Are Economics-Based and Psychology-Based Measures of Ability the Same?

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1 Are Economcs-Based and Psychology-Based Measures of Aly he Same? Solomon W. Polachek* Deparmen of Economcs Sae Unversy of New York a Bnghamon and IZA [email protected] Trhaanmoy Das Deparmen of Economcs Sae Unversy of New York a Bnghamon [email protected] Rewa Thamma-Aproam Faculy of Economcs Kasesar Unversy Thaland [email protected] Sepemer 20, 20 Key words: Lfe-Cycle Model; Cognve Aly; Earnngs JEL Classfcaons: J24; J29 ; J3; J39 ABSTRACT Economss rely on psychology-ased IQ and achevemen es scores o assess aly. Ye human capal models of lfeme earnngs propagaon enal human capal producon funcon parameers ha ncorporae aly parameers. Ths paper makes use of human capal heory o derve a hghly nonlnear, u emprcally racale, earnngs funcon whch when esmaed yelds parameers represenng cognve aly. Gven ha he Naonal Longudnal Survey NLS-Y now has up o 22 years of daa on each ndvdual responden, we esmae hese earnngs funcons for each ndvdual o exrac ndvdual-specfc esmaes of aly. We hen compare our esmaed aly parameers wh ndependenly oaned nellgence es scores for hese same ndvduals n he NLS-Y daa. We fnd a sgnfcan posve correlaon eween our measures and he ndependenly oaned psychologcally-ased cognve es scores. These measures adhere o predced relaonshps regardng ypes of aly and schoolng. We fnd a posve correlaon eween nellecual prowess he aly o creae new human capal from old and years of school, and a negave relaon eween years of school and socks of knowledge, as predced y human capal heory. However, unlke he psychology-ased measures, our aly esmaes yeld a weaker relaonshp wh race, herey mplyng he possly of greaer racal ases n he psychologcallyased measures han our economcs-ased measures. * Ths paper was parly wren whle Polachek was a Vsng Scholar a he NBER n Camrdge, Massachuses. I was presened a he 20 IZA Cognve and Non-Cognve Sklls Workshop n Bonn, Germany. We hank Vkesh Amn, Chrsan Belzl, Armn Falk, Rchard Freeman, Clauda Goldn, James Heckman, Danel Henderson, Larry Kaz, Gerald Marschke, Denns Pxon, Arna Roy, Davd Schaffer, Xangn Xu, and Bong Joon Yoon for valuale advce and dscusson.

2 . Inroducon Cognve aly reflecs an ndvdual s capacy o perform profcenly n nellecual pursus. For our purposes, we characerze cognve aly o comprse nellgence as well as knowledge ased sklls. We vew nellgence as he aly o hnk and solve prolems, and knowledge as he aly o recall and use pror learned maerals. Two srands of research measure aly. The frs, and mos common, s ased n psychology. Ths srand orgnaed n 904 when he French governmen commssoned Alfred Bne o develop ess, now known as he IQ nellgence quoen, o measure varous aspecs of cognve sklls. Nowadays here s a myrad of such ess. They examne readng comprehenson, arhmec and algerac sklls, spaal relaons, vocaulary, and oher componens of cognve aly. 2 The second research srand s ased n economcs, u s less well known. Ths laer approach uses lfe-cycle human capal heory o derve an esmale nonlnear earnngs funcon ha accordng o he leraure egnnng wh Ben-Porah, 967 conan human capal producon funcon parameers denong nellgence as well as a parameer denong knowledge. Currenly praconers, ncludng socal scence research scholars as well as economss, generally gnore he economcs-ased approach when hey measure aly, mosly ecause he economcs-ased echnque s dffcul o mplemen. In order o denfy aly parameers for parcular ndvduals, he economcs-ased echnque requres a hghly nonlnear specfcaon ncorporang suffcenly long panel daa, whch a leas n he pas were no readly avalale. Thus, nsead of dong her own esmaon, economss usually rely on psychologss IQ and achevemen ess o denfy aly. Typcally, o accoun for aly, economss use hese measures as ndependen varales The whole noon of esng daes ack a leas o 2200BC when he Chnese emperor had hs offcals esed every hree years o deermne f hey were f. Wren ess coverng cvl law, mlary affars, agrculure, revenue and geography were nroduced y he Han Dynasy 202BC o 200 AD, u hese were desgned o measure knowledge more so han nellgence Gregory, 20. Currenly, ess egn a rh wh he Apgar es, and connue hroughou lfe n school, encompassng ess for learnng dsales, gfedness, vocaonal neres, college admsson, drver s lcenses, maral compaly, and more. The mansay of psychologcal ess enals measurng aspecs of personaly and nellgence. Lke n emprcal economcs, psychologcal ess represen a lmed sample of ehavor from whch he examner draws nferences aou he oal doman of relevan ehavor. For example, he numer of words defned n he vocaulary suse of he Wechsler es sgnals he examnee s general knowledge of vocaulary. Makng such nferences s known as assessmen n he psychology leraure. 2 We concenrae mosly on he AFQT ecause s used wdely y economss o conrol for aly n earnngs funcon and oher sascal analyses, and ecause s conaned n he Naonal Longudnal Survey of Youh NLS-Y. However, as a rousness check, we presen some addonal resuls for ffeen oher IQ ype ess.

3 n smple earnngs funcon regressons. When panel daa are avalale, hey ofen rely on fxed-effecs echnques o hold ndvdual-level aly consan.. Earnngs funcons ha ncorporae nellgence ess as ndependen varales esmae he effecs of aly, raher han measure aly self. The same can e sad for fxed-effecs regressons whch are desgned o ne ou ndvdual specfc heerogeney, ncludng aly. However, wh he adven of speeder compuers, eer opmzaon programs, and longer panels, measures of aly ased on human capal heory can now e rereved y esmang parameers of a nonlnear earnngs funcon. Wh suffcenly long panels one can esmae such aly parameers for specfc ndvduals. From hese esmaes, one can aggregae he daa o esmae average aly for seleced groups, such as all hose employees wh a gven level of schoolng or all hose employees of a parcular racal group. 3 The advanage of hs economcs-ased approach s one can oan measures of aly founded on he economcs prncple of opmzaon whch resuls when ndvduals accumulae human capal o maxmze he presen value of lfeme earnngs, raher han e rooed n he psychology prncples underlyng nellgence esng of whch here s a large leraure Hogan, Oanng aly measures usng economcs-ased models s mporan for a numer of reasons. Frs, he economcs-ased approach yelds several dsnc ypes of aly whch enales one o es heores emanang from human capal heory. For example, heory predcs ha nellecual prowess wha we wll defne as he aly o creae new human capal from old causes one o ge more schoolng whereas a greaer nnae sock of knowledge causes one o go o school less. Addonally, heory predcs hgher dscoun raes whch our model also esmaes are assocaed wh less years of school. Checkng he srengh of hese predcons serves o es he valdy of he lfecycle human capal models. Second, oanng aly measures usng economcs-ased models s mporan ecause enales one o compare hese new economcs ased aly measures o prevously oaned psychology ased measures. If hey dffer, one can queson he 3 As wll e dscussed laer, he economcs-ased approach s lmed o hose who have a work hsory. Whereas, hs lmaon could u proaly does no as nferences aou he non-workng populaon, does no as conclusons comparng he economcs-ased and psychology-ased approaches for oservaonally equvalen workers, whch s he man pon of hs paper. 2

4 valdy of one or he oher. Though desgned for dfferen purposes, credence s enhanced regardng he relaly of each f oh correlae wh each oher. Thrd, he aly measures ased on he economcs approach can e used n a Mncer-ype earnngs funcon along wh psychology ased measures o see whch eer explans earnngs varaon. One mgh e relucan o use psychology-ased es scores raher han economcs-ased measures should he explanaory power of he economcsased measures appear o have more explanaory power han he sandard AFQT aly measures when accounng for earnngs varaon. Fourh, and perhaps more conroversal u even more mporan, one can es wheher radonal IQ ype ess are racally ased, as many allege s he case. Ths s a real possly gven ha he dfferen culures of mnory groups are ypcally no aken no accoun when formulang quesons for psychologcally-ased nellgence ess. 4 As wll e shown, he economcs-ased aly parameers we esmae are oaned from a model concepually ndependen of race. As such, noons of race do no ener he srucural defnon of our human capal ased aly measure, hough hey do ener he esmaon process f racal dscrmnaon affecs earnngs. Thus a leas from a heorecal sandpon, our aly measures are concepually race neural. From oh pedagogcal and polcy perspecves hs race neuraly s mporan ecause fndng no racal dfferences n economcs-ased aly measures would e srong evdence ha IQ ype measures are ndeed racally ased, snce hose measures do dffer y race, whereas our economcs-ased measures would no. On he oher hand, should our economcsased measures dffer y race n he same way IQ measures dffer y race, one can make eher he case ha neher measure s racally ased, or alernavely one can make he case ha wage dscrmnaon s racally ased n exacly he same way ha culural 4 A long hsory of nellgence es culural ases and her mplcaons egns when Henry Goddard, a promnen Amercan psychologs, loed for resrcve mmgraon laws ased on hs fndng ha over 80% of he Jewsh, Hungaran, Ialan, and Russan mmgrans he esed usng ranslaed Bne-Smon IQ ess were feele-mnded Goddard, 92. He somewha recaned n 928, u noneheless Goddard s nellgence esng opened up he queson of culural ases n mplemenng such ess. The same can e sad for achevemen and numerous oher ype ess Gregory, 20. 3

