American Economic Association
Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records
Author(s): Joshua D. Angrist
Source: The American Economic Review, Vol. 80, No. 3 (Jun., 1990), pp. 313-336 Published by: American Economic Association
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Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security
Administrative Records By JOSHUA D. ANGRIST*
The randomlyassigned risk of inductiongenerated by the draft lottery is used to construct estimates of the effect of veteran status on civilian earnings. These estimates are not biased by thefact that certain types of men are more likely than others to service in the military. Social Security administrativerecords indicate that in the early 1980s, long after their service in Vietnam was ended, the earnings of white veterans were approximately15 percent less than the earnings of comparablenonveterans.(JEL 824)
A central question in the debate over mili- tary manpower policy is whether veterans are adequately compensated for their service. The political process clearly reflects the de- sire to compensate veterans: since World War II, millions of veterans have enjoyed benefits for medical care, education and training, housing, insurance, and job place- ment. Recent legislation provides additional benefits for veterans of the Vietnam era. Yet, academic research has not shown conclu- sively that Vietnam (or other) veterans are worse off economically than nonveterans. Many studies find that Vietnam veterans earn less than nonveterans, but others find posi- tive effects, or effects that vary with age and
*Department of Economics, Harvard University, Cambridge, MA 02138. Grateful thanks go to Warren Buckler, Cresston Smith, Ada Enis, and Bea Matsui for their assistance in producing the Social Security data; to Chester Bowie for his help in producing the SIPP data; and to Mike Dove for providing DMDC administrative records. Special thanks also go to David Card and Whitney Newey, from whose instruction and comments I have benefited greatly, and to Alan Krueger and an anonymous referee, whose careful reviews of an earlier draft led to substantial improvement. Data collection for this project was funded by the Princeton Industrial Relations Section. Funds for computation and financial support of the author were provided by the Industrial Relations Section, the Princeton Department of Eco- nomics, the Sloan Foundation, and the Olin Founda- tion.
schooling. Regarding the general position of veterans, a member of the Twentieth Cen- tury Fund’s Task Force on Policies Toward Veterans concludes that “Within any age group, veterans have higher incomes, more education, and lower unemployment rates than their nonveteran counterparts.”‘
The goal of this paper is to measure the long-term labor market consequences of mil- itary service during the Vietnam era. Previ- ous research comparing civilian earnings by veteran status may be biased by the fact that certain types of men are more likely to serve in the armed forces than others. For exam- ple, men with relatively few civilian opportu- nities are probably more likely to enlist. Es- timation strategies that do not control for differences in civilian earnings potential will incorrectly attribute lower civilian earnings of veterans to military service. The research reported here overcomes such statistical problems by using the Vietnam era draft
‘The quote is from Michael Taussig (1974, p. 51). Legislation pertaining to veterans benefits is outlined in Veterans Administration (1984) and in other annual reports of the Veterans Administration. Studies by Sherwin Rosen and Paul Taubman(1982), Saul Schwartz (1986), and Jon Crane and David Wise (1987) find that Vietnam veterans earn less than nonveterans. Dennis DeTray (1982) and Mark Berger and Barry Hirsch (1983) find some positive effects for different age and schooling classes, and Veterans Administration (1981a) researchefs find an overall positive effect.
313
314 THE AMERICAN ECONOMIC REVIEW JUNE 1990
lotteriesto set up a naturalexperimenthat randomlyinfluencedwho servedin the mili- tary.2
SectionIV tests the hypothesisthatveter- ans earn less than nonveteransbecausethey have less civilian labor marketexperience. Resultsin this sectionsuggestthat the earn- ings loss to white veteransis equivalento a loss of two years of civilian labor market experience.Section V reviewssome of the potentialpitfallsinestimationbasedonthe draftlottery.SectionVI offersconclusions and indicatesdirectionsfor futureresearch.
SectionI describesthe SocialSecurityad-
ministrativerecords used in the empirical
work and providesbackgroundon the draft
lotteries.In each lottery,priorityfor induc-
tion was determinedby a RandomSequence
Number (RSN) from 1-365 that was as-
signed to birthdatesin the cohort being
drafted. Men were called for inductionby
RSN up to a ceilingdeterminedby the De-
fenseDepartment,andonlymenwithlottery
numbersbelow the ceilingcouldhavebeen
drafted. Therefore,men with lottery num-
bersbelowtheceilingarereferredtohereas Therewerefivedraftlotteriesduringthe
“draft-eligible.”
The empiricalanalysisbeginsin SectionII
VietnamWar period.The 1970 lotterycov- ered19- to 26-year-oldmenbornin 1944-50, althoughmost of the men draftedin 1970 werebornin 1950.Otherlotterieswerere- stricted to 19- and 20-year-olds.The 1971 lottery coveredmen born in 1951, the 1972 lotterycoveredmenbornin 1952,andso on, through1975. However,no one was drafted after 1972, and congressionalconscription authorityexpiredin July1973.
with estimatesof the effectof drafteligibility
on earnings.If drafteligibilityis correlated
with veteran status but uncorrelatedwith
other variables related to earnings, then
earningsdifferencesby draft-eligibilitsytatus
can be attributedto militaryservice.In Sec-
tion III, informationon the proportionsof
draft-eligibleand draft-ineligiblemen who
actually served in the military is used to
convertestimatesof the effectof drafteligi-
bilityinto estimatesof theeffectof military
service.The assumptionsunderlyingthis
procedurearethosethatjustifyinstrumental 195in1970,RSN125in1971,andRSN95
variablesestimation;inprinciple,anyfunc- tion of the RSN providesa legitimateinstru- ment for veteranstatus.In the secondpart of SectionIII,aninstrumentavlariablesesti- mation strategyis developedwhichis more efficientthan one basedsolelyon draft-eligi- bility status.Resultsin SectionIII indicate that white veteransearn approximately15 percentless thannonveteransas muchas ten yearsaftertheirdischargefromthe military.
2A candid assessment of the problems caused by nonrandom selection for military service is given by Crane and Wise (1987), who note they were unable to use econometric sample selection models to generate robust estimates of the effects of military service on civilian earnings. The first researchersto use the lottery to solve the selection problem were Norman Hearst, Tom Newman, and Stephen Hulley (1986), who present lottery-based estimates of delayed effects of military service on mortality.
in1972-were announcedlaterintheyear, once Defense Departmentmanpowerneeds wereknown.As a consequenceof thisdelay, manymenwithlownumbersvolunteeredfor the militaryto avoid being draftedand to improve their terms of service (Angrist 1989b). There was even a behavioralre- sponse to the lotteryin enlistmentratesfor the 1953 cohort, althoughno one born in 1953 was drafted.In the analysisthat fol- lows, the “draft-eligibilityceiling”for men born in 1953 is set at RSN 95, the highest lotterynumbercalledin 1972.
3This section draws on Curtis Tarr (1981) and the Selective Service System (1986).
4Men born from 1944-49 were already of draft age when the 1970 lottery was held on December 1, 1969. For nonveterans in this group, subsequent liability for service was determined by 1970 lottery numbers.
I. BackgroundandData
A. National RandomSelection3
Draft lottery RSNs were randomly as- signed in a televised drawingheld a few monthsbeforemenreachingdraftagewere tobecalled.4Draft-eligibilityceilings-RSN
VOL. 80 NO. 3 ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY 315
Onlytheinitialselectionprocesswasbased on RSN order.Subsequentselectionfrom the draft-eligible, nondeferred pool was based on a numberof criteria.The most important screeningcriteriawere the pre- inductionphysicalexaminationanda mental aptitude test. In 1970, for example,half of allregistrantsfailedpre-inductionexamina- tions and 20 percentof those who passed wereeliminatedby physicalinspectionscon- ducted at induction(SelectiveServiceSys- tem, 1971). Of course,the fact that armed forces selection criteriawere ultimatelynot randomdoes not meanthat the initial prior- ity for inductionwas not randomlyassigned by RSN.
The year 1970 was the last time men over the age of 20 were drafted. In principle, nonveteransborn between 1944 and 1949 continued to be at risk of inductionin the 1970 lottery, but the majorityof men who ended up serving from these cohorts had alreadyenteredthe militaryby the time of the1970lotterydrawingV.eteransbornfrom 1944-49 who managedto avoidserviceuntil 1970 may not constitutea representative sample. Therefore,the analysis here is re- strictedto men who turned19 in the year they were at risk of induction.This sample includesmen who werebornbetween1950 and 1953.
B. SocialSecurityEarningsData
Earningsdatausedin thisstudyaredrawn from the Social SecurityAdministration’s (SSA) Continuous Work History Sample (CWHS).The CWHSdata set, describedin detail in the Appendix, is a one percent sampledrawnfromall possibleSocialSecu- ritynumbers.TheCWHSincludestwoearn- ings series:the firstcontainsinformationon the 1964-84 earningsof menin employment coveredby FICA (SocialSecurity)up to the Social Security taxable maximum.It also includes FICA taxable earningsfrom self- employment.The secondseries,beginningin 1978, contains total compensationas re- ported on InternalRevenueServiceForm W-2, excluding earningsfrom self-employ- ment.In principle,theW-2earningsdataare neithercensorednorlimitedto earningsfrom
Social Securitytaxableemployment.How- ever,becauseSSAproceduresforthecollec- tion of W-2 forms are relativelynew, W-2 earningsdataareprobablylessreliablethan the FICA data.
The original CWHS data set does not contain informationon date of birth. SSA programmersmatcheddateof birthvari- ables to the CWHSin a specialextractcre- ated for this project.Lotterynumberswere thenmatchedto datesof birth,usingtables published in the 1969-73 SemiannualRe- ports of the Directorof SelectiveService.
The InternalRevenueServicelimits dis- closure of data collected for tax purposes. To adhereto these disclosurerequirements, the SSA could releaseonly aggregatedata. The aggregate data set contains sample statistics for cells definedby year of earn- ings,yearof birth,race,andfiveconsecutive lottery numbers. Cell statistics include means, variances, fraction with earnings equalto the taxablemaximumf,ractionwith earningsabove the taxablemaximum,frac- tion with zero earnings,and numberof ob- servationsineachcell.
II. TheEffectof DraftEligibility on Earnings
Figure 1 shows the historyof FICA tax- able earningsfor draftlotteryparticipants bornbetween1950and1953. Foreachco- hort there are two lines drawn: one for draft-eligiblemen, and one for men with lottery numbersthat exemptedthem from the draft.
