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let e(a) represent the fraction of inen who smoke as a ftsaction of age, and 2?(a) represant the mortality ratio of male smoker to nonsmoker as a function of age, then Q~(a) 1 • fa(a)(1 • t?(a)) and Q$(a) - e(a) x (4s(a) where C?M(a) is the anmzal death probability of male nonsmokers as a function of age and QS(a) is the aaausl death probability for male smokers. The formulas for vomen are identical with all the superscripts changed to v's. The appendix tables displaye tha assumptions for 1?(a) and I?(a) , derived from 8ammond (1966), and for fa(a) and e(a) for the 1920 cohort, derived from Harris (1983). They also show the results for QNS(a), QS(a), Q~S(a), and QS(a). Table 2 offers some summary statistics based on these derived life tables. Our life tables for the 1920 birth cohort show that 85,798 males and 88,787 females out of 100,000 births live to age 20. It is well kaown that smoking affects the mortality of vomen less than men. That is partially due to the fact that women smokers smoke less, iabale less, and are more likely to smoke filter cigarettes. Again, out of 100,000 births, 53,051 male smokers (who began smoking at age 20) survive until age 65, whereas 67,464 male nonsmokers survive until that traditional retirement age. Conditional on living to age 20, almost 79 percent of nonsmokers make it to 65, whereas slightly less than 7

2sbls 2 Lifs Emp.ctaacF, li.dim Age at D.ath, And Svrviviag Populitioa at Ages 20 and 63 For 1920 Eirr.h Cohort Susvivors at age 20 out of Susvivors at ag. 65 out of Lif. expectancy Life sxpsctaacy Isidisa age of d.ath '.S.dian age of dsath 100,000 100,000 conditioaal coaditioaai conditional conditional births births on age 20 on age 65 oa age 20 oa ags 65 Smoksrs 85,758 53,051 68.7 78.8 70 77 Noasmokars 85,758 67,465 75.1 81.5 77 81 Wos.a Ssoicars 88,787 ' 69,303 77.2 84.6 79 84 Noasaokars 88,787 74,461 80.5 86.6 84 86 a

62 percent of smokers do so. At age 20, nale smokers have a life expectancy . 6.4 years shorter than male nonsmokers, and a median age of death 7 years youmger. Conditional on surviving to 65, male smokers have a remaining life expectancy which is 2.7 years less than their nonsmoking cohort members. The figures for women show that the life expectancy difference at age 20 is 3.3 years, while the difference at age 65 is 2 years. Our life tablei cs++not sort out causality and correlation. It is certaialy true that smokers would not become identical to nonsmokers if they stopped smoking. Smokers drink more alcohol tban nonsmokers, have a higher incidence of suicide, and, in general, may face higher mortality risks than nonsmokers for reasons correlated with smoking but not caused by smoking per se. Qe have not been able to separate these effects, although it is our belief that most of the higher mortality risks faced by smokers are due directly to the cigarette-consvmption. However, it should be kept in mind when interpreting our results that we have attributed all of the mortality difference to the cigarette consumption. 3. SIMLTIATION OF 'ffiE SOCIAL SECUBITI COSTS OF SMORI3G. ae aY9mi*+~ the Social Security consequences of smoking for 100,000 man born in 1920 and 100,000 women born in 1923. 'Ihe three year difference approximates the average age gap in marriage for this cohort. The 1920 cohort life tables compiled by Social Security are taken to be applicable to the men and women in our study. Re calculate the Social Security outcomes separately for single men, single women, and one and t•.ro earner couples. We assume that each person's probability of death is given by the life tables, and therefore is independent of the status of their spouse. The rnzmbet of women who become widowed in each year until the husbands retire is noted, and each "widow cohort• is then tracked as a separate population. This is necessary, because 9

at retireaent widows msist choose between a benefit basad on thair o+rn work record and one based on that of their spouse. In the case of the one earnar couples, we assume that the husband is employed until retirement or death. If the husband should die before retirement, the widow is asstmod to Voric cmtil rstirsaent or death. We have not been very sophisticated in davaloping our earnings profiles. The earnings series used are median aarnings for men and woaen vorldng full- time year-round, tskan from the Cansus Bureau Current Population Seport P-60, No. 142 (1982). Earnings before 1955 and 1982 are estimated using a related series from the Depart:mant of Isbor's Employment, Hours, and Earnings report. The earnings series are then adjusted to reflect a life-cycle pattern of lifetime earnings, %ising Census data on mean incomes for different age groups from Report P-60, No. 137. Our analysis for low waga earners exam{res those who earn 60 percent of the median earnings profiles. There are several factors vh3c3s could be added to our earnings series. First. we do not take into account the effect of the iacraased morbidity of smokers on their earnings pattern. This is probably a relatively minor adjnstment, but one which is conceptually desirable. Second, nonworking wives entering the workforce when widowed are assumed to immedistaly earn the median (or 60 percent of the median) amount for their age. This is cert.zinly optimistic regarding their prospects. Finally, we do not take into account spells of uaamployment, employment in the uncovered sector, or disability. The surviving members of the cohort are assumed to retire at aga 65 and begin to recaive benefits based on the 1985 Social Sacurity law. Q* assume that the initial benefit received is fully indexed for inflation for their remaining life. The women in the simtsiations retire chree. years later, simply =e="lect:ng that they are three years younger than the men. Because the median earnings of man exceed those for women, the Social Security OASI benefit based on a man's 10

