## Social Security and Race

No. 236
Monday, October 02, 2000
by Liquin Liu and Andrew J. Rettenmaier

## Calculating Expected Net Present Values and Expected Rates of Return

"Virtually all of today's workers can expect to pay more in taxes than they will receive in benefits."

As we have seen, deaths at early ages result in survivors benefit payments to children and spouses based on just a few years of tax payments. Deaths at later ages represent investments that may involve many years of tax payments and such benefits as a retirement pension for the worker, an additional retirement pension for a spouse and survivors benefits. Thus for each possible year of death, there is a well-defined stream of taxes and benefits. To calculate the expected net present value for an individual we multiply the probability of dying at each age times the tax and benefit stream associated with that age. Summing over all possible life spans in this way yields the expected net present value of Social Security. The internal rate of return is the discount rate at which the present values of expected taxes and expected benefits are equal.8

"Even today's 65-year-old men would have done better investing their payroll tax dollars at a 4 percent rate of return."

We use 4 percent as the real discount rate because it represents a conservative estimate of the real rate of return workers could receive elsewhere. Several earlier studies used real discount rates that ranged from 2 percent to 3 percent, while more recent studies have used rates between 4 percent and 5 percent.9 The higher rates are justified for several reasons, including the evidence on the historically higher rates of return on stock market portfolios.10 Using stock market returns from 1802 to 1997, Jeremy Siegel (1998) calculated that for holding periods of 30 years the lowest annualized rate of return was 2.6 percent and the highest was 10.6 percent. Over that same span the average annual real rate of return was 7.0 percent.

"On the average, white males do worse than black males."

Racial Differences in Net Present Values for Single Men. Figure IV summarizes the net present values for single men based on their race and the year in which they were born. All figures are presented in 1999 dollars and are calculated at the age of 25. In this case, there are no surviving children benefits, no spousal benefits and no surviving spouse benefits.11 As a result, deaths that occur prior to attaining the retirement age trigger no benefit stream. The graph has three significant features:

• First, all of the present values are negative. On average, even men born in 1935 (today's 65-year-olds) would have done better if they could have invested their payroll tax dollars at a 4 percent rate of return.
• Second, the present values decline over time, with those just retiring paying \$19,485 more in taxes than they can expect to receive in benefits, while those entering the labor market pay \$42,762 more in taxes than they can expect to receive in benefits.
• Third, the net present value for single white men is less (that is, more negative) than for single black men. For example, a single black man born in 1980 can expect to pay almost \$41,000 more in taxes than he receives in benefits, while a single white man can expect to pay almost \$45,000 more in taxes than he receives in benefits.

"The losses for single women are smaller than for single men."

Racial Differences in Net Present Value for Single Women. Some of the same features revealed in the graph for single men also appear in Figure V. From the figure the net present values are negative for all but the first birth year. This means that all groups pay more in taxes than they can expect to receive in benefits. The net present values for single women are higher than for single men. This is due in part to longer expected lives and lower predicted earnings. Longer lives imply more years of receiving retirement benefits and lower earnings are associated with higher replacement rates, both of which work to produce higher net present values.

As the graph shows:

• First, the present values are negative for all single black women, even those born in 1935 (today's 65-year-olds).  They are negative for all women regardless of race born in 1940 or later.  On average, all of these women would have done better if they could have invested their payroll tax dollas at a 4 percent rate of return.
• Second, the present values decline over time, with those just retiring receiving \$883 more in benefits than they paid in taxes, while all those entering the labor market pay over \$30,000 more in taxes than they can expect to receive in benefits.
• Third, the net present value for single white women is less (that is, more negative) than for single black women; for example, a single black woman born in 1980 can expect to pay a lifetime tax of almost \$32,000 more than she receives in benefits while a single white woman can expect to pay almost \$35,000 more.

"Among 20-year-olds, white women lose more than black women, but among the middle-aged, the reverse in true."

Distribution of Benefits Among Retirees, Wives and Widows. Given that most people marry, how closely do the results for single men and single women approximate people's actual experiences?12 Retired workers account for 71 percent of beneficiaries under the OASI program. Of these, women account for 46 percent. About 22 percent of the wives of retired men, or about 8 percent of all OASI beneficiaries, collect retirement benefits on their husband's accounts. So for these women either their benefit amount based on their own earning history was less than 50 percent of their husband's benefit amount, or they did not work enough to qualify for a benefit. The percentage of women receiving benefits based on their husband's accounts has declined and will continue to do so as increasing numbers of women draw Social Security benefits based on their own earnings histories.

