubles, rising from 3.00 to 6.11, when we reintroduce the income floor as it disproportionately reduces the incentive that low income, low wealth households, the majority of whom are black, have to save. Finally, reintroducing differences in lifespan risk causes the ratio of median wealth to rise from 6.11 to 6.95, which is just 3.5% higher than the value of 6.71 observed in the data. Our results suggest that one does not need to appeal to racial differences in preferences or returns on investment in order to explain how observed income differences between black and white households lead to large racial disparities in wealth.6 This is not to say that other factors such as legacies of discrimination are unimportant for understanding racial disparities in wealth. Indeed, there is an extensive literature documenting how both statistical and taste-based discrimination may be of primary import for explaining racial differences in labor market outcomes, which our model suggests have important implications for racial wealth inequality.7 What our findings do imply, however, is that the racial wealth gap is a direct result of racial differences in labor income in the presence of bequest motives, intergenerational transfers of wealth, and social insurance. To put it differently, if income differences were eliminated in our model, racial disparities in wealth would eventually disappear.8 Our findings thus underscore the importance of identifying the causes of racial differences in income for understanding racial disparities in wealth. To our knowledge, there are only two other papers that use a quantitative-theoretic model to explore the racial wealth gap: White (2007) quantifies the extent to which conditions at the time of Emancipation and segregated schooling can explain observed trends in racial income and wealth inequality, and Aliprantis et al. (2018), in a study contemporaneous to

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Based on the 1989–2016 waves of the SCF. See the Online Appendix for details. See, for example, Blau and Graham (1990), Oliver and Shapiro (1995), Avery and Rendall (1997), Menchik and Jianakoplos (1997), Gittleman and Wolff (2000), Barsky et al. (2002), Altonji and Doraszelski (2005), and Thompson and Suarez (2015). 4 Our model takes income differences as given. There is a related literature that seeks to identify the underlying source of these income differences. See, for example, Rauh and Valladares-Esteban (2018). 5 By “family structure” we specifically mean the number of adults present in the household. 6 Charles et al. (2009) find that racial differences in preferences are not required to explain divergent patterns of expenditures on visible consumption goods across black and white households. Racial differences in returns on investment could, in principle, result from discrimination in financial markets (Black et al., 1978; Loury, 1998; Edelberg, 2007), intergenerational inertia in portfolio choice (e.g. Chiteji and Stafford, 1999), or gaps in financial literacy (e.g. Lusardi and Mitchell, 2007; Lusardi and Mitchelli, 2007). However, Gittleman and Wolff (2004) find no evidence that returns on investment are higher for white households than black households. 7 See the recent survey of the literature by Lang and Lehmann (2012) and references therein. 8 While our findings do suggest that racial disparities in steady state wealth would disappear if income differences were eliminated, White (2007) and Aliprantis et al. (2018) point out that it may take many decades after the income gap is closed for the economy to converge to a new steady state in which the racial wealth gap is eliminated. 3

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ours, compute the transition path of the racial wealth gap as income differences fall at a deterministic rate.9 Instead, we focus on identifying and evaluating potential mechanisms capable of explaining how observed differences in income lead to large disparities in wealth. The model studied by White (2007) features dynastic households that face no idiosyncratic risk. In contrast, the overlapping-generations, life-cycle economy that we develop features a parsimoniously calibrated stochastic income process which produces rich heterogeneity across households, thereby allowing us to more precisely assess the effect of income differences on racial differences in wealth. While the model employed by Aliprantis et al. (2018) is similar to ours along a number of dimensions, it abstracts from racial differences in family structure, the likelihood and persistence of realizing zero labor income, and income volatility, all of which we find are quantitatively important for explaining racial wealth inequality. Using a quantitative-theoretic model to assess the ability of income differences to explain the racial wealth gap has a number of advantages over the empirical approaches employed to date. In particular, it allows us to (1) isolate the effect of income on wealth and (2) identify and evaluate potential amplification mechanisms capable of explaining how observed income differences between black and white households result in vast differences in median wealth. While exploring the origins of the racial wealth gap is important on its own, our approach also sheds light on the factors driving wealth inequality more generally. Just as explaining the extreme concentration of wealth in the U.S. requires understanding why the rich save so much, we demonstrate that accounting for the racial wealth gap requires understanding why black households save so little relative to their white counterparts.10 Our results highlight the potential role that voluntary bequests, an income floor, and differences in lifespan risk play in driving a wedge between the saving rates of black and white households. The role of bequests in accounting for the racial wealth gap has been explored extensively in the empirical literature.11 This literature concludes that bequests, on their own, can account for no more than one quarter of the racial wealth gap at the mean and likely matter far less at the median.12 Following De Nardi (2004), we model bequests as luxury goods. This induces the richest households in our model, the majority of whom are white, to save more in order to leave a larger estate to their offspring. This mechanism is consistent with Smith (1995), who argues that differences in intergenerational transfers of wealth arise not because white households have a stronger bequest motive, but because they are more able to “afford” bequests. Simulations of our model suggest that voluntary bequests, through their differential impact on household saving behavior within a generation and their cumulative effects on wealth accumulation over many generations, can explain the entire portion of the racial wealth gap in levels not accounted for by income differences alone. There is considerable debate in the empirical literature regarding the impact that public assistance programs have on household saving.13 In their influential theoretical analysis, Hubbard et al. (1995) argue that the low saving rate exhibited by the poorest households in the U.S. can be rationalized as a utility maximizing response to the presence of means-tested social insurance. In our model, the income floor disproportionately inhibits precautionary saving by black households since they earn less income and hold less wealth, on average, than white households and are, therefore, more likely to qualify for and benefit from this form of social insurance. As a result, the median wealth of black households declines more in percentage terms in response to the presence of the income floor, which causes the ratio of median wealth to more than double and enter into an empirically plausible range. Exogenous shocks to family structure and their implications for wealth inequality have been studied previously in overlapping generations life cycle economies.14 For example, Cubeddu and Ríos-Rull (2003) develop a model with exogenous marriage and divorce shocks in which uncertainty over the characteristics of one’s future spouse and divorce risk affect saving incentives and, therefore, household wealth. To maintain computational tractability, we assume perfect assortative mating on race, education, income, and wealth, equal sharing of assets upon divorce, and homothetic preferences at the household level over consumption per adult. Marriage and divorce shocks in our model are risky in so far as they determine the properties of the exogenous stochastic income process that households’ face and, therefore, affect wealth accumulation over the life cycle mechanically through their impact on household formation and destruction. Despite this simplification, we find that exogenous racial differences in marriage and divorce shocks, and the racial marriage gap that arises as a result, do play an important role in explaining racial wealth inequality.15

9 In a related study, Love and Schmidt (2015) investigate differences in the wealth accumulation patterns of immigrants and natives through the lens of a quantitative life cycle model with housing and bequests. 10 Smith (1995) draws a similar conclusion using data from the Health and Retirement Study. The seminal result in the quantitative wealth inequality literature is that a standard Bewley (1977) model fails to explain the extreme concentration of wealth in the U.S. from observed levels of income inequality. Savings mechanisms that have been proposed to address this deficiency include preference heterogeneity (Krusell and Smith, 1998), intergenerational transfers of wealth and ability (De Nardi, 2004; De Nardi and Yang, 2014), entrepreneurship (Quadrini, 1999), and higher earnings risk for the top earners (Castaneda et al., 2003), among others. See Cagetti and De Nardi (2008) and De Nardi and Fella (2017) for comprehensive surveys of this literature. 11 See, for example, Avery and Rendall (1997), Menchik and Jianakoplos (1997), Gittleman and Wolff (2000), and Altonji and Doraszelski (2005). 12 See Scholz and Levine (2002). 13 See, for example, Neumark and Powers (1998), Gruber and Yelowitz (1999), Ziliak (2003), and Hurst and Ziliak (2006). 14 There is also a related literature in which family structure is endogenously determined. See, for example, Aiyagari et al. (2000) and Greenwood et al. (2003) and references therein. 15 See the Online Appendix for details. For a discussion of the potential causes and consequences of the racial marriage gap, see Caucutt et al. (2018) and references therein.

