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Smoking taxing health and social security.

Cigarette smoking is the largest single health risk in the United States, accounting for approximately 440,000 deaths each year (U.S. Department of Health and Human Services [USDHHS] 2004b). The financial cost of smoking-attributable health care expenditures and lost productivity has been well documented (Centers for Disease Control and Prevention [CDC] 2003). In general, smokers have higher health care expenditures and more sick days than do nonsmokers (Max 2001). However, the effects of smoking-attributable mortality on income distributions are less well known.

Premature death attributable to smoking may redistribute Social Security income in unanticipated ways that affect behavior and reduce the economic well-being of smokers and their dependent spouses and children (Rice et al. 1986). Knowledge of how smoking redistributes both individual and household Social Security benefits and taxes is important not only from the perspectives of informing smoking cessation efforts (Rice et al. 1986) and evaluating proposals to improve family welfare through reductions in system inequities or promotion of social adequacy but also from the standpoint of managing the Social Security System's finances. Social Security is financed by a pay-as-you-go tax levied on earnings; thus, if the harmful health effects of smoking reduce individual or household hours of work, these effects have implications for the system's funding.

Economists employ the comprehensive marginal tax rate to assess the distortionary effect of taxation on labor supply and welfare (Armour and Pitts 2004). One important component of this comprehensive marginal tax rate in the United States is the Social Security payroll tax, which is assessed on individual earnings up to the annual taxable maximum. In 2002 approximately 94 percent of all U.S. workers earned less than the annual taxable maximum of $84,900, thus incurring an Old-Age and Survivors Insurance (OASI) Social Security payroll tax at the margin. (1) For these individuals, Social Security is a benefit tax for which an extra dollar of earnings may increase their future benefits at retirement. Therefore, the net marginal Social Security tax rate (NMSSTR)--defined as the difference between the statutory payroll tax rate and the present value of the stream of future benefits to which an additional dollar of earnings entitles the covered worker--should be used in calculating the marginal tax rate for the purpose of assessing the effect of taxation on labor supply and welfare. (2)

Studies that have used the NMSSTR to examine the distributional effects of Social Security concluded that Social Security benefit and tax rules create NMSSTRs that treat workers differently depending on age, gender, race, dependency status, earnings, insurance status, and income-related life expectancy (for example, Aaron 1977; Browning 1985; Burkhauser and Turner 1985; Feldstein and Samwick 1992; Armour and Pitts 2004). To our knowledge, no study has looked at lifestyle and the harmful health effects of an addictive habit such as smoking on NMSSTR estimation. This study contributes to the literature by examining the distributional effects of smoking-attributable mortality on NMSSTR estimation.

Methods

Social Security benefit determination. The Social Security benefits to which a covered worker is entitled at retirement depend on lifetime earnings. Average indexed monthly earnings (AIME) is the measure of lifetime earnings on which benefits are based. Earnings are indexed by multiplying a worker's taxable earnings by an indexing factor for each year after 1950 through the indexing year. The indexing year is defined as the year a worker attains age sixty. The indexing factor for each year, t, is obtained by dividing average covered worker earnings in the indexing year, [[bar.E].sub.60,t], by average covered worker earnings at each age, a, in each year, [[bar.E].sub.a,t]. The AIME for individuals retiring in year t is

(1) AIME = [1/n] [1/12] [[summation].sub.t[member of]A][[[bar.E].sub.60,t]/[[bar.E].sub.a,t]][E.sub.t] + [[summation].sub.t[member of]B][E.sub.t].

For individuals attaining age sixty-two after 1991, the AIME is based on the highest thirty-five years of earnings. However, for each year a worker is born before 1929, the number of years, n, in the computation period is reduced by one. To convert the AIME from an annual to a monthly basis, it is divided by 12. [E.sub.t] denotes worker earnings in year t. The set of all years through age sixty that will be counted among the highest thirty-five or n years of earnings is denoted by A. B denotes the set of years between age sixty and the year prior to retirement ill which a year of unindexed earnings replaces a year of indexed earnings in the benefit formula.

Once the AIME is determined, the primary insurance amount (PIA)--the amount of monthly benefits payable at retirement--may be calculated. (3) The benefits formula for a covered worker attaining age sixty-two in 2002 is

(2) PLA = [0.90 x (AIME [less than or equal to] $592)] + [0.32 x ($592 < AIME [less than or equal to] $3,567)] + [0.15 x (AIME > $3,567)].

The PIA is composed of two parts: the bend points (the dollar amounts defining the AIME bracket in the benefit formula) and the marginal replacement rate (the applicable percentage used to determine the PIA). (4)

The benefit formula illustrates one fundamental feature of the system: the progressive structure of Social Security. Low-earning workers are afforded proportionately greater benefits with a marginal replacement rate of 90 percent when compared with average-earning and high-earning workers, whose marginal replacement rates are 32 percent and 15 percent, respectively. Because the Social Security benefit formula classifies workers into one of three earnings groups, the NMSSTR by sex and age is calculated for a representative worker in each group.

Calculation of the NMSNTR. NMSSTRs by sex, age, and earnings classification are calculated under two alternative scenarios. The first scenario uses a common mortality assumption, and the second scenario accounts for smoking-attributable mortality in calculating the NMSSTR.

The NMSSTR is [??] = T- [B.sub.PV]. T denotes the OASI statutory rate, which is defined as the combined employee-employer legislated rate. The combined employee-employer tax rate was 10.6 percent in 2002. (5) This analysis assumes that the employee pays the tax. (6)

Primary beneficiary (single). The present value of the change in anticipated future benefits resulting from a $1 change in earnings is

(3) [B.sub.PV] = [1/n] [[partial derivative]PIA/[partial derivative]AIME][(1 + g).sup.max (60-a)][i.sub.s,f,[bar.t],t][N.summation over (j=f)] [P.sub.s,t](j|a)[(1 + r).sup.a-j].