5 ases have nculcaed he psychologcally-ased es score measures. In eher case, he academc professon wll e eer nformed how aly dffers y race. In addon, here are oher relaed prolems wh sandardzed aly ess ha ge less aenon. For example, ess can e naccurae f examnees have undagnosed dsales. Ths s especally rue wh chldren who are ofen poor nformans of her capales. Vernon and Brown 964 repor he case of a young grl admed o a hospal for he menally rearded for fve years ecause she scored a 29 on he Sanford- Bne es. The chld was released when hospal aendans fnally realzed she was deaf and had an IQ of 3 when measured on a performance-ased nsead of oral es. Chldren who lnk, squn, or loose her place could e vsually mpared whch also could affec resuls on hese ess. Smlarly here s a whole leraure on how race, experence, ehncy and oher characerscs of he examner can affec es resuls e.g., Terrell, e al.,984. The same can e sad for examnee ackground and movaon ncludng prolems regardng es anxey. These mperfecons n psychologcal ess and he nerpreaon of her resuls could mply a need for a compleely dfferen mehodology for assessng aly. The economcs-ased approach s one possly hough no applcale o chldren snce one needs daa on laor marke experence. Fnally, ffh, one oher mporan aspec of hs paper s how emphaszes ndvdual heerogeney. Currenly lerally hundreds of arcles accoun for unoserved ndvdual heerogeney y neng ou person-specfc effecs. Sudes ha assume person-specfc parameers are of hree genres. Frs, random coeffcen models and exensons ncludng he correlaed random coeffcens model Heckman, e al assume ndvdual parameers vary across ndvduals n accord wh a parcular dsruon u do no denfy each ndvdual s acual parameer values. Nor are hey usually ceran of he underlyng parameer dsruon, whch one usually assumes o e normal. Second, oher panel daa models adjus for person-specfc slope parameers Polachek and Km, 994; and Pesaram, 2006, u hese are ofen lmed o one parameer esdes he nercep. Fnally non-paramerc approaches ge a heerogeney essenally y groupng ndvduals accordng o relaed neghorng measured 4

6 characerscs whn opmal and wdhs Racne and L, Raher han ndvdual-specfc parameers, hey oan group-specfc parameers. Our approach makes use of long enough panels o oan ndvdual specfc measures for each coeffcen n he earnngs funcon model we employ, ncludng parameers specfyng aly. Of course a numer of assumpons underle he economcs-ased approach. Frs, he approach assumes ndvduals plan her human capal nvesmen sraegy ased on expecaons ha hey seek o work each year of her workng lfe. Ths means ndvduals do no leave he laor force for famly reasons and ha hey do no aler her nended human capal nvesmen plans ased on unexpeced spells of unemploymen. I s why we concenrae on males who generally have connuous work hsores. 5 Second, he approach assumes a relavely smple human capal producon funcon. We assume ndvduals use her me and exsng human capal o creae new human capal, u we gnore oher npus such as ooks and compuers as well as parenal, eacher, and school qualy npus whch can also e used o creae addonal human capal. In our model hgh aly people can creae a gven amoun of human capal wh smaller me npus. Thrd, we gnore non-cognve sklls, u hese could e ncorporaed y modfyng he human capal producon funcon. Fourh, he approach assumes laor markes reward ndvduals ased on her exsng sock of human capal, and ha neher ncomplee nformaon nor ncenve pay governs worker earnngs. Ffh, we assume all human capal producon funcon parameers reman consan hroughou each person's lfe. In he conex of our model, hs means we assume ha aly does no change over one s lfeme hough modfcaons can e made o parameerze changes n measured aly as envronmenal facors such as jo, ndusry, or locaon change. Fnally sxh, reles on ndvduals wh a sgnfcan work hsory. Ovously, hose wh a work-hsory consue a selec sample of he populaon. However, n our case, hs selecvy does no preclude nferences oaned when comparng he economcs-ased and psychology 5 One poenal as we face n comparng whes and lacks s ha lacks may selec dfferen ypes of jos f hey expec more spells of unemploymen han whes. If lacks nsure agans rsk hey mgh seek jos wh more human capal nvesmen herey mgang oserved dfferences n our aly measures. We adjus for hs somewha y comparng lacks fully employed n every year o hose wh unemploymen spells. 5

7 ased mehods ecause precsely he same ndvduals are used n evaluang he wo approaches. On he oher hand, selecvy ases could come aou when makng nferences aou racal dfferences n aly f whe workers are dfferen n aly han lack workers, for example, f lack workers are relavely more ale han whe workers compared o lack and whe non-workers. However, as wll e shown laer, we fnd ha he aly advanage of workers o non-workers s smlar for oh lacks and whes, so ha hs as s a wors very small. The remander of our paper s organzed as follows: Secon 2 derves a heorecal model from whch we are ale o denfy hree measures of cognve aly. Secon 3 descres he daa. Secon 4 presens he esmaon procedure and emprcal resuls. In hs secon, we llusrae how our parameers are conssen wh populaonwde esmaes from pas sudes, and how our aly parameers are conssen wh aly measures from psychology-ased ess. Furher, n hs secon, we presen evdence ha nellecual aly s posvely assocaed wh school level whereas knowledge-ased sklls are no, as predced y human capal heory. Fnally, n ha secon we dscuss ssues regardng selecvy and rousness. Fnally, Secon 5 concludes. 2. Usng he Lfe-Cycle Human Capal Model o Esmae Aly Mos emprcal sudes adop sngle equaon log-lnear Mncer earnngs funcons o parameerze earnngs. The eauy of esmang smple Mncer earnngs funcons s compuaonal ease. Assumng schoolng and experence are exogenous, Mncer earnngs funcons are easly esmaed y OLS. Alhough more recen analyses queson wheher such OLS esmaon procedures are free of economerc ases Heckman, Lochner and Todd, , n realy he Mncer model s a smplfcaon ased on Taylor approxmaons of a more complex funcon. Underlyng he Mncer model s a lfe-cycle 6 There are also some concepual ases regardng how o nerpre such parameers as he schoolng and experence coeffcens whch many ake o measure raes of reurn o school and experence. 6

8 earnngs generang process ha yelds a hghly nonlnear earnngs funcon. 7 From hs nonlnear funcon one s ale o denfy several cognve aly parameers ased on he producon funcon of human capal. We defne wo of hese parameers o depc nellgence ecause hey measure he ease whch an ndvdual can creae new human capal from old human capal, a process whch enals nnovave hnkng, u no necessarly roe recall of facs. The frs of hese parameers s he ndvdual s human capal producon funcon oupu elascy, and he second s he ndvdual s human capal producon funcon oal facor producvy parameer. These wo nellgence measures of cognve aly are dsnc from one s knowledge ase, whch n our framework s defned more as roe knowledge and depced as he ndvdual s earnngs power devod of human capal nvesmens. In our framework, hs s one s human capal a he me one egns school. We also provde esmaes of a comnaon of nellgence and knowledge whch s our esmae of one s human capal sock measured a he me one graduaes from school and eners he laor marke. The dervaon of he earnngs funcon conanng hese parameers enals he ypcal economcs-ased maxmzaon paradgm. I assumes an ndvdual nvess n human capal o maxmze he presen value of expeced lfeme earnngs. Based on hs opmzaon process, one can derve opmal human capal nvesmen, opmal human capal sock, and opmal earnngs over a person s lfeme. In he model one s earnngs over he lfe-cycle are drecly proporonal o one s human capal sock. Each year one s human capal sock s augmened y he amoun of new human capal one creaes hrough schoolng and on-he-jo ranng, and one s human capal sock s dmnshed y he amoun human capal deprecaes. Creang new human capal enals usng me and exsng human capal o produce new human capal, gven one s aly. The greaer one s aly he more human capal one can produce, and he more rapdly one can ncrease earnngs power from year-o-year Ben-Porah, 967. The resul s a nonlnear earnngs funcon wh hree parameers reflecng dfferen knds of aly. 7 Mncer s log e -lnear specfcaon ges around hese nonlneares y assumng me-equvalen human capal declnes lnearly wh age. In realy, he me pah of human capal acquson s more complcaed. Takng hs no accoun yelds a hghly nonlnear earnngs funcon. 7