earnings history exceeds the benefit based on a voman's work record. ds a result, husbands and widowers will always elect to take their own benefit. Wives choose between their own benefit and oae-half of their husband's, while widows may elect to receive their oxn benefit or the benefit which their husband would receive were he alive and had not worked since the year he actually died. In other vords, a voaan vhoae husband died in 1965 could taks the benefit he would be receiving had he stopped working in 1965 and lived to receive his benefit, or she could take her own benefit. In the tsro-earmer cohort, her benefit is based on her earnings from 1940 to her retirement in 1988, while in the one-earner cohort her benefit is based on a shorter work history, 1965 - 1988, since we assuae she only begins work upon her husband's death. This means that a vidow's benefit may depend on when h.r husband died (and in the one-e.raer case must depend on it), necessitating our keeping track of the 'widov cohorts' mentioned above. Qives over the age of 65 whose husbands are still alive will alsrays receive one-half of their husband's benefit in the oae-earner family, since they have no earnings history of their o.rn. In the txo-eaxaer case, wives-will take their own benefit since their benefit exceeds half their husband's, given our earnings series. All benefits are calculated in real dollars, so coaparfuon of 1985 and 1988 benefits is valid. The results for singles are shown in Table 3. All figures are stated in 1985 dollars, and the real discount rats used for cash flovs occurring at other times is 3 percent. Rith those assumptions, the figures in the upper portion of the table for single men with median wage profiles in this cohort show that nonsmokers can expect to receive a net transfer from Social Security of $3,436, while the expected benefits received by smokers fall $17,782 short of the expected contributions. All of these figures are conditioaa]l on having survived to age 20. The Social Security cost of smoking for single men with median C iI

Tabls 3 Present valus of Social S.cnrit7 Benefits and ?mus (in 1985 $) And Intsrasl Rats of Rsturn to the Social S.curity Program For 2ismb.rs of the 1920 birtb Cohort Raal Nst Intarnal. Ezpsctsd F.zp.ctsd Present Rsts of Present Prss.nt 14.t valu. Real Ratsira value vatus b*.ctad Conditional Intarasl Conditional of QASI of OeSI Present On Surviving Rats of On Surviving a.n.fits Sass Value Until Ag. 65 Hstvrn Until Ags 65 Median Earnings Profile NAM Smokers 53,497 71,279 •17,782 3,721 1.87 3.18 Nonsmokars 79,436 76,000 3,436 18,218 3.17 3.78 vom.n Smk.rs 65,512 57,386 8,126 21,843 3.45 4.03 Nonsmokers 75,788 58,395 17,394 28,283 3.87 4.27 Low (60% Median) Earnings Profile d.a Smokers 41,378 50,342 •8,964 8,918 2.25 3.57 Nonsmokers 61,441 53,433 8,008 20,130 3.53 4.15 Aom.n ~ Smokers 47,159 34,431 12,728 23,166 4.06 4.65 Q ~ Nonsmokers 54,556 35,036 19,520 27,801 4.47 4.88 CD M'r 12

earnings patterns thus exceeds $21,000. The internal rats of return, which equates the expected value of payouts and payins, is 1.87 percent real for smokers and 3.17 percent for nonsmokers. If one only looked at those who survived until 65, the rates of return would naturally be higher. In that case, the real internal rats of return for median wag. aale smoicars in this cohort is 3.18 percent, rrhereas the rate for nonsmokers is 3.78 percent. The dollar difference in the net transfer between nale smokers and nonsmokers, conditional on surviving to 65, is still about $14,500. Table 3 indicates that the Social Security cost of smoking is smaller for single women than for single men. In general single women get a higher rate of return from Social Security for two reasons. First, they have longer life expectancies, and, second, they have lower earnings and'the system is progressive. Conditional on age 20, the diffsrence in the net transfer to median wage women nonsmokers and smokers is slightly more than $9,000. The real intaraal rate of return for smoking voman is 3.45 percent, while the figure is 3.87 percent for nonsmokers. Conditiona7l on reaching age 65, the dollar difference between smoking and not is about $6500 for median wage single women. The lower portion of Table 3 shows ttie results for single individuals with earnings 60 percent of the median for their age and cohort. The loss due to smoking in the expected transfer from Social Security is almost $17,000 for men and $7,000 for women at this earnings level. Re conclude that the Social Security cost of smoking is not terribly sensitive to earnings levels. The corresponding results for one and two earner married couples with median earnings profiles ars shown in Table 4. One earner couples receive larger transfers and a higher rate of return from Social Securitq because of the benefits received by the nonworking spouse. The Social Security expected cost of smoking is similar for couples in either circnmstance. The net 13