The future benefits that an additional dollar of earnings entitles an individual to at retirement depend on the marginal replacement rate, ([partial derivative]PIA)/([partial derivative]AIME), and the age, a, at which the individual plans to retire. Workers are assumed to retire at the full benefit retirement age, f. (7) The indexing factor at each age, [(1 + g).sup.max(60-a)], is estimated assuming that earnings grow at a real rate of 1.1 percent. (8) The probability that an individual of sex s and age a in year t will be eligible for benefits at age fin year [??] ([??] = t + f- a) is denoted by [i.sub.s,f,[??],t]. (9) The probability of an individual of sex s surviving from age a to age j is denoted by [P.sub.s,t]j\a). N is the age at which all persons are assumed to be dead and is set at 100 in all calculations. The rate at which a worker discounts future benefits, r, is set at 3 percent in all calculations. (10)

To illustrate, consider the case of a man who is fifty-five years old in 2002 and plans to retire at age sixty-six in 2011. Because he will attain age sixty-two after 1991, the AIME is based on the highest thirty-five years of earnings. Earnings through age sixty are indexed to the growth rate in average covered earnings. Assuming that real earnings grow at a rate of 1.1 percent annually, then [(1 + g).sup.max(60-55)] = 1.056. An additional dollar of earnings at age fifty-five increases average indexed earnings by $(1/35)(1.056) [approximately equal to] $0.03.

Assuming that the fifty-five-year-old man is a lifetime average wage earner, his marginal replacement rate is 0.32, and an extra dollar of earnings at age fifty-five would increase the PIA by $ (0.03)(0.32) [approximately equal to] $0.0097. The present value of the change in anticipated future benefits resulting from a $1 change in earnings is 0.0097 [[summation].sup.N=100.sub.j=66] [P.sub.f,t](j\55)[(1 + r).sup.55-j]. The discounted sum of survival probabilities for a man aged fifty-five is 7.838. Multiplying 0.076 (0.0097 x 7.838) by the probability that a fifty-five-year-old man will be eligible for Social Security benefits at the full benefit retirement age, 0.931, yields an estimate of [B.sub.PV] [approximately equal to] 0.0705. Subtracting 0.0705 from the statutory rate yields 0.0355, or 3.55 percent.

NMSSTRs for representative low-, average-, and high-earning workers by sex and select ages in 2002 are shown in Table 1. The estimates reveal that men and women at each age face an NMSSTR that is less than the statutory rate and that the NMSSTR declines with age. The age differential is the result of higher conditional survival probabilities and the fact that older workers have a shorter period over which to discount future benefits. Also, low-earning workers incur the lowest NMSSTR, as expected given the progressive nature of the benefit formula.

Across earning classes, women at most ages incur a lower NMSSTR than do men. The estimated NMSSTR for a low-earning woman aged fifty-five is 1.12 percentage points lower than the rate faced by her male counterpart (-10.34 percent compared with -9.22 percent). Gender differences in the NMSSTR are approximately 0.4 percentage points for average-earning individuals and 0.2 percentage points for high earning individuals aged fifty-five; this differential is attributable to the longer life expectancy of females. The NMSSTR for a woman aged sixty-five with average lifetime earnings is 0.9 percentage points higher than the rate for her male counterpart. Older women incur a higher NMSSTR because they have less of an attachment to the labor force and thus have a lower probability of being fully insured for benefits. (11)

Primary beneficiary and dependent spouse. Women who are married and do not work outside the home or fail to qualify for benefits based on their own earnings histories may qualify for dependent spouse benefits. Thus the present value of anticipated future benefits also depends on whether a primary beneficiary claims benefits for a dependent spouse. (12) A dependent spouse is entitled to an additional 50 percent of the primary beneficiary's benefit amount at retirement. In addition, if the primary beneficiary dies, the widow is entitled to 100 percent of the primary beneficiary's benefit. (13) The formula (obtained from Feldstein and Samwick 1992) for calculating the present value of the change in anticipated future benefits resulting from a $1 change in earnings for a male worker age a with a dependent spouse is shown in equation (4);

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where 1 = male, 2 = female, and a dependent wife is assumed to be the same age as her husband. The definitions of the other characters are identical to those for a single primary beneficiary.

The first term of equation (4) denotes the expected value of the widow's benefits conditional on the worker dying at age a. The second term denotes the expected value of the primary beneficiary's retirement benefit conditional on attaining the full benefit retirement age, f. The third term denotes the expected value of the dependent spouse's benefit conditional on both parties reaching the full benefit retirement age.

Because beneficiaries with a dependent spouse do not pay any additional taxes for the additional benefit, they incur a lower NMSSTR than do singles. The NMSSTR for an average-earning man aged fifty-five with a dependent spouse, assuming a discount rate of 3 percent, is -0.02 percent (see Table 1). This negative tax rate is a net marginal subsidy and is lower than the rate incurred by female dependent spouses, whose NMSSTR equals the statutory rate of 10.6 percent.

Smoking-attributable mortality. The progressivity of the Social Security benefit formula is based on a common mortality assumption. However, the literature contains evidence that smoking reduces life expectancy (USDHHS 2004b). Life tables published by the National Center for Health Statistics are used to construct and account for differences in life expectancy among current and former smokers as well as people who have never smoked in determining NMSSTRs. The approach utilizes the mortality ratios of Thun et al. (1997) and current and former smoking prevalence estimates for persons aged thirty-five through sixty-four made available by the CDC (2007). The method of estimation is described below.