9 Whereas no everyone eleves n he human capal approach as he ass for one s earnngs, he model s surprsngly rous compared o oher models n explanng lfe-cycle earnngs paerns. For example, screenng models explan why educaon enhances earnngs; occupaonal segregaon models explan why women earn less; effcency wage models explan ceran wage premums; and producvy enhancng conrac models explan upward slopng hough no necessarly concave earnngs profles; u none of hese heores smulaneously explan all of hese ssues as does he human capal model. Bu more mporan, hese oher models allow no one o denfy aly from esmaed parameers. For hs reason we adop he human capal model o approach he prolem of measurng aly The Ben Porah Model The Ben-Porah 967 model assumes ndvduals nves n hemselves o maxmze expeced lfeme earnngs. 9 Invesmen s governed y a producon funcon n whch one comnes own me and aly along wh pas human capal nvesmens o creae new human capal. A he margn, one equaes he margnal cos and margnal gans of creang new human capal. The margnal cos of each un of nvesmen s essenally he foregone earnngs of he me needed o produce a margnal un of human capal. 0 The margnal gan s he presen value of each addonal un of human capal. Ben- Porah s nnovaon was o realze ha he fne lfe consran mples he margnal gan declnes monooncally over he lfe-cycle a leas for ndvduals ha work connuously hroughou her lves. The equlrum mples a human capal sock ha rses over he lfe-cycle a a dmnshng rae. Ths yelds he commonly oserved concave earnngs profle. 8 Some have crczed he Mncer s dervaon of he earnngs funcon ecause does no explan why people choose a parcular amoun of educaon snce equlrum n hs orgnal model 958 enals ndvduals who dffer n schoolng u have no dfference n lfeme earnngs. However, Johnson 978 shows how schoolng levels dffer across ndvduals ased on he aly parameers of he human capal producon funcon, whch we esmae ndvdual-y-ndvdual n hs paper. 9 Incorporang laor supply enales one o maxmze uly poenally enalng one o denfy specfc ase parameers, u dong so requres a numer of addonal assumpons o denfy key earnngs funcon parameers. 0 In more complcaed models hs cos also ncludes expenses for goods such as uon, ooks, compuers, and oher maeral npus o creae human capal. as does Mncer we assume he goods componens are offse y earnngs durng he nvesmen process. See Polachek 975 for he case of dsconnuous laor force parcpaon. 8

10 The closed-form soluon o Ben-Porah s earnngs funcon s hghly nonlnear. A he me of s dscovery n 967 few compuers were fas enough o easly esmae he parameers. However, shorly hereafer, Haley 976 was ale o esmae a verson, u he smplfed he esmaon ecause no all parameers were readly denfale. Gven hese compuaonal dffcules, mos scholars reled on a lnearzaon. Ths lnear-n-he-parameers specfcaon has ecome known as he Mncer log-lnear earnngs funcon, or smply he Mncer earnngs funcon. One prolem s ha Mncer s smplfcaon does no allow one o denfy aly. Gven he adven of faser compuers and longer panels of ndvdual daa, we feel now s a good me o reexamne Haley s approach. Furher, as menoned aove, gven suffcenly long panels for parcular ndvduals, he approach enales one o compue aly parameers person-y-person. Oanng person-specfc aly measures addresses one aspec of unoserved heerogeney, a relavely mporan ssue n mcroased economerc research. 2.2 The Haley Model The human capal model assumes an ndvdual s poenal earnngs could earn n me perod are drecly relaed o human capal sock * Y wha a person E. As such, * Y = RE where for smplcy R s assumed o e he consan renal rae per un of human capal. 2 Human capal sock s accumulaed over one s lfeme y pruden nvesmens n oneself va schoolng and on-he-jo ranng as well as healh, jo search and oher 2 Polachek 98 assumes he renal rae can vary y ype of human capal. Polachek and Horvah 977 assume he renal rae can vary y geographc locaon. However, relaxng he assumpon aou a consan renal rae n hese wo ways s unnecessary for hs applcaon, nor s a common pracce n he human capal leraure. As such, we assume he same renal rae for he enre populaon and ha hs renal rae s deermned y supply and demand n he marke. 9

11 earnngs augmenng ypes of human capal. 3 The rae of change n human capal., sock, E s expressed as he amoun of human capal produced K & mnus deprecaon so ha E & = K & E 2 where s he consan rae of sock deprecaon. For smplcy, we assume ndvduals creae human capal usng a Co-Douglas producon funcon such ha where & = K 3 K K s he fracon of human capal sock renvesed n me perod and parameers [0,] and are producon funcon parameers.4 The parameer reflecs he rae a whch curren human capal sock s ransformed o new human capal. I reflecs how one acqures new knowledge from old, and as such reflecs how quckly one learns. We denoe o depc he scale a whch one learns. As such, ecause measures how well one ransforms pas knowledge no new knowledge, can e consrued as relaed o he nellecual aly, perhaps wha should e measured y psychologcal IQ ype ess snce represens how well one ransforms pas knowledge no new knowledge. The parameer s he echnology parameer. I represens oal facor producvy. In realy IQ and apude ess measure a comnaon of and. The ndvdual s ojecve s o maxmze dscouned dsposale earnngs, Y, over he workng lfe-cycle. 5 Ths goal s acheved y choosng he amoun of human capal K o renves each year n order o maxmze he presen value of lfeme earnngs 3 Specfc ranng s also ncluded ecause accordng o Kuraan 973 n equlrum workers receve remuneraon for he exac same poron of specfc ranng hey pay for, whch hey fnance y akng lower wages durng he ranng perod. 4 As already menoned, we assume no oher npus oher han one s own human capal. Less smplfed producon funcons could enal ndvduals employng goods npus such as eachers, ooks, and sudy 2 me. For example, Ben-Porah 967 assumes q = K D where D equals oher npus. Laer emprcal analyss precludes akng accoun of hese oher facors of producon ecause no daa are avalale for hese oher npus. Thus we adop he aove more smplfed human capal producon funcon used y Haley As already menoned, we asrac from laor supply. 0

12 Max K J N r = e Y d 4 0 where J s he oal dscouned dsposale earnngs over he workng lfe-cycle, r s he personal me dscoun rae and N s he numer of years afer whch one reres assumed known wh ceranly. 6 Dsposale earnngs are Y = R E K ] 5 [ Maxmzaon of 4 sujec o equaons 2 and 3 can e done y maxmzng he followng Hamlonan. r H K, E, λ, = e R[ E K ] λ [ K E ] 6 wh consrans E K 0, whch means one canno nves usng more human capal han one currenly has.e., no orrowng; and he ransversaly condon λ = 0, whch ndcaes a zero laor marke gan from human capal nvesng n one s fnal year a work. The soluon nvolves hree phases: Specalzaon n human capal nvesmen when K =E whch can e defned as eng n school snce one s spendng full-me nvesng; 2 Workng whch defnes he me perod when one oh works and nvess; and 3 Reremen when one ceases nvesng compleely. We are concerned wh Phase 2 snce hs s he only me perod one can oserve earnngs. In school one plows ack all one s earnngs poenal no more human capal nvesmen and hence has no ne earnngs. Lkewse durng reremen one does no work so here are no earnngs hen eher. N Ths maxmzaon yelds a nonlnear n he parameers earnngs funcon 7 Y = A * * r N 0 e A [ e ] A2[ e ] 7 where 6 For smplfcaon ecause we have no daa on ndvdual nvesmens pror o school we defne =0 o e he me when one egns full-me schoolng. 7 Appendx A conans he dervaon. Noe hs dffers a from he Haley specfcaon ecause n our dervaon we assume a one-erm Taylor expanson whereas Haley uses a wo-erm Taylor expanson. Our approach yelds a slghly smpler earnngs funcon.

13 A 0 = R E 0 e * A = R A 2 = R r r and where * s he age a whch one graduaes from school.e., he age when Phase ends, N s he ancpaed reremen age whch we ake as 65, a reasonale assumpon for hs cohor, and E 0 s one s human capal when one egns ranng. In realy, parens egn ranng her chld a or pror o rh, u for our purposes we consder hs me o e when one sars formal schoolng ecause hs s he pon we know chldren spend full-me learnng. Fnally, gven measuremen error and oher unoservale facors, one need add a me varyng error erm ε for each ndvdual One pon aou E 0 s noeworhy efore we descre how we esmae 7. In he formal model see Appendx A, E 0 corresponds o human capal sock when one egns specalzaon, ha s when one egns school. Ths E 0 parameer s undenfed n he Mncer earnngs funcon, whch nsead esmaes poenal earnngs a he me formal school ceases and one egns work. However, wh our model, one can also derve esmaes for poenal earnngs when one jus egns work. We do so y defnng E S as he amoun of human capal upon compleng school. E S s compued y augmenng E 0 y he amoun of human capal produced n each year of school. Mulplyng E S y he renal rae per un of human capal yelds poenal earnngs. Of course, a hs sage of he lfe-cycle poenal earnngs exceed acual earnngs ecause ndvduals are sll heavly nvesng n human capal, hough no full-me. Laer n lfe, he gap eween poenal earnngs and acual earnngs should dmnsh as he proporon of avalale me spen nvesng declnes. Laer n he paper, when presenng our emprcal esmaes, we verfy he valdy of hese predcons. Haley esmaes a varan of 7 usng ncome y age daa aggregaed from he 956, 958, 96, 964, and 966 CPS surveys. Hs esmaes can e consrued as 2

14 populaon averages. However, y employng suffcenly long panel daa, equaon 7 can e esmaed person-y-person. To do so one can ulze nonlnear esmaon echnques along wh daa on experence and earnngs for each ndvdual. 2.3 Idenfcaon Sraegy Equaon 7 conans sx parameers: R,,, r,, and E 0. The parameers r,, and all have no dmenson. The parameers r and are percens. The parameer s he oupu elascy n he human capal producon funcon 3. I reflecs reurns o scale of human capal. I also can e consrued as an aly parameer snce measures he producvy of old human capal n creang new human capal. These parameers are echncally oservale. The parameers, and E 0 are nomnaed n erms of uns of human capal sock whereas R s dmensoned as dollars per un of human capal. Comnng he wo yelds E /, 0 whch s dmensonless. Thus we also rea E / as a sngle parameer. We wre R as 0 where wˆ w * = [ R ] = w = R whch s he parameer we esmae. Fnally, o conserve degrees of * freedom and qucken convergence we assume a unform human capal deprecaon rae. Based on Haley 976, we assume hs o e As a resul of hese denfcaon 8 resrcons we end up esmang four parameers: ˆ =, 0 E E ˆ =, wˆ * R =, and r ˆ = r for each ndvdual usng nonlnear leas squares for hose ndvduals wh a leas welve years of daa. For he esmaon we employ a recenly avalale parallel processng algorhm used y ologss n genec research Czarnzk and Doherr, Ths algorhm reaches an opmum more effcenly han radonal Newon-Raphson hll-clmng 8 Expermenaon wh oher deprecaon raes dd no qualavely aler our resuls. 3