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Finally, we also contribute to that body of the literature which attempts to carefully measure earnings risk and study its implications for consumption and saving behavior.16 In light of well-documented racial differences in incarceration rates and labor force non-participation rates, particularly for men, we augment the canonical permanent-transitory framework for labor income with a Markov process governing discrete jumps between positive and zero labor income.17 In addition, our approach explicitly allows for the possibility that black and white households with identical education and family structure face different income processes, both at the mean and variance levels. In other words, we allow the returns to observable skills, both in terms of average income and income volatility, to vary with race, education, and family structure. This is a key innovation because, as we show here, differential exposure to income risk, which affects both the consistency and reliability of a household’s income stream, has important implications for differences in the patterns of wealth accumulation between black and white households. The remainder of this paper is structured as follows. Section 2 describes our model. Section 3 presents our quantitative results. Finally, Section 4 concludes. 2. Model Our model economy is populated by overlapping generations of adults, each with measure one and linked to previous generations through intergenerational transfers of wealth and labor market ability. Households consist of either one or two adults. We refer to the number of adults in a household as the household’s family structure. Prior to retirement, adults within the same cohort marry and divorce at exogenously given rates that vary by age, education, and race. During retirement, adults face mortality risk that varies with age, education, and race. Changes in family structure during retirement, therefore, occur only via stochastic mortality. Prior to retirement, households earn a stochastic income endowment of the homogeneous consumption good, the properties of which depend on their race, education, and family structure. During retirement, households earn a non-stochastic income endowment of the homogeneous consumption good that depends on their income at retirement, race, education, and family structure. There is one asset, a risk free bond, which households can use to self-insure against labor market and lifespan risk.18 Finally, there is a government that levies income taxes on households and insures households against adverse income shocks via an income floor. 2.1. Demographics Adults enter the model at age T 0 , work until retirement at age T R , and live to the maximum age T M . Adults belong to one of six race-education groups (white/black, high school dropout/high school graduate/college graduate) indexed by j and form households consisting of n = 1 or n = 2 adults.19 We refer to n as the household’s ‘family structure.’ Retired adults face a race and education-specific probability s j ,t of surviving to age t + 1 conditional on surviving to age t. Upon the death of all adults in a household, a bequest is made to their heirs. A fraction ϒ of the bequest is transfered to the grandchildren of the deceased who then enter the model, while the remainder is transfered to the children of the deceased.20 Thus, each adult in the model has either a parent or a child that is also active in the model in any given period. The demographic patterns are assumed to be stable, meaning that age t adults make up a constant fraction of the population at every point in time. Since we consider only stationary environments, all variables are indexed by the age t of adults within a household with the index for time left implicit.

16 Important contributions to this literature include Zeldes (1989), Carroll et al. (1992), Hubbard et al. (1995), Carroll and Samwick (1997), Low et al. (2010), and Guvenen et al. (2015), among others. 17 See, for example, Western (2002), Neal and Rick (2014), and Bayer and Charles (2018). Using micro-level data from the PSID to examine racial differences in the mean and variance of earnings itself is not new. See, for example, the seminal contributions in Duncan (1984). Carroll (1997) uses data from the PSID to estimate a similar income process. However, his income process does not allow for persistence in the zero labor income state, nor is it race or family structure-specific. 18 While housing equity is the largest source of wealth for most households with positive wealth (Wolff, 1998), our model abstracts from a household’s rent versus own decision. Given that our main interest is in whether or not income difference can explain wealth differences, housing would only be important in so far as it serves as a mechanism through which relatively small income differences are amplified into large differences in median wealth. While income and wealth are empirically correlated with homeownership, there exists considerable disagreement about whether or not housing is a useful means for building wealth. For example, Goodman and Mayer (2018) argue that housing is beneficial for wealth accumulation, while Li and Yang (2010) find that the average real return to investment in housing is negative. 19 For the purposes of mapping the model to the data in the calibration section that follows, to be considered a college graduate, the head of household must have at least a four year college degree. Thus, high school graduates include those with some college experience, for example, heads of households that have an associates degree or were college dropouts. 20 De Nardi (2004) develops a model with intergenerational transfers of wealth in which bequest timing is stochastic and children infer the size of the bequest they are likely to receive by observing their parent’s labor productivity at entry into the model. However, this comes at the cost of increasing the model’s state space and, therefore, the required computational time. To reduce our computational burden, we assume that bequests are unanticipated by their recipients, both in terms of timing and size.

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2.2. Preferences Households have time separable preferences with the constant subjective discount factor β over consumption per adult, which can be represented by the utility function

u (c ) =

c 1 −γ 1−γ

,

where γ is the coefficient of relative risk aversion and c is consumption per adult. Households also have preferences over the size of the bequest d they leave to their heirs which can be represented by the utility function

 v (d) =

χ1 1 − χ1

γ 

χ1 (1 − χ1 )−1 χ2 + d 1−γ

 1 −γ

−γ

if χ1 ∈ (0, 1),

v (d) = χ2 (d) if χ1 = 1, and v (d) = 0 if χ1 = 0, where χ1 ∈ [0, 1] governs the strength of the bequest motive and determines the extent to which bequests are a luxury good.21

χ2 ≥ 0

2.3. Stochastic household income process Prior to retirement, the labor income of household i in race-education group j which consists of n age t adults is given by

zi , j ,n,t = ψi , j ,n,t exp( f j ,n,t + e i , j ,n,t + νi , j ,n,t ), where ψi , j ,n,t is an indicator function that is equal to one if the labor income of the household is positive and zero otherwise (i.e. employed or unemployed), f j ,n,t is a race, education, and family structure-specific deterministic function of age, e i , j ,n,t ∼ N (0, σe, j ,n ) is an i.i.d. idiosyncratic transitory shock with race, education, and family structure-specific volatility σe, j ,n , and νi, j,n,t is a persistent component which evolves according to the random walk process

νi, j,n,t = νi, j,n,t −1 + ζi, j,n,t , where ζi , j ,n,t ∼ N (0, σζ, j ,n ) is an i.i.d. idiosyncratic persistent shock with race, education, and family structure-specific volatility σζ, j ,n .22 We assume that the indicator function ψi , j ,n,t evolves according to a two-state Markov process with p ,q race, education, and family structure-specific transition matrix j ,n , where π j ,n = Pr j ,n (ψi , j ,n,t +1 = q|ψi , j ,n,t = p ). The post-retirement income endowment of retired households is equal to the race and education-specific fraction λ j of the persistent component of their labor income at retirement. Thus, the post-retirement income endowment of household i in race-education group j which consists of n age t adults is given by

zi , j ,n,t = λ j exp( f j ,n, T R + νi , j ,n, T R ). 2.4. Intergenerational transfers of labor market ability Following De Nardi (2004) we assume that, in addition to a bequest, children inherit part of the labor market ability of their parents. To maintain tractability, we assume that the process governing the intergenerational transmission of educational attainment is independent of the intergenerational transmission of wealth and income. Specifically, when an individual enters the model, they draw their education level from the conditional distribution G (Education|Parent’s Race and Education) and the persistent component of their labor income endowment from the stochastic process

νi, j,n,T 0 = ρ ν˜ ˜i, ˜j,˜n,t˜ + ωi, j,n , where ν˜ ˜i , ˜j ,˜n,t˜ is the persistent component of their parent’s labor income endowment in the period that they enter the model and ωi , j ,n ∼ N (0, σω ) is an i.i.d. idiosyncratic shock.

21 This functional form is taken directly from Lockwood (2018). It represents a re-parameterized version of the functional form used by De Nardi (2004) and nests as special cases nearly all of the functional forms that are commonly used in the literature. See Lockwood (2018) for further details. 22 For computational reasons, we assume that both transitory and persistent shocks to a household’s income endowment are bounded and, in particular,



that e i , j ,n,t ∈ e j ,n , e j ,n





and ζi , j ,n,t ∈ ζ

j ,n

 , ζ j ,n ∀ j , n.

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2.5. Shocks to family structure Prior to retirement, adults marry and divorce at exogenously given age, race, and education-specific rates. In particular, adults marry other adults with identical age, race, education, persistent component of labor income, and wealth with prob1, 2 1, 1 1, 2 ability φ j ,t to form a new household (and remain single with probability φ j ,t = 1 − φ j ,t ).23 A household formed as a result of marriage has two adults, identical persistent component of labor income, identical education, and twice the wealth of 2, 1 each spouse prior to the marriage. Households with two adults divorce to form two new households with probability φ j ,t 2, 2

2, 1

(and remain married with probability φ j ,t = 1 − φ j ,t ). A household formed as a result of divorce has one adult, identical persistent component of labor income, identical education, and half of the wealth of the household prior to the divorce.24 During retirement, changes in family structure occur only as a result of stochastic mortality. Thus, retired households with two adults transition to having only one adult with probability 2(1 − s j ,t )s j ,t (i.e. one adult dies), while both adults die with probability (1 − s j ,t )(1 − s j ,t ). 2.6. Financial assets The only asset available to households is a one-period, risk free bond. Let b i , j ,n,t denote the quantity of bonds owned by household i in race-education group j which consists of n age t adults. Households can sell bonds (i.e. borrow, b i , j ,n,t < 0) up to their natural borrowing constraint b i , j ,n,t at interest rate rd and can buy bonds (i.e. save, b i , j ,n,t > 0) at interest rate r s . 2.7. Taxes and transfers Households pay income taxes which we model after the U.S. tax code. The total income of household i in race-education group j which consists of n age t adults is

y i , j ,n,t ≡ zi , j ,n,t + r s b i , j ,n,t Ibi, j,n,t >0 . The household’s taxable income is given by





y˜ i , j ,n,t = max 0, zi , j ,n,t + ξ r s b i , j ,n,t Ibi, j,n,t >0 − sn , where ξ is the fraction of capital income that is taxable and s is the standard deduction per adult. The taxes paid by a household are given by T ( y˜ i , j ,n,t , n), which is increasing in taxable income and decreasing in the number of adults. An income floor per adult y is provided via transfer payments to households. The transfer payment is equal to the difference between the total income floor and the household’s after-tax income:



 ( y i , j ,n,t , y˜ i , j ,n,t , n) = max 0, yn − y i , j ,n,t − T ( y˜ i , j ,n,t , n) .

