Wealth Accounting Framework Patterns of Wealth Accumulation by Race

Interestingly, economic theory does not offer unambiguous predictions about the ef- fect of racial discrimination in the small business credit market with respect to the rate of return to business ownership for African Americans relative to whites. If such discrim- ination occurs in the form of higher credit costs, it can lower the relative rate of return. If, however, a lack of access to credit causes African Americans to be unable to start businesses that a similarly qualiŽed white would be able to, then, on average, African American entrepreneurs able to start businesses would be expected to be better qualiŽed than their white counterparts, and thus have a higher rate of return. The various models that have been developed to study the behavior of consump- tion have implications for the pattern of household saving rates by race Browning and Lusardi 1996; Browning and Crossley 2001. Life-cycle models predict that, because African Americans have shorter life expectancies and larger families, they will consume at a faster rate than whites. Though economists have not yet reached a consensus on the importance of precautionary saving and the appropriate proxy for the uncertainty that generates it Browning and Lusardi 1996; Carroll, Dynan, and Krane 1999, African Americans experience greater income uncertainty Gittle- man and Joyce 1996; Mazumder 2001. In buffer-stock saving models, the volatility of income increases the necessity of building up savings, but also makes it more likely that reserves will have to be drawn down Carroll 1997. Differences by race also may emerge because saving as a proportion of current income tend to rise with current income, and whites have higher levels of current income than do African Americans. In standard models, this relationship between saving rates and current income may occur because households with high levels of transitory income may be saving at a faster clip to offset expected lower income in the future Dynan, Skinner, and Zeldes 2000. A number of other economic explanations also have been offered, in addition to an array of psychological and sociological theories Beverly 1997; Carney and Gale 1999. These economic theories include that relative to the rest of the population, low-income households may be more impatient Lawrance 1991, have a higher Social Security replacement rate, and have more limited access to institutionalized saving mechanisms such as 401k plans. Further, the saving behavior of African Ameri- cans may be more affected than that of whites by the presence of asset-based, means- tested social insurance programs, because of the higher concentration of African Ameri- cans in the low-income population. Programs such as AFDCTANF and Medicaid may depress saving by providing a consumption oor and thereby reducing income uncer- tainty and thus the need for precautionary saving, and by imposing assets limits that, in some circumstances, effectively tax assets at a rate of 100 percent for those who are income-eligible for a program but have savings above the threshold Hubbard, Skinner, and Zeldes 1995.

B. Wealth Accounting Framework

To examine differences in wealth accumulation by race, we employ a simple wealth accounting framework. The wealth of a household at any point in time can be repre- sented by the following formula: for each household on the basis of the actual portfolio composition of each household. They concluded that racial differences in rates of return were not important in explaining racial differences in wealth levels. 1 W ft 5 A a51 p aft W aft where W 5 net worth in constant dollars, p represents the share of each asset in the portfolio, f is the index for family, t for time, and a for asset. Assuming that there are no changes in portfolio allocation, the change in wealth between periods t and t 11 can be expressed as follows: 2 DW f 5 A a 5 1 r aft p aft W aft 1 s ft I ft 1 T ft where r represents the rate of return, s the rate of saving out of income, I family income and T the amount of inheritances or gifts received by the family. 6 It is possible that gifts can come from nonrelatives, though for ease of exposition we will some- times refer to them as family transfers. It may be worth emphasizing that given what may be substantial differences across families in the path of asset prices within the broad groups of assets noted above, the rates of return are family- and period-spe- ciŽc,. Finally, the rate of change in wealth is the ratio of the Equation 2 to Equation 1: 3 DW f W ft 5 A a 5 1 r aft p aft W aft 1 s ft I ft 1 T ft W ft Formula 3 makes clear that the rate of accumulation for a family starting the period with wealth W ft depends on Žve factors: 1 the rates of returns on assets; 2 portfolio allocation; 3 the saving rate; 4 the income level; and 5 the amount of transfers. All Žve factors may differ by race and thus are potential causes of disparate patterns of wealth accumulation by race. Because our sample restriction that the head of household must be the same over time does allow for some changes in household composition that have an important inuence on wealth—for example, marriage, divorce, and death of spouse— it is also necessary to take account of changes in household composition on wealth. 7 In addition, as noted above, ows of funds related to pension annuities are not included in net worth and need to be tracked as well. Augmenting Equation 3 to take into account the effects of changes in household composition and of ows related to pension annuities, we have: 3 ¢ DW f W ft 5 A a 5 1 r aft p aft W aft 1 s ft I ft 1 H ft 1 P ft W ft 6. Because the PSID does not track gifts made by a family, we assume that these gifts do not exist. 7. As is discussed in greater detail in the Appendix, because the PSID classiŽes the male as the head of household in the case of couples, a male respondent going through changes in marital status is tracked, but a female respondent who changes marital status is not tracked. Because some households are not tracked, the effects of household composition would not be expected to net to zero, as they should for the population as a whole. Another reason is that we exclude from the analysis households undergoing major changes in composition, so that children who, between waves, leave the parental home to head their own households are not included in the analysis. where H is the net change in wealth resulting from assets being brought into or removed from family holdings as a result of changes in household composition and P is the net ow of funds out of pension annuities.

C. Descriptive Analysis 1. Wealth Levels