15 echnques. We easly denfy he ndvdual-specfc and r parameers. To denfy and E 0 we adop he followng approach: Frs, we specfy o equal e where s he populaon average and e s he ndvdual devaon. Second, we rewre 8 as Takng he logarhm, yelds = e. 9 w * R ln w ˆ * = ln R ln ln e. 0 Esmang 0 usng each ndvdual s values oaned from he parameerzaon we employ o esmae 7 gves a populaon value of R he coeffcen of, he average he consan erm, and ndvdual-specfc values of oaned y akng he an-log e of he sum of he laer wo erms n 0. Ulzng and values along wh he coeffcen 0 E Eˆ = oaned from esmang 7 yelds ndvdual- specfc E The Daa Nowadays here are a numer of panel mcro-daa ses conanng nformaon on schoolng, work experence, and earnngs over he lfe-cycle. However, as far as we know, only he Naonal Longudnal Survey of Youh 979 also conans exensve ndependen psychology-ased nformaon on aly. These nclude AFQT scores for much of he sample as well as varous oher aly ess admnsered o smaller samples of he NLS youh. For hs reason we ulze he NLSY79 daa n order o compare our own ndvdual-specfc aly parameers o he ndependen aly measures ased on psychologcal ess. As s well known, he NLSY79 s a naonally represenave sample of young men and women aged 4 o 22 years old when frs surveyed n 979. The surveys have een conduced annually unl 994, and hen performed every oher year. We ulze he 2006 NLSY79, whch conans up o 22 years of daa for each responden. The NLSY79 4

16 represens varous groups such as men, women, Hspancs, lacks, non-hspancs and non-lacks, as well as he economcally dsadvanaged. There are hree sugroups comprsng he NLSY79. The frs s a cross-seconal sample represenng nonnsuonalzed cvlan youhs lvng n he Uned Saes aged 4-22 n 979. The second sample s a cross-seconal supplemenal desgned o oversample cvlan Hspanc, lack, and economcally dsadvanaged nonlack/non-hspancs eween 4 and 22 n 979. The hrd s a cross-seconal mlary sample of youhs ha represen he populaon, aged 7-22 n We do no apply samplng weghs snce we are examnng each ndvdual separaely raher han ryng o use each ndvdual s daa o uld a naonwde mean. 20 To esmae 7 we use daa on weekly earnngs.e., annual earnngs dvded y numer of weeks worked deflaed y he uran CPI ndex, 2 age, and years of schoolng. From hese we compue he experence level from he me when schoolng sopped *. Because our earnngs funcon specfcaon s desgned for hose who work connuously, we concenrae only on he males ecause females are more lkely o have dsconnuous laor force parcpaon, makng he measuremen of experence more dffcul and resulng n a hghly more nonlnear earnngs equaon Polachek, 975. In addon, curren human capal acquson s affeced y fuure nermen parcpaon. No eng ale o predc when and how long a woman wll drop ou precludes esmang female earnngs funcons, a leas for he purposes of hs paper. Furher, we use daa only on ndvduals ha have compleed school ecause hose workng whle n school or hose workng wh he nenon of gong ack o school earn less han commensuraely schooled ndvduals who compleed her educaon Lazear, 977. As was already menoned, for he purposes of hs sudy, he man vrue of he NLSY79 daa s he nformaon on aly whch was oaned ndependen of economc and demographc varales. For mos respondens hs consss of a leas one of 28 possle nellgence/apude ess. Of hese we concenrae on he 980 AFQT ecause 9 The daa and furher explanaons can e explored from he wese hp:// 20 We use he sample weghs when we aggregae he resuls o ge nferences aou parcular segmens of he populaon. 2 We also esmaed 7 usng annual earnngs daa for full-me workers and found very lle dfference n he resuls. 5

17 s he mos wdely used es n he NLS-Y and s avalale for nearly all respondens. 22 Neverheless, o check rousness of our fndngs, we also presen resuls usng he scores on 5 addonal ess repored n he NLS-Y. 23 Dealed descrpons of each aly es are gven n Appendx B. As already ndcaed, we compare hese psychology-ased cognve aly scores responden-y-responden o he ndvdual-specfc aly parameers we esmaed usng 7 and Esmaon Resuls As dscussed aove, we use non-lnear leas-squares o evaluae 7 for each person wh 2 or more years of daa. 24 We employ an algorhm denoed as GA used n genec research Czarnzk and Doherr, 2007 whch s less susceple o geng suck a local opma han radonal graden opmzaon echnques. We esmae four crucal parameers. They are he aly parameer ˆ, he dscoun rae rˆ, and he compose parameers ˆ E0 = and * wˆ R E =. Tale conans esmaes for he enre sample as well as for lacks and whes separaely. 26 Whe, W, and E values exceed hose of lacks, whereas, as s found n oher sudes, he lack dscoun rae exceeds he 22 The 980 AFQT score dffers slghly from he 989 and 993 scores ecause of he way each componen s weghed. 23 We are no ale o use all 25 ess ecause we drop ndvduals wh less han welve years of earnngs daa whch we requre o esmae he nonlnear earnngs funcons dscussed aove. The sxeen ess are: he Armed Forces Qualfcaon Tes AFQT, he Amercan College Tes Mah, he Amercan College Tes Veral, he Calforna Tes of Menal Maury, he Cooperave School and College Aly Tes, he Dfferenal Apude Tes, he Henmon-Nelson Tes of Menal Maury, he Kuhlman-Anderson Inellgence Tes, he Lorge-Thorndke Inellgence Tes, he Sanford-Bne, he Os-Lennon Menal Aly Tes, he Prelmnary Scholasc Apude Tes Mah, he Prelmnary Scholasc Apude Tes Veral, he Scholasc Apude Tes Mah, he Scholasc Apude Tes Veral, and he Wechsler Inellgence Tes for Chldren. 24 For mos ndvduals we have eween 7 and 22 years of daa. 26 We elmnae Hspancs ecause here were far fewer oservaons for hose wh 2 or more years of earnngs daa whch would make dffcul o form nferences for hs group. Furher, Hspancs end o e more heerogeneous han whes or lacks gven ha many Hspancs mmgrae from several Spansh speakng counres e.g., Mexco, Peuro Rco, Cua where levels of developmen vares Borjas and Tenda,

18 whe dscoun rae. We shall dscuss he mplcaons of hese parameer values shorly, u frs we address sascal sgnfcance whch we compue va oosrap echnques. For hs, we run 200 nonlnear regresson replcaons ulzng up o 2 randomly drawn oservaons wh replacemen from he avalale 2-22 oservaons per person. 27 Mean values of he coeffcen sandard errors averaged across all ndvduals are gven n row 2 of each panel and medan values whch deemphasze oulers are gven n row 3. On average, mos oservaons conan coeffcens ha are sascally sgnfcan wh he excepon of r, for whch a numer oulers produce an anormally hgh average sandard error. These oulers are apparen when nong how he medan sandard error of hese r coeffcens decreases dramacally o.03 for he populaon., E 0 Based on he denfcaon sraegy we descred earler, we ge values for, E s and r, and a populaon-wde value of R. Mean values across all ndvduals are gven n Tale 2 along wh mean values for each of he 6 es scores conaned n he NLS-Y ha were menoned aove. Ovously, sample szes vary among he non- AFQT scores ecause no all ndvduals ook each es. 4. Conssency wh Pror Populaon-Wde Esmaes Ineresngly, mean values of our parameers compare favoraly o pas sudes ha esmae aggregae earnngs funcons. For example, we oan an r of 0.08 compared o Haley s We oan a mean of 0.35 compared o Haley s 0.57, Heckman s , Heckman e al. s , Song and Jones s , and Lu s Smlarly, we oan a weekly renal rae per un of human capal R of $24.7 compared o Lu s $4.7. Of course, our resuls are ased on weghed averages of ndvdual values whereas he oher sudes examne one funcon for he populaon as a whole. Furher, each uses slghly dfferen human capal producon funcons. 27 These compuaons ook 275 hours usng wo 7-vpro chp parallel processor compuers runnng en STATA programs n andem each ulzng he GA algorhm. 7