2.8. The recursive problem of a household The problem of a household can be formulated recursively. We consider the problem of a working household (t < T R ) separately from the problem of a retired household (t ≥ T R ). The value function of a working household with bond holdings b, permanent component of labor endowment ν , and transitory component of labor endowment e in labor income state ψ and race-education group j which consists of n age t adults is given by







V j ,t (b, n, ν , e , ψ) = max u (c ) + βEn ,ζ  ,e ,ψ  V j ,t +1 b , n , ν  , e  , ψ  n, ν , ψ



c ,b ≥b

subject to

b = 1 + In >n − 0.5In
 



b 1 + rd Ib<0 + y − T ( y˜ , n) + ( y , y˜ , n) − cn



y = z + r s bIb>0

(2)

y˜ = z + ξ r s bIb>0 − sn

 ( y , y˜ , n) = max 0, yn − y − T ( y˜ , n) 



z = ψ exp( f j ,n,t + e + ν ) 23 24

(1)

In other words, we assume perfect assortative mating based on age, race, education, income, and wealth. Thus, we assume that wealth is divided equally in the event of divorce and that each spouse has an equivalent future expected earnings potential.

(3) (4)

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e  ∼ N (0, σe, j ,n )

ν = ν + ζ  ζ  ∼ N (0, σζ, j ,n )  ψ =  n =

j

1

with probability πψ,1

0

otherwise

1

t, j

with probability φn,1

2 otherwise

.

The value function of a retired household with bond holdings b and permanent component of income at retirement race-education group j which consists of n = 2 age t adults is











ν in

 

W j ,t (b, 2, ν ) = max u (c ) + β s2j ,t W j ,t +1 b , 2, ν + 2(1 − s j ,t )s j ,t W j ,t +1 b , 1, ν + (1 − s j ,t )2 v b c ,b ≥b

subject to equations (1) – (4) and

z = λ j exp( f j ,n, T R + ν ).

(5)

The value function of an identical retired household which consists of n = 1 age t adult is







 

W j ,t (b, 1, ν ) = max u (c ) + β s j ,t W j ,t +1 b , 1, ν + (1 − s j ,t ) v b  c ,b ≥b

subject to equations (1) – (5). The terminal period value function W j , T M +1 (b, n, ν ) is set equal to v (b) and we assume that V j , T R (b, n, ν , e , ψ) = W j , T R (b, n, ν ) for all e and ψ . 3. Quantitative results In this section, we first describe how we calibrate our incomplete markets life cycle economy. We then evaluate the model’s ability to replicate key empirical facts related to the racial wealth gap. Finally, we perform a decomposition analysis that allows us to quantify the relative importance of income differences, voluntary bequests, the income floor, and differences in lifespan risk in accounting for the racial wealth gap. 3.1. Calibration There are two sets of parameters: those that can be estimated independently of the model or are based on estimates provided by other studies (Table 4), and those that are chosen so that the model-generated data match a given set of targets (Table 5). We first discuss the parameters calibrated outside of the model, beginning with those related to demographics. Each model period represents one calendar year. Adults enter the model at age T 0 equal to 25, retire at age T R equal to 65, and live to a maximum age T M of 95. The race and education-specific probabilities s j ,t of surviving to age t + 1 conditional on surviving to age t are set equal to the corresponding estimates reported by Masters et al. (2012), averaged across males and females, which we depict in Fig. 1.25 In 2016, 61.3% of the population was white (non-Hispanic) and 13.3% was black (non-Hispanic) or African American (U.S. Census Bureau). Our model consists of only white and black adults, so we assume that 82.2% of adults are white and the remainder are black. We calibrate the process governing the intergenerational transmission of educational attainment, represented by the conditional distribution G (Education|Parent’s Race and Education), using data from the U.S. Department of Education’s Longitudinal Study of 2002 reported in Table 1. 1, 2 2, 1 We estimate the age, race, and education-specific marriage and divorce probabilities φ j ,t and φ j ,t using data from the 2008–2017 waves of the American Community Survey downloaded from the IPUMS-USA database (Ruggles et al., 2018). Our resulting estimates are depicted in Fig. 2.26 We also use this dataset to estimate the race and education specific fraction of households with two adults present at age 25. For white households, we find that 36.0% of high school dropouts, 36.6% of high school graduates, and 25.2% of college graduates are married at age 25. For black households, we find that 9.8% of high school dropouts, 16.0% of high school graduates, and 13.2% of college graduates are married at age 25. We set the corresponding fractions of households with two adults present at age 25 in our model accordingly. Next we turn to the preference parameters. We set the coefficient of relative risk aversion γ equal to 1.6, which is consistent with the corresponding estimate reported by Attanasio et al. (1999). Lockwood (2018) estimates the parameters

25 We avoid keeping track of the gender of members of each household during retirement by assuming that individuals face mortality rates that represent the average of that for males and females. 26 See the Online Appendix for a description of the data, sample selection, and estimation procedures.

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Fig. 1. Survival probabilities during retirement conditional on race, education, and age. Source: Masters et al. (2012), averaged across males and females.

Table 1 Educational attainment conditional on parent’s education by race. Parent’s education

White households High school dropout

High school graduate

College graduate

High school dropout

Black households High school graduate

College graduate

High school dropout High school graduate College graduate

11.5% 3.5% 0.8%

82.1% 75.2% 48.0%

6.4% 21.3% 51.2%

14.7% 6.9% 3.9%

80.0% 80.6% 64.7%

5.3% 12.5% 31.3%

Source: U.S. Department of Education, NCES, Education Longitudinal Study of 2002, High School Sophomores.

of the utility function representing preferences over bequests using data from the Health and Retirement Study. He finds that setting the parameter that governs the strength of the bequest motive χ1 equal to 0.95 and the parameter that determines the extent to which bequests are a luxury good χ2 equal to 0.494 times median household income provides the best fit of age-wealth profiles during retirement. We set the corresponding parameters in our model accordingly. We estimate the stochastic income process for households in each of the six race-education groups conditional on family structure using data from the PSID.27 Fig. 3 depicts the estimated age-income profiles and Table 2 reports the estimated Markov transition probabilities, age-income profile coefficients, and volatilities of persistent and transitory shocks to income. Love (2013) uses the PSID to estimate income replacement rates during retirement for high school dropouts, high school graduates, and college graduates. His estimates are 81.8%, 76.9%, and 75.7%, respectively, and we set the corresponding values for λ j in our model accordingly.28 We take the persistence of the income inheritance process ρ to be 0.40 and the volatility σω to be 0.37 from De Nardi (2004). We adopt a modified version of the tax schedule used by Chatterjee and Eyigungor (2015). The tax rates are listed as a function of taxable income per adult relative to median household income in Table 3. The standard deduction per adult s is set equal to 0.062 times median household income and the fraction of financial asset returns that are taxable ξ is set equal to 0.40. The income floor per adult y is set equal to 0.135 times median household income since the consumption floor for two adult households in 1992 was $8,159 (Scholz et al., 2006), while median household income was $30,042 (U.S. Census Bureau). The final parameter calibrated outside of the model is the interest rate on household savings r s , which we set equal to 2% following Campbell and Viceira (2002). Table 4 summarizes this portion of our calibration. The parameters calibrated within the model include the subjective discount factor β , the interest rate on household debt rd , and the fraction of bequests left to the grandchildren of the deceased ϒ . We calibrate these parameters jointly to match corresponding targets in the data. In particular, we set the subjective discount β equal to 0.980 to match median wealth across all households of $115,320 (2016 USD, SCF). We set the interest rate on household debt rd equal to 9.0% to match the 10th percentile of the distribution of wealth across all households of −$281 (2016 USD, SCF). Finally, we set the fraction of bequests left to the grandchildren of the deceased ϒ equal to 0.107 to match median wealth across all age 25 households of $18,864 (2016 USD, SCF). Table 5 summarizes this portion of our calibration.