The impactof drafteligibilityon the earn- ings profilesis striking.Thereappearsto be no differencein earningsuntil the year of conscriptionriskin thedraftlottery.Subse- quently,the earningsof draft-eligiblewhite menbornin 1950-52 fallbelowtheearnings of draft-ineligiblewhitemenbornin 1950- 52. The earningsof draft-eligiblenonwhites also fall below the earningsof other non-
5Eamings are in 1978 dollars. The deflator used for all tabulations is the CPI on p. 313 of The Economic Report of the President (Council of Economic Advisors, 1988).
316 THE AMERICAN ECONOMIC REVIEW
JUNE 1990
<. D. o
3000 -
2000-
1000- * 0'
U-2000 -
-3000
Notes: The figure plots the history of FICA taxable earnings for the four cohorts born 1950-53. Foreachcohort,separatelinesaredrawnfordraft-eligibleanddraft-ineligible men. Plotted points show average real (1978) earnings of working men born in 1953, real earnings+ $3000 for men born in 1950, real earnings+ $2000 for men born in 1951, and real earnings+ $1000 for men born in 1952.
FIGURE 1. SOCIALSECURITYEARNINGSPROFILESBY DRAFT-ELIGIBILITY STATUS
- 0.08 -0.04 0
0.04 0.08
0.12 0.16
whites, but the gap appearsto narrowand become positive for some nonwhitecohorts in later years.The fact that earningsdo not differ by draft-eligibilitystatus before the lotteries is a consequenceof the random assignmentofdrafteligibilityT.heonlything that distinguishesdraft-eligiblemen from draft-ineligiblemen is the higher conscrip- tion risk faced by eligible men after the lottery.
Figure2 presentsa magnifiedview of the effect of draft eligibilityon earnings.This figureplots the time-seriesof differencesin earningsby draft-eligibilitystatus for each cohort. As in Figure1, Figure2 shows no differenceduringthe yearsbeforethe yearof conscriptionrisk,whilein subsequentyears, the earningshistoriesdiverge.Figure2 also shows that the loss of earningsto draft-eligi- blewhitemenwaslargestduringtheperiod they were most likely to be in the service.
However,the earningsof draft-eligiblewhite men continuedto lag behindthe earningsof draft-ineligiblewhitemen through1984.
The picture for nonwhitesis less clear. Theearningsofdraft-eligiblneonwhitesborn in1950and1951exceedthoseofdraft- ineligible nonwhites in some of the later years.On the otherhand,for nonwhitesborn in 1952, time-seriesvariation in earnings differencesby eligibilitystatusis similarto that of whites. The generalimpressionfor the threeolder cohortsof nonwhitesis that the earningsof draft-eligiblemen at least had caughtup with the earningsof draft-in- eligiblemenby 1984.
Earningsof white men born in 1953 do not appearto differby draft-eligibilitysta- tus. The earningsof draft-eligiblenonwhites born in 1953 generallyexceed the earnings of nonwhiteswho werenot draft-eligible. Differencesbetweenthe effectof drafteligi-
PROBABILITRYESIDUAL
VOL. 80 NO. 3
ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY 317
uJ z uA
X LL_
LL
0- Z~~~~~~
0-
I-
____
___ _ _ _- _ _ _ _
,- _ _
-_ ,
Z2 W0-4-4 I-
< ui
0B 1951
IJJ
66 68 70 7274
BORN 1950
BORN 1951
BY DRF-LGBLT BORN 1952
BORN 1953
rel(1978
dollars.
6668
FIGUR
70 7274 76 78 8082 YEAR
84
z
--
76 78 808284 YEAR
STATUS
COHORT
2T1.L-k 0IFREC INi EANIG
Notes: The figure plots the difference in FICA taxable earnings by draft-eligibility status for the four cohorts born 1950-53. Each tick on the vertical axis represents $500 real (1978) dollars.
FIGuRE 2. THE DIFFERENCEIN EARNINGSBy DRAFT-ELIGIBILITYSTATUS
bility on men born in 1953 and the effecton the threeoldercohortsmightbe explained by the transitionto an All-VolunteerForce in 1973. Men who volunteerfor the military areprobablylesslikelythandrafteesto suf- fera careerdisadvantagefromtheirservice.
Estimatesof the effect of draft eligibility are reportedin Table1 for both FICA earn- ingsandW-2earnings.Standarderrorsasso- ciated with the estimatesare reportedin parentheses.The statisticsin Table 1 show that the loss in FICA earningsto draft-eli- gible white men is sometimesstatistically significantand amountsto 2-3 percentof earnings.EstimatedW-2earningslossesare similar,but tend to be largerand morevari- able than the estimatedlossesin FICA earn- ings. In contrast,differencesin earningsby draft-eligibilitystatus for nonwhitesrarely exceedtheirstandarderrors.
Elsewhere(Angrist1989c),I have shown that draft-eligiblewhite men are less likely to have earningsabove the FICA taxable maximumthan draft-ineligiblewhite men.
The effect of draft eligibilityon nonwhites' probabilityof being at the taxablemaxi- mum, althoughimpreciselymeasured,also appearsto go in the same directionas the effectof drafteligibilityon meanearnings. Theseresultsareworthnotingbecause,when the effectof drafteligibilityon the probabil- ity of being censoredhas the same sign as the effect on earnings,estimatestabulated using censoreddata tend to underestimate the trueeffect.6
6Theeffectof censoringon estimatedtreatmentef- fects is discussedin the appendix.Angrist(1989c)also reportsestimatesof the effectof drafteligibilityon the probabilityofhavingnorecordedearningsT.hesetabu- lationsindicatethatdraft-eligiblwehitesweresomewhat morelikelyto havehadFICAearningsduringtheyears in whichtheywerein theservice,andthatdraft-eligible nonwhitesare more likely to have had no earningsin recentyears.Thereis no statisticallysignificantevi- dence for eitherrace,however,of any lastingeffectof drafteligibilityon theprobabilityof havingzeroearn- ings.
318
THE AMERICAN ECONOMIC REVIEW
JUNE 1990
Year 66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
1950 1951
-21.8
(14.9)
-8.0 13.1 (18.2) (16.4)
-14.9 12.3
(24.2) (19.5) -2.0 18.7 (34.5) (26.4)
- 233.8 -44.8 (39.7) (36.7)
- 325.9 - 298.2 (46.6) (41.7)
- 203.5 -197.4 (55.4) (51.1)
1952 1953
-8.9
(19.2)
11.4 -4.0
(22.7) (18.3) -5.0 32.9 (29.3) (24.2)
- 29.4 27.6 (40.2) (30.3)
-261.6 2.1 (46.8) (42.9)
1950
1951
1052
1953
TABLE 1-DRAFT-ELIGIBILITY TREATMENT EFFECTS FOR EARNINGS
FICA Taxable Earnings
Total W-2 Compensation
- 226.6 - 228.8 - 357.7 - 56.5
(56.2) -402.7
(68.3) - 295.2 - 99.2 - 304.5
(67.8) (61.6) - 243.0 -155.4
(81.4) (75.3)
(94.4) (89.7)
- 314.2 - 86.8 (106.6) (102.9)
- 262.6 - 274.2 (117.9) (112.2)
- 205.3 - 203.8 (132.7) (127.0)
- 339.1 - 267.9 (183.2) (175.3)
(79.6)
- 263.6
(160.5) (152.3)
(153.9) - 312.1
(148.7) (1,575.6) (1,590.5) - 93.8 -1,028.1 85.6
- 60.5
(127.3)
- 236.8 89.2 -1,588.7 523.6
- 580.8 - 557.9 (736.7) (750.1)
- 581.3 -428.7 (309.1) (341.5)
-440.5 - 109.5 (265.0) (245.2)
- 514.7 18.7
(54.8) -15.0
(68.1) - 28.3
(85.0)
- 370.7 -145.5
(98.2) - 396.9
(111.1) -467.1
(93.0) - 85.5 (107.1) - 65.3 (123.1)
1,059.3 (2,159.3)
233.2 (1,609.4)
175.3 (1,567.9)
-1,974.5 (912.1)
Whites
(178.2) (170.7) (756.8) - 342.8 34.3 - 589.6
(599.8) - 71.6 (423.4) - 72.7 (372.1)
- 435.8 - 358.3
(210.5) (203.6) (206.8) (199.0) (299.4)
- 320.2 -117.3 (235.8) (229.1)
- 349.5 - 314.0 (261.6) (253.2)
-235.1 29.4 - 305.5
(232.3) (222.6) -437.7 - 96.3
(296.5) - 915.7
(281.9) 30.1
(441.2) (426.3) - 484.3 - 398.4 -436.0 - 228.6 -1,143.3 - 809.1
(286.8) (279.2) (281.9)
(272.2)
III. TheEffectof MilitaryService on Earnings
A. Estimates UsingDraft Eligibility
where f,B is a cohort effect, at
Estimates of the effects of military service are based on a simple linear model for earn- ings. Denote the earnings of man i in cohort c at time t by Yd, and let si be an indicator of veteran status. Then we may write
(1) ycti==AC+ at+ sia + uit
(257.5) (248.7)
(345.4)
- 512.9 - 896.5
(318.1) - 767.2 - 164.2
(395.2)
(492.2) (380.9) (376.0) (366.0)
iS a period effect common to all cohorts, and uit is a residual. The coefficient a is the effect of military service on civilian earnings. If si is correlated with the unobserved components of the earnings equation, then a will not be consistently estimated by Ordinary Least Squares (OLS). For example, correlation be-
tween si and u,, may arise because the armed forces' eligibility criteria are correlated with earnings, but not accounted for by the econometrician, or because veterans are
VOL. 80 NO. 3
ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY 319
Year 66 67 68 69 70 71 72 73 74 75
76
77
78
79
80
81
82
83
84
1950
-11.8 (27.6)
12.9 (34.2)
- 29.5 (44.5) -5.1 (66.8)
- 99.8 (78.5)
-164.8 (92.7)
-188.8 (113.6) -85.7 (137.7)
-179.3 (165.0)
-190.3 (189.3)
-105.3 (214.7)
112.4 (238.5) 163.6 (272.6) 187.0 (317.2) 203.2 (363.1) 534.5 (413.5) 285.1 (461.2)
96.0 (512.6)
- 76.8 (548.2)
1951
-4.0 (30.6) -6.2 (37.3)
67.8 (53.4) 62.2 (75.7)
- 144.3 (86.4)
-156.7 (105.7)
-134.8 (127.0) - 96.7 (160.1)
1952
-12.0 (35.0)
3.4 (43.4)
24.7 (62.2)
-25.0 (85.1)
-208.2 (104.2)
-175.6 (129.0)
-181.4 (155.6)
-183.7 (185.8)
- 308.9 (216.5)
-251.1 (248.5)
-424.9 (279.4)
1953
-42.4 (36.4) -9.0 (44.9)
18.2 (60.7) 60.4 (92.8)
115.5 (119.4) 216.5 (145.1) 111.6 (166.9)
-46.4 (199.3)
153.5 (233.5) 381.9 (275.7)
1950 1951
1952
1953
FICA Taxable Earnings
Total W-2 Compensation
-
236.1 (186.8)
TABLE1-CONTINUED Nonwhites
- 333.7 (215.4)
- 206.8 (240.4)
-108.6 (269.2)
-210.3 (323.0)
4.8 (368.4)
313.2 (419.1) 175.4 (471.6) 419.5 (538.1)
-223.1
(562.8) (568.5) (568.2) (804.0) (771.5) (721.0) (716.8)
-1,145.0 (2,395.6)
2,978.2 -4,676.2 (2,869.6) (1,393.1)
-482.7 (2,206.0)
-391.7 312.0 4,005.4 1,545.0 - 494.7 -1,043.3
(324.8) -212.6
(372.5) - 305.8
(429.1) - 262.5
(476.7) -177.3
(326.3) 344.0 (370.3) 717.8 (433.7) 810.4 (486.3) 543.6 (523.2)
(2,721.2) 790.2
(648.1) 802.5 (524.6)
(2,191.1) 376.4
(533.6) 415.9 (745.1)
(2,683.8) - 292.7
(440.9) - 272.3
(492.8) -160.2
(590.0) - 53.6 (643.4)
(1,660.2) 288.6
(416.4) 784.4 (503.1) 675.1 (564.1) 462.3 (638.9)
(531.5)
-123.3 641.3 - 287.4 -718.6
- 288.0 827.3
326.0 - 244.3
(608.9) 315.4 (720.0)
(647.8) 254.3 (767.5)
errors in parentheses.