19 Smlarly our resuls are conssen wh compuaons of Mncer s meequvalen pos-school nvesmen as well as wh he predcon ha me-equvalen nvesmen decreases wh age. Fgure plos poenal and acual earnngs for ndvduals who egan work mmedaely followng school. 28 Acual earnngs come from he daa and as such are oserved for each person. Poenal earnngs are compued y mulplyng predced human capal sock E S y he populaon-wde marke renal rae per un of human capal sock R, oh of whch are parameer esmaes. Theory predcs poenal earnngs exceed acual earnngs; and one can see hs o e he case from he wo dsruons. The mode for acual weekly earnngs s $00 per week n dollars and he modal value for poenal earnngs s aou $250. Ths mples a me-equvalen nvesmen for new enrans o e aou 0.60 whch compares favoraly o he 0.7 range ased on Mncer s orgnal earnngs funcon regressons. 29 Recompung hese wo dsruons for older workers Fgure 2 shows a defne narrowng of he dsance eween poenal and acual earnngs, as predced y heory. In shor, older workers renves less of her exsng human capal as hey age. 4.2 Conssency wh Sandardzed Tess Nex we deermne wheher he economcs-ased ndvdual aly parameers,, E 0 and E s are correlaed wh sandardzed aly es scores. One way o see how our economcs-ased aly measures compare o he psychologcally-ased es measures s o plo ou kernel densy funcons of our measures and he psychologcally ased es scores. To do so, we mus scale each es score ecause each has a dfferen measuremen range. For example, our aly measure s an exponen n a producon funcon. I ranges from almos zero o 0.50 wh a mean of 0.36 and a sandard devaon of 0.0. SAT scores are coded eween 200 and 800, u for our sample hey vary eween 200 and 750 for mah and eween 200 and 770 for veral. Each of he oher aly ess also has unque scores. To compare he overall 28 These exclude hose wh very low schoolng levels and hose who ook a year or more o fnd her frs jo. 29 One oans 0.56 and 0.8 respecvely when one solves for k 0 he equvalen of our E 0 usng Mncer s 974 Gomperz specfcaon G2a and G2, p

20 dsruons each mus e scaled o have he same range of values. To do so, we scale x L each measure x of es y where L s he lowes es score value and H s he H L hghes es score value. Ths yelds a scalng eween zero and one, where ndexes each parcular es. Fgures 3-7 plo he kernel densy funcons for AFQT,,, and E 0 E 0, E The AFQT and kernel denses are relavely smlar. Boh are lef-skewed wh modal values n he range. The kernel densy for s ell-shaped wh a slgh rgh-skew, and E 0 s unched a he lower levels whch makes sense snce hs s he amoun of nal human capal efore nvesng over he lfe-cycle. Anoher way o see how our economcs-ased aly measures compare o he psychologcally-ased measures s o examne scaer plos of our aly esmaes agans AFQT. We do so n Fgures 8- y plong mean,, E0, and E S levels assocaed wh each AFQT score. For each of our aly measures, hese yeld srong posve correlaons. 4.3 The Dsruon of Aly y Race Nex, n Fgure 2, we plo lack and whe dfferences n hese kernel denses for,, E0, and AFQT usng hese same ndvduals. Generally lacks sold lne fare worse han whes dashed lne snce for each es score he lack dsruon s furher o he lef han he whe dsruon. However, noeworhy s he large dfference for AFQT compared o our esmaed aly ased on he lfe-cycle model. Thus we fnd smaller aly dfferences y race n our economcs-ased measure han s oserved n he psychology-ased measures. Kolmogorv-Smrnov ess for he dfference n hese dsruons are gven n Tale 3. The race dfferences for each dsruon are sgnfcanly dfferen sascally, u he dsance measure s larges for he AFQT. 30 The AFQT es scores are gven n percenles rangng from o 99. Because of hs we compue raw scores ased on summng he scores for each componen par. We hen scale hese as ndcaed aove. These rescaled scores are wha are conaned n Fgure. To conserve space we do no presen kernel densy plos for he oher psychology-ased ess, u we laer n he paper we presen evdence how he oher ess correlae wh our human-capal ased measures. 9

21 4.4 Paerns n he Aly Coeffcens Clearly, gven he large numer of ndvduals, we canno presen coeffcens for each person. Insead we presen aggregae esmaes for varous groups. These are gven n Tales 4 for each of he sxeen achevemen ess. Column gves he mean score for each es; column 2 he numer of respondens akng parcular ess; columns 3-6 our esmaes of he economcs-ased aly measures for hese same ndvduals; column 7 our esmaes of he me-dscoun raes; and fnally column 8 hese respondens AFQT scores. A numer of paerns can e noed n he daa. Frs AFQT scores are hgher for whes han lacks. The same s rue for he economcs-ased aly, E, E, 0 measures, u slghly less so. Second,, E 0, E S and AFQT appear o e posvely correlaed. AFQT scores as well as, E 0, and E S values are larger for respondens wh hgher psychology-ased es scores. Thrd,,, E 0, E S and he achevemen es scores are posvely correlaed. Respondens wh hgher psychology-ased es scores end o have hgher values of, E 0, E S and AFQT. Fourh, AFQT and he psychology-ased es scores are also posvely correlaed. S 4.5 Conssency wh Human Capal Theory Our aly measures as well as AFQT are relaed o schoolng n a predcale way. Tale 5 conans coeffcen averages y years of school. Agan he ale s dvded eween lacks and whes. Column conans he numer of oservaons, columns 2-5 conans he esmaed human capal ased aly coeffcens, column 6 gves he esmaed me dscoun rae, and column 6 presens he AFQT score of hese ndvduals. Here, oo, a few paerns are noeworhy. Frs, even whn schoolng groups,,, E 0, and E S values are hgher for whes han lacks, u only margnally so, u here reman large dfferences n AFQT. Second, he and values rse sgnfcanly wh years of school. AFQT scores also rse wh years of school. Of course, a posve correlaon eween aly and schoolng level s predced y human capal heory ecause hgher aly rases he amoun of human capal one can produce per un of me. Holdng 20

22 renal raes per un of human capal consan, hs lowers he opporuny coss of gong o school, herey ncreasng he amoun of school purchased. On he oher hand, E 0 does no rse wh schoolng level eher for acks or whes. Ths s expeced ecause an ndvdual s hgher nal human capal susues for schoolng, and as Ben-Porah 967 predcs, leads one o sop schoolng earler. Fnally, he esmaed me dscoun rae r decreases wh he level of school. Ths laer resul s noeworhy ecause hgher me dscoun raes should mply fewer years of schoolng snce ndvduals wh hgh dscoun raes are more relucan o pu off he grafcaon of curren marke earnngs gven ha hey dscoun he fuure heavly. These paerns are also presened n Tale 6 whch conans specfc regressons. 3 Row ndcaes a hgher aly score for whes for all aly measures. However, he race dfference s aou en mes larger for he AFQT han our human capal ased measures. Row 2 ndcaes he posve relaonshp eween and schoolng level, and schoolng level, E 0 and schoolng, and AFQT and schoolng. However, as noed n Tale 5, he same s no rue for nnae human capal E 0. Also, as n Tale 5, he esmaed dscoun rae and schoolng are negavely relaed. Thus, as predced y human capal heory, ndvduals wh hgh cognve aly and posvely sor, ndvduals wh hgh nnae human capal E 0 negavely sor, and ndvduals wh hgh dscoun raes negavely sor wh schoolng level. 4.6 Selecvy Equaon 7, from whch we oan aly parameers, are esmaed only for hose ndvduals wh suffcenly long work hsores. Clearly hs sample s a selec group ecause does no nclude hose respondens wh shorer or no work hsores. The workers we choose may e and mos lkely are dfferen n aly and proaly oher characerscs han he non-workers we do no nclude. As such, makng nferences aou he whole populaon usng our selec sample may yeld ased resuls ecause our aly esmaes are no averaged over he enre populaon; u our purpose s no o 3 Noe ha each aly measure s scaled n percenles so comparsons can e easly made wh AFQT scores. 2

23 oan populaon-wde esmaes of aly. Insead, our pon s o use he dfference n psychology-ased and economcs-ased measures for he same workers o denfy wheher oh mehods of assessng aly dffer form each oher. In essence, we ulze he dfference eween he wo measures holdng oservale and unoservale ndvdual characerscs consan. On he oher hand, one mgh argue ha lack workers workng 2 or more years are relavely more ale han whe workers workng 2 or more years ecause only he relavely eer lacks compared o whes are ale o susan such a long work hsory. One can assess hs as y ulzng he psychology-ased es scores for non-workers of each race. If he worker compared o non-worker aly advanage s greaer for lacks han whes, hen our measures oversae lack compared o whe aly, and as a resul undersae he racal aly gap. In conras, f he relave aly advanage s greaer for whes, hen he oppose s rue, and as such, we hen undersae lack-whe aly dfferences. Tale 7 presens dfferences n AFQT scores eween hose workng 2 or more years our sample and he remander of he populaon hose no meeng he work requremen roken down y level of educaon. In seven educaonal caegores he aly advanage for workers s hgher for whes han lacks, whle n fve he aly advanage favors lacks. A -es rejecs he hypoheses ha hese dfferences are unequal. In shor, hose workng 2 or more years end o e more ale han hose workng less han 2 years, or no a all; u he dfference eween lack workers and nonworkers s no dfferen sascally han for whe workers and non-workers. Ths resul s conssen wh small, f any, selecvy ases when consderng racal dfferences n aly y concenrang on lacks and whes workng a leas 2 years of her lfeme. 4.7 Rousness Check 22