27 In particular, we use similar empirical methods to those employed by Neumuller (2015), who uses the PSID to estimate stochastic income processes at the industry level. See the Online Appendix for a detailed description of the data and our sample selection and estimation procedures. 28 These income replacement rates are similar to those estimated by Lusardi et al. (2017) and are close to estimates of total retirement income in the literature (e.g. Aon Consulting, 2008). Note that they are higher than those based solely on Social Security benefits since retired households also derive income from part-time work, employer pension benefits, annuities, etc.

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Fig. 2. Marriage and divorce rates conditional on race, education, and age. Source: Authors’ estimates using data from the 2008–2017 waves of the American Community Survey.

Fig. 3. Average age-income profiles conditional on race, education, and family structure. Source: Authors’ estimates using data from the 1968–2015 waves of the PSID.

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Table 2 Estimated stochastic household income processes conditional on race, education, and number of adults. High school dropout One adult

j ,n π11 j ,n π22

θˆ0, j ,n θˆ1, j ,n θˆ2, j ,n

σˆ e, j,n σˆ ζ, j,n

High school graduate Two adults

One adult

College graduate Two adults

One adult

Two adults

White

Black

White

Black

White

Black

White

Black

White

Black

White

Black

0.939

0.890

0.986

0.973

0.977

0.936

0.994

0.984

0.989

0.987

0.997

0.998

0.645

0.685

0.511

0.705

0.564

0.556

0.491

0.599

0.417

0.300

0.414

0.000

10.160 (0.534) −0.0204 (0.028) 0.0343 (0.035)

7.902 (0.399) 0.0609 (0.021) −0.0586 (0.026)

9.421 (0.174) 0.0666 (0.009) −0.0839 (0.011)

9.348 (0.243) 0.0471 (0.0124) −0.0667 (0.015)

9.535 (0.191) 0.0338 (0.010) −0.0366 (0.013)

8.597 (0.237) 0.0512 (0.012) −0.0531 (0.016)

9.588 (0.079) 0.0704 (0.004) −0.0800 (0.005)

9.430 (0.159) 0.0572 (0.008) −0.0735 (0.010)

9.061 (0.246) 0.0774 (0.013) −0.0926 (0.016)

7.855 (0.468) 0.115 (0.022) −0.136 (0.029)

8.750 (0.113) 0.123 (0.006) −0.136 (0.007)

8.234 (0.328) 0.131 (0.016) −0.157 (0.020)

0.170 (0.057) 0.308 (0.061)

0.340 (0.026) 0.163 (0.100)

0.150 (0.008) 0.143 (0.016)

0.172 (0.008) 0.169 (0.017)

0.169 (0.057) 0.310 (0.061)

0.175 (0.016) 0.256 (0.022)

0.150 (0.008) 0.143 (0.016)

0.163 (0.006) 0.138 (0.015)

0.097 (0.022) 0.221 (0.018)

0.130 (0.020) 0.153 (0.037)

0.086 (0.006) 0.175 (0.006)

0.115 (0.015) 0.150 (0.023)

Source: Authors’ estimates using data from the 1968–2015 waves of the PSID. The age-income profile, expressed in 2016 dollars, is given by f j ,n (ai , j ,t ) = θ0, j ,n + θ1, j ,n ai , j ,t + θ2, j ,n a2i , j ,t (10)−2 , where ai , j ,t is the age of the head of household i in race-education group j which consists of n adults in year t.

Bootstrapped estimates of the biennial√ transitory and permanent income shock volatilities. Annualized estimates of income shock volatilities can be obtained by dividing the biennial estimates by 2. Standard errors in parentheses. See the Online Appendix for details.

Table 3 Income tax schedule. Taxable income per adult relative to median income

Tax rate

0.00–0.37 0.37–0.88 0.88–1.34 1.34–2.40 2.40–∞

0.15 0.28 0.31 0.36 0.39

Source: Chatterjee and Eyigungor (2015).

Table 4 Parameters calibrated outside of the model. Parameter (s)

Value (s)

Source

Initial age, T 0 Retirement age, T R Maximum age, T M Survival probabilities, s j ,t Fraction of adults that are white Intergenerational transmission of education, G (Education|Parent’s race and education)

25 65 95 See Fig. 1 0.822 See Table 1

n/a n/a n/a Masters et al. (2012) U.S. Census Bureau NCES, ELS of 2002

See Fig. 2 1.6 0.950 and 0.494 See Fig. 3 and Table 2 See Text 0.40 0.37 See Table 3 0.135 2%

2008–2017 Waves of the ACS Attanasio et al. (1999) Lockwood (2018) 1968–2015 Waves of the PSID Love (2013) De Nardi (2004) De Nardi (2004) Chatterjee and Eyigungor (2015) See text Campbell and Viceira (2002)

1,2

2,1

Marriage and divorce probabilities, φ j ,t and φ j ,t Coefficient of relative risk aversion, γ Bequest parameters, χ1 and χ2 Stochastic household income processes Income replacement rate during retirement, λ j Persistence of income inheritance process, ρ Volatility of income inheritance process, σω Tax schedule Income floor per adult, y Interest rate on household savings, r s

3.2. Model fit In this section, we evaluate the calibrated model’s ability to replicate some key empirical facts related to the racial wealth gap. To begin, Fig. 4 compares the distribution of wealth across all households in the calibrated model to that observed in the data.29 While the model is calibrated to match just the 10th and 50th percentiles of this distribution, it replicates the

29

See the Online Appendix for a discussion of the data and our sample selection and estimation procedures.

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Table 5 Parameters calibrated to match moments in the data. Moment

Data

Model

Median wealth across all households 10th percentile of the distribution of wealth across all households Median wealth at age 25 across all households

$115,320 −$281 $18,864

$115,994 $173 $19,266

Parameter

Value

Subjective discount factor, β Interest rate on household debt, rd Fraction of bequests left to the grandchildren of the deceased, ϒ

0.980 9.0% 0.107

Note: Wealth levels expressed in 2016 USD. Estimated using data from the 1989–2016 waves of the SCF.

Fig. 4. Distribution of wealth across all households. Source: Calibrated model and authors’ calculations based on data from the 1989–2016 waves of the SCF.

Fig. 5. Distribution of wealth across households by race. Source: Calibrated model and authors’ calculations based on data from the 1989–2016 waves of the SCF.

distribution well from the 10th percentile up until around the 80th percentile. From that point on, however, the model tends to under-predict the wealth held by households.30 Fig. 5 compares the distributions of wealth conditional on race in the calibrated model to those observed in the data. The model replicates the distribution of wealth for white households reasonably well from the 10th percentile up through

30 This deficiency of the model is particularly acute in the far right tail of the distribution. For example, households at the 95th and 99th percentiles of the distribution in the model have wealth equal to $1.4 million and $2.6 million, respectively, compared to $1.9 million and $7.6 million in the data. The inability of our model to match the far right tail of the wealth distribution is consistent with De Nardi (2004) whose model also features a realistically parameterized stochastic household income process and intergenerational links. In her model, the richest 1% and 5% of households, respectively, hold just 18% and 42% of total wealth compared with 29% and 53% in the data. Since the focus of this paper is on understanding racial differences in median wealth, the inability of the model to precisely replicate the far right tail of the wealth distribution is of considerably less importance than its performance in the middle which is reasonably good.

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Fig. 6. Median wealth of black and white households over the life cycle. Source: Calibrated model and authors’ estimates using data from the 1989–2016 waves of the SCF.

the 90th percentile of the distribution. The model also replicates the distribution of wealth for black households reasonably well from the 10th percentile up through around the 80th percentile of the distribution. From that point on, however, the model tends to under-predict the wealth held by black households. The model performs particularly well at and around the median of each respective distribution—the median white household in the model has wealth equal to $154,831 versus $146,790 in the data, while the median black household in the model has wealth equal to $22,267 versus $21,866 in the data. The model-implied racial wealth gap at the median in levels (white–black) is thus $132,564 versus $124,924 in the data, meaning that the model accounts for ($132, 564/$124, 924) = 106.1% of the racial wealth gap in levels. Moreover, the ratio of median wealth (white/black) in the model is 6.95, which is just 3.6% higher than the value of 6.71 observed in the data. Thus, in addition to generating an empirically plausible degree of wealth inequality unconditional on race, the model also produces an empirically plausible degree of racial wealth inequality throughout the middle of the wealth distribution. Figs. 6(a) and (b) compare the model-generated patterns of wealth accumulation over the life cycle for the median white and black household, respectively, to those observed in the data. The model reproduces the hump-shaped pattern, consisting of rapid wealth accumulation prior to retirement followed by the slow decummulation of wealth during retirement, exhibited by white households reasonably well up until around age 85 at which point the model fit begins to deteriorate. The model is also able to match the pattern of wealth accumulation prior to retirement exhibited by black households reasonably well, but cannot explain why wealth rises during retirement and instead predicts a rapid fall in wealth as black households progress through retirement and into old age.31 This deficiency of the model potentially explains why the model also under-predicts the amount of wealth held by black households in the far right tail of the wealth distribution (see Fig. 5). Given that our calibrated model is able to replicate the majority of these key empirical facts reasonably well, we now use it to quantify the extent to which income differences can explain the racial wealth gap. We then explore the mechanisms by which relatively modest income differences are amplified into vast racial disparities in wealth. 3.3. Income differences and the racial wealth gap In our model, black and white households differ along a number of dimensions, including educational attainment, the mean and variance of lifetime earnings, family structure, and the likelihood and persistence of realizing zero labor income. The cumulative effect of racial differences along each of these dimensions corresponds to the income differences that we observe in the data. In this section, we use our calibrated model to quantify the relative importance of each of these factors in accounting for the racial wealth gap. We begin with a version of our calibrated model in which means-tested social insurance and bequest motives are shut down (i.e. y = 0 and χ1 = 0), accidental bequests are equally distribution across recipient households, life expectancy is independent of race, and there are no income differences between black and white households (i.e. black and white households have identical educational attainment, mean and variance of lifetime earnings, family structure, and likelihood and