the difference in earnings by lottery-determined draft-eligibility status.
Notes: Standard
The table shows
Eligibility ceilings are RSN 195 for men born in 1950, RSN 125 for men born in 1951, and RSN 95 for men born in 1952 and 1953.
Earnings data are from the Social Security Administration CWHS, described in the text and the Appendix.
self-selected on the basis of unobserved characteristics.
The draftlotteryfacilitatesestimationof (1) because functionsof randomlyassigned lottery numbersprovideinstrumentalvari- ablesthatarecorrelatedwithsi,butorthog-
onal to the error term, uir. For example, one such instrumentis a dummyvariable,di, that equals one if the ith individualwas draft eligible. Supposethat attentionis re- strictedto a singlecohort.Then,use of d1 and a constant as instrumentalvariables
320 THE AMERICAN ECONOMIC REVIEW
JUNE 1990
leads to the following estimator for a.,
eligibility on veteran status for whites born 1950-52 range from 0.10 to 0.16. Thus, a rule of thumb for conversion of draft-eligi- bility treatment effects into estimates of the effects of military service is to multiply by 1/0.15 = 6 2/3.
Wald estimates of the effect of military service for selected cohorts and years are presented in Table 3. The sample is re- stricted to the subset of whites born 1950-52 because the results in Table 2 suggest that this is the group for whom draft eligibility is most likely to be a useful instrument. Earn- ings variables are for 1981-84 because the impact of military service in these years rep- resents a long-term effect. Furthermore,as a practical matter, both FICA and W-2 earn- ings data are likely to be more reliable in recent years-the FICA data because of in- creased employment coverage and the W-2 data because of improvements in data collec- tion procedures.
Table 3 reports three sets of estimated draft-eligibility effects for use in the numera- tor of the Wald estimator. Column (1) pre- sents estimates for FICA earnings and col- umn (3) presents estimates for W-2 earnings; the figures in both of these columns are copied directly from Table 1. In addition, column (2) reports estimates for an earnings
(2)
?&= (ye - -n)/( pe _ pn)
is the proportion of the cohort
A
where
actually entering the military,
earnings, and superscript e and superscript n denote the draft-eligible and draft-ineligi- ble samples. Note that the numerator of (2) consists of estimates of the effect of draft eligibility plotted in Figure 2.
Intuitively, equation (2) simply adjusts earnings differences by draft-eligibility status for the fact that not all draft-eligible men actually served in the military, while some men who were not draft eligible voluntarily enlisted for service. The justification for esti- mation of the effects of military service in this manner is clear: it is assumed that noth- ing other than differences in the probability of being a veteran is responsible for differ- ences in earnings by draft-eligibility status. This formula may also be recognized as an application of Abraham Wald's (1940) grouping method, where the data have been grouped by draft-eligibility status. Applica- tions of this formula will therefore be re- ferred to here as "Wald estimates."
-
is mean
In addition to draft-eligibility treatment
effects, implementation of the Wald estima-
tor requiresestimatesof pe and An. These series constructed by applying a simple
estimates are tabulated from a special ver- sion of the 1984 Survey of Income and Pro- gram Participation (SIPP). The SIPP data used here were matched to an indicator of draft-eligibility status from information on birthdates included in the Census Bureau's in-house version of the SIPP file. Additional details on the SIPP data are provided in Section 7 of the Appendix.
In the upper panel of Table 2, the columns labeled pe and An show probabilitiesof veteran status tabulated using the SIPP. Be- cause of the small number of observations available for single-cohort statistics, each SIPP estimate is actually the average for three consecutive cohorts. For example, SIPP estimates assigned to men born in 1951 are based on data for men born in 1950, 1951, and 1952. The last column of Table 2, la- beled pe _ Apn, shows the differencein the probability of military service by draft-eligi- bility status. Estimates of the effect of draft
non-parametric correction for censoring to the FICA earnings data. The correction pro- cedure is described in detail in Section 6 of the Appendix. Briefly, data are adjusted for censoring by using the fraction with recorded earnings at the taxable maximum, combined with mean earnings above the taxable maxi- mum estimated from Current Population Surveys, to estimate population mean earn- ings from censored mean earnings. Note that the effects estimated using the adjusted data are usually bracketed by the effects esti- mated using the unadjusted FICA and W-2 data. Therefore, only Wald estimates con- structed from the adjusted data are reported in the table.
Wald estimates for adjusted FICA earn- ings, reported in column (5) of Table 3, indicate that white veterans suffered an an- nual earnings loss of roughly $2000 constant (1978) dollars of $3,500 current dollars. This is approximately 15 percent of annual W-2
VOL. 80 NO. 3 ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY 321
Data Set SIPP(84)a
DMDC/CWHSb
Data Set SIPP (84)a
DMDC/CWHSb
Cohort Sample 1950 351
1951 359 1952 336 1953 390 1950 16119 1951 16768 1952 17703 1953 17749
P(Veteran)
0.2673 (0.0140) 0.1973 (0.0127) 0.1554 (0.0114) 0.1298 (0.0106) 0.0633 (0.0019) 0.1176 (0.0025) 0.1515 (0.0027) 0.1343 (0.0026)
pe
0.3527 (0.0325) 0.2831 (0.0390) 0.2310 (0.0473) 0.1581 (0.0339) 0.0936 (0.0032) 0.2071 (0.0053) 0.2683 (0.0065) 0.1548 (0.0053)
pe
0.1957 (0.0699) 0.2014 (0.0827) 0.1449 (0.1040) 0.1980 (0.0865) 0.0548 (0.0042) 0.1173 (0.0076) 0.1439 (0.0095) 0.0984 (0.0079)
pn
0.1933 (0.0233) 0.1468 (0.0180) 0.1257 (0.0146) 0.1153 (0.0152) 0.0279 (0.0019) 0.0708 (0.0024) 0.1102 (0.0027) 0.1268 (0.0029)
pn
0.1354 (0.0491) 0.1514 (0.0448) 0.1287 (0.0373) 0.1612 (0.0470) 0.0271 (0.0032) 0.0599 (0.0040) 0.0794 (0.0042) 0.0904 (0.0046)
pe - -n
0.1594 (0.0400) 0.1362 (0.0429) 0.1053 (0.0495) 0.0427 (0.0372) 0.0657 (0.0037) 0.1362 (0.0059) 0.1581 (0.0071) 0.0280 (0.0060)
pe_ ph
0.0603 (0.0854) 0.0500 (0.0940) 0.0161 (0.1105) 0.0367 (0.0984) 0.0276 (0.0053) 0.0574 (0.0086) 0.0644 (0.0104) 0.0080 (0.0092)
TABLE2-VETERAN STATUSAND DRAFT ELIGIBILITY Whites
Notes: Standard errors in parentheses. pe conditional on being draft eligible; p" is the on being ineligible.
of being a veteran probability of being a veteran conditional
Cohort Sample 1950 70 1951 63 1952 52 1953 55 1950 5447 1951 5258 1952 5493 1953 5303
P(Veteran)
0.1625 (0.0292) 0.1703 (0.0292) 0.1332 (0.0275) 0.1749 (0.0305) 0.0417 (0.0027) 0.0794 (0.0037) 0.0953 (0.0040) 0.0925 (0.0040)
Nonwhites
aWave I, Panel I of the 1984 Survey of Income and Program Participation. Probabilities are for service in the Vietnam era. Estimates are weighted by the SIPP sampling weight and smoothed over 3 cohorts.
bDefense Manpower Data Center Administrative Records' information on acces- sions, from 1970-73, combined with information on cohort size from the Social Security Administration Continuous Work History Sample.
compensation for white men between 1981 and 1984. The similarity of coefficient esti- mates across cohorts and years suggests that the Wald estimates provide a robust measure of the impact of military service. Taken indi- vidually, however, few of the estimates are
statistically significant at conventional levels.7
7The'asymptoticstandarderrorof the Wald esti- mates is derived from the limiting distributionof
is the probability
322
THEAMERICANECONOMICREVIEW
JUNE 1990
rn e -
Cohort 1950
1951
1952
FICA Earnings
Year (1)
1981 - 435.8 (210.5)
1982 - 320.2 (235.8)
1983 - 349.5 (261.6)
1984 -484.3 (286.8)
1981 - 358.3 (203.6)
1982 -117.3 (229.1)
1983 -314.0 (253.2)
1984 - 398.4 (279.2)
1981 - 342.8 (206.8)
1982 -235.1 (232.3)
1983 -437.7 (257.5)
1984 -436.0 (281.9)
Adjusted FICA Total W-2 Earnings Earnings
(2) (3)
-487.8 - 589.6 (237.6) (299.4)
-396.1 - 305.5 (281.7) (345.4)
-450.1 -512.9 (302.0) (441.2)
- 638.7 -1,143.3 (336.5) (492.2)
-428.7 - 71.6 (224.5) (423.4)
- 278.5 - 72.7 (264.1) (372.1)
-452.2 - 896.5 (289.2) (426.3)
- 573.3 - 809.1 (331.1) (380.9)
- 392.6 -440.5 (228.6) (265.0)
- 255.2 - 514.7 (264.5) (296.5)
- 500.0 - 915.7 (294.7) (395.2)
- 560.0 - 767.2 (330.1) (376.0)
pe _ (4)
0.159 (0.040)
0.136 (0.043)
0.105 (0.050)
Service Effect in 1978$ (5)
-2,195.8 (1,069.5)
-1,678.3 (1,193.6)
-1,795.6 (1,204.8)
-2,517.7 (1,326.5)
-2,261.3 (1,184.2)
-1,386.6 (1,312.1) -2,181.8 (1,395.3)
- 2,647.9 (1,529.2)
- 2,502.3 (1,556.7)
-1,626.5 (1,685.8)
- 3,103.5 (1,829.2)
- 3,323.8 (1,959.3)
TABLE3-WALD ESTIMATES Draft-EligibilityEffectsin Current$
Notes: Standard errors in parentheses.