24 As descred aove, each NLS-Y responden could have aken any of sxeen IQ-ype ess. We dvde he populaon no sxeen groups, each represenng all respondens who ook ha parcular es. For each responden we have he psychology-ased es scores as well as our own esmaes of aly. A posve correlaon eween and IQ s conssen wh our nerpreaon ha he parameers, E, E, 0 S measure aly. Tale 8 conans hree ses of four columns. The four columns n each se gve correlaon coeffcens eween each of our aly measures and he aly es of each row, he op row eng he AFQT. The frs se of columns depcs he correlaon for he populaon of es akers ndependen of race. The second and hrd ses depc correlaons separaed y race. AFQT scores are srongly relaed o each of our aly measures. As a rousness check, n vrually all oher cases our compued aly parameers and he psychologcally-ased aly es scores are also posvely correlaed. Ths means ha despe eng compued compleely ndependenly, he psychologcallyased ess founded on long hsory of measurng nellgence and achevemen and our aly parameers ased on a nonlnear esmaon of ndvdual-specfc human capal producon funcon parameers correlae well. Ths posve assocaon eween our aly measure sand all he es scores adds credence o our aly measures compued ased on he lfe-cycle earnngs model. Several oher paerns n Tale 8 are noeworhy. Recall he nerpreaon of our esmaed parameers, E, E, 0 S. The parameers and depc one s aly o creae new human capal from old. The E0 parameer reflecs nnae human capal sock when one egns school. Fnally ES s a comnaon of all hree, reflecng human capal a he me one graduaes school and eners he laor marke. The psychology ased aly ess vary n nerpreaon, u y and large hey ncorporae oh nellgence and achevemen, encompassng oh knowledge and he aly o use hs knowledge for logcal reasonng. Tes quesons no only encompass vocaulary, smple readng passages, easy mah conceps, u n addon nclude veral relaons esed va analoges as well as arhmec and algerac reasonng esed va mah prolems of varous levels of sophscaon. To he exen psychology-ased ess measure oh 23

25 achevemen and nellgence, hey should e mos correlaed wh our ES measure snce ha oo esmaes oh achevemen, ased on wha s learned n school, and nellgence, ased on he aly o use hs knowledge o creae new knowledge. Clearly, he correlaon eween AFQT and ES s hgher han he correlaon of AFQT and our oher aly measures. Ths paern s also generally rue for all oher psychology-ased ess, hough he magnudes vary. Ineresngly, E 0, whch reflecs nnae knowledge a he me school egns, s leas correlaed wh each psychology-ased es, as mgh e expeced f psychology-ased es deemphasze hs nal knowledge. The and correlaons wh AFQT are n eween whch also mgh e expeced f and are purely nellgence ased measures. 4.8 Explanaory Power One fnal way o measure he mporance of our esmaed aly ndcaors s o examne how much addonal varaon n earnngs s explaned when ncorporang hese aly measures no a ypcal earnngs funcon. Tale 9 repors adjused R 2 measures for such earnngs funcons. AFQT ncreases he adjused R 2 y only.03 over he asc Mncer log e -lnear f, whereas and ncrease adjused R 2 y.06 and.7 respecvely, and y.27 ogeher wh E 0. Incorporang AFQT adds nohng o he explaned poron of varance when ncludng our hree aly measures Concluson Ulzng psychology-ased es scores has he advanage of measurng aly early n one's lfeme. On he oher hand, here s some conroversy regardng how well such es scores really reflec cognve aly. Furher, here s a grea deal of conroversy regardng race dfferences n hese measures Fraser, We do no nclude E s ecause ha ncludes he effecs of schoolng. 24

26 Based on an enrely dfferen paradgm, economss ulze conceps of aly n modelng earnngs. In such models ndvduals creae earnngs power y producng human capal. Two of he parameers and reflec he nellgence necessary o creae new human capal form old. A hrd parameer E 0 depcs nal knowledge efore formally enerng school. A fourh parameer r depcs me-preference. We esmae hese parameers for each ndvdual n he Naonal Longudnal Survey of Youh who has suffcen earnngs nformaon. In addon, for each such responden, we compue E S depcng he amoun of human capal a he me hs responden fnshed school and jus enered he laor force. Asde from esmang hese parameers, our am n hs paper s frs o es wheher hese economcs-ased aly parameers are conssen wh predcons from he human capal model, and second, o compare our economcs-ased aly measures wh ndependenly oaned psychology-ased measures also conaned n he NLS-Y daa. Comparng oh measures s mporan for a numer of reasons. Frs, serves as an ndependen check of he underlyng paradgms upon whch each s ased. Second, enales one o gan some nsgh no he queson of possle racal ases nheren n psychologcally-ased ess, as s ofen alleged. Thrd, serves as an example of how one can use newer and longer panels o measure aspecs of he ndvdual heerogeney. The resuls ndcae an uncanny parallel eween our economcs-ased aly measures and psychology-ased measures from he daa s varous achevemen es scores. Frs, we fnd oh measures o e posvely correlaed wh each oher. Second, we fnd oh o ndcae hgher levels of measured aly for whes compared o lacks, hough he correlaon s weaker for our measure han for he sandardzed ess. From hs we nfer he possly of greaer racal ases n he psychologcally-ased measures han our economcs-ased measures. Thrd, as predced y human capal heory, we fnd oh nellgence measures and o e hgher for hose wh greaer levels of schoolng. Ovously, E S s also posvely correlaed wh school, u neresngly, as s also predced, we fnd our measure of nal knowledge E 0 o e nversely correlaed wh levels of schoolng compleed. Ths means hgh nellgence ndvduals ge more 25

27 educaon, u hose wh more nal raw knowledge do no. Fourh, we fnd an nverse correlaon eween our measure of me preference r and school, agan as s predced y human capal heory. Of course, employng an economcs-ased model s no a panacea for measurng aly. Even f he economcs-ased approach provdes a vale alernave o he psychologcally ased achevemen ess, s no nformave early n one s lfe ecause requres earnngs daa for a perod of me long afer one ermnaes school. Furher, oh dscrmnaon n he avalaly of hgh qualy schoolng, as well as dscrmnaon n he laor marke self can cause racal ases n esmang aly parameers usng earnngs daa. In hs case racal dscrmnaon n he laor marke manfess self n a smlar way culural ases mgh nculcae psychologcally-ased models. Techncal smplfcaons could also mar nerpreaon of our resuls. Underlyng our approach are he ypcal assumpons ncorporaed n lfe-cycle models. Ovously, our resuls may e suspec f earnngs are deermned y oher frameworks such as ncenve conracs or deferred compensaon schemes. In addon, for compuaonal smplcy, we ulze a relavely smple human capal producon funcon, whch n our case only has wo aly parameers. We envson more complcaed versons ncorporang non-cognve sklls n he human capal producon funcon. These laer models would yeld more complex earnngs funcons han he ones we already use. On he oher hand, we feel srongly ha our resuls are no smply verfyng he well-known fac ha hgh aly people smply earn more. Our aly measures are unrelaed o earnngs level. Insead, hey arse from he curvaure of he earnngs profle. Our resuls are promsng enough o warran pursung he approach furher. For example, denfyng varous ypes of aly mgh enale one o gan nsghs no occupaonal choce decsons ncludng answerng quesons relang o gender dfferences n one's nclnaon o go no scenfc professons. 26

28 Fgure Dsruon of poenal and acual earnngs Wh zero years of experence x Acual Poenal Fgure Dsruon of poenal and acual earnngs Age group x Acual Poenal 27

29 Fgure 3 Raw AFQT, Dsruon of raw AFQT AFQT, 980 Fgure 4 kdensy ss Dsruon of : scaled 28 score0-00

30 Fgure 5 Dsruon of ea kdensy ssea ea: scaled score0-00 Fgure 6 Dsruon of Eo kdensy sseo Eo: scaled score

31 Fgure 7 kdensy Es Dsruon of Es Es: scales score 0-00 Fgure and AFQT AFQT 30

32 Fgure 9 ea and AFQT ea AFQT Fgure 0 Eo and AFQT Eo AFQT 3

33 Fgure Es and AFQT Es AFQT Fgure 2 Dsruon of ales y race Sold: Blacks, Dash: Whes kdensy ss kdensy ssea ea kdensy sseo Eo :scaled score ea:scaled score Eo:scaled score AFQT Es kdensy ssrafq kdensy sses AFQT raw:scaled score Es: scaled score 32

34 Tale Earnngs Funcon Parameer Esmaes* W E r All Average coeffcen esmae SEmean SEmedan Proporon of oservaons wh sg5% Blacks Average coeffcen esmae SEmean SEmedan Proporon of oservaons wh sg5% Whes Non lack/non hspanc Average coeffcen esmae SEmean SEmedan Proporon of oservaons wh sg5% * Row of each panel gves average parameer esmaes of 7 over he enre sample. Rows 2 and 3 gve mean and medan oosrapped sandard errors. Each oservaon s weghed y he NLS Y weghs when compung he averages and he medans. 33

35 Tale 2 Descrpve Sascs weghed: Indvdual specfc parameers and aly es scores OBS Mean SD ea Eo Es r AFQT ACT-MATH ACT-VERBAL CALIF COOP DIFFEREN HENMON KUHLMAN LORGE OTIS PSATMATH PSATVERBAL SATMATH SATVERBAL STANFORD WECHSLER Source: Compued from NLS-Y. The values of, ea, E 0, and r are averages parameer values oaned y esmang equaon 7 separaely for each ndvdual. The remanng varales refer o specfc achevemen/aly es scores conaned n he NLS-Y. The specfc ess are descred n Appendx B. Oservaons dffer y ype es ecause only he AFQT was admnsered o all respondens. Tale 3 Kolmogorv-Smrnov Tes for he Dfference n Dsruons of Indcaed Aly Varale for Blacks and Whes Ho: They are from he same dsruon Dsance P-value ea Eo AFQT The p-value s PD[m,n] >Do Ho, for he hypohess ha lack and whe aly measures are from he same dsruon, where Do s he oserved value of he wo sample K-S es sasc. 34