31 Thompson and Suarez (2015) document a similar divergence between the age-wealth profiles of black and white households in the SCF. The authors propose a potential explanation, namely, differences in labor force participation at and around retirement which we abstract from in our quantitative model. Another potential explanation for this interesting feature of the data are racial differences in the allocation of wealth. While the typical white household shifts their wealth away from real estate and into stock and equity mutual funds prior to retirement, the typical black household does precisely the opposite — the fraction of wealth held in the form of real estate rises as retirement approaches, while the fraction of wealth invested in stock and equity mutual funds falls (see Fig. 2 of the Online Appendix). Imperfections in the housing market, which make it difficult to access wealth held in the form of real estate, combined with the increasing share of real estate in the average black household’s portfolio may therefore explain why the median black household draws down their wealth during retirement more slowly than the median white household whose wealth is mainly held in the form of highly liquid financial assets.

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Table 6 Decomposing the effects of income differences on the racial wealth gap. Counter-factual simulation (1)

(2)

(3)

(4)

(5)

Educational attainment Age-income profiles Volatility of income shocks Family structure Zero income transition matrix

Yes No No No No

Yes Yes No No No

Yes Yes Yes No No

Yes Yes Yes Yes No

Yes Yes Yes Yes Yes

Median wealth gap % of wealth gap explained

$9,494 7.2%

$36,248 27.3%

$47,468 35.8%

$55,235 41.7%

$56,961 43.0%

Source: Calibrated model. Median wealth gap is expressed in 2016 dollars. Percent of wealth gap explained is equal to (Median Wealth Gap in Model X)/ (Median Wealth Gap in Baseline Model)×100%.

persistence of realizing zero labor income). We then sequentially add back racial differences in educational attainment, mean and variance of lifetime earnings, family structure, and likelihood and persistence of realizing zero labor income. For each counter-factual simulation, we recompute the distribution of wealth by race holding all other model parameters fixed. Table 6 summarizes the results of this exercise, reporting the model-implied level difference in median wealth and the percentage of the wealth gap in levels explained for each counter-factual simulation, the latter of which is computed as follows:

% of Wealth Gap Explained =

(Median Wealth Gap in Model X) × 100%. (Median Wealth Gap in Baseline Model)

Column (1) of Table 6 reports the results of our model when we allow only for racial differences in educational attainment. Black households are more likely to be high school dropouts and less likely to be college graduates. As a result, white households will earn more, on average, than black households simply because they are more educated, not because white households earn more than black households conditional on education. Through the lens of our model, the impact of differences in educational attainment on differences in median household wealth is quite modest. This is because even though black households are more likely to be high school dropouts and less likely to be college-educated than white households, the median black household is still a high school graduate. The racial wealth gap in this simulation is $9,494, implying that differences in educational attainment account for 7.2% of the gap. In column (2) of Table 6, we allow for differences in age-income profiles conditional on education, in addition to differences in educational attainment itself. Fig. 3 shows that black households, on average, earn significantly less income throughout the life cycle than white households with identical education and family structure. The marginal impact of these lower age-income profiles on differences in median wealth are substantial — the racial wealth gap increases by $26,754 when differences in age-income profiles are introduced, implying that this feature of our model can explain 27.3% − 7.2% = 20.1% of the gap. In column (3) of Table 6, we introduce differences in the volatility of income shocks, in addition to differences in education and age-income profiles. Table 2 suggests that black households face a higher degree of transitory income uncertainty than white households conditional on education and family structure, while white households tend to face a higher degree of persistent income uncertainty. Since the coefficient of relative risk aversion γ in our calibrated model is greater than one, households are prudent. As a result, higher levels of income uncertainty raise their precautionary saving motive, inducing them to save more to self-insure against income risk. On net, the impact of higher persistent income uncertainly for white households slightly dominates and the racial wealth gap increases by $11,220, implying that volatility differences account for 35.8% − 27.3% = 8.5% of the gap. In column (4) of Table 6, we allow for differences in family structure, in addition to differences in education, age-income profiles, and the volatility of income shocks. In our calibrated model, black households are less likely to have two adults present than white households due to racial differences in the fraction of households married at entrance into the model and racial differences in marriage and divorce rates over the life cycle. Given that households with only one adult present earn substantially less income than those with identical race and education but two adults present and that black households with only one adult present tend to earn less, on average, than white households with identical education but only one adult present (see Fig. 3), allowing for racial differences in family structure reduces the average labor income of black households. The net impact is an increase in the racial wealth gap by $7,767, implying that differences in family structure account for 41.7% − 35.8% = 5.9% of the gap. In column (5) of Table 6, we introduce differences in the likelihood and persistence of realizing zero labor income, in addition to differences in education, age-income profiles, volatility of income shocks, and family structure. Non-college educated black households are more likely to transition to, and remain in, the zero labor income state than white households with identical education and family structure. In addition, black households are more likely than white households to have only one adult present, and households with only one adult present are more likely to transition to, and remain in, the zero labor income state than those with two adults present. As a result, non-college educated black households face a

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Table 7 Decomposing the model-implied racial wealth gap. Model (1)

(2)

(3)

(4)

(5)

Income differences Bequest motives Unequal bequests Income floor Differences in lifespan risk

Yes No No No No

Yes Yes No No No

Yes Yes Yes No No

Yes Yes Yes Yes No

Yes Yes Yes Yes Yes

White median household wealth Black median household wealth Ratio of median wealth

$166,050 $109,089 1.52

$238,546 $143,611 1.66

$193,668 $64,556 3.00

$153,968 $25,201 6.11

$154,831 $22,267 6.95

Median wealth gap % of median wealth gap explained

$56,961 43.0%

$94,935 71.6%

$129,112 97.4%

$128,767 97.1%

$132,564 100.0%

Note: Levels of wealth are expressed in 2016 dollars. Differences in income represents the combined effect of racial differences in educational attainment, mean and variance of lifetime earnings, family structure, and likelihood and persistence of realizing zero labor income. % of Median Wealth Gap Explained = (Median Wealth Gap in Model X)/(Median Wealth Gap in Baseline Model)×100%.