Columns (1) and (3) are taken from Table 1.
Column (2) reports draft-eligibility treatment effects on earnings adjusted for censoring at the FICA taxable maximum. The adjustment procedure is described in the Ap- pendix. Column (4) reports SIPP estimates of the effect of draft eligibility on veteran status, taken from Table 2. Column (5) reports estimates of the effect of military service on civilian earnings is implied by columns (2) and (4).
B. EfficientInstrumental VariablesEstimates
The Wald estimator is based solely on earnings differences by draft-eligibility sta- tus. A more efficient estimator exploits all the information on RSNs in the aggregate data by fitting earnings model (1) to obser- vations on mean earnings for each group of
mulas.
five consecutive lottery numbers. Consider the following grouped version of (1), where Yctjis mean earnings for members of cohort
c at time t with lottery numbers in group j, and is the fraction of cohort c with lottery numbers in group j who served:
(3) Yctj=3c+St+P-a +uCtj
Intuitively, estimation of (3) simply general- izes Wald's method to grouped data with more than two groups.
Generalized Least Squares (GLS) esti- mates of (3) may easily be shown to have an instrumental variables interpretation (Angrist, 1988). In this case, the instrument set includes dummy variables that indicate
e - -"). The standarderroris therefore equal to 1/( e - n) times the standard error of the numerator because the numerator has a nondegenerate limiting distribution, while (pe - p) converges to a constant. The same standard error formulas arise from application of conventional InstrumentalVariables for-
yn)l(
pn
VOL. 80 NO. 3 ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY 323
groups of five consecutive lottery numbers for each race, cohort, and year of earnings. There are 73 dummy variables for a particu- lar race, cohort, and year; the first indicates men with lottery numbers 1-5 and the 73rd indicates men with lottery numbers 360-365. Furthermore, the quadratic form minimized by the GLS estimator is an overidentifica- tion test statistic associated with the use of dummy variables as instruments. This statis- tic tests the exclusion of lottery number group dummies from equation (1). It may also be viewed as a measure of the goodness- of-fit of the cell means to equation (1).8
In principle, implementation of the esti- mation strategy based on (3) is straightfor- ward-the estimates are simply coefficients from GLS regressions of mean Social Secu- rity earnings on estimates of fi.. The SIPP sample is too small to allow accurate estima- tion of a full set of P , however. Thus, a second set of probabilities was estimated from a combination of Defense Manpower Data Center (DMDC) administrativerecords and CWHS data on cohort size. Detailed descriptions of the DMDC administrative records may be found in Angrist (1989b). Briefly, the DMDC data show the total num- ber of new entrants to the military by race, cohort, and lottery number from July 1970 through December 1973.
DMDC and CWHS administrativerecords are used to estimate 1bj by first counting the number of entrants to the military by race, cohort, and lottery number interval. These numbers are the numerator of the c . Esti- mates of overall cohort size, to be used in the denominator of Pj3, are derived from the CWHS. Recall that the CWHS is a one percent sample, so that if the CWHS sam- pling frame is identified with the population
8
A general reference on overidentification testing is
Whitney Newey (1985). See also Angrist (1988), where GLS on grouped data is shown to be the minimum variance linear combination of all the Wald estimators that can be computed from any division of grouped observations into linearly independent pairs. The overi- dentification test statistic for dummy variable instru- ments is also shown to be the same as the Wald statistic for equality of alternative Wald estimates.
at risk, an estimate of total cohort size is simply 100 times the CWHS cohort size. For example, to estimate the probability of being a veteran conditional on being draft eligible, the number of draft-eligible men in the DMDC data is divided by 100 times the number of men in the CWHS with lottery numbers below the induction ceiling. Stan- dard errors for these estimates are computed by applying the usual formula for a binomial proportion.9
For comparison with the SIPP estimates, DMDC/CWHS estimates of pe and pn are reported in the lower panel of Table 2. These figures show that, with the exception of the 1950 cohort, the SIPP and DMDC/CWHS procedures give reasonably similar estimates of _- p". Inaccuracy of the DMDC/ CWHS estimates for 1950 is a consequence of the fact that DMDC administrative records are unavailable before July 1970. Therefore, despite the limitations of the SIPP data, the SIPP must be used to construct probabilities for the 1950 cohort. The SIPP sample is too small to allow estimation of a complete set of p for all lottery number cells in 1950. Consequently, SIPP estimates for 1950 are computed for only two cells, defined by draft-eligibility status, and CWHS earnings data for men born in 1950 are also grouped by draft eligibility. Thus, for each race and year, the sample used to estimate equation (3) includes 73 cell means for each of the three cohorts born from 1951-53, plus two cell means for the 1950 cohort.
A graphical version of equation (3) is de- picted in Figure 3, which shows the relation- ship between probabilities of veteran status (PCJ)and mean W-2 compensationin 1978 dollars (jctJ) between 1981 and 1984. Plot- ted in the figure are the average (over four years of earnings) residuals from a regression
4Theformula used is j '(1 - ')/n,], where p is the estimated proportion of servers and nC is the number in the CWHS cohort. For example, 5749 draft eligible white men in the CWHS were born in 1951, and DMDC administrative records show that 119,062 draft-eligible white men born in 1951 served between July 1970 and December 1973. pe is therefore119,062/574,900 = 0.21, with estimated variance equal to (0.21 * 0.79)/5749.
324 THE AMERICAN ECONOMIC REVIEW
JUNE 1990
(I)~~~~~~~~~~~U a 16000
a
1950
14500
0g12500 0500
-J 14000 a 12000
a) i2(-i) z
/i
-
w
4000-
#,-/
CO
_
6500.
2000,f,~ I 11111I1III
66r68e7702i74
80t827h68478
YEAR Z
66 68 70 72 74 7678 8082 84 YEAR
_ -_ /
COHORT1950 1951 1952 1953
ELIGIBLE INELIGIBLE --.
1953 _- _ _ DRAFT
Notes: The figure plots mean W-2 compensation in 1981-84 against probabilities of veteran status by cohort and groups of five consecutive lottery numbers for white men born 1950-53. Plotted points consist of the average residuals (over four year-sof earnings) from regressions on period and cohort effects. The slope of the least squares regression line drawn through the points is - 2,384 with a standard error of 778, and is an estimate of a in the equation
Yctj==fc + at+ P a+ iu4t
FIGURE3. EARNINGSANDTHEPROBABILITYOFVETERANSTATUSBYLOTTERYNUMBER
of earningsand probabilitieson periodand cohort effects.10Thus,the slope of the ordi- nary least squares regressionline drawn throughthe points correspondsto an esti- mate of a. This slope is equal to -2,384 dollars,with a standarderrorof 778 dollars. An interestingfeatureof the figureis the apparentheteroscedasticityof the earnings residuals.Dispersionaroundthe regression line is reducedfor cells with high probabili-
ties of veteranstatus.Thisheteroscedasticity also appearsin comparison(snot shownhere) of cell variancesby draft-eligibilitystatus; draft-eligiblemen have somewhatless vari- able earnings.
As pointedout earlier,estimationof (3) is the same as instrumentalvariablesestima- tion of (1) using dummyvariablesas instru- ments.However,inferencefor the casewhere the estimationstrategyis implementedby regressing CWHS mean earnings on DMDC/CWHS or SIPP probabilities is complicatedby theuseof datafrommultiple samples.Assumingthat the samplesused to calculatemean earningsand the sampleused to calculateA3areindependentt,he optimal
l?There are 221 points plotted in the figure: 4 years
of earnings times 3 cohorts with 73 cells plus 4 years of
earnings times one cohort with 2 cells (men born in
1950) = 884, divided by four to compute the average
overyears. Two-SampleInstrumentaVlariables(TSIV)
5 500-
2500 'A
*
1990
VOL. 80 NO. 3 ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY 325
estimator has a simple form that may be
-
able maximum using the procedure de- scribedin section6 of the Appendix.
The results in Table 4 show that white veteransborn from 1950-52 sufferedan an- nual earnings loss of between $1,500 and $2,100constant(1978)dollars.Theseresults generally are similar in magnitudeto the Waldestimatesreportedin Table3. Also, as in Table 3, regressionestimatesfor adjusted FICA earningstend to be bracketedby the resultsfor unadjustedFICA and W-2 earn- ings. Although many of the estimates for individualcohortsin Model1 arenot signif- icant, the combinedestimatesfor whites in Model 2 are substantiallylargerthan twice theirstandarderrors.In contrast,resultsfor nonwhitesshownoevidenceofastatistically
significantearningsloss to veterans.
The overidentificationtest statistics re- ported in Table 4 take on valuesless than theirdegreesof freedom,suggestingthatthe
residualsin equation(1) are not correlated with lottery-basedinstruments.12It should be noted,however,thatlowvaluesof thetest statisticsmay indicatelow powerin a test with so many degreesof freedom.On the other hand, withouta particularalternative hypothesisin mind, it seems naturalto re- port the omnibusgoodness-of-fitest.