36 Tale 4: Descrpve Sascs y Race Blacks Whes IQ ea Eo Es r AFQT IQ ea Eo Es r AFQT AFQT AMERCOLL AMERCOLL CALIF COOP DIFFEREN HENMON KUHLMAN LORGE OTIS PSATMATH PSATVERBA SATMATH SATVERVAL STANFORD WESCHLER Source: Compued from he NLS-Y. Average values across ndvduals akng ndcaed es ased on esmaon of equaon 7 weghed y NLS-Y weghs. Tale 5 Aly Measures y Level of Schoolng usng NLS weghs Black Whe Schoolng ea Eo Es r AFQT80 ea Eo Es r AFQT80 < <= Source: Compued from he NLS-Y. Average weghed y NLS weghs values across ndvduals ased on esmaon of equaon 7. Tale 6 Aly and Race: How Human Capal Producon Funcon Measured Aly and AFQT Are Relaed o Each Oher and Race for Un-scaled and Scaled Aly Measures Dependen Varales ea Eo Es r AFQT Whe dummy 2.606* 2.905*** 2.754*** 3.77*** *** Schoolng.840*** 0.753*** *** -.56*** 6.077*** Consan ***.244*** 0.788*** -25.4*** 34.84*** *** R OLS regressons of,, E 0, E S, r, and AFQT on race and schoolng level. *** denoes sgnfcance a 0.0, ** denoes sgnfcance a 0.05, * denoes sgnfcance a

37 Tale 7 Average AFQT80 weghed Dfference n AFQT Dfference n AFQT Years of School Black Workers and Black Non Workers Whe Workers and Whe Non Workers Compued from NLS Y 36

38 Tale 8 Correlaons Beween Economcs-Based Measured Aly and Psychology-Based Aly* All Blacks Whes ea Eo Es ea Eo Es ea Eo Es AFQT AMERCOLLMAT AMERCOLLVE~ CALIF COOP DIFFEREN HENMON KUHLMAN LORGE OTIS PSATMATH PSATVERBAL SATMATH SATVERBAL STANFORD WECHSLER * For each es row gves he correlaon, row 2 he sascal sgnfcance, and row 3 he numer of oservaons. 37

39 Tale 9 Goodness of F Acheved y Incorporang Aly n an Earnngs Funcon* Varales n Earnngs Funcon Adjused R2 s,exp,exp s,exp,exp2, AFQT 0.36 s,exp,exp2, 0.39 s,exp,exp2,ea 0.50 s,exp,exp2,e s,exp,exp2,,ea,e s,exp,exp2,,ea,e0,afqt 0.60 * Adjused R 2 repored for Mncer-ype log e -lnear earnngs funcons of he form ln Y 2 = 0 αs α 2 exp α 3 exp α 4 α Aly ε where Y s weekly earnngs, S s years of school, exp s years of experence, and Aly consues each ype aly measure descred n he ex. 38

40 Appendx A: Dervaon of he Human Capal Earnngs Funcon Assume he ndvdual s ojecve s o maxmze dscouned dsposale earnngs, Y, over he workng lfe-cycle. 33 Ths ojecve s acheved y choosng he amoun of human capal K o renves each year n order o maxmze he presen value of lfeme earnngs N r Max J = e Y d K A 0 where J s he oal dscouned dsposale earnngs over he workng lfe-cycle, r s he personal dscoun rae and N s he numer of years one works, assumed known wh ceranly. Dsposale earnngs are Y = R E K ] A2 [ where E denoes human capal sock n me perod and K he amoun of human capal sock renvesed n me perod o creae new human capal. We assume he ndvdual egns wh an nnae sock of human capal E0 whch can e augmened y nvesng all or par of hs. The perod-o-perod change n human capal s denoed y E& = Q E = K E A3 where we assume s a consan rae of sock deprecaon of exsng human capal sock and where we assume ndvduals creae human capal usng a Co-Douglas producon Q = K. Maxmzaon of A sujec o equaons A2, A3 and A4 enals maxmzng he Hamlonan r H K, E, λ, = e R[ E K ] λ [ K E ] A4 wh consrans E K 0. and makng use of he ransversaly condon λ = 0. The funcon λ s he margnal conruon o he oal dscouned dsposale earnngs f here s one more un of human capal nvesmen. Assumng ha no corner soluons are ndng, he necessary condons are as follows. H A5. = 0 K H. = λ E H. = E λ A5.2 N A As noed n he ex, we asrac from laor supply consderaons. 39

41 40 = 0 N λ A5.4 From equaon A5.2, we oan Re r λ λ = &. Solvng hs dfferenal equaon and usng he ranversaly condon A5.4 we oan [ ] N r r e e r R = λ A6 From A6, 0 < λ &, ndcang a dmnshng value of human capal over me. From A5. Re 0 = = r K K H λ mplyng ha Re = r K λ r R e = λ A7 Susung A6 no A7 yelds, N r e r K = for ], [ * N. A8 Of course, E K = durng school snce one devoes full-me o nvesng whle n school. To oan human capal sock E, we comne A8 wh A3 and A5.3 whch yelds a dfferenal equaon whose closed form soluon enals an nfne hypoergeomerc seres [ ], *,, / / 0 * N r j e j r Be E j N r j j = = A9 where. / / * 0 * 0 j N r j j r j e j r r e E B = = A0

42 Haley shows ha he nfne hypergeomerc seres converges o a parcular value from he second erm. In Haley s dervaon he convergence creron s se for 6 decmal pons. A smpler form can e oaned y seng he convergence a 4 decmal pons level. Noe ha Haley s convergence ale shows ha converges from he frs erm.e. j=0 a 4 decmal pons. We use hs slghly less srngen convergence creron o consruc he earnngs funcon. VALUE OF THE INFINITE SUM FOR j = 0,...,34 AND = /8,, = 75, EO= 50, R =.38, yj =.08, 5 =.03, N = 65, AND = J Sum A j = 0, he nfne sum of he hyper-geomerc seres ecomes j= 0 * j r N e j j r j r = Thus, / * / / r B = [ E0 e ] r r or, B = [ E r / * / / 0 e ] A Thus he sock of human capal a me can e expressed as * / r E = Be r or / * E = Be r or 4

43 42 / / / / / 0 } ] {[ * * r e r e E E = or ] [ / / / 0 / * * * e r e e E E = A2 Oserved earnngs can e expressed as followng ] [ K E R Y = where, R s he renal rae of human capal. Thus, 2 0 ] [ ] [ * * N r e A e A e A Y = A3 where * 0 0 e E R A = r R A = 2 r R A =

44 Appendx B: Descrpon of Aly Measures Conaned n he NLSY79. Armed Forces Qualfcaon Tes AFQT Armed Forces Qualfcaon Tes scores are calculaed from some porons of Armed Servces Vocaonal Apude Baery ASVAB whch s admnsered y he Mnsry of Defense. The man purpose of he AFQT s o deermne he enlsmen elgly for ranches of he Armed Servces. The es self comprses wo chef pars whch are he Mah and he Veral. The Veral par conans Word Knowledge and Paragraph Comprehenson and he Mah conans Arhmec Reasonng and Mahemacs Knowledge. However, o calculae he score of AFQT, whch s repored as a percenage, he Mah secons are couned only once, whls he Veral pars are couned wce. In pracce, for example, he percenles elow he 30 h generally are no elgle for eng par of any ranches of he Armed Forces. 2. Amercan College Tes Mah The Amercan College Tes ACT s used o assess hgh school sudens performances n general educaon developmen and her ales o complee a degree a he college level. Ths mulple-choce es consss of four pars: Englsh, Mahemacs, Readng, and Scence. Also, here s an oponal par of he es ha s ascally supposed o measure aly n plannng and wrng a shor essay. As for he Mahemacs par, he es conans Pre-Algera, Elemenary Algera, Inermedae Algera, Coordnae Geomery, Plane Geomery, and Trgonomery. The oal numer of quesons for hs par s 60, whch s almos one-fourh of he 25 quesons on he enre es Amercan College Tes Veral Anoher secon of he Amercan College Tes s he Veral. Ths par measures he Englsh aly n he areas of Usage/Mechancs, Rheorcal Sklls, ec. The oal numer of quesons s 75. Ths secon s weghed he mos heavly. Addonally, he score of he whole es, every secon comned, can range from o 36, and he raw scores, he numer of correc answers, would e convered o he scale scores efore he fnal scores are repored Calforna Tes of Menal Maury The Calforna Tes of Menal Maury CTMM, admnsered y Calforna Tes Bureau, was prmarly desgned for sudens from Grades 7-4; s man ojecve s o gauge he menal ales of sudens. Ths dagnosc evaluaon s closely relaed o suden success n a wde range of school acves, so ha he eacher can e drecly nformed of who has learnng dffcules Carroll, 982. Moreover, provdes comprehensve measuremen of he funconal capales essenal o learnng, prolemsolvng, and respondng o new suaons Cooperave School and College Aly Tes Ths aly es was desgned o assess oh veral and mahemacal ales, prmarly for sudens Grades 4-2. Raher han dagnosng ndvduals, s focus s on predcng suden success n relaed areas of acvy. There are wo forms of he es, A 43