substantially higher likelihood and persistence of realizing zero labor income than similarly educated white households. This has two competing effects. First, since households are prudent, this raises the precautionary saving motive for black households relative to white households, inducing black households to save more in an effort to self-insure against this additional income risk. Second, realizing the zero labor income state inhibits the ability of households to build wealth. Since black households are at higher risk of realizing the zero labor income state, this effect is more acute for black households than their white counterparts. Our results suggest that this latter effect slightly dominates, leading to a further reduction in the median wealth of black households relative to white households. The racial wealth gap rises by $1,726 when we introduce differences in the likelihood and persistence of realizing zero labor income, implying that this feature of our model accounts for just 43.0% − 41.7% = 1.3% of the gap. In our model, income differences are represented by the sum of differences in education, age-income profiles, income volatility, family structure, and the likelihood and persistence of realizing zero labor income. Our results thus suggest that income differences, in the absence of the income floor, voluntary bequests, and racial differences in lifespan risk, can explain 43.0% of the racial gap in the level of median household wealth. 3.4. Accounting for the racial wealth gap Differences in lifespan uncertainty, the income floor, bequest motives, and unequal bequests likely interact with income differences in quantitatively important ways, thereby allowing our model to fully account for the racial wealth gap observed in the data. In this section, we use our model to quantify the relative importance of each of these factors in accounting for racial differences in median household wealth. We again begin with a version of our calibrated model in which the income floor and bequest motives are shut down (i.e. y = 0 and χ1 = 0), accidental bequests are equally distributed across recipient households, life expectancy is independent of race, and there are no income differences between black and white households. We then sequentially add back racial differences in income (represented by the combined effect of racial differences in educational attainment, mean and variance of lifetime earnings, family structure, and likelihood and persistence of realizing zero labor income), intergenerational transfers of wealth, bequest motives, the income floor, and racial difference in lifespan risk. In each case, we recompute the stationary distribution of wealth holding all other model parameters fixed. Table 7 summarizes the results of this exercise, reporting the model-implied median wealth gap and the percentage of the wealth gap explained in each case. Column (1) of Table 7 reports the results of our model when we allow only for racial differences in income, which are represented by the combined effect of racial differences in educational attainment, mean and variance of lifetime earnings, family structure, and likelihood and persistence of realizing zero labor income. In this counter-factual simulation, the model slightly over-predicts the wealth held by the median white household ($166,050 in the model vs. $146,790 in the data), but severely over-predicts the wealth held by the median black household ($109,089 in the model vs. $21,866 in the data). The model-implied racial wealth gap in levels (white–black) is thus $56,961 versus a value of $124,924 in the data, while the model-implied ratio of median wealth (white/black) is 1.52 versus a value of 6.71 in the data. In order to explain the remainder of the racial wealth gap, the model requires additional mechanisms that disproportionately hinder the ability of the median black household to accumulate wealth. Fig. 7 compares the distributions of wealth in this counter-factual simulation to those observed in the data. In order to better fit the data, these mechanisms should also increase the wealth held by white households above the median and decrease the wealth held by black households throughout the distribution. We now explore the extent to which bequest motives, unequal bequests, the income floor, and differences in lifespan risk bring the model closer to the data along each of these dimensions. In column (2) of Table 7, we reintroduce bequest motives (i.e. χ1 > 0) but continue to assume that bequests are equally distributed across recipient households. This counter-factual exercise therefore isolates the effect of the bequest motive to

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Fig. 7. Distribution of wealth across households by race. Model (1) isolates the effect of income differences in the absence of the income floor, differences in lifespan risk, and bequest motives, where accidental bequests are equally distributed across recipient households. Model (2) introduces bequest motives. Model (3) allows for direct intergenerational transfers of wealth between family members. Model (4) introduces the income floor. Model (5) allows for racial differences in lifespan risk and, thus, corresponds to the baseline model.

save from the cumulative effect of differences in intergenerational transfers of wealth over many generations. Since bequests in our calibrated model are luxury goods, the marginal incentive to save in order to leave a larger bequest is increasing with household wealth. As white households hold more wealth than black households, introducing a plausibly calibrated bequest motive raises the saving rate of white households relative to black households, particularly for households in the upper quantiles of the wealth distribution. However, because bequests are equally distributed across recipient households, the wealth held by both black and white households increases at the median (Table 7) and throughout each respective distribution (Fig. 7). While the ratio of median wealth remains largely unchanged when we introduce bequest motives (1.66 versus 1.52), the racial wealth gap in levels rises by $37,974, implying that bequest motives can explain 71.6% − 43.0% = 28.6% of the gap. In column (3) of Table 7, we allow for direct intergenerational transfers of wealth between family members. Moving from an environment in which bequests are equally distributed across recipient households to an environment with unequal bequests necessarily reduces wealth held by low income, low wealth households relative to their high income, high wealth peers. Moreover, the cumulative effect of differences in intergenerational transfers of wealth over many generations substantially increases the concentration of wealth in the upper tails of the distribution, the majority of whom are white. From Fig. 7, we see that allowing for unequal bequests reduces the wealth held by black households throughout the distribution and the wealth held by white households in the bottom three quarters of the distribution. Conversely, wealth increases for white households in the upper quartile of the distribution as it is these households that are most likely to give and receive large bequests. The ratio of median wealth rises from 1.66 to 3.00 and the racial wealth gap in levels increases by $34,177, implying that direct intergenerational transfers of wealth between family members, in the presence of bequest motives, can explain 97.4% − 71.6% = 25.8% of the gap.

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In column (4) of Table 7, we reintroduce the income floor (i.e. y > 0). Recall that black households, on average, earn less income than white households and are far more likely to transition to and remain in the zero labor income state. Black households in our model are, therefore, more likely to qualify for and benefit from this form of social insurance. As a result, reintroducing the income floor disproportionately reduces the precautionary saving motive of black households relative to white households, particularly for those in the lower portions of the wealth distribution. The income floor thus amplifies the effect of income on wealth by reducing the incentive of low income, low wealth households to accumulate wealth while leaving the incentive of high income, high wealth households to accumulate wealth unchanged (as they are less likely to qualify for and benefit from the income floor). From Fig. 7 we see that, when the income floor is introduced, wealth falls for black households throughout the distribution and for white households in the bottom three quarters of the distribution. The effects are proportionately larger, however, for black households. While the median wealth of white households falls by 20.5% in response to reintroducing the income floor, the median wealth of black households drops by 61.0%. The net result is a more than doubling in the ratio of median wealth from 3.00 to 6.11. However, because the median wealth of white and black households falls by approximately the same amount in levels, the median wealth gap remains largely unchanged and, in fact, decreases slightly. Thus, while the income floor brings the model-generated distributions of wealth closer to the data and causes the ratio of median wealth to more than double, this feature of the model accounts for just 97.1% − 97.4% = −0.3% of the racial wealth gap. Finally, in column (5) of Table 7, we reintroduce racial differences in lifespan risk. The results presented in column (5) thus correspond to those of our baseline model. On the one hand, black households face substantially higher mortality rates, particularly early in retirement, which reduces their incentive to save for retirement relative to white households. On the other hand, higher mortality rates reduce the age at which black households expect to leave a bequest relative to white households, which raises the present value of utility from bequests for black households relative to white households. On net, the former force slightly dominates the latter, as the median wealth of black households falls by 11.6%, which causes the ratio of median wealth to rise by 13.7% to 6.95. However, the wealth gap in levels increases by just $3,797. Thus, while differences in lifespan risk bring the model-implied ratio of median wealth within just 3.6% of the value observed in the data, this feature of the model explains just 100.0% − 97.1% = 2.9% of the racial wealth gap in levels. 3.5. Intergenerational transfers of wealth Given the important role that intergenerational transfers of wealth appear to play in accounting for racial disparities in wealth, in this section we explore how the distribution of transfers in the model compares to that observed in the data. As our basis for comparison, we document the empirical distribution of bequests using data from the RAND Health and Retirement Study (HRS) Longitudinal File 2014 (v2), which is an easy-to-use dataset based on the HRS core data.32 This file was developed at RAND with funding from the National Institute on Aging and the Social Security Administration. We use wealth in the last period in which an individual is alive as a proxy for realized bequests since it is better-measured than actual bequests. This approach is consistent with De Nardi (2004), De Nardi et al. (2010), and Lockwood (2018), among others. Fig. 8 compares the model generated distributions of realized bequests, conditional on race, to those observed in the HRS data. Importantly, no moments of either bequest distribution were directly targeted as part of our calibration exercise. The model does a good job at matching the majority of the distribution of bequests left by black adults, including the relatively large fraction who leave zero bequests to their descendants. The distribution generated by the model for white adults compares very well to the HRS data, including the relatively large fraction who leave zero bequests to their descendants, until around the 60th percentile of the bequest distribution. From this point on, the model predicts larger bequests than those observed in the HRS data. This discrepancy is similar to that identified by De Nardi (2004), who compares bequests in her model to the distribution of estates documented by Hurd and Smith (1999) using AHEAD data for single decedents.33 These discrepancies between model and data are likely due in large part to the fact that the HRS does not over-sample rich households. Indeed, Sierminska et al. (2008) find that while the top 1% of households in the SCF, which does over-sample rich households, hold nearly 33% of all wealth held by the elderly, the corresponding statistic in the HRS, which does not over-sample rich households, is just 17%. We also compare the model’s predictions for the total volume of bequested wealth to that observed in the data. Kotlikoff and Summers (1981) find that intergenerational transfers account for the vast majority of aggregate wealth in the U.S. In particular, the authors estimate the stock of transfer wealth in the U.S. was $3.151 trillion in 1974. The authors then estimate that, in order to account for this vast sum of wealth, the annual flow of transfers would need to be approximately $70 billion. Given a total net worth for the household sector of $3.884 trillion in 1974, the implied ratio of annual intergenerational transfers of wealth to the stock of household wealth is 0.0180. Using a similar approach, Gale and Scholz (1994) estimate that the total flow of intergenerational transfers in 1986, including bequests and college payments, was $203 billion. Given a total net worth for the household sector of $11.976 trillion in 1986, the implied ratio of annual intergenerational transfers

32 The HRS (Health and Retirement Study, 2019) is sponsored by the National Institute on Aging (grant number NIA U01AG009740) and is conducted by the University of Michigan. 33 See Fig. 3 in De Nardi (2004). Also note that AHEAD is an HRS auxiliary study.