Subtractingthe test statisticfor Model 1 from the test statisticfor Model 2 gives a chi-squaretest for the restrictionof equal treatmenteffects acrosscohorts.The set of restrictionsimposedby equaltreatmentef- fects has three degreesof freedom.None of the chi-squarestatisticsfor Model 2 are larger than the correspondingstatisticsfor Model 1 by as muchas three,indicatingthat
of freedom for the overidentification tests are calculated as follows. For each race, the data consist of four years of earnings for three cohorts with 73 lottery number cells each. The fourth cohort, men born in 1950, has four years of earnings with 2 lottery num- ber cells each. This gives a total of 884 cells or, equiva- lently, 884 categorical instruments. Model 1 includes 4 cohort dummies, 3 year dummies, and 4 treatment effects. 884 minus 11 parameters gives 873 degrees of freedom. Model 2 has 3 fewer parameters than model 1 and consequently the chi-square statistic for model 2 has 876.degrees of freedom.
denotethe vector of Jctj' p denote the vector of
brieflydescribedas follows.Let
and iu(O)denote the vectorof uct.,where0 in parenthesesrepresentsthe dependenceof residualson the parametervector.Also, let
V( ) denote the covariancematrix of the argument.Then the optimalTSIVestimator chooses 0 to minimize
@)'[V( y)+ a2V(fp)] u(e)
which is also the GLS minjimandfor (3).11 The minimizedvalueof m(O)is an overi-
dentificationtest statisticfor the validityof dummyvariablesasinstrumentsI.fsomeof these dummy variablesare correlatedwith the regressionerror,then m(O) should be largerelativeto a chi-squaredistributionwith degreesof freedomequal to the difference betweenthe numberof instrumentsand the numberof estimatedparameters.
Table 4 presentstwo sets of TSIV esti- matesof equation(3) for 1981-84 earnings in 1978dollars.Model1 allowstheeffectof veteranstatuson earningsto varyby cohort, while Model 2 restrictsestimatedserviceef- fects to be the same across cohorts. Note that, as in Table 3, the heading"adjusted FICA earnings" refers to FICA-taxable earningsadjustedfor censoringat the tax-
"1See Angrist (1989d) for details. Estimates of a for
use in the formula for (D were computed by weighted
least squares using the inverse of the sampling variance
-
of the
discussed in Section 5 of the Appendix. Note that the TSIV estimator may also be motivated as an application of Optimal Minimum Distance (OMD) techniques such as those described by Gary Chamberlain(1982). Ignor- ing period and cohort effects, OMD estimates for the current problem are tabulated by choosing a and p to minimize
as weights. Estimates of V(y) and V(p) are
q(a,P) =
[y - PC' V(y) LP-Pp Lo
0 1 V(p')]
y_pal L-P p
By concentrating out the estimate of p, it is easy to show that q(a, p) = m(0).
12Degrees
326
THE AMERICAN ECONOMIC REVIEW
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Cohort
Model 1 1950
1951
1952
1953
X2(873)
Model 2 1950-53
X2(876)
Cohort
Model 1 1950
1951
1952
1953
X2(873)
Model 2 1950-53
X2(876)
FICA Taxable Earnings
-1709.2 (946.8)
-1457.1 (959.3)
-1724.0 (863.1)
1223.8 (3232.1)
578.3
-1562.9 (521.8)
579.1 Nonwhites
FICA Taxable Earnings
3893.7 (5358.5) - 891.3 (4397.1)
- 3182.9 (3997.4)
- 5928.3 (10296.3)
616.7
-643.3 (2407.5)
618.4
Adjusted FICA Earnings
- 2093.7 (1108.8)
- 1983.7 (1036.1)
- 1943.0 (927.2)
900.7 (3505.3)
630.3
-1920.4 (575.9)
631.0
Adjusted FICA Earnings
3891.9 (6244.5) - 333.4 (4664.2)
- 3457.7 (4195.2)
- 8571.4 (10697.1)
681.7
- 999.7 (2602.5)
683.4
Total W-2 Compensation
-1895.0 (1333.1)
- 2431.4 (1152.1)
- 2058.7 (1001.9) -488.6 (3936.0)
569.5
- 2094.5 (646.3)
569.7
Total W-2 Compensation
5711.8 (7206.0) 2609.0 (4894.6)
- 3068.0 (4229.2)
- 6325.8 (11410.6)
693.6
366.7 (2734.2)
695.6
TABLE4-TWO-STAGE INSTRUMENTALVARIABLESESTIMATES Whites
Notes: Standard errors in parentheses.
The table shows estimates of the effect of military service on average 1981-84 earnings in 1978 dollars. The estimation method is optimally weighted Two-Sample Instrumental Variables, described in the text. FICA and W-2 earnings are from the Social Security CWHS. The adjusted FICA series is described in the Appendix.
the estimated treatment effects are not statis- tically different across cohorts.
IV. MilitaryServiceandLossofLabor MarketExperience
The simplest explanation for a veteran earnings penalty is that military experience
is a poor substitutefor lost civilian labor marketexperience.As evidencefor this hy- pothesis, Grilichesand Mason (1972) show thatthelongertheywerein themilitary,the less veteransearnrelativeto nonveteransA. test of the loss-of-experiencehypothesisis developed here using the functional form commonlyemployedin empiricalstudiesof
VOL. 80 NO. 3 ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTER Y 327
humancapital.The earningsfunctionmoti- vated by the theory of human capital is loglinear in years of schooling and log- quadraticin years of labor market exper- ience. This functional form puts testable restrictionson the time-seriesof earnings differencesby veteranstatus.'3
Adapting the human capital earnings functionfor the problemat hand,the earn- ings of individual i in cohort c at time t may be written
(4a) Yca= 8t + wi,o + /Oxic, + yx 2 +U,
where yci now denoteslog earnings,8, is a
time-varyingintercept, y, and are BoL, So
parameters.xict is the civilianlabor market experienceof man i in cohort c at time t, taken here to be equal to [t - (c + 18)- w,- sil], where wi is the deviationof i's school- ing fromthe samplemeanlevelof schooling, and 1 is years of militaryexperiencefor veterans.As before, si is a dummyvariable that indicatesmilitaryservice.
To focus on parametersthat can be esti- mated using Social Securitydata, equation (4) is rewrittenas
(4b) Ycti= Sit
+/30(X -sil) + y(XCt- Sil)2
- (2ywixct -2ylwisi) + ui,
where xct = t - (c + 18) and 8t = St+ W(8O
- 1h)+ yw7. Now, as in the previousanaly- sis, assumethat schoolingdoes not varyby lottery number.Assumealso that schooling is independentof cohort-this seems rea- sonablefor the smallcohortrangeconsid- eredhere.Finally,to focussolelyon the loss of labor
schoolingis independentof veteranstatus. Thenusingdummyinstrumentavlariablesto group equation (4b) by cohort, year, and lottery number, average log earnings for membersof cohort c at time t in lottery- numbercell j are
market experience, assume that
Models (5) and (6) both have the follow- ing reducedformin termsof unrestricted regressioncoefficients:
(7) Yctj= a + /oxct + yx t
+ 7TPcj + 72( Pc*jxcx) + uct
Note that the reducedformveteraneffectis cty 1+ 'T2Xct Thus, thesemodelsparame- terize a time-varyingveteranstatus coeffi- cient as a linear functionof labor market
Averaging over c, t, and j eliminates (d yw,x, - aywisi) because wi is orthogonal to x,, and s, by assumption. Using the fact that E(s,jc, j) = E(s2lc, j) = pcj, (4) simplifies to (5). Note that (5), (6), and (7) are not estimable if allowance need be made for cohort as well as period effects. Qualitatively similar estimates to those reported below were obtained when t was dropped in favor of cohort effects, although the good- ness-of-fit test leads to rejection of models without period effects.
13See Mincer (1974) for theoreticaljustification of the human capital earnings function. A recent survey of the human capital literature is Willis (1986).
(5)
Yctj= 8t+ floxot + YXct - [,3l - y12] A-
- [2-yl] Cxct ) + Uct,
where 8Anow includesthe periodmean of '4
it.
A generalizationof model (5) allows the linearexperiencetermto varywithveteran statusby lettingtheslopeforindividuali be Pi3= f8 + Pls,. In this case, mean cell earn- ings are characterizedby
(6)
Yctj= 8a+ f3OXc+ yx2 - [30l-yl2+I3ll]pC
- [2yl - fil](P-xCt) + iCt
328
THE AMERICAN ECONOMIC REVIEW
JUNE 1990
Parameter
Experience Slope, ,80
Experience Squared, y
Veteran Effect on Slope, 3,8
Veteran Loss of Experience, /
s7T= - [fol- y12 + 3l]
,g2 = - [2yl - l]
Age at Which Reduced Form VeteranEffect(7r1+ 7r2xc,)=0
X2(dof)
Model (5): Loss of Experience (1)
0.1022 (0.007) - 0.0027
(0.0003)
2.08 (0.38)
1.41(1)
Model (6):
Loss of Experience, Reduced Growth Rate (2)
0.1016 (0.007) - 0.0025
(0.0003) - 0.0035
(0.0023) 1.84
(0.43)
Model (7): Unrestricted Reduced Form (3)
0.1016 (0.007) - 0.0025
(0.0003)
-0.189 (0.052)
0.006 (0.004)
50.1 (15.9)
813.57(1247)
TABLE5-EARNINGS-FUNCTION MODELSFORTHEVETERANEFFECT, WHITESBORN 1950-52
Notes: Standard errors in parentheses.
The table reports estimates of experience-earningsprofiles that include parameters for the effect of veteran status. Estimates are of equations (5), (6) and (7) in the text. The estimating sample includes FICA taxable earnings from 1975-84 for men born 1950, 1976-84 earnings for men born in 1951, and 1977-84 earnings for men born 1952. The estimation method is optimally weighted Two-Sample Instrumental Variables for a nonlinear model in columns (1) and (2), and for a linear model in column (3).
experience.Excludingthe time-varyinginter- cept, model (6) containsfour structuralpa- rameters;80,81,y,and1,andfourreduced form parameters;fLo,y, 7T,and 7T2.Model (5) imposesone testablerestrictionon the reducedformby settingfB= 0.15
Table5 showsresultsfromnonlinearGLS estimationof (5) and (6), and resultsfrom LinearGLS estimationof (7), usingdata on the real FICA earningsof white men born from 1950 to 1952. The weightingmatrix used in estimationwas derivedin a manner similarto the weightingmatrixused to con- struct the estimatesin Table 4.16 Because
'5A third model is derived by letting both y and ,B vary with veteran status. This model leads to a reduced form similar to (7), with the only modification being the addition of a linear term of the form T3( cj * x2,). In the empirical work, however, no evidence was found that such a term belongs in the earnings function re- duced form.
16The only modification arises from the fact that for equations (5)-(7), reduced form treatment effects ap- pearing in the weighting matrix are time varying. Let Fc denote the vector of act for the time-series of
earningsfunctionsare commonlyfit in logs, the dependentvariableis takento be the log of meanearningsforeachcell.Thelogof the meanis not the sameas the meanof the log, but the CWHSdataset does not contain the mean of log earnings.If earningsare approximatelylognormallydistributed,use of the log of the meanwill providea reason- able approximationI.n practice,estimatesof
earnings by cohort c and suppose that each time-series is of length T. Then the second term in the optimal weighting matrix has the following block corresponding to the time series of earnings for lottery number cell j of cohort c:
(l/ncj) fc
X IeTeT'
] [Pcj
Pcj)]}rf C,
where eT is a vector of T l's. In practice, lc is replaced by weighted least squares estimates (weights are the inverse sampling variances of Yctj) of the re- duced form equation, (7). Estimates of models for the log of earnings replace V(5) with delta-method esti- mates of the covariance matrix of log(.P).
VOL. 80 NO. 3 ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY 329
models in levels resulted in inferences simi- lar to those arising from estimates of models in logs.
The sample used to estimate equations (5)-(7) begins in the fifth year after the lottery in which members of the cohort were drafted. For example, the sample begins in 1975 for men born in 1950. This allows for three years of service and one year of read- justment to civilian life. Median length of service of Vietnam era veterans was 37 months (Veterans Administration 1981b, p. 16). Evidence from Table 4 suggests that veteran effects are essentially zero for the 1953 cohort, so it was excluded from the estimation.
Estimates of models (5), (6), and (7) are presented in columns (1), (2), and (3) of Table 5. The chi-square statistic in column (3) is an overidentification test statistic for the overall goodness-of-fit of the reduced form and the chi-square statistic in column (1) is for the restriction fB= 0. Restricting f, to be zero does not affect the overall fit. The effect of veteran status on earnings growth, although negative, is not statistically significant. The sum of the test statistics in columns (1) and (3) is an overidentification test statistic for the overall goodness-of-fit of model (5). This statistic also takes on a value less than its degrees of freedom, indicating that the simplest loss-of-experience model is not at odds with the data.
The loss of experience estimated using model (5) is approximately 2 years. This is somewhat low relative to the median length of service, suggesting that military experi- ence may be a partial substitute for civilian experience. Table 5 also shows the age at which the reduced form veteran effect finally reaches zero. This occurs when xct = - 7TJ1
sT2 so that act = 0. The reduced form esti- mates in column (3) imply that the loss of earnings to veterans decays to zero around age 50 with a standarderror17of 16.
V. Caveats
The consistency of lottery-based estimates of the effects of military service turns on two key assumptions. First, earnings model (1) must be an accurate representation of the impact of military service. Second, functions of the draft lottery must be valid instru- ments for s, in the earnings regressions. Three models leading to the failure of these assumptions are discussed briefly below. The first two, incorporating treatment effect het- erogeneity and missing covariates, merely re- sult in a reinterpretation of the estimates. The third model, allowing for earnings-mod- ifying draft-avoidance behavior, calls into question the assumption that earnings dif- ferences by lottery number can be attributed solely to veteran status.
A. TreatmentEffect Heterogeneity
The effect of veteran status can only be estimated for those who served in the armed forces. If veterans are more or less likely to benefit from military service than the rest of the population, then the estimated veteran status coefficient does not characterize the impact of veteran status on a random sam- ple. This problem is formalized in the ran- dom coefficients model for treatment effect heterogeneity:
Ycti= 13c+ St+ sia5i+ uit ai= ao + eie
where ai is the effect of military service on the earnings of person i, with population mean equal to a0. If ei is uncorrelated with the instruments, an instrumental variables estimator of the random coefficients model identifies a0 + E(,ilsi = 1), and not a0 (James Heckman and Richard Robb, 1985).
Related to the problem of treatment effect heterogeneity is the fact that not all Vietnam era accessions to the military were induced by the draft. A substantial fraction of enlist- ments were made by "true volunteers" who would have volunteered for service in the absence of a draft (Tarr, 1981). Suppose that the impact of military service on the earn- ings of true volunteers differs from the im-
17
square root of (a1/7T22) - (2'g127Tl/T) +(?2712/X24),
where a1, cF2,and aJ12 aretheelementsof thecovariance matrix of the estimated 7T, and 7T2. a12 is estimated to be - 0.00019, and the square roots of a1 and a2 appear in Table 5.
Delta method standard errors are given by the
330 THE AMERICAN ECONOMIC REVIEW JUNE 1990
pact on the earnings of draftees and men who enlisted because of the draft. Then us- ing functions of the draft lottery as instru- ments will only identify the effect of military service for the latter group. To see this, let fi be an indicator for the veteran status of draftees and draft-motivated volunteers and let gi be an indicator of veteran status for true volunteers. Write
aisi = affi + aggi
for the treatment effect experienced by i. Note that functions of draft lottery numbers will only be correlated with fi. Conse- quently, af is identified by lottery-based IV estimators, but aggi becomes part of the regression error.
B. TheAbsenceofCovariates
An additional problem arises because So- cial Security data contain no information on covariates other than race and age. This may be of concern if the impact of veteran status is primarily through its effect on covariates. For example, veterans might have a higher level of educational attainment because of financial aid available through the GI Bill. In the absence of data on education, esti- mated veteran effects confound the "pure" effect of military service with its effect on education. Formally, the need for covariates may be represented by replacing at with xiA in (1). In this case, instrumental variables estimates identify
a= [E(xilsi =1) -E(xilsi = O)]8 + a.
In many applications, however, it may be a that is actually the parameterof interest. For example, the fact that veteran status influ- ences civilian earnings primarily through its influence on third variables might be of little importance for issues related to veterans compensation.
C. Earnings-ModifyingDraft AvoidanceBehavior
Perhaps the most serious problem arises if the risk of induction affected earnings for
some other reason than through an effect on the probability of military service. For exam- ple, it is sometimes argued that during the Vietnam era, students went to college to avoid the draft and that educational stan- dards were reduced to avoid having to flunk students out of school. Lawrence Baskir and William Strauss (1978) claim that Vietnam era college enrollment was 6-7 percent higher than normal because of the draft.
If draft-avoidance behavior is correlated with lottery numbers and with variables re- lated to earnings besides veteran status, then lottery-based instruments will be correlated with the regression error in equation (1). Such correlation will bias estimates of the effects of military service constructed using the lottery. But in a previous study using micro data (Angrist, 1989a), specification tests provided no evidence of a relationship between lottery numbers and characteristics other than veteran status. The overidentifi- cation test statistics reported here also show no evidence of omitted variables bias. Fi- nally, even if having a low lottery number is correlated with a tendency to stay in school, the fact that earnings rise with schooling implies that lottery-based estimates of the effect of veteran status will tend to underes- timate the true effect.
VI. Conclusions
Estimates based on the draft lottery indi- cate that as much as ten years after their discharge from service, white veterans who served at the close of the Vietnam era earned substantially less than nonveterans. The an- nual earnings loss to white veterans is on the order of $3,500 current dollars, or roughly 15 percent of yearly wage and salary earn- ings in the early 1980s. In contrast, the esti- mated veteran effects for nonwhites are not statistically significant.
In light of the results reported here, some more conventional estimates of the effect of Vietnam era veteran status do not appear to be too far off the mark. Rosen and Taubman (1982) report estimates close to these, finding a 19 percent annual earnings loss to Vietnam era veterans. Crane and Wise (1987) find an 11 percent reduction in 1979 weekly earn-
VOL. 80 NO. 3 ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY 331
ings. On the other hand, Mark Berger and Barry Hirsch (1983) find essentially no effect on 1977 weekly earnings, and Angrist (1989a) reports OLS coefficients of zero when using the National Longitudinal Survey (NLS) to estimate the effects of veteran status on hourly wages. In contrast to the OLS esti- mates, lottery-based estimates from the NLS indicate that white veterans had lower hourly wages in 1981 than their nonveteran coun- terparts. Similar results from the SIPP are reported in Angrist (1989c). Thus, lottery- based estimates from a variety of sources provide conclusive evidence that white Viet- nam veterans were disadvantaged by their service.18
This paper also proposes a simple expla- nation for the loss of earnings to white veter- ans: they earn less because their military experience is only a partial substitute for the civilian labor market experience lost while in the armed forces. Goodness-of-fit tests sug- gest that for whites, the time-series of vet- eran status coefficients is consistent with this hypothesis. Experience-earningsprofiles esti- mated using Social Security data imply that white veterans suffered an earnings reduc- tion equivalent to the loss of two years civil- ian labor market experience.
The analysis reported here leads naturally to further research on a number of topics. One of these is the question of alternatives to the loss-of-experience explanation for the reduction in white veterans' earnings. Vet- eran status may be a screening device, as suggested by DeTray (1982), or there may be cohort size effects such as those discussed by Finis Welch (1979). Because the Social Secu- rity data include information on variances, testable implications of these theories might also include restrictions on second, as well as first, moments. Another question for future research is whether draft eligibility affected educational and career plans independently of its effect on military service. The lottery
18Lottery-based estimates from the SIPP and NLS suggestthatnonwhiteveteransmayhavehighermonthly and hourly earnings than comparable nonveterans. The estimates for nonwhites are too imprecise, however, to be viewed as conclusive.
may provide a useful tool for research on changing educational attainment in the 1960s and 1970s.
Finally, there remains the question of rec- onciling the loss of earnings to Vietnam era veterans with the apparent benefits of mili- tary service to veterans of World War II and other eras (Rosen and Taubman, 1982; Berger and Hirsch, 1983). Elsewhere, Alan Krueger and I have argued that the need for reconciliation is, at least in part, illusory (Angrist and Krueger, 1989). Although OLS regressions usually show that the effect of World War II veteran status is large, posi- tive, and significant, these results may actu- ally be a consequence of selection bias. By exploiting the fact that World War II vet- eran status is also correlatedwith exact date of birth, we have implemented an instrumen- tal variables estimation strategy similar in spirit to the one used here. The results of this procedure indicate that the true impact of World War II veteran status on earnings is no larger than zero and may well be negative.
APPENDIX: DATA SOURCES AND
METHODS
1. CWHS Data Collection9
The Social Security Administration maintains the
earnings histories of covered employees in a data base known as the Summary Earnings Record (SER). Ap- proximately one year after the SER has been updated with the latest year's earnings, a one percent sample of earnings histories is extracted. The sampling frame con- sists of all issued Social Security numbers, and the sample is stratified using the regional information coded in the numbers.
Prior to 1978, the FICA taxable earnings of employ- ees were reported to the SSA by employers on a quar- terly basis. Self-employed workers report their earnings annually on schedule SE of Internal Revenue Service (IRS) Form 1040, which is forwarded to the SSA by the IRS. Since 1978, employers have no longer been re- quired to make quarterly reports. Instead they file IRS form W-2 with the SSA, as well as with the IRS, on an annual basis.
After 1978, all earnings, including those above the FICA taxable maximum, are to be reported to the SSA on form W-2. Furthermore, all employers are required
19This sectiondrawsonWarrenBucklerandCresston Smith (1984), U.S. Department of Health and Human Services (1987), and personal correspondence and con- versationsiwith Buckler and Smith.
332 THE AMERICAN ECONOMIC REVIEW JUNE 1990
to file W-2s with the SSA regardless of whether their employees are engaged in FICA taxable employment. In practice, however, many employers do not report the earnings of those engaged in non-FICA-taxable employ- ment. A further shortcoming of the W-2 series is the poor quality of the data during the first years of annual reporting.
2. Coverage and Truncation of the CWHS Earnings Series
FICA coverage includes most wage and salary and self-employment earnings. For the sample period used here, the most important coverage exceptions are the majority of federal civilian employees, some state and local government employees, some agricultural and do- mestic workers, and the employees of some nonprofit organizations. A view of coverage by industry in 1981 is given in Robert Meyer (1985, Table 2.1). Meyer's fig- ures for state, local, and civilian federal government employees imply that by 1981, roughly 58 percent of all civilian government workers were covered.
FICA taxable maximums are reported in Appendix Table Al. The combined effects of limited coverage and censoring at the taxable maximum are conveniently summarized by the percentage of all earnings that are reported to the SSA. These statistics, reported in De- partment of Health and Human Services (1987, Table 30), show that after 1981 over 90 percent of wage and salary earnings and over 75 percent of self-employment earnings were reported to the SSA.
The W-2 earnings series excludes earnings from self-employment. Unpublished estimates indicate that roughly 6.4 percent of men born between 1944 and 1953 with nonzero earnings in 1984 had self-employment earnings only (figures from private correspondence with SSA employees). Other differences between FICA and W-2 earnings coverage are described by Mary Millea and Beth Kilss (1980).
3. Matching Dates of Birth to the CWHS
In the CWHS, information on race and sex is ob-
tained from a computerized record of applications for a Social Security number called the NUMIDENT file. For this project, dates of birth were also matched from the NUMIDENT file to the CWHS. Draft lottery num- bers were then matched to the dates of birth using lottery number tables in Selective Service System Semi- annual Reports for 1969-73. A small number of indi- viduals were discarded from the final data set because there was no information on either their sex, race, or exact date of birth.
4. CWHS Descriptive Statistics
Descriptive statistics for the CWHS cohorts studied
here are reported in Table Al. The combined statistics for four cohorts were constructed by computing weighted averages of cohort means. Unless otherwise noted, statistics in the table refer to men with positive earnings. Sample sizes decline over time due to attrition from mortality.
The descriptive statistics indicate that after 1972 the fraction of men in the sample with zero FICA earnings varies roughly between 15 and 22 percent for whites and
between 33 and 36 percent for blacks. To evaluate these figures, note that the author's tabulations show that roughly 10 percent of white men in these cohorts have zero recorded wage and salary earnings in the late 1970s' Current Population Surveys. Suppose that of the 90 percent who work, 12 percent are in the uncovered sector so that only 79 percent of the cohort may be expected to have positive FICA wage and salary earn- ings. Adding an estimated 5 percent who only have FICA self-employment earningsimplies that 16 percent should have zero FICA earnings of any type. Thus, 14-18 percent of CWHS earnings being zero for whites between 1973 and 1980 does not seem unreasonable.
In recent years, the fraction with zero earnings ap- pears to be too high to be accounted for by labor force participation or employment in the uncovered sector. This is probably because of the long delay in filing and recording Social Security taxable earnings. In their anal- ysis of Social Security data, Card and Sullivan (1988) also note the problems caused by filing delay. Problems of undercoverage and filing delay may be especially severe for nonwhites. The 15 percent of CPS nonwhites with zero wage and salary earnings is not large enough to explain the approximately 34 percent of nonwhites with zero FICA earnings in the CWHS.
The fraction with FICA earnings at the taxable max- imum is more variable than the fraction with zero earnings, ranging from 3 to 15 percent for whites and between 2 to 10 percent for blacks. The FICA earnings of men with multiple employers can exceed the taxable maximum because reported earnings are censored by source. The fraction of men with FICA earnings above the taxable maximum is around 1-2 percent. The W-2 and FICA earnings series show roughly equal fractions at or above the FICA taxable maximum, suggesting that both variables are drawn from the same underlying distribution. But problems with early years of the W-2 series are clearly reflected in the sample statistics. For example, the standard deviation of whites' W-2 earnings in 1978 is six times the mean and does not fall below the mean until 1981. Another disturbing feature of the W-2 series is that nominal earnings appear to fall from 1978-80. The W-2 series also has a substantially higher fraction of zeros than the FICA series does. However, part of this difference is caused by the inclusion of self-employment earnings in the FICA series. Also, gen- erally there are some individuals with FICA taxable earnings but no federally taxable compensation (Millea and Kilss, 1980).
5. Covariance Estimates for Social Security Earnings and for p
Information on second moments in the aggregated CWHS is restricted to variances. Therefore, off-diagonal elements of the covariance matrix of Social Security earnings must be estimated. Recall that y denotes the vector of Yctj, where c indexes cohort, t indexes year of earnings, and j indexes lottery number cells. The co-
-
variance matrix of
elements for the covariance between Yc,j and ickj' and zeros everywhere else. Thus, there is only correlation between elements of the time-series of earnings for a particular cohort and lottery number group. The in-
is block diagonal, with nonzero
VOL. 80 NO. 3
ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY
333
Race White
Year N 69 68,407 70 68,339 71 68,244 72 68,154 73 68,053 74 67,966 75 67,882 76 67,794 77 67,691 78 67,598 79 67,503 80 67,413 81 67,316 82 67,265 83 67,190 84 67,114 69 21,514 70 21,501 71 21,475 72 21,443 73 21,412 74 21,380 75 21,339 76 21,310 77 21,275 78 21,243 79 21,200 80 21,167 81 21,130 82 21,109 83 21,077 84 21,042
Maximum EarningS
7,800 1,473 (1,457) 7,800 1,977 (1,825)
7,800 2,581 (2,233) 9,000 3,614 (2,802)
10,800 4,738 (3,460) 13,200 5,727 (4,170)
14,100 6,459 (4,843) 15,300 7,698 (5,548)
16,500 8,974 (6,206) 17,700 10,441 (7,050)
22,900 12,388
(8,455) 25,900 13,769 (9,678) 29,700 15,641
(11,129) 32,400 16,743 (12,371) 35,700 18,046
(13,621) 37,800 19,717 (14,883) 7,800 1,306
(1,471) 7,800 1,711 (1,865) 7,800 2,197
(2,275) 9,000 3,072 (2,922) 10,800 3,992
(3,609) 13,200 4,802 (4,359) 14,100 5,404
(5,015) 15,300 6,453 (5,836) 16,500 7,510
(6,616) 17,700 8,751 (7,541) 22,900 10,262
(8,938) 25,900 11,405 (10,147) 29,700 12,986
(11,628) 32,400 14,045 (12,849) 35,700 15,101
(14,167) 37,800 16,391 (15,237)
Nonwhite
TABLEAl-DESCRIPTIVE TaXable FICA
FICA at Limita,b
0.003 0.010 0.030 0.040 0.046 0.034 0.053 0.078 0.107 0.149 0.092 0.092 0.089 0.092 0.089 0.103 0.002 0.007 0.020 0.025 0.029 0.021 0.031 0.049 0.071 0.096 0.061 0.063 0.063 0.067 0.067 0.077
FICA Zeros
0.321 0.241 0.194 0.157 0.141 0.145 0.169 0.167 0.163 0.165 0.166 0.175 0.183 0.200 0.210 0.219 0.464 0.417 0.388 0.352 0.330 0.336 0.359 0.350 0.341 0.338 0.329 0.331 0.335 0.354 0.358 0.353
W-2 W-2 at EarningSc Limita
W-2 Zerosa
STATISTICSFORMEN BORN 1950-53
Notes: Statistics are from the Social Security Adminiatration CWHS. Standard deviations of earings in parentheses. Amounts are in current dollars. Sample statistics are weighted averages of cells for each race, year of birth, and five consecutive lottery numbers.
aFractions at limit are fractions of nonzero earnings at or above FICA taxable maximum. Fractions zero are fractions of all nondecedents with zero earings.
bFICA earings are wage and salary and self-employment earnings in Social Security taxable employment. FICA taxable earings are censored at the taxable maximum except for those with multiple sources. Multiple sources are censored by source.
cW-2 earnings are total W-2 form wage and salary compensation, not censored at the Social Security taxable maximum. W-2 earings do not include earings from self-employment.
15,435 0.167 (91,032)
14,786 0.097
(65,359)
14,561 0.096
(28,180)
16,363 0.092
(15,295)
17,907 0.093
(16,298)
19,595 0.089
(22,470)
21,595 0.101
(20,856)
0.244 0.261 0.272 0.272 0.282 0.275 0.281
13,439 0.116 (63,722)
13,581 0.067 (63,244)
11,716 0.067 (13,895)
13,421 0.063 (14,644)
14,983 0.065 (16,112)
16,271 0.065 (19,089)
17,905 0.073 (20,784)
0.391 0.393 0.397 0.388 0.408 0.396 0.387
334 THE AMERICAN
ECONOMIC REVIEW JUNE 1990
tertemporal correlation structure is assumed constant across lottery number groups so that the 73 cells avail- able for each race and cohort may be used to estimate correlation matrices for all race-cohort combinations. Correlations are converted to covariances using the within cell variances available from the CWHS data. This procedure is also applied to the adjusted FICA series described in Section 6 of the Appendix, with the modification that adjusted standard errors (diagonal elements of Q) are used to convert correlations to covariances.
The covariance matrix of p is also block diagonal, with elements equal to the variance of PCj in every element of the block corresponding to the time series for cohort c and lottery cell j. The variance of Pcj is estimated using the standard formula for an estimated proportion. The sample size in the formula is taken to be the size of the SIPP cohort for those born in 1950 and the size of the CWHS cohort for those born from 1951 to 53.