45 and B, whch have een proven equvalen n erms of aly measuremen and relaly. In erms of scores, percenles and convered scores are repored for each grade level Kaya, Dfferenal Apude Tes Dfferenal Apude Tes DAT was desgned o measure an ndvdual s aly o learn or o succeed n varous areas. Ths es consss of 8 areas: veral reasonng, numercal aly, asrac reasonng, percepual speed and accuracy, mechancal reasonng, space relaons, spellng, and language usage. All of he DATs are mulplechoce, wh me lms rangng from 2 o 25 mnues. 5 In addon, one of he enefs of hs es over ohers s ha provdes a rankng for he suden agans naonal averages n he respecve areas. The DAT resuls can e nerpreed as an ndcaor of suden progress wh an denfed fuure plan n pursung a vocaonal program or college Henmon-Nelson Tes of Menal Maury Henmon-Nelson Tes of Menal Maury was fundamenally desgned o measure a varey of areas of menal ales ha are crucal for success oh n academc work and ousde he classroom. In deal, hs es can e denfed as four dfferen levels: approprae for Grades 3-6, Grades 6-9, Grades 9-2, and college level. 7 I would e mos accurae f he es aker s age s eween 2 and 8. The 90 mulple-choce quesons are dvded no hree pars: word prolems, numer prolems, and graphcal represenaon. The overall score s eleved o adequaely represen he ndvdual s general cognve ales Kuhlman-Anderson Inellgence Tes Smlar o oher nellgence ess, Kuhlman-Anderson Inellgence Tes was specfcally desgned o measure an ndvdual s academc poenal y assessng general cognve sklls peranng o he learnng process. 9 Ths es s a well-known sandardzed nellgence group es ha can e gven o Grades K-2. Orgnally developed n he 920 s, has een updaed several mes as he numer of es-akers has ncreased. There are veral and nonveral ems n hs es whose scores can ndcae performances among chldren y oh chronologcal age and grade level Lorge-Thorndke Inellgence Tes The Lorge-Thorndke Inellgence es s anoher sandardzed, groupadmnsered es suale for Grades K-8 sudens. Is average score can e represenave of he naonwde school populaon. Accordng o he manual for hs es, was prmarly nended o measure reasonng ales, no he profcency n parcular sklls augh n school. The es n general consss of wo pars, whch are veral and nonveral. Furhermore, has een acknowledged ha he Lorge-Thorndke Tes s one of he es paper-and-pencl general nellgence ess Jensen, Os-Lennon Menal Aly Tes The Os-Lennon Menal Aly Tes s he fourh generaon of Os seres, whch daes ack o 98. Ths revsed edon s a susanal mprovemen on s 44

46 predecessors u sll focuses on educaonal sengs. Raw scores are easly convered o varous ypes of normave scores, and normave daa are repored oh y age- and grade-ased reference groups Groelueschen, 969. There are hree ypes of ales ha are mean o e measured y hs es: comprehenson of veral conceps, quanave reasonng and reasonng y analogy. Suale for sudens n Grades 8-9, hs es s also a group nellgence es whose norms can e updaed annually.. Prelmnary Scholasc Apude Tes Mah Admnsered y he College Board and Naonal Mer Scholarshp Corporaon, he Prelmnary Scholasc Apude Tes PSAT s a sandardzed es ha s usually gven o hgh school junors. No only does hs es provde an opporuny o pracce for he SAT, u can also pnpon he es-aker s weaknesses. Furhermore, f he scores are hgh enough, hey mgh qualfy for a scholarshp from he Naonal Mer Scholarshp compeon. Lke oher sandardzed apude ess, PSAT s desgned o measure a varey of sklls. Ths mulple-choce es s comprsed of hree prmary pars: Crcal Readng, Mahemacs, and Wrng Sklls. Focusng on he Mah par, conans 28 mulple choce and 0 grd-n quesons ha am a esng sklls n asc mah, algera, geomery, measuremen, daa analyss, and sascs, as well as asc proaly. 2 There are fve possle answers provded for he mulple choce quesons, whle he grd-n quesons requre he es akers o deermne her own answers. Generally, he sraeges used for PSAT Mah are same as for SAT Mah, u he alloed me for PSAT s somewha shorer han SAT for Mah and he oher secons. 2. Prelmnary Scholasc Apude Tes Veral As for he Veral par, hs es conans 48 mulple quesons ha focus on oh senence compleons and crcal readng sklls passage-ased readng. The Veral quesons are arranged n random order; however, he es srucure has 3 quesons for senence compleons and 35 quesons for he passage-ased readng. The oal amoun of me allowed o complee hs secon s 50 mnues Scholasc Apude Tes Mah The Scholasc Apude Tes SAT s perhaps he naon s mos wdely acceped college-enrance exam, and s admnsered y he College Board. The SAT s ypcally aken y hgh-school junors and senors. I can reflec how well sudens are n erms of sklls and knowledge hey have acqured n and ousde of he classroom, as well as how hey hnk, communcae, and solve prolems. Ths es s used y mos schools as one of he es predcors of how successful he sudens are n college. Smlar o he PSAT, he SAT comprses hree pars: Crcal Readng, Mahemacs, and Wrng. Each secon of he SAT s scored on a scale of The ypes of Mah quesons are fve-choce mulple-choce and sudenproduced responses. In furher deal, hs secon ams a esng sklls of sudens n he followng areas: exponenal growh, asolue value, funconal noaon, lnear funcons, manpulaons wh exponens, properes of angen lnes, esmaon, and numer sense. 5 45

47 4. Scholasc Apude Tes Veral The SAT Veral par, currenly known as he crcal readng secon, s also smlar o he PSAT Veral, assessng crcal and senence-level readng. More specfcally, ess sudens readng comprehenson, senence compleons, and paragraph-lengh crcal readng. Quesons may e ased on one or wo readng passages. Some quesons, on he oher hand, are no ased on passages; nsead, sudens need o complee senences Sanford Achevemen Tes Frs pulshed n 926, he Sanford Achevemen Tes Seres measures elemenary and secondary school sudens academc knowledge, and as such provdes a measure of achevemen. I was Is conen s desgned o reflec school currcula and es nsruconal pracces ased on sae and naonal sandards. Each em s desgned o measure up o four achevemen parameers: conen cluser, process cluser, cognve level and nsruconal sandard. The ess nclude hree ypes of quesons: mulple choce, shor answer, and exended response. Besdes requrng a wren answer of fve or sx senences, he exended response may also requre he suden o graph, llusrae or show work. Such answers are usually ncluded whn he areas of scence or mahemacs. 6. Wechsler Inellgence Tes for Chldren The Wechsler Inellgence Tes for Chldren was orgnally developed y Davd Wechsler n 949 o measure he ndvdual s nellgence, especally for chldren aged 6 years o 6 years and monhs. Theorecally, s eleved ha human nellgence s complex and mulfaceed, so hs es s desgned o reflec hs elef hrough esng oh veral and nonveral performance ales. The veral IQ score s derved from scores on 6 suess: nformaon, dg span, vocaulary, arhmec, comprehenson, and smlares. The nonveral score s from 6 suess: pcure arrangemen, lock desgn, ojec assemly, codng, mazes, and symol search. In addon o s uses n nellgence assessmen, hs es s also used n neuropsychologcal evaluaon, specfcally wh regard o ran dysfuncon. Susanal dfferences n veral and nonveral scores may ndcae some poenal prolems of ran damage. 7 Kaplan Prep Tes and Admssons, hp:// ASVAB/ML_afq_esovervew.hml 2, 3 Amercan College Tesng Programs, 4 York Unversy, hp:// 5 Socey for Human Resource Managemen, hp:// 6 Swarz Creek Communy Schools, hp:// %20Inerpreaon%20Meeng.pp2_fles/frame.hm 7 York Unversy, hp:// 8 See Hoge Deparmen of Psychology, The College of New Jersey, hp://psychology.deparmen.cnj.edu/ /documens/tes_invenoryls.00.doc 0 Famly Educaon Nework, hp://school.famlyeducaon.com/gfed-educaon/educaonalesng/40939.hml Educaonal Research Cenre, hp:// 2 Sudy Gude Zone Company, hp:// 46

48 3 Aou.com Company, hp://esprep.aou.com/od/psa/a/psat_cr.hm 4 The College Board, hp:// 5 The College Board, hp:// 6 The College Board, hp:// 7 Encyclopeda of Menal Dsorders, hp:// 8 Naonal Longudnal Survey of Youh, hp:// %20User%20Gude/79ex/achess.hm 9 ASVAB Prep Informaon, hp://asvaprepnfo.com/ 47

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51 Song, Xueda and John Jones 2006 The Effecs of Technologcal Change on Lfe-Cycle Human Capal Invesmen, Workng Paper. Terrell, F. Terrell, S. and J. Taylor 98 Effec of Race of Examner and Culural Msrus on he WAIS performance of Black Sudens, Journal of Consulng and Clncal Psychology 49: Vernon, M. C. and D. W. Brown 964 A Gude o Psychologcal Tess and Tesng Procedures n he Evaluaon of Deaf and Hard-of-Hearng Chldren, Journal of Speech and Hearng Dsorders 29: