Simulations Simulations and Sensitivity Analysis

Table 9 Racial Differences in the Rate of Wealth Appreciation African American – White, 1984– 94 Type of regression OLS OLS OLS Median Median Median Period 1984– 89 20.057 0.007 20.082 20.164 20.087 20.149 0.142 0.142 0.139 0.057 0.066 0.051 1989– 94 0.120 0.168 0.093 20.088 20.025 0.033 0.341 0.343 0.345 0.058 0.055 0.059 1984– 94 0.041 0.174 0.015 20.293 20.044 20.066 0.385 0.385 0.383 0.145 0.103 0.080 Other Income 1 Income 1 regressors None Income others None Income others Notes: The rate of wealth appreciation is deŽned as the change in wealth divided by initial wealth. Rates are calculated only if the denominator is positive. The racial difference is the coefŽcient on a dummy variable for African Americans. Standard errors are in parentheses. Total family income over the time span and its square are the income variables, while the other regressors are initial wealth and its square, age of head and its square, sex and education of head, marital status at start and end of period, number of children and inheritances over the period. The trimmed longitudinal samples are used for OLS and the untrimmed ones for median regressions for details, see the appendix on the JHR website. Regressions use PSID family weights multiplied by wealth at the start of period. signiŽcant at 10 percent level signiŽcant at 5 percent level signiŽcant at 1 percent level appreciation of African Americans relative to whites. Because of this reduced gap and to the imprecision of the estimates, the OLS results do not show any statistically signiŽcant differences by race. For the median regressions, the baseline regressions match the results of Table 5, where whites have a substantially higher rate of wealth appreciation for 1984– 89 and 1984– 94. The statistical signiŽcance of this difference remains when other controls are added for 1984– 89, but not for 1984– 94. As noted above, in their multivariate analysis of wealth accumulation, Hurst, Luoh, and Stafford 1998 do not usually Žnd the coefŽcient for the race dummy to be statisti- cally signiŽcant.

IV. Simulations and Sensitivity Analysis

A. Simulations

In this section, we conduct counterfactual experiments to calculate what the racial wealth gap would have been at the end of each period had the behavior of African Americans been identical to that of whites with respect to the following dimensions: 1 portfolio allocation; 2 rate of return on capital; 3 saving as a share of income; 4 family income; 5 inheritance; and 6 changes in household composition. The experiments are performed both by changing one of these dimensions at a time and by changing all six simultaneously. We examine changes in mean values only be- cause of the difŽculty of conducting such experiments to examine counterfactuals for median wealth. The traditional Blinder-Oaxaca method is based on a regression framework to divide racial wage differentials into a productivity component and a residual that is usually interpreted as resulting from discrimination. The difŽculty of knowing which wage structure would exist in the absence of discrimination is typically addressed by performing two decompositions— the Žrst using the regression coefŽcients for whites and the second using the regression coefŽcients for African Americans. In more recent work, Oaxaca and Ransom 1994 demonstrate that under certain as- sumptions it is appropriate to make the calculations using the wage structure derived from a regression that pools both races. Though our application is quite different because we employ the wealth accounting framework of Equation 3 ¢ rather than a regression framework and do not try to estimate the portion of the wealth gap attribut- able to discrimination, we follow an analogous approach. In particular, in our count- erfactual experiments we calculate what the racial wealth ratio would have been at the end of the period if the behavior of African Americans and whites were, on average, identical to that of the full sample. For example, in the saving rate simula- tions we recalculate the change in both African American and white wealth that would have occurred had the share of income devoted to saving for each race equaled that for the sample as a whole. We, thus, avoid the need to produce two sets of results—one where we assume that African Americans have the same saving rate as whites, and the other the converse. We have nonetheless checked the pooled re- sults against these two alternatives and Žnd little difference. The most striking Žnding to emerge from the results of the 1984– 94 simulation shown in Table 10 is that decades would be required for the wealth gap to close or even for the wealth ratio to approach the income ratio, when one component is changed at a time. Indeed, even with the dramatic changes in behavior implied by these experiments changes that no policy could easily accomplish, simulated Afri- can American wealth levels remain at just a fraction of those of whites. There are other Žndings of note for the 1984– 94 period. First, raising the saving of African Americans either by equalizing the unconditional saving rates or by equalizing fam- ily incomes of African Americans and whites also would have very modest effects, raising the mean wealth ratio over the actual 1994 level by only 5 to 6 percentage points. However, on the basis of the regression analysis reported above in Table 6, the impact of equalizing the conditional saving rate would be reduced while that of equalizing family incomes increased if the simulations were performed with sav- ing as a function of income. Second, with the caveat that calculations using asset-speciŽc returns should be interpreted with caution, the simulations show that if both races had the same portfo- lio allocation, the wealth gap would have been narrowed by Žve percentage points in 1994. The simulated narrowing of the wealth gap stems from the higher share of stocks in the portfolio of whites in comparison to African Americans. Table 10 Mean Wealth Ratios Recalculated Under Counterfactual Assumptions: Accounting Framework Method 1984– 89 1989– 94 1984– 94 Actual, start period 0.23 0.22 0.25 Actual, end period 0.23 0.27 0.28 Characteristic from full sample assumed to hold for both Portfolio allocation 0.23 0.30 0.33 Rate of return 0.21 0.24 0.25 Saving rate 0.27 0.29 0.34 Family income 0.25 0.30 0.33 Inheritance 0.25 0.29 0.32 Inows from changes in household composition 0.24 0.27 0.30 All characteristics above 0.34 0.33 0.45 Notes: Ratios refer to mean wealth for African Americans divided by mean wealth of whites. Calculations use PSID family weights and the trimmed longitudinal samples for de- tails, see the appendix on the JHR website. Third, as noted earlier, eliminating racial differences in the rate of return on capital would actually widen by 3 to 4 percentage points the racial wealth gap by the end of the period. However, this result may be peculiar to the period under the study. In fact, the increase in the stock market since 1994 has probably pushed up the overall rate of return on capital for whites relative to African Americans because of the greater weight of stocks in the portfolio of the whites. Fourth, equalizing inheritances and transfers between African Americans and whites would result in a Žve percentage point increase in the racial wealth ratio. Fifth, standardizing for wealth inows related to household composition shifts would have little effect on the racial wealth gap.

B. Sensitivity of the Results