"The results for married people will approach the results for single men and women over time."

Widows account for another 13 percent of total OASI beneficiaries. Recall that widows and widowers are entitled to 100 percent of their spouses' benefits after the spouse dies. Thus while a husband and wife are both alive, most beneficiaries draw pensions based on their own earnings, but upon the death of their husbands, women whose own benefits are less than their husbands' will then draw the higher benefits. Together, workers, wives and widows make up 92 percent of all beneficiaries. With the exception of survivors benefits, the realized results for any group of workers will approach the results for single men and women over time, with most members of the group receiving benefits based on their own earnings.

"Among men with nonworking wives, the losses are about the same for young black and white families."

Racial Differences in Net Present Value for Married Men with Nonworking Spouses and Children. Figure VI presents the net present values for married men with nonworking spouses. To make these estimates, we assume that men marry, at age 22, women of the same age. At age 25 we assume the couple has twin children, and we further assume that the wife does not work while the children are 18 or younger. Thus survivors benefits are paid in the case of the husbands' premature deaths between ages 25 and 43.13 These assumptions produce the largest possible net present value. A couple in which both spouses work would have a net present value that falls in between the result for the singles and for the married men as defined here. Relative to the results for single men, the net present values improve significantly because of the survivors benefits and spousal benefits. When the effects of these benefits are included, as depicted in Figure VI, the net lifetime tax has been relatively constant since 1960 at about \$13,000.

Racial Differences in Internal Rates of Return for Single Men. The internal rates of return for black and white single men appear in Figure VII. The graph has three significant features:

• In general, the returns decline across time and blacks have persistently lower rates of return.
• For men born in 1980, benefits were equal to only 34 percent of costs for blacks but 47 percent of costs for whites.
• Similarly, the internal rate of return for whites is higher - 1.8 percent versus 0.7 percent for blacks.

"Black men have persistently lower rates of return than white men."

How can this be reconciled with the previous results, which showed higher present values for black men? Although projected future earnings are lower for black men and thus a larger percentage of their income will be replaced by the benefit formula, their probability of receiving benefits is lower. The net present values indicate how much an individual loses by participating in Social Security: single white men lose more than single black men. The net present values identify the magnitude of the redistribution. But based on rates of return, which measure the relative progressivity of the system, black men do worse. Here Social Security is regressive.

"Although black women do better than black men, they have lower rates of return that white women."

Racial Differences in Internal Rates of Return for Women. Among single women, blacks continue to have a lower rate of return than do whites, as shown in Figure VIII. The graph has three significant features:

• In general, the returns decline across time and black women have persistently lower rates of return.
• Single black women born in 1935 can expect 89 cents in benefits for every dollar paid in taxes, while single white women born in 1935 can expect \$1.11.
• Single black women born in 1980 can expect 46 cents in benefits for every dollar paid in taxes, while single white women born in 1980 can expect 54 cents.
• The internal rate of return for blacks born in 1935 is 3.6 percent versus 4.4 percent for whites, and the rate of return for blacks born in 1980 is only 1.7 percent, compared to a rate for whites of 2.2 percent.

"If blacks do better than whites on present values, why do they do worse on rates of return?"

Racial Differences in Internal Rates of Return for Married Men. As Figure IX shows, the rates of return for married men with nonworking spouses and children are quite similar prior to 1950, but from that point on the rates for blacks fall below the rates for whites.

• By birth year 1980 the internal rate of return for married white men is 3.5 percent and the rate for married black men is 3.0 percent.
• Including survivors and spousal benefits narrows the gap between the rates of return to only 0.5 percentage points.
• Given that blacks are more likely to die at younger ages, the inclusion of survivors benefits awarded in the event of preretirement deaths tends to decrease the gap in rates of return.

Finally, the internal rates of return for the 1960 and later birth cohorts are quite similar. The decline in rates of return between the 1935 and 1960 birth cohorts is the result of higher payroll tax rates (and thus higher lifetime taxes) for younger workers and an increase in their retirement age from 65 to 67. The higher retirement age will be fully phased in by the time individuals born in 1960 retire; at this time no further increases in the retirement age are scheduled. Though individuals born in 1965 and beyond will face higher tax rates over their lifetimes, their increased longevity coupled with a fixed retirement age produce relatively stable rates of return.