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Fig. 8. Cumulative distribution function of wealth in the last wave/period in which an individual is alive among individuals who die during the sample period. Source: Calibrated model and authors’ calculations using the RAND HRS Longitudinal File 2014 (v2) which includes data from the 1992–2014 waves of the Health and Retirement Study.

of wealth to the stock of household wealth is 0.0170. The calibrated model compares favorably along this dimension as well. Specifically, the ratio of annual intergenerational transfers of wealth to the stock of household wealth in the calibrated model is 0.0158, which is 12% less than the corresponding estimate reported by Kotlikoff and Summers (1981) and just 7% less than the corresponding estimate reported by Gale and Scholz (1994). 4. Conclusion We study the racial wealth gap through the lens of a quantitative, overlapping-generations, incomplete markets, life-cycle model. The calibrated model generates an empirically plausible degree of wealth inequality, both conditional and unconditional on race, and is broadly consistent with observed patterns of wealth accumulation over the life cycle. Simulations of the model suggest that income differences alone can explain 43.0% of the racial wealth gap in levels (white–black). Once we account for realistic, race-independent bequest motives, however, the model is able to explain the entire racial wealth gap in levels. While the income floor and differences in lifespan risk explain very little of the racial wealth gap in levels, they

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differentially reduce the incentive for low income, low wealth households, the majority of whom are black, to save, which leads to a more than doubling of the model-implied ratio of median wealth (white/black), bringing it into an empirically plausible range. Our results have a number of important policy implications. First, differences in labor income appear to be the proximate cause of the racial wealth gap. This is to say that, if the income gap in our model were eliminated, racial disparities in wealth would eventually disappear. Thus, policies aimed at reducing income differences are likely to be the most direct and potent means for reducing the racial wealth gap. Second, to the extent that income differences prove too difficult to eliminate via policy intervention, there may be scope for redistribution policies aimed at directly reducing racial disparities in wealth. Insofar as intergenerational transfers of wealth are an important driver of racial wealth inequality, and our results suggest that this is indeed the case, then it might prove fruitful for policy makers and researchers to explore how changes to estate taxation laws impact racial wealth inequality. Finally, although the social safety net clearly plays an important role in insuring low-income, low-wealth households against labor market risk, our results suggest that welfare programs which act as an income floor may in fact contribute in a meaningful way to observed racial disparities in wealth via their disproportionate impact on precautionary saving by black households. Our results highlight the need for policy makers to consider the potential for welfare programs which act as an income floor to differentially impact saving incentives and, as a result, exacerbate racial wealth inequality. It has been known for some time that income differences are a significant factor in understanding racial wealth inequality. The typical approach in the literature prior to this study was to employ a Blinder-Oaxaca means-coefficient analysis, using regressions estimated separately by race.34 However, estimates of how much of the racial wealth gap can be attributed to differences in income vary widely depending on whether the coefficients employed are from the white or black regression equations.35 As a result, the existing empirical literature has failed to reach a consensus regarding the quantitative importance of income differences in accounting for the racial wealth gap. The results presented here shed some light on why this might be. In our model, the extent to which bequest motives and the presence of an income floor affect a household’s incentive to save is strongly correlated with income and wealth. In particular, low income, low wealth households are more likely to qualify for and benefit from welfare programs, which reduces their incentive to save. To the extent that bequests are a luxury good (and there is considerable evidence in support of this view) the bequest motive to save is essentially non-existent for these same households. Conversely, high income, high wealth households are largely unaffected by the presence of an income floor and have a sizable bequest motive to save. Differences in the bequest motive to save lead to large differences in the distribution of bequests, which have large cumulative effects over many generations on wealth inequality. For these reasons, the relationship between income and wealth in our model is highly non-linear. Given that black and white households tend to populate vastly different regions of the income distribution, it is not at all surprising that estimates of how much of the racial wealth gap can be attributed to differences in income vary widely depending on whether the coefficients employed are from the white or black regression equations. Indeed, one key benefit of approaching this question through the lens of a quantitative, incomplete markets, life-cycle model is that we need not place any restrictions a priori on the relationship between income and wealth. While our study makes a meaningful contribution to the literature that aims to understand the causes of racial wealth inequality in the U.S., it is not without its limitations. First and foremost, the only decision households face in our model is how much to save (and leave as a bequest)—they can’t adjust along any other margin. Second, the only vehicle for saving is a risk-free bond. Third, intergenerational transfers of wealth and income are assumed to be independent of the process governing the intergenerational transmission of education. One potential avenue for future research would therefore be to explore whether the results presented here hold up in environments that include, for example, a labor-leisure decision, endogenous marriage and divorce, investment in human capital (i.e. education), risky financial assets, and/or housing investment, the latter of which may prove particularly useful in understanding why the median black household draws down their wealth during retirement far more slowly than is predicted by our model. Finally, to maintain tractability, we focus our analysis here exclusively on the steady state of our model economy. This is in contrast to previous work by White (2007) and contemporaneous work by Aliprantis et al. (2018), each of which study how the racial wealth gap evolves along the transition path of their respective model economies. An implicit assumption in our analysis, therefore, is that the environment is stationary. While this is a standard assumption in quantitative models of wealth inequality (see, for example, Cagetti and De Nardi, 2008, and De Nardi and Fella, 2017), the validity of this assumption for the question at hand is tenuous at best. Over the last few decades, for example, increases in the incarceration rate of black males likely induces time variation in the likelihood and persistence of the zero income state for black households. In addition, marriage and divorce rates are known to vary across cohorts, educational attainment has been rising for both black and white households over the last few decades, and marginal tax rates in the U.S. have changed multiple times in

34 See, for example, Smith (1995), Oliver and Shapiro (1997), Hurst et al. (1998), Blau and Graham (1990), Avery and Rendall (1997), Menchik and Jianakoplos (1997), and Altonji and Doraszelski (2005), among others. 35 In an effort to resolve these empirical challenges, Barsky et al. (2002) use a nonparametric model to simulate white wealth over the black earnings distribution and find that differences in income can explain about two-thirds of the wealth gap.