6. FICA Earnings Adjusted for Censoring
For economy of notation, in this section all cells are indexed by j. The relationship between the expectation of censored earnings and the expectation of uncensored
earnings for cell j is given by
-
=C +Pj
where y? is the mean of uncensored earnings, [j is the mean of censored earnings, [ is the mean of earnings above the taxable maximum, Lj is the taxable maxi- mum, and pl is the fraction with earnings at or above the taxable maximum.20
The FICA earnings series is adjusted for censoring by applying this formula using estimates of 4 tabulated from March Current Population Surveys (CPS) for each year, race, and cohort. Although this procedure involves
20This formula ignores the fact that the censored earnings of men with multiple employers may be above the taxable maximum. The formula may be used to analyze the bias in treatment effects estimated from censored data. Suppose that cell j is for a sample of draft-eligible men and that cell k is for a sample of draft-ineligible men. The draft-eligibility treatment ef- fect estimated from the difference between CWHS cen- sored mean earnings in cells j and k is the sample analogue of
no parametric distributional assumptions, the adjust- ment is only approximate because the CPS estimates of ,Ljdo not vary by lottery number. However, the adjust- ment does incorporate variation in p by lottery num- ber.
Data on earnings above the FICA taxable maximum (,ul.) are taken from the Mare-Winship March CPS Uniform files. Cohort was determined on the basis of age in 1985; ages 34-35 were assigned 1950, ages 33-34 were assigned 1951, ages 32-33 were assigned 1952, and ages 31-32 were assigned 1953. The CPS reports wage and salary earnings in the year preceding the survey year. To compute the adjusted 1981-84 earnings series used in Tables 3 and 4, data from the CPSs for 1982-85 were used to compute separate a I by cohort and race for each year. Additional details and summary statistics for the CPS data are reportedin Appendix A of Angrist (1989c). It should be noted that CPS earnings data are also censored-at $75,000 for 1981-83 earnings and at $100,000 for 1984 earnings.
Standard errors for the adjusted series are calculated as follows. Let m = [m m 'm ]' denote the vector of sample moments corresponding to /,uCp', and gLand let
ij(=i,j=1,2,3) denote the correspondingblocks of the covariance matrix of m. The covariance matrix of m is assumed to be given by
(11 112 0 712 122 0 0 0 233
The delta-method covariance matrix for the vector of adjusted earnings, ml + m2(m3 - L), is
= 11+2112(m3- L)
-c -
= ( -p?k) +(Pj pk)( L--IL'.)
+ Pk( lk 1'-
A simplified procedure, described in Section 5 of this Appendix, is used to estimate the nonzero off-diagonal elements of Q directly from the adjusted cell means.
7. Matching Draft-Eligibility Status to the SIPP
The Survey of Income and Program Participation is a Census Bureau longitudinal survey of approximately 20,000 households in the civilian noninstitutional popu- lation (U.S. Department of Commerce, 1985). Data for the first wave of the first SIPP panel were collected from
four rotation groups in 1983 and 1984.
The SIPP public-use tapes contain year and month
of birth. A Census Bureau "in-house" version of the
Assuming that the effect of draft eligibility on both pi and tl is of the same sign as the effect on o,u this expression shows that treatment effects estimated from the censored data differ from the true treatment effect by terms that are opposite in sign from the true effect.
+ -
22 (m3-L)2+
m2233.
Only the diagonal elements of Q are estimated using the above formula. Estimates of diagonal elements of F., and 122 are available from the CWHS cell statistics, while diagonal elements of 233 are estimated from the CPS micro data. An estimator for diagonal elements of
212
is easily shown to be (Angrist, 1989c)
012j [i( L- Kji)IInj-
VOL. 80 NO. 3 ANGRIST: LIFETIME EARNINGS AND VIETNAM ERA DRAFT LOTTERY 335
SIPP contains information on day of birth, which is not released to the public. At the author's request, this information was used to match a dummy variable for draft-eligibility status to the public use version of SIPP Panel I. Draft eligibility was determined by the official RSN ceiling for men born from 1944-52 and by RSN 95 for men born in 1953. Vietnam era veteran status is coded from the SIPP variablesVETSTAT,which records veteran status, and from U-SRVDTE, which records the period of service.
REFERENCES
Angrist,JoshuaD., "Grouped Data Estima- tion and Testing in Simple Labor Supply Models," Industrial Relations Section Working Paper, no. 234, Princeton Uni- versity, July 1988.
, (1989a),"Using the Draft Lottery to Measure the Effects of Military Service on Civilian Labor Market Outcomes," in Re- search in Labor Economics, 10, Ron Ehrenberg, ed., Greenwich: JAI Press, 1989.
, (1989b),"Selection for Military Ser- vice in the Vietnam Era," Industrial Rela- tions Section Working Paper, no. 250, Princeton University, April 1989.
, (1989c),"Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," Industrial Relations Section Working Pa- per, no. 251, Princeton University, April 1989.
, (1989d),"InstrumentalVariables Re- gression with Moments from Two-Sam- ples," Chapter 3 in EconometricAnalysis of the Vietnam Era Draft Lottery, unpub- lished Princeton University doctoral dis- sertation, October 1989.
and Krueger,Alan,"Why Do World War II Veterans Earn More?" National Bureau of Economic Research Working Paper, no. 2991, May 1989.
Baskir, LawrenceM. and Strauss,WilliamA., Chance and Circumstance:The Draft, The War and the Vietnam Generation, New York: Alfred A. Knopf, 1978.
Berger, Mark C. and Hirsch, BanryT., "The Civilian Earnings Experience of Vietnam- Era Veterans," Journal of Human Re- sources, Fall 1983, 18, 455-79.
Buckler, Warren and Smith, Cresston, "The Continuous Work History Sample
(CWHS): Description and Contents," in Statistical Use of AdministrativeRecords: Recent Research and Present Prospects Volume I, Department of the Treasury, Internal Revenue Service, Statistics of In- come Division, March 1984.
Card, David and Sullivan,Daniel, "Measuring the Effect of Subsidized Training Pro- grams on Movements In and Out of Em- ployment," Econometrica, January 1988, 56, 497-530.
ChamberlainG,ary,"MultivariateRegression Models for Panel Data," Journalof Econo- metrics, January 1982, 18, 5-46.
Crane, Jon R. and Wise, David A., "Military Service and the Civilian Earnings of Youths," Chapter 6 in Public Sector Pay- rolls, D. A. Wise, ed., Chicago: University of Chicago Press, 1987.
DeTray, Dennis N., "Veteran Status as a Screening Device," American Economic Review, March 1982, 72, 133-42.
Griliches,Z. and Mason,William,"Education, Income and Ability," Journal of Political Economy, May/June 1972, 80, Part 2: S74-S103.
Hearst,Norman,Newman,TomB. andHulley, StephenB., "Delayed Effects of the Mil- tary Draft on Mortality: A Randomized Natural Experiment," New England Jour- nal of Medicine, March 6, 1986, 314, 620-24.
Heckman,JamesJ. andRobb,Richard,"Alter- native Methods for Evaluating the Impact of Interventions," in J. Heckman and B. Singer, eds., LongitudinalAnalysis of La- bor Market Data, New York: Cambridge University Press, 1985.
Meyer, Robert J., Social Security, 3rd ed., Homewood, IL: Richard D. Irwin, 1985. Millea,MaryT. andKilss,Beth,"Exploration
of Differences Between Linked Social Se- curity and Internal Revenue Service Wage Data for 1972," in Studies from Intera- gency Data Linkages, Report No. 11: Measuring the Impact on Family and Per- sonal Income Statistics of Reporting Dif- ferences Between the Current Population and Administrative Sources, U.S. Depart- ment of Health, Education and Welfare, Social Security Administration, March 1980.
336 THE AMERICAN ECONOMIC REVIEW JUNE 1990
Mincer, Jacob, Schooling, Experience and Earnings, New York: National Bureau of Economic Research, 1974.
Newey,WhitneyK.,"GeneralizedMethodof Moments Specification Testing," Journal of Econometrics, September 1985, 29, 229-56.
Rosen,SherwinandTaubmanP,aul,"Changes in Life Cycle Earnings: What Do Social Security Data Show?" Journal of Human Resources, Summer 1982, 17, 321-38.
Schwartz,Saul, "The Relative Earnings of Vietnam and Korean-Era Veterans," In- dustrial and Labor Relations Review, July 1986, 39, 564-72.
Tarr,CurtisW., By the Numbers: The Reform of the Selective Service System 1970-72, Washington: National Defense University Press, 1981.
Taussig,MichaelK.,"The Rationale for Veter- ans Benefits," in Those Who Served: Re- port of the 20th CenturyFund Task Force on Policies Toward Veterans, New York:
The 20th Century Fund, 1974. Wald,Abraham",TheFittingofStraightLines
If Both Variables Are Subject to Error," Annals of MathematicalStatistics, Septem- ber 1940, 11, 284-300.
Welch, Finis, "The Effect of Cohort Size on Earnings: The Baby Boom Babies Finan- cial Bust," Journal of Political Economy, October 1979, Part 2, 87, S69-S97.
Willis, Robert J., "Wage Determinants: A Survey and Reinterpretation of Human CapitalEarningsFunctions,"in0. Ashen-
felter and R. Layard, eds., The Handbook of Labor Economics, Amsterdam: North- Holland, 1986.
CouncilofEconomicAdvisorsE,conomicReport of the President, February 1988, Washing- ton: USGPO, 1988.
SelectiveServiceSystem,Officeof PublicAffairs, "AShortHistoryoftheSelectiveService System," Washington: USGPO, 1986.
, Semiannual Report of the Director of Selective Service for the Period July 1 to December 31, 1970, Washington: USGPO, 1971.
(1969-1973), Semiannual Report of the Director of Selective Service, selected issues, Washington: USGPO, 1969-73.
U.S. Departmentof HealthandHumanServices, Social Security Administration, Social Se- curity Bulletin Annual Statistical Supple- ment, Washington: USGPO, 1987.
U.S. Departmentof Commerce,Bureauof the Census, Survey of Income and Program Participation: Wave I Rectangular File, Washington: USGPO, 1985.
VeteransAdministration(1981a),Reports and Statistics Service, Research Monograph 15: Educational and Income Characteris- tics of Veterans, March 1979, Washington: USGPO, August 1981.
, (1981b),Office of Reports and Statis- tics, Data on Vietnam Era Veterans, Washington: USGPO, September 1981.
, (1984), Administrator of Veterans Affairs, Annual Report 1983, Washington: USGPO, 1984.