Estimates of the total number of survivors, [l.sub.a], by sex, s, and exact age, a, are shown in Table 2. The probability of an individual of sex s surviving from age a to age j is [P.sub.s](j|a) = [l.sub.j/[l.sub.a]. The mortality rate at each age is calculated by subtracting survival probabilities at each age from 1.

The mortality ratio, which is the ratio of one group's death rate to that of the population, was used to split the table into three categories: current smokers, former smokers, and those who never smoked. The mortality ratio (M) by smoking status (SS) at each age (a) is [M.sub.SS,a] = [q.sub.SS,a]/[q.sub.T,a]. The mortality rate for the total population is [q.sub.T,a], and [q.sub.SS,a] denotes the mortality rate by smoking status. For example, the mortality rate for current smokers by sex and exact age is calculated as [q.sub.CS,a] = [M.sub.CS,a] x [q.sub.T,a]. For persons aged twenty-one through thirty-five, the mortality ratio for male and female current and former smokers was assumed to be 1. For men aged thirty-five and older, the mortality ratios for current smokers and former smokers were 2.30 and 1.46, respectively. For female current and former smokers aged thirty-five and older, the mortality ratios were 1.92 and 1.30, respectively. (14)

To determine the number of survivors by smoking class, we initially assumed that 23.2 percent of men were current smokers and 34.3 percent were former smokers. For women, we assumed that 18.7 percent were current smokers and 22.9 percent were former smokers. (15) We subtracted mortality rates by sex for current smokers from 1 and multiplied by the number of current smokers that survived to age a - 1 to estimate the number of current smokers by sex surviving to age a. The number of surviving former smokers by sex and age was calculated in a similar manner. The number of people who have never smoked of sex s surviving to age a was estimated by subtracting the number of current and former smokers from the total number of survivors. The number of survivors at each age in the three smoking classes, as shown in Table 2, is then used to calculate the probability that a person age a will survive to age j. For each smoking class, the survival probabilities are in turn used to calculate [B.sub.PV].

NMSSTRs for single primary beneficiaries that account for smoking-attributable mortality by age, gender, and earnings class are shown in Table 3. As expected, a comparison of the results in Tables 1 and 3 reveals that a smoker's shorter life expectancy increases the NMSSTR at each age. A single male current smoker aged fifty-five with lifetime average earnings faces a net tax rate of 6.51 percent, which is approximately 3 percentage points higher than the rate estimated under the common mortality assumption (3.55 percent). The NMSSTR for a single male former smoker aged fifty-five with average lifetime earnings is 4.92 percent, which is approximately 1.4 percentage points higher than the rate estimated under the common mortality assumption. The NMSSTR for a single man aged fifty-five who never smoked with average lifetime earnings is 1.25 percent--5.3 percentage points lower than the rate for a current smoker and 3.7 percentage points lower than the rate for a fifty-five-year-old former smoker of the same age.

A single female current smoker aged fifty-five with lifetime average earnings faces an NMSSTR of 5.13 percent, which is approximately 1.4 percentage points lower than the rate estimated for a fifty-five-year-old current smoking man with lifetime average earnings. The gender differential in NMSSTRs for both current and former smokers at each age is larger than the differential estimated under the common mortality assumption. In addition, sixty-five-year-old female current and former smokers now incur a lower NMSSTR than do their male counterparts. These gender differences result from males smoking at higher rates than females and having a higher smoking-attributable mortality risk.

As shown in Table 4, a fifty-five-year-old male current smoker with lifetime average earnings and a dependent spouse who also smokes incurs an NMSSTR of 3.17 percent, which is more than 3 percentage points higher than the rate estimated under the common mortality assumption (-0.02). In addition, this rate is 1.69 percentage points higher than the rate incurred by a fifty-five-year-old male former smoker with lifetime average earnings and a dependent spouse who formerly smoked (1.48 percent) and approximately 5.5 percentage points higher than the rate incurred by a fifty-five-year-old male who never smoked with lifetime average earnings and a dependent spouse who never smoked (-2.49 percent).

Results and Discussion

As previous studies have shown, we find that Social Security treats single people and dual-income couples less equitably than single-income couples. This study's results add to previous findings by showing that NMSSTRs also vary by smoking status. (16) The higher tax rates that smokers incur may reduce their labor supply. (17) Given that Social Security is financed by a payroll tax on earnings, any reduction in the labor supply will have implications for the system's funding. However, the aggregate effect of smoking on the OASI Trust Fund's finances would depend on how smoking redistributes benefits from smokers to people who never smoked and the resulting labor supply response to changes in marginal tax rates.

While Social Security has reduced poverty among elderly Americans, young widows are at increased risk of living in poverty because of the premature death of their spouse (Redja 1994; Engelhardt and Gruber 2004; Sevak, Weir, and Willis 2004). Many individuals who smoke die prematurely. Approximately 536,000 adults in the United States under age sixty-five died of smoking-attributable illnesses between 1997 and 2001. (18) Widows with no children under age sixteen in their care who were married to fully insured workers who died prematurely may be ineligible for Social Security benefits until they reach age sixty. Estimates suggest that 15 percent of women aged fifty-four, too young to qualify for Social Security benefits, fall into poverty following the death of their husband (Sevak, Weir, and Willis 2004). (19) As a result, it has been suggested that Social Security is failing to live up to one of its primary goals--providing adequate survivors insurance for older low-earning Americans (Gustman and Steinmeier 2002). One proposal to improve Social Security's adequacy is to lower the eligibility age for widows from sixty years to fifty-five years (Redja 1994). (20) In addition to the establishment of private accounts, two of the three plans proposed by the President's Commission to Strengthen Social Security (2001) recommended an increase in benefits for low-earning widows and widowers.

