Multivariate Analysis Patterns of Wealth Accumulation by Race

the distribution that is truncated rises, the racial gap in the saving rate and capital gains tends to narrow. We now turn to multivariate analysis to explore whether the racial differences remain after controlling for other characteristics.

D. Multivariate Analysis

It is well known that multivariate analysis using wealth data poses special chal- lenges because of the skewness of the wealth distribution. In order to avoid the undue inuence of extreme observations, researchers have sometimes transformed the data by taking logarithms. Analysts who take this step must then make a decision with respect to the large proportion of observations that cannot be transformed because they are zero or negative, with some electing to truncate the sample, and others arbitrarily assigning a value, such as zero, for the log of zero or negative wealth Carroll, Dynan, and Krane 1999. Irrespective of one’s view of such an approach, the use of a log transformation is not practical for an analysis of changes in wealth because of an even larger proportion of the sample with zeroes or negative numbers. For instance, for the 1984– 94 longitudinal sample, about 15 percent of the observa- tions have zeroes or negative numbers for the level of wealth in 1984, while the corresponding share for changes in wealth is more than twice that. Instead of a log transformation we make use of two complementary approaches: The Žrst is quantile regression, which is not sensitive to outliers and thus can be used on the full longitudinal samples to examine the determinants of the rates of saving, capital gains and wealth appreciation at their medians. The second is OLS, which will be employed on the longitudinal samples with the top and bottom percen- tiles trimmed for an examination of tendencies at the means. For the analysis of saving rates, we Žrst run a baseline regression where a dummy variable for African Americans is the only independent variable, then add controls for income to see if any racial differences can be accounted for by income differences, and then include additional controls for age, education and sex of head, change in marital status, and number of children. The same controls are used for an analysis of inheritances. When the rate of return to capital and the rate of wealth appreciation are the dependent variables, controls for wealth and its square at the start of the period are also included. In Columns 1 and 4 of Table 6, we Žrst reproduce on the basis of OLS and median regressions, respectively, the earlier Žnding that with no controls whites save a higher share of their income than do African Americans. However, after accounting for income, we Žnd that this relationship no longer holds, as shown in Columns 2 and 5. In fact, for two of the three median regressions, the coefŽcients for African Ameri- cans become positive and signiŽcant. As already noted, these results are consistent with those of Dynan, Skinner, and Zeldes 2000, who use the Survey of Consumer Finances and the Consumer Expenditure Survey in addition to the PSID to document a positive relationship between personal saving rates and lifetime incomes. As shown in Columns 3 and 6, adding the remaining demographic controls leaves none of the coefŽcients signiŽcant, with the changes in the median regressions largely attribut- able to the fact, that conditional on income, saving rates rise somewhat faster with age for African Americans than for whites. Regression analysis of racial differences in mean rates of return on capital, sum- marized in Table 7, is hampered by the fact that returns to capital gains can be Table 6 Racial Differences in Saving Rates African American2White, 1984– 94 Type of regression OLS OLS OLS Median Median Median Period 1984– 89 20.052 20.012 0.003 20.034 0.003 0.005 0.029 0.029 0.029 0.007 0.005 0.005 1989– 94 20.024 0.027 0.008 20.022 0.013 20.007 0.026 0.026 0.026 0.008 0.006 0.007 1984– 94 20.037 0.003 0.004 20.031 0.010 0.003 0.020 0.020 0.021 0.008 0.005 0.007 Other Income 1 Income 1 regressors None Income others None Income others Notes: The saving rate is deŽned as the ratio of saving over the period divided by family income over the same time span. 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 age of head and its square, sex and education of head, marital status at start and end of period, and number of children. 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 income at start of period. signiŽcant at 10 percent level signiŽcant at 5 percent level signiŽcant at 1 percent level calculated only with respect to positive wealth. Thus, we are forced to exclude from the OLS analysis households with nonpositive wealth—about 15 to 17 percent of the sample, depending upon the period. 13 Calculations not shown here reveal that the racial difference in mean rates of return to capital is somewhat smaller when only positive wealth holders are included. With this caveat in mind, we Žnd that the coefŽcient for African Americans is positive in the baseline OLS regressions, though the estimate is too imprecise to be signiŽcant at conventional levels. Likewise, as we found in Table 5, signiŽcant differences in rates of return are not evident at the median. This situation scarcely changes when additional controls are added, as the race coefŽcient is almost always positive but almost never estimated precisely enough to achieve statistical signiŽcance. For our multivariate analysis of inheritances, we forego median regressions, be- cause only a small portion of the sample received an intergenerational transfer during the periods. We use tobit regressions instead of OLS because inheritances are a censored variable, not at zero in this case but at 10,000 in nominal currency, the threshold used in the PSID questionnaire. In light of substantial differences by race in the share who receive inheritances 12 percent for whites and 1 percent for African 13. These observations are also excluded in the median regressions and in the median calculations for Table 5, so that there is no inconsistency in comparing the two sets of regression results. Table 7 Racial Differences in the Rate of Return on Capital African American2White, 1984– 94 Type of regression OLS OLS OLS Median Median Median Period 1984– 89 0.048 0.043 20.043 0.000 0.014 0.014 0.121 0.121 0.121 0.003 0.010 0.019 1989– 94 0.106 0.082 0.056 0.000 0.001 0.007 0.142 0.142 0.143 0.000 0.000 0.008 1984– 94 0.107 0.102 0.022 20.003 0.008 0.005 0.264 0.263 0.265 0.024 0.043 0.037 Other Income 1 Income 1 regressors None Income others None Income others Notes: The rate of capital gains is deŽned as capital gains 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, and number of children. The trimmed longitudi- nal 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 Americans and the higher average inheritance among those who receive one 75,236 versus 48,946, it is no surprise that there is a large difference by race evident from the baseline analysis, shown in Table 8. We use the parameters of the tobit regression to predict the average difference by race if inheritances had not been censored at 10,000, and for the sake of comparison, show this prediction under the assumption that there were, in fact, no inheritances below the 10,000 threshold. Though the estimation is not particularly precise because of the small number of positive values and their high level of skewness, the results suggest that little bias arises from assuming that there are no transfers below 10,000. The results reported here are, moreover, broadly similar to those reported in Wolff 1998 on the basis of the 1995 Survey of Consumer Finances SCF. According to the SCF, 24 percent of white households had reported an inheritance on or before 1995, compared to 11 percent of African American households, and the average bequest for inheritors was 115,000 among whites and 32,000 for African Americans. The results of the other tobit regressions indicate that racial differences in income and various demographic characteristics account for only a small portion of racial differences in inheritances. In Table 9, we consider racial differences in the overall rate of wealth appreciation. As in our analysis of the rate of return on capital, we are forced to exclude households with nonpositive wealth from the analysis. This truncation lowers the rate of wealth G ittle m an and W olff 217 Table 8 Racial Differences in Inheritances, Tobit Regressions African American2White, 1984–94 Predicted Predicted Predicted Predicted Predicted Predicted Average Average Average Average Average Average Difference, Difference, Difference, Difference, Difference, Difference, Censored Censored Censored Censored Censored Censored Period CoefŽcient at Zero as in Survey CoefŽcient at Zero as in Survey CoefŽcient at Zero as in Survey 1984–89 2748,015 28,726 28,647 2701,255 27,506 27,431 2628,738 25,161 25,098 56,307 1,169 1,173 53,926 1,077 1,080 49,997 786 786 1989–94 2830,827 29,031 28,977 2784,920 27,658 27,607 2738,266 26,798 26,749 60,468 1,502 1,510 58,472 1,310 1,315 56,311 1,165 1,167 1984–94 2761,886 217,204 217,128 2707,897 215,114 215,040 2643,932 213,032 212,961 50,996 2,304 2,312 48,996 1,999 2,007 46,697 1,788 1,792 Other Income 1 regressors None Income others Notes: Respondents are asked about dollar amount of inheritances only if they have received an amount of 10,000 or more in nominal currency. The coefŽcient shown in the table is for a dummy variable for African Americans from a Tobit regression, and reects differences in latent variables. Standard errors are in parentheses. “Predicted Average Difference” uses the Tobit results to predict differences by race in the amount of inheritances in 1998 dollars, with censoring at zero and at 10,000 as in the actual survey. Standard errors are calculated by bootstrapping. Total family income over the time span and its square are the income variables, while the other regressors are age of head and its square, sex and education of head, marital status at start and end of period, and number of children. Trimmed longitudinal samples are used for details, see the appendix on the JHR website. Regressions use PSID family weights. signiŽcant at 10 percent level signiŽcant at 5 percent level signiŽcant at 1 percent level 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