Table 4 Present Value of Social Security Bsn.fits and 2sxas (in 1985 $) .Aad Internal 8sta of Rst~ua to the Social S.eurity Progrm For li.abars of the 1920 Birth Cohort 2S.disa Esraiags Profile Real 14st Internal FsF.ctad Ezp.etad Pres.at Bste of Present Prueat Nst Valu. Real Return vslue Value Fsp.atad Coaditionsl Zataraa.l Conditional of OASI of OASI Present On Surviving Rita of On Surviving Benefits T.xss valus Until Ag. 63 Return Until Age 63 Narriad (one saraar) Both Smoks 118,223 79,466 38,757 81,270 4.40 5.41 Nonsmokers 149,229 81,004 68,225 95,872 5.14 5.63 Mala smoker 128,748 79,722 49,026 92,123 4.67 5.67 female nonsmoker F.mal• smoker 139,353 male nonsmoker 80,860 58,493 87,010 4.93 . 5:43 Married (two .uaars) Both Smoics 126,687 128,664 -1,977 38,639 2.95 3.87 Nonsmokers 162,985 134,395 28,590 56,371 3.68 4.18 Male smoker 138,313 129,673 ' 8,640 48,103 3.22 4.04 femala nonsmoker Female smoker 151,494 male nonsmoker 133,386 18,108 48,402 3.46 4.05 v02E: Figures ire per honsanold. 14

expected present value of participation in Social Security is $29,467 lower for one earaer couples who both smoke relative to one earner couples where neither spouse smokes. If only the man smokes, the loss in the expected transfer from the system is $19,199, vhereas if only the wife smokes the loss is $9,732 relative to a one earner couple in which neither smokes. To put these figures in perspective, one might note that the median earnings of 64 year old men in this cohort were $20,315. Thus, the Social Security loss for both smoking amounts to almost 1.5 years labor income. In fact, the loss in slightly greater than that given that Social Security benefits are taxed more favorably than labor income. The nssobers for two earner couples are that their expected nst Social Security transfer is $30,567 less if both spouses smoke than if neither does. The real internal rate of return for two earner couples in which both smoke is 2.95 percent, whereas it is 3.68 percent if neither smokes. The cost of the husband only smoking is $19,950, and the cost of the wife only smoking is $10,482. For reference, the median aaaual earnings of women is about $12,500, so the loss if they both smoke is roughly equivalent to 2.4 years of the wife's earnings. Table 5 contains the results for low wage one and tvo-earaer couples. For c one earner couples, we find that the cost of both smoking is roughly $22,500. For two earner couples, the cost of both smoking is $23,500. Once again, the cost is roughly twice as large for msn as it is for women. The dollar costs to smoking are greater relative to earnings for low wage households than for median earners. The gain in Social Security benefits that accrue to the nonsmoker, or to the smoker .Tho quits, represents an equal :uid opposite drain on Social Security fnnds. This drain is only partially offset by the. increase in preretirement N 0 N W W N ~ 0 ~ ~ ?5

If Table 5 Prsssnt valise of Social Security Baufits and Taxes (in 1985 $) And Intasaal Bzts of Utura to the Social Sacurity Prograa For M.mbsrs of the 1920 Birth Cohort . Lov (60% dsdian) Earaings Profil. Real 8.t Intsrnal Fsp.ctad Fzp.ctad Present Rsta of Prasant Present Net vslne Beal Raurn vs].ue vslua ExFectad Conditional Internal Conditional of OASI of OASI Present On Survivia; Rsta of On Sur7iving Banafits Tas.s vilu. Until Age 65 Raturn Until Ags 65 Marriad (one sasaar) Both Smoka 91,761 53,146 36,614 70,896 4.78 5.81 Honssokars 115,531 56,327 59,204 81,313 5.50 5.99 Msle ssolcsr 99,952 55,300 44,652 79,101 5.05 6.07 faaala nonsmoksr Fsale ssoic.r 107,878 56,241 51,637 74,672 5.29 5.79 nals aonsmokar larried (tvo eaznars) B.ah Smoke 96,843 84,772 12,071 45,609 3.47 4.43 Nonsmokers 124,085 88,469 35,616 58,131 4.13 4.70 Msla smoker 105,689 85,378 20,311 52,959 3.74 4.61 female noasmoltsr Female saoicar 115,429 87,864 27,566 52,003 3.97 4.56 msla nonsmoker *iOTE: Figures are per household. N 0 / :6