Because low-earning workers are more likely to smoke and smokers are more likely than people who have never smoked to die prematurely, an unintended distributional effect of enacting proposals that would reduce widows' retirement age or increase retirement benefits among low-earning widows and widowers would be to redistribute benefits from people who have never smoked to smokers, thus benefiting behavior that is detrimental to health. As with life insurance, perhaps this unintended effect could be offset by smokers' paying a higher premium, in this case a smoker's insurance tax rate. The revenue generated from a tax levied on current smokers could be added to the OASI Trust Fund and used to reduce financial hardship currently faced by young widows and widowers by paying increased benefits or paying benefits at an earlier age. In addition, the higher tax penalty associated with smoking may increase cessation. The aggregate in, pact of such a change on the various trust fund finances would be a valuable addition to the debates surrounding the system's solvency and ways to reduce poverty among widows and widowers.

As in previous studies, these results are limited in that they are based on hypothetical workers; thus, the relative importance of various economic assumptions and differences is an empirical question. (21) Because analysis with money flows over time may be sensitive to the choice of discount rate, selective results shown in Tables 1, 3, and 4 for workers with average lifetime earnings were reestimated under alternative discount rate assumptions. As shown in Table 5, a lower discount rate reduces the NMSSTR at each age. (22)

Although the calculations presented are complex, they oversimplify the Social Security program in a number of ways. First, we focus on OASI and ignored the DI and HI components of Social Security. Second, we ignore benefits for dependent children of young widows or widowers. Third, we ignore the possibility of divorce and remarriage. Fourth, the employer portion of the payroll tax is tax exempt, and given the progressive nature of income taxation, this exemption disproportionately benefits higher-earning individuals. Thus, the NMSSTR for high-earning individuals may be lower than the estimates reported. Fifth, smoking prevalence is held constant across earnings classes. Because lower-earning individuals have a higher smoking prevalence than do higher-earning individuals, low-earning individuals' NMSSTRs may be higher than the rates reported whereas average- and high-earning individuals may have NMSSTRs that are lower than the rates reported.

A final potential limitation to our results is that the mortality risk measures used to account for the mortality difference among current and former smokers are adjusted for sex and age only. Other risk factors such as educational status, diet, and alcohol consumption that are correlated with smoking were unaccounted for in the mortality risk measure that was used. As a consequence, the NMSSTR estimates may overstate the tax penalty associated with smoking (Shoven, Sundberg, and Bunker 1987; Thun et al. 1997). However, this limitation may not pose too great a problem because evidence in the literature suggests that when behavioral and demographic factors correlated with smoking were taken into account, the higher mortality risks faced by smokers did not change much (Malareher et al. 2000; Thun et al. 1997).

Conclusion

The analyses reveal that smokers will incur higher net marginal tax rates than people who never smoked and may reduce their labor supply. (23) Any reduction in labor supply among smokers will have implications for the system's funding. Knowledge of the distributional effects of smoking on Social Security is important not only from the standpoint of the system's funding but also from the perspective of informing smoking cessation efforts (Rice et al. 1986). People can avoid higher net marginal tax rates by never smoking or reduce them by quitting smoking. Finally, smoking status should be considered in assessing Social Security legislative proposals designed to reduce system inequities or promote social adequacy--in particular, amendments designed to reduce poverty among young widows and widowers. Failure to do so may unintentionally promote behavior that is detrimental to health.

REFERENCES

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Anzick, Michael A., and David A. Weaver. 2001. Reducing poverty among elderly women. Social Security Administration Working Paper No. 8, January.

Armour, Brian S., and Melinda M. Pitts. 2004. Incorporating insurance rate estimates and differential mortality into the net marginal Social Security tax rate calculation. Public Finance Review 32, no. 6:588-609.

Brittain, John A. 1972. The incidence of Social Security payroll taxes. American Economic Review 61, no. l:110-25.

Browning, Edgar K. 1985. The marginal Social Security tax on labor. Public Finance Quarterly 13, no. 3:227-51.

Burkhauser, Richard V., and John A. Turner. 1985. Is the Social Security payroll tax a tax? Public Finance Quarterly 13, no. 3:253-67.

Centers for Disease Control and Prevention (CDC). 2003. Cigarette smoking-attributable morbidity--United States, 2000. Morbidity and Mortality Weekly Report 52, no. 35:300-3.

--. 2007. Smoking-attributable mortality, morbidity, and economic costs (SAMMEC): Adult SAMMEC and maternal and child health (MCH). SAMMEC software. <http://apps.nccd.cde.gov/sammec/login.asp> (July 20, 2007).

Engelhardt, Gary V., and Jonathan Gruber. 2004. Social Security and the evolution of elderly poverty. National Bureau of Economic Research Working Paper No. 10466, May.

Feldstein, Martin, and Andrew A. Samwick. 1992. Social Security rules and marginal tax rates. National Tar Journal 45, no. 1:1-22.

Garrett, Daniel M. 1995. The effects of differential mortality rates on the progressivity of Social Security. Economic Inquiry 33, no. 3:457-75.

Gustman, Alan L., and Thomas L. Steinmeier. 2002. The new Social Security commission personal accounts: Where is the investment principle? National Bureau of Economic Research Working Paper No. 9045, July.

Krueger, Alan B., and Bruce D. Meyer. 2002. Labor supply effects of social insurance. National Bureau of Economic Research Working Paper No. W9014, June.

Leimer, Dean R. 1995. A guide to Social Security money's worth issues. Social Security Bulletin 58, no. 2:3-20

Malarcher, Ann M., Jane Schulman, Leonardo Epstein, Michael J. Thun, Paul Mowery, Ben Pierce, Luis Escobedo, and Gary A. Giovino. 2000. Methodological issues in estimating smoking-attributable mortality in the United States. American Journal of Epidemiology 152, no. 6:573-84.

Max, Wendy. 2001. The financial impact of smoking on health-related costs: A review of the literature. American Journal of Health Promotion 15, no. 5:321-31.

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Redja, George E. 1994. Social insurance and economic security. Englewood Cliffs, N.J.: Prentice Hall.

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Sevak, Prowl, David R. Weir, and Robert J. Willis. 2004. The economic consequences of a husband's death: Evidence from HRS and AHEAD. Social Security Bulletin 65, no. 3:31-44.

Shoven, John B., Jeffrey O. Sundberg, and John P. Bunker. 1987. The Social Security cost of smoking. National Bureau of Economic Research Working Paper No. 2234, May.

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Thun, M.J., C. Day-Lally, D.G. Myers, E.E. Calle, W.D. Flanders, B.P. Zhu, and M.M. Namboodiri. 1997. Trends in tobacco smoking and mortality from cigarette use in Cancer Prevention Studies I (1959 through 1965) and II (1982 through 1988). In Changes in cigarette-related disease risks and their implication for prevention and control. Smoking and tobacco control monograph 8. National Institutes of Health Publication No. 97-4213. Washington, D.C.: NIH.

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--. 2004a. Annual statistical supplement to the Social Security Bulletin. Washington, D.C.: Social Security Administration.

--. 2004b. The health consequences of smoking: A report of the Surgeon General. Atlanta: U.S. Department of Health and Human Services, Public Health Service, CDC, Center for Chronic Disease Prevention and Health Promotion, and the Office on Smoking and Health.

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(1.) These figures are estimated from information in USDHHS (2004a, table 4.B4).

(2.) While many researchers recognize the link between the payroll tax levied on an additional dollar of earnings and anticipated future benefits, their analysis typically calculates the comprehensive marginal tax rate using the Social Security statutory rate; as a consequence, their results are overstated (Browning 1985; Burkhauser and Turner 1985).

(3.) The benefit amount that family members may receive each month is limited. The limit varies but generally equals about 150 to 180 percent of PIA. If the sum of the benefits payable to family members exceeds this limit, their benefits will be reduced. However, any benefits paid to a surviving divorced widow or widower do not count toward this maximum amount (see USDHHS 2004a).

(4.) The 1977 amendments to the Social Security Act indexed the benefit formula's bend points to the growth rate in average covered earnings. The marginal replacement rates were fixed at 90, 32, and 15 percent, respectively (see USDHHS 2004a).

(5.) The tax rate ignores the disability insurance (DI) and health insurance (HI) contribution rates. Including both rates increases the net marginal Social Security tax rate by the statutory amount. In 2002 the combined employee-employer DI and HI rates were 1.8 and 2.9 percent, respectively (see USDHHS 2004a).

(6.) Brittain (1972) found that the payroll tax reduced employee earnings by the full amount of the tax.

(7.) The formula in equation (3) estimates the actuarial present value of anticipated future benefits relative to some benchmark retirement age. The age chosen here, f; is defined as the full benefit retirement age, which corresponds to the age at which an individual is first eligible for retirement benefits without actuarial adjustment. Following legislation implemented in the 1983 amendments to the Social Security Act, the full benefit retirement age increased two months per year, from sixty-five to sixty-six, from 2000 to 2005. Between 2005 and 2016 the full benefit retirement age will remain at sixty-six. In 2017, the full benefit retirement age is scheduled to increase two months per year and will be fixed at age sixty-seven for those attaining age sixty-two after the year 2022. The retirement age for workers with a full benefit retirement age in terms of years and months is rounded to the next full year in all calculations.

(8.) The economic assumptions used in the calculations are based on the 2005 Social Security Board of Trustees' best-cost estimates (USDHHS 2005).

(9.) To qualify for Social Security benefits, an individual must be fully insured. The measure used to determine whether a worker is eligible for retirement benefits is quarters of coverage. Under current legislation, a worker is fully insured if he obtains one quarter of coverage for each year after 1950 (or age twenty-one, if later) and before the year he dies, becomes disabled, or attains age sixty-two (USDHHS 2001). The minimum number of quarters required to be fully insured ranges from six to forty.

Unpublished insurance rate estimates were provided by the Social Security Office of the Actuary. The data contained projections covering the period 2002 by sex and age for the number of fully insured workers as a percentage of the total population.

(10.) A rate of 3 percent was chosen to approximate an individual's rate of time preference. As before, this rate was chosen on the basis of recommendations contained in USDHHS (2005).

(11.) The probability that a man aged sixty-five was fully insured for benefits in the year 2002 was 0.929. In comparison, the probability that a sixty-five-year-old female was fully insured was 0.741. These unpublished estimates were provided by the Social Security Office of the Actuary.

(12.) The Social Security Administration estimates that, of the 21.4 million women aged sixty-two and older in 2000, 8.2 million were entitled to primary benefits only, 5.9 million were dually entitled, and 7.4 million were solely entitled to benefits as a dependent spouse and failed to qualify for benefits based on their own earnings history (USDHHS 2001).

(13.) Widows and widowers become eligible to receive survivor benefits at age sixty. However, children and disability may lower the age of eligibility. A detailed explanation of how these criteria may affect the age that survivors may be first eligible for benefits is contained in USDHHS (2001).

(14.) Mortality ratios for current and former smokers were obtained from Thun et al. (1997).

(15.) Smoking prevalence data for current and former smokers were obtained from the CDC (2007).

(16.) It has been suggested that premature deaths attributable to smoking save Social Security money (Shoven, Sundberg, and Bunker 1987). One should not infer from these results that because smokers incur a higher NMSSTR they pay more than their fair share to Social Security; the higher NMSSTR may cause smokers to reduce their labor supply and thereby reduce Social Security contributions. In addition, Social Security disability payments to persons with smoking-attributable diseases and payments to dependents and survivors of deceased smokers will offset reductions in future system liabilities that stem from smoking-attributable death.

(17.) In addition to reducing hours of work, an increase in taxes may decrease labor force participation. Specifically, smoking may lead to a reduction in labor supply through early retirement. Retirement studies have typically used average life expectancy by age as opposed to predictions based on health status in their analysis (Social Security Advisory Council 1997). Those smokers in poor health who retire early may be responding to financial incentives that are masked in analyses that use average life expectancies.

(18.) These estimates are unpublished and were estimated from Smoking-Attributable Mortality Morbidity and Economic Cost (SAMMEC) data maintained by the Office on Smoking and Health at the CDC. SAMMEC estimates are available at <http://apps.nccd.cdc.gov/sammec/>.

(19.) We do not know how many widows under age sixty are ineligible for benefits. However, we do know that in the year 2000, 45,680 widows received benefits because they had a child under age sixteen in their care (USDHHS 2001, table 5.F1).

(20.) It is unclear why age fifty-five is recommended. Widows under age fifty-five whose eligibility is based solely on age would continue to be ineligible for Social Security benefits, and the system would fail to live up to one of its main goals of providing adequate retirement security. Additional information on proposals aimed at changing Social Security survivorship benefits and poverty among widows is available from Anzick and Weaver (2001).

(21.) However, this methodology is the best one can do since the actual data are unavailable (Garrett I995). For a discussion of the usefulness of results based on hypothetical worker data, see Leimer (1995).

(22.) The calculations shown in Tables 1, 3, and 4 ignored the personal income tax bracket at which Social Security retirement benefits will be taxed during retirement. Thus, the estimates shown in Table 5 assumed that Social Security benefits will be subject to a federal income tax rate of 15 percent. For a single male current smoker aged fifty-five, assuming a discount rate of 3 percent, taxation of benefits increased his NMSSTR by 0.3 percentage points (6.51 percent versus 6.81 percent).

(23.) The evidence is mixed on the impact of Social Security on the labor supply although the predominant research in this area has focused on the labor supply responses of older workers (Krueger and Meyer 2002).

BRIAN S. ARMOUR AND M. MELINDA PITTS

Armour is a health scientist at the Centers for Disease Control and Prevention (CDC) in Atlanta. Pitts is a research economist and associate policy adviser in the regional group of the Atlanta Fed's research department. The authors thank Ralph Caraballo, Scott Grosse, and Corinne Husten for helpful comments. This article reflects the authors' views and not those of the CDC.
Table 1
Net Marginal Social Security Tax Rate Estimates for Single
Beneficiaries and Primary Male Beneficiaries with a Dependent
Spouse by Earnings Classification and Age in 2002

 Single female Single male

Age in Low Average High Low Average High
2002 earning earning earning earning earning earning

35 -4.68 5.17 8.05 -2.11 6.08 8.48
45 -8.24 3.90 7.46 -4.94 5.07 8.01
55 -10.34 3.15 7.11 -9.22 3.55 7.30
65 -15.33 1.38 6.28 -17.86 0.48 5.86

 Male beneficiary
 and dependent spouse

Age in Low Average High Uninsured
2002 earning earning earning female

35 -9.75 3.37 7.21 10.6
45 -13.54 2.02 6.58 10.6
55 -19.26 -0.02 5.62 10.6
65 -31.37 -4.32 3.60 10.6

Note: Workers are assumed to retire at the full benefit retirement
age. Low-earning workers expect a marginal replacement rate of 0.9.
and average- and high-earning workers expect rates of 0.32 and 0.15,
respectively. A real discount rate of 3 percent is assumed. The
growth rate in real earnings is set at 1.1 percent.

Table 2
Life Tables Used in Net Marginal Social Security
Tax Rate Estimation of Survivors by Smoking Status

Age in Total Current Former Never
2002 population smoker smoker smoked

Females

20 98,922 18,538 22,604 57,780
21 98,877 18,530 22,593 57,754
22 98,827 18,520 22,582 57,725
23 98,781 18,512 22,571 57,698
24 98,736 18,503 22,561 57,672
25 98,688 18,494 22,550 57,644
26 98,639 18,485 22,539 57,615
27 98,589 18,476 22,528 57,586
28 98,539 18,466 22,516 57,557
29 98,483 18,456 22,503 57,524
30 98,424 18,445 22,490 57,489
31 98,362 18,433 22,476 57,453
32 98,296 18,421 22,461 57,415
33 98,225 18,407 22,444 57,373
34 98,148 18,393 22,427 57,328
35 98,064 18,363 22,402 57,299
36 97,970 18,329 22,374 57,267
37 97,869 18,293 22,344 57,232
38 97,759 18,253 22,311 57,195
39 97,640 18,210 22,276 57,153
40 97,500 18,160 22,234 57,105
41 97,355 18,109 22,192 57,055
42 97,194 18,051 22,144 56,999
43 97,023 17,990 22,093 56,940
44 96,830 17,921 22,036 56,873
45 96,627 17,849 21,976 56,802
46 96,405 17,770 21,910 56,724
47 96,176 17,689 21,843 56,644
48 95,928 17,602 21,769 56,557
49 95,654 17,505 21,689 56,460
50 95,364 17,403 21,603 56,357
51 95,059 17,297 21,513 56,249
52 94,724 17,179 21,415 56,130
53 94,380 17,060 21,314 56,007
54 93,989 16,924 21,199 55,866
55 93,572 16,780 21,077 55,716
56 93,095 16,616 20,937 55,542
57 92,629 16,456 20,801 55,372
58 92,084 16,270 20,642 55,172
59 91,491 16,069 20,469 54,953
60 90,826 15,845 20,275 54,706
61 90,138 15,614 20,076 54,448
62 89,374 15,360 19,854 54,159
63 88,552 15,089 19,617 53,846
64 87,657 14,796 19,359 53,502
65 86,680 14,479 19,079 53,122
66 85,631 14,143 18,779 52,709
67 84,512 13,788 18,460 52,264
68 83,281 13,402 18,110 51,768
69 81,982 13,001 17,743 51,238
70 80,556 12,567 17,342 50,647
71 79,026 12,109 16,914 50,004
72 77,410 11,633 16,464 49,313
73 75,666 11,130 15,982 48,554
74 73,802 10,604 15,470 47,729
75 71,800 10,051 14,924 46,824
76 69,639 9,470 14,340 45,828
77 67,366 8,877 13,732 44,757
78 64,935 8,262 13,088 43,585
79 62,372 7,636 12,416 42,320
80 59,621 6,989 11,704 40,928
81 56,681 6,327 10,954 39,400
82 53,660 5,680 10,195 37,785
83 50,324 5,002 9,371 35,951
84 47,075 4,382 8,585 34,109
85 43,542 3,751 7,747 32,045
86 39,919 3,151 6,909 29,859
87 36,246 2,595 6,083 27,569
88 32,571 2,090 5,281 25,201
89 28,943 1,643 4,516 22,784
90 25,411 1,258 3,800 20,354
91 22,024 936 3,141 17,947
92 18,828 675 2,549 15,604
93 15,862 471 2,027 13,364
94 13,158 317 1,578 11,264
95 10,737 205 1,200 9,332
96 8,613 127 892 7,594
97 6,785 75 646 6,064
98 5,245 42 455 4,747
99 3,977 23 312 3,642
100 2,954 12 208 2,735