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recent years. Another potential avenue for future research would thus be to explore how the relationship between income and wealth, and the implied racial wealth gap, varies over time in an economy that is far from its steady state. Appendix. Supplementary material Supplementary material (Online Appendix) related to this article can be found online at https://doi.org/10.1016/j.red. 2019.06.004. References Aiyagari, S.R., Greenwood, J., Guner, N., 2000. On the state of the union. Journal of Political Economy 108 (2), 213–244. Aliprantis, D., Carroll, D., Young, E., 2018. The dynamics of the racial wealth gap. http://cicm.pbcsf.tsinghua.edu.cn/Public/Uploads/upload/cicm_paper/ Inequality%20in%20Macroeconomics-02-Eric%20Young.pdf. Altonji, J.G., Doraszelski, U., 2005. The role of permanent income and demographics in black/white differences in wealth. The Journal of Human Resources 40 (1), 1–30. Aon Consulting, 2008. Replacement Ratio Study: A Measurement Tool for Retirement Planning. Aon, Global Corporate Marketing and Commmunications, Chicago. Attanasio, O.P., Banks, J., Meghir, C., Weber, G., 1999. Humps and bumps in lifetime consumption. Journal of Business & Economic Statistics 17 (1), 22–35. Avery, R.B., Rendall, M.S., 1997. The Contribution of Inheritances to Black-White Wealth Disparities in the United States. Cornell University, Ithaca New York. Barsky, R., Bound, J., Charles, K.K., Lupton, J.P., 2002. Accounting for the black–white wealth gap: a nonparametric approach. Journal of the American Statistical Association 97 (459), 663–673. Bayer, P., Charles, K.K., 2018. Divergent paths: a new perspective on earnings differences between black and white men since 1940. The Quarterly Journal of Economics 133 (3), 1459–1501. Bewley, T., 1977. The permanent income hypothesis: a theoretical formulation. Journal of Economic Theory 16 (2), 252–292. Black, H., Schweitzer, R.L., Mandell, L., 1978. Discrimination in mortgage lending. The American Economic Review 68 (2), 186–191. Blau, F.D., Graham, J.W., 1990. Black-white differences in wealth and asset composition. The Quarterly Journal of Economics 105 (2), 321–339. Cagetti, M., De Nardi, M., 2008. Wealth inequality: data and models. Macroeconomic Dynamics 12 (S2), 285–313. Campbell, J.Y., Viceira, L.M., 2002. Strategic Asset Allocation: Portfolio Choice for Long-Term Investors. Clarendon Lectures in Economic. Carroll, C.D., 1997. Buffer-stock saving and the life cycle/permanent income hypothesis. The Quarterly Journal of Economics 112 (1), 1–55. Carroll, C.D., Hall, R.E., Zeldes, S.P., 1992. The buffer-stock theory of saving: some macroeconomic evidence. Brookings Papers on Economic Activity 1992 (2), 61–156. Carroll, C.D., Samwick, A.A., 1997. The nature of precautionary wealth. Journal of Monetary Economics 40 (1), 41–71. Castaneda, A., Díaz-Giménez, J., Ríos-Rull, J.-V., 2003. Accounting for the US earnings and wealth inequality. Journal of Political Economy 111 (4), 818–857. Caucutt, E.M., Guner, N., Rauh, C., 2018. Is Marriage for White People? Incarceration, Unemployment, and the Racial Marriage Divide. Charles, K.K., Hurst, E., Roussanov, N., 2009. Conspicuous consumption and race. The Quarterly Journal of Economics 124 (2), 425–467. Chatterjee, S., Eyigungor, B., 2015. A quantitative analysis of the US housing and mortgage markets and the foreclosure crisis. Review of Economic Dynamics 18 (2), 165–184. Chiteji, N.S., Stafford, F.P., 1999. Portfolio choices of parents and their children as young adults: asset accumulation by African-American families. The American Economic Review 89 (2), 377–380. Cubeddu, L., Ríos-Rull, J.-V., 2003. Families as shocks. Journal of the European Economic Association 1 (2–3), 671–682. De Nardi, M., 2004. Wealth inequality and intergenerational links. The Review of Economic Studies 71 (3), 743–768. De Nardi, M., Fella, G., 2017. Saving and wealth inequality. Review of Economic Dynamics 26, 280–300. De Nardi, M., French, E., Jones, J.B., 2010. Why do the elderly save? The role of medical expenses. Journal of Political Economy 118 (1), 39–75. De Nardi, M., Yang, F., 2014. Bequests and heterogeneity in retirement wealth. European Economic Review 72, 182–196. Duncan, G.J., 1984. Years of Poverty – Years of Plenty: The Changing Economic Fortunes of American Workers and Families. Institute for Social Research, Ann Arbor, MI. Edelberg, W., 2007. Racial Dispersion in Consumer Credit Interest Rates. Gale, W.G., Scholz, J.K., 1994. Intergenerational transfers and the accumulation of wealth. The Journal of Economic Perspectives 8 (4), 145–160. Gittleman, M., Wolff, E.N., 2000. Racial Wealth Disparities: Is the Gap Closing? Levy Economics Institute Working Paper No. 311. Gittleman, M., Wolff, E.N., 2004. Racial differences in patterns of wealth accumulation. The Journal of Human Resources 39 (1), 193–227. Goodman, L.S., Mayer, C., 2018. Homeownership and the American dream. The Journal of Economic Perspectives 32 (1), 31–58. Greenwood, J., Guner, N., Knowles, J.A., 2003. More on marriage, fertility, and the distribution of income. International Economic Review 44 (3), 827–862. Gruber, J., Yelowitz, A., 1999. Public health insurance and private savings. Journal of Political Economy 107 (6), 1249–1274. Guvenen, F., Karahan, F., Ozkan, S., Song, J., 2015. What do Data on Millions of us Workers Reveal About Life-Cycle Earnings Risk? Technical report. NBER. Health and Retirement Study, 2019. RAND HRS Longitudinal File 2014 (v2) public use dataset. Produced and distributed by the University of Michigan with funding from the National Institute on Aging (grant number NIA U01AG009740). Hubbard, R.G., Skinner, J., Zeldes, S.P., 1995. Precautionary saving and social insurance. Journal of Political Economy 103 (2), 360–399. Huggett, M., 1996. Wealth distribution in life-cycle economies. Journal of Monetary Economics 38 (3), 469–494. Hurd, M.D., Smith, J.P., 1999. Anticipated and Actual Bequests. Technical report. National Bureau of Economic Research. Hurst, E., Luoh, M.C., Stafford, F.P., Gale, W.G., 1998. The wealth dynamics of American families, 1984–1994. Brookings Papers on Economic Activity 1998 (1), 267–337. Hurst, E., Ziliak, J.P., 2006. Do welfare asset limits affect household saving? Evidence from welfare reform. The Journal of Human Resources 41 (1), 46–71. Kotlikoff, L.J., Summers, L.H., 1981. The role of intergenerational transfers in aggregate capital accumulation. Journal of Political Economy 89 (4), 706–732. Krusell, P., Smith Jr, A.A., 1998. Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy 106 (5), 867–896. Lang, K., Lehmann, J.-Y.K., 2012. Racial discrimination in the labor market: theory and empirics. Journal of Economic Literature 50 (4), 959–1006. Li, W., Yang, F., 2010. American dream or American obsession? Business Review (Federal Reserve Bank of Philadelphia) 20 (30). Lockwood, L.M., 2018. Incidental bequests and the choice to self-insure late-life risks. The American Economic Review 108 (9), 2513–2550. Loury, G.C., 1998. Why more blacks don’t invest. The New York Times, 70–71. Love, D., Schmidt, L., 2015. Comprehensive Wealth of Immigrants and Natives. University of Michigan Retirement Research Center Working Paper 328. Love, D.A., 2013. Optimal rules of thumb for consumption and portfolio choice. The Economic Journal 123 (571), 932–961. Low, H., Meghir, C., Pistaferri, L., 2010. September. Wage risk and employment risk over the life cycle. The American Economic Review 100 (4), 1432–1467. Lusardi, A., Michaud, P.-C., Mitchell, O.S., 2017. Optimal financial knowledge and wealth inequality. Journal of Political Economy 125 (2), 431–477.

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Lusardi, A., Mitchell, O.S., 2007. Baby boomer retirement security: the roles of planning, financial literacy, and housing wealth. Journal of Monetary Economics 54 (1), 205–224. Lusardi, A., Mitchelli, O.S., 2007. Financial literacy and retirement preparedness: evidence and implications for financial education. Business Economics 42 (1), 35–44. Masters, R.K., Hummer, R.A., Powers, D.A., 2012. Educational differences in U.S. adult mortality: a cohort perspective. American Sociological Review 77 (4), 548–572. Menchik, P.L., Jianakoplos, N.A., 1997. Black-white wealth inequality: is inheritance the reason? Economic Inquiry 35 (2), 428–442. Neal, D., Rick, A., 2014. The Prison Boom and the Lack of Black Progress After Smith and Welch. Technical report. National Bureau of Economic Research. Neumark, D., Powers, E., 1998. The effect of means-tested income support for the elderly on pre-retirement saving: evidence from the SSI program in the US. Journal of Public Economics 68 (2), 181–206. Neumuller, S., 2015. Inter-industry wage differentials revisited: wage volatility and the option value of mobility. Journal of Monetary Economics 76, 38–54. Oliver, M.L., Shapiro, T.M., 1995. Black Wealth/White Wealth. Routledge, New York. Oliver, M.L., Shapiro, T.M., 1997. Black Wealth, White Wealth: A New Perspective on Racial Inequality. Routledge. Quadrini, V., 1999. The importance of entrepreneurship for wealth concentration and mobility. The Review of Income and Wealth 45 (1), 1–19. Rauh, C., Valladares-Esteban, A., 2018. Wage and employment gaps over the lifecycle–the case of black and white males in the US. Technical report, mimeo. Ruggles, S., Flood, S., Goeken, R., Grover, J., Meyer, E., Pacas, J., Sobek, M., 2018. IPUMS USA: Version 8.0 [dataset]. Scholz, J.K., Levine, K., 2002. US black-white wealth inequality: a survey. University of Wisconsin-Madison. Manuscript. Scholz, J.K., Seshadri, A., Khitatrakun, S., 2006. Are Americans saving “optimally” for retirement? Journal of Political Economy 114 (4), 607–643. Sierminska, E., Michaud, P.-C., Rohwedder, S., 2008. Measuring Wealth Holdings of Older Households in the US: A Comparison Using the HRS, PSID and SCF. Smith, J.P., 1995. Racial and ethnic differences in wealth in the health and retirement study. Journal of Human Resources, S158–S183. Thompson, J.P., Suarez, G., 2015. Exploring the Racial Wealth Gap Using the Survey of Consumer Finances. FEDS Working Paper No. FEDGFE2015-76. Western, B., 2002. The impact of incarceration on wage mobility and inequality. American Sociological Review 67 (4), 526–546. White, T.K., 2007. Initial conditions at emancipation: the long-run effect on black–white wealth and earnings inequality. Journal of Economic Dynamics and Control 31 (10), 3370–3395. Wolff, E.N., 1998. Recent trends in the size distribution of household wealth. The Journal of Economic Perspectives 12 (3), 131–150. Zeldes, S.P., 1989. Optimal consumption with stochastic income: deviations from certainty equivalence. The Quarterly Journal of Economics 104 (2), 275–298. Ziliak, J.P., 2003. Income transfers and assets of the poor. Review of Economics and Statistics 85 (1), 63–76.