Males

20 98,436 22,778 33,724 41,934
21 98,299 22,746 33,677 41,875
22 98,157 22,714 33,629 41,815
23 98,021 22,682 33,582 41,757
24 97,882 22,650 33,534 41,698
25 97,746 22,618 33,488 41,640
26 97,614 22,588 33,443 41,584
27 97,479 22,557 33,396 41,526
28 97,352 22,527 33,353 41,472
29 97,225 22,498 33,309 41,418
30 97,091 22,467 33,263 41,361
31 96,954 22,435 33,216 41,302
32 96,813 22,403 33,168 41,242
33 96,678 22,371 33,122 41,185
34 96,526 22,336 33,070 41,120
35 96,367 22,251 32,990 41,125
36 96,196 22,161 32,905 41,131
37 96,016 22,065 32,815 41,136
38 95,823 21,963 32,719 41,141
39 95,610 21,851 32,612 41,147
40 95,381 21,731 32,498 41,152
41 95,128 21,598 32,373 41,157
42 94,859 21,458 32,239 41,163
43 94,577 21,311 32,099 41,167
44 94,266 21,150 31,945 41,171
45 93,929 20,976 31,778 41,175
46 93,569 20,791 31,600 41,178
47 93,171 20,587 31,404 41,179
48 92,755 20,376 31,199 41,180
49 92,296 20,144 30,974 41,178
50 91,809 19,900 30,735 41,174
51 91,286 19,639 30,480 41,167
52 90,722 19,360 30,205 41,157
53 90,138 19,073 29,921 41,144
54 89,505 18,765 29,614 41,126
55 88,850 18,449 29,298 41,103
56 88,102 18,092 28,938 41,072
57 87,369 17,746 28,586 41,037
58 86,542 17,360 28,191 40,991
59 85,644 16,945 27,764 40,935
60 84,637 16,487 27,287 40,863
61 83,612 16,028 26,805 40,779
62 82,483 15,530 26,276 40,677
63 81,255 14,998 25,705 40,552
64 79,946 14,442 25,101 40,403
65 78,556 13,865 24,463 40,228
66 77,071 13,262 23,788 40,021
67 75,501 12,641 23,081 39,779
68 73,809 11,989 22,326 39,494
69 72,012 11,318 21,532 39,162
70 70,087 10,622 20,692 38,773
71 68,039 9,908 19,809 38,322
72 65,864 9,180 18,884 37,800
73 63,621 8,461 17,945 37,215
74 61,202 7,721 16,949 36,532
75 58,680 6,989 15,930 35,761
76 56,028 6,262 14,878 34,887
77 53,251 5,549 13,802 33,901
78 50,398 4,865 12,722 32,811
79 47,454 4,211 11,637 31,606
80 44,370 3,582 10,533 30,255
81 41,252 3,003 9,452 28,797
82 38,102 2,475 8,399 27,228
83 34,798 1,982 7,335 25,481
84 31,719 1,578 6,388 23,753
85 28,478 1,207 5,435 21,836
86 25,296 897 4,548 19,851
87 22,212 646 3,739 17,828
88 19,266 449 3,015 15,803
89 16,494 300 2,381 13,812
90 13,925 193 1,840 11,893
91 11,585 118 1,388 10,078
92 9,490 69 1,022 8,399
93 7,648 38 732 6,877
94 6,059 20 510 5,529
95 4,715 10 345 4,360
96 3,601 4 226 3,371
97 2,698 2 143 2,553
98 1,982 1 88 1,894
99 1,426 0 52 1,374
100 1,005 0 29 975

Note: "Survivors" refers to the number of persons by smoking status
reaching age a during the year among the stationary population.

Source: Constructed from life tables published by the National Center
for Health Statistics

Table 3
Net Marginal Social Security Tax Rate Estimates for Single Primary
Beneficiaries by Sex, Smoking Status, Earnings Classification,
and Age in 2002

 Current smoker Former smoker

Age in Low Average High Low Average High
2002 earning earning earning earning earning earning

 Females

35 -0.14 6.78 8.81 -2.87 5.81 8.35
45 -2.83 5.83 8.36 -6.09 4.67 7.82
55 -4.77 5.13 8.04 -8.13 3.94 7.48
65 -9.84 3.33 7.19 -13.13 2.16 6.64

 Males

35 3.96 8.24 9.49 0.73 7.09 8.96
45 2.21 7.62 9.20 -1.61 6.26 8.57
55 -0.91 6.51 8.68 -5.37 4.92 7.94
65 -8.84 3.69 7.36 -13.68 1.97 6.55

 Never smoked

Age in Low Average High
2002 earning earning earning

 Females

35 -6.84 4.40 7.69
45 -10.78 3.00 7.04
55 -12.86 2.26 6.69
65 -17.62 0.57 5.90

 Males

35 -7.68 4.10 7.55
45 -11.16 2.86 6.97
55 -15.69 1.25 6.22
65 -23.50 -1.53 4.92

Note: Workers are assumed to retire at the full benefit retirement
age. Low-earning workers expect a marginal replacement rate of 0.9,
and average- and high-earning workers expect rates of 0.32 and 0.15,
respectively. A real discount rate of 3 percent is assumed. The growth
rate in real earnings is set at 1.1 percent.

Table 4
Net Marginal Social Security Tax Rate Estimates for Male Primary
Beneficiaries with a Dependent Spouse by Earnings Classification,
Smoking Status, and Age in 2002

 Primary beneficiary Primary beneficiary
 current smoker former smoker
 Dependent spouse Dependent spouse

Age in Current Former Never Current Former Never
2002 smoker smoker smoked smoker smoker smoked

 Low earner

35 -4.39 -6.41 -8.68 -5.56 -7.14 -8.97
45 -6.53 -8.57 -10.87 -8.53 -10.18 -12.10
55 -10.30 -12.38 -14.71 -13.31 -15.05 -17.05
65 -20.9 -22.95 -25.18 -24.76 -26.51 -28.47

 Average earner

35 5.27 4.55 3.75 4.86 4.29 3.64
45 4.51 3.78 2.97 3.80 3.21 2.53
55 3.17 2.43 1.60 2.10 1.48 0.77
65 -0.60 -1.33 -2.12 -1.97 -2.59 -3.29

 High earner

35 8.10 7.77 7.39 7.91 7.64 7.34
45 7.75 7.40 7.02 7.41 7.14 6.82
55 7.12 6.77 6.38 6.62 6.33 5.99
65 5.35 5.01 4.64 4.71 4.42 4.09

 Primary beneficiary
 never smoked
 Dependent spouse

Age in Current Former Never
2002 smoker smoker smoked

 Low earner

35 -13.77 -15.42 -17.44
45 -18.21 -20.01 -22.22
55 -24.26 -26.21 -28.57
65 -35.42 -37.38 -39.68

 Average earner

35 1.94 1.35 0.63
45 0.36 -0.28 -1.07
55 -1.80 -2.49 -3.33
65 -5.76 -6.46 -7.28

 High earner

35 6.54 6.26 5.93
45 5.80 5.50 5.13
55 4.79 4.46 4.07
65 2.93 2.60 2.22

Note: Workers are assumed to retire at the full benefit retirement
age. Low-earnings workers expect a marginal replacement rate of 0.9,
and average- and high-earning workers expect rates of 0.32 and 0.15,
respectively. A real discount rate of 3 percent is assumed. The growth
rate in real earnings is set at 1.1 percent.

Table 5
Net Marginal Social Security Tax Rate Estimates for Average Earner
Primary Beneficiaries and Dependents by Sex, Smoking Status,
and Age in 2002

 Primary beneficiary

 Single female Single male

Age in Current Former Never Current Former Never
2002 smoker smoker smoked smoker smoker smoked

 2.2 percent discount rate

35 5.83 4.56 2.69 7.69 6.23 2.35
45 5.08 3.68 1.64 7.19 5.59 1.52
55 4.76 3.42 1.50 6.28 4.54 0.45
65 3.42 2.18 0.47 3.85 2.08 -1.58

 3.0 percent discount rate

35 7.07 6.17 4.87 8.42 7.35 4.59
45 6.18 5.11 3.57 7.84 6.58 3.44
55 5.54 4.44 2.89 6.81 5.35 1.95
65 3.88 2.79 1.32 4.20 2.61 -0.62

 3.7 percent discount rate

35 7.87 7.21 6.25 8.90 8.09 6.02
45 6.95 6.10 4.89 8.30 7.28 4.77
55 6.13 5.20 3.90 7.22 5.95 3.06
65 4.25 3.28 1.97 4.49 3.04 0.13

 Smoking status of male primary
 beneficiary and dependent spouse

Age in Both current Both former Both never
2002 smokers smokers smoked

 2.2 percent discount rate

35 5.34 4.30 0.50
45 4.68 3.35 -0.95
55 3.49 1.83 -2.88
65 0.07 -1.84 -6.32

 3.0 percent discount rate

35 5.67 4.77 1.38
45 4.97 3.76 -0.19
55 3.73 2.17 -2.28
65 0.24 -1.60 -5.94

 3.7 percent discount rate

35 5.90 5.09 1.96
45 5.18 4.06 0.34
55 3.92 2.43 -1.83
65 0.38 -1.42 -5.63

Note: Workers are assumed to retire at the full benefit retirement
age. Average-earning workers expect a marginal replacement rate of
0.32. The growth rate in real earnings is set at 1.1 percent.
Estimates account for smoking-attributable mortality and taxation
of benefits.
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Author:Armour, Brian S.; Pitts, M. Melinda
Publication:Economic Review (Atlanta, Ga.)
Geographic Code:1USA
Date:Jul 1, 2007
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