An EmpiricalAnalysis ofthe Risk Properties ofHumanCapital Returns

By IGNACIO PALACIOS-HUERTA*

Humancapital resources are a crucialpart of considerableprogress has been made in the anindividual’ s capitalholdings and comprise recentliterature toward understanding the prop- muchof thetotal aggregate wealth in theUnited ertiesand implications of investment returns, Statesand other economically advanced na- andalthough human capital assets are the main tions.During the last few decades,much en- form ofindividual and aggregate investments, ergyhas been devoted to the analysis of thisprogress has not reached the human capital humancapital and its empirica lregularities. literature.As aresult,a numberof crucialques- Theresult has been the accumula tionof a tionsremain unanswered. For instance,consider largeamount of evidenc esupportingthe im- theissues raised by Gary S.Becker(1993, p. portanceof humancapital to thestructure and 205): evolutionof earnings ,occupations,employ- mentand unemplo yment,fertility ,andeco- Thischapter adds several dimensions to nomicgrowth and development. 1 theevaluation of the effects of college Onlyrelatively recently, however, have econ- educationon earningsand productivity by omistsbegun to undertakea systematicanalysis comparing privateand social gains from oftheproperties of investmentreturns and their collegeeducation with those of other in- vestments. Thesecomparisons permit a implicationsfor modelsof dynamiceconomies. determinationof how much is gained or Muchof thisanalysis has been concerned with lostby individuals and society from in- theanalysis of risky and riskless Ž nancialas- vestmentin the former ratherthan in the sets,and their implications for intertemporal latter,and are essential to determine modelsof consumer optimization. Although whetherthere is underinvestment in col- legeeducation; they also help determine whethercapital market difŽ culties, the *Department ofEconomics,Brown University, Box B, lackof knowledge and liquidity, etc., ... Providence,RI 02912(e-mail: [email protected]).I haveserious impediments to the  owof owe adebtof deepgratitude to Gary S.Becker, KevinM. resourcesinto college education (italics Murphy,and Guillermo Mondino for their helpful com- added). ments onearlier drafts,encouragement, and several stimu- latingdiscussions. I alsobeneŽ ted from conversations with Thesearguments apply not only to college and MosheBuchinsky, John Cochrane, Andrew Foster, Lars highschool education but to anyeducation level Hansen,Kenneth Judd, Paul Romer, Sherwin Rosen, Stan- leyZin, from the suggestions of two anonymous referees, orother forms ofhuman capital. A suitable andfrom the audiences at seminars heldat theUniversity of comparisonof the properties of different risky Chicago,Stanford University, Brown University, the Uni- humancapital returns, and of humancapital and versityof Cambridge, London Business School, the Amos Žnancialreturns, can then provide crucial infor- TuckSchool of Business,and the University of Miami.I am especially thankfulto Giorgio De Santisfor his program- mationabout these key matters. These compar- mingassistance, tothe National Fellows Program at the isons,which also are of great relevance to HooverInstitution and the George J. StiglerCenter at the publicpolicy, represent the subject matter of the Universityof Chicago for their hospitality and Ž nancial analysisin this paper. support,and to SurreyWalton for research assistance. Any Interestingly,there is relatively little research errors are mine alone. 1 SherwinH. Rosen(1987) reviews thehuman capital intheliterature that helps us understandhow the literatureand its impact upto the last decade. Dale W. risk-returntrade-off for differenthuman capital Jorgensonand Barbara Fraumeni(1989) estimate thatthe investmentsand for Žnancialinvestments may share ofhuman capital wealth inthe aggregate wealth ofthe compareat themargin. Moreover, the approach UnitedStates during1948 – 1989was arounda remarkable 93percent. At theaggregate level, labor receives at least adoptedin the literature is unsatisfactory and two-thirdsof total income in the United States andother generallyinvalid. The procedure usually fol- economicallyadvanced nations. lowedis to compare average levelsof human 948 VOL.93 NO. 3PALACIOS-HUERTA:RISK PROPERTIES OF HUMANCAPITAL RETURNS 949 capitalrates of return,ignoring the role of risk, Theanalysis in this paper overcomes these andrestricting the intertemporal marginal rate twoimportant impediments by exploiting the ofsubstitution (IMRS) ofthe consumer to a propertiesof somerecently developed method- particularfunction of observed data. The Ž rst ologiesfor theanalysis of asset returns and aspectis pointed out in Becker (1993, p. 4)who, intertemporalutility-based models. In particu- withregard to his own in uential book, says: lar,in recent years the Ž nanceliterature has witnessedan increasing use of tests for mean- Thereis a moreserious error in my dis- variancespanning, as Ž rst introducedby Gur cussionof the riskinessof investments in Hubermanand Shmuel Kandel (1987). The lit- education. Iignoredthe then developing eratureon mean-variance spanning analyzes the literatureon optimal portfolios, and did effectsthat the introduction of additionalassets notderive my measure of marginalrisk— thevariance in therateof return—from an hason the mean-variance frontier of certain analysisof utility maximization (italics benchmarkassets. There is mean-variancespan- added). ningif the frontier of the benchmark assets alonecoincides with the frontier of the bench- Unfortunately,this error hasnever been cor- markassets plus the new assets. For instance, rectedin thehuman capital literature. Moreover, consideran individual investing in human cap- noanalysis has even attempted to compare the ital.If thefrontier associated with his human risk-returnproperties of differenthuman capital capitalassets alone coincides with the frontier assets.Therefore, no reliable estimates of in- ofthe human capital assets plus a Žnancial vestmentgains or losses by individuals and asset,then mean-variance spanning means that societyexists. theindividual will not be ableto improveupon Thepurpose of this paper is to begin to Ž ll hishumancapital investment by investingin the thisgap by providing an empirical comparison Žnancialasset. If thefrontiers do not coincide, oftheproperties of risk-adjustedhuman capital thenthe mean-variance characteristics of his ratesof return.As Beckerremarks, the principal originalinvestment could be enhanced by also challengeis to incorporate the role of riskiness investingin theŽ nancialasset. Empirically, it is ofinvestmentsin education into the comparison importantto note that recent research shows that ofinvestmentreturns: How canmarginal risk be laborincome risk represents an important per- derivedfrom utilitymaximization? How then vasiverisk factor at the aggregate level that canreturns, or returnsrelative to their variabil- requiresa substantialrisk premium in Ž nancial ity,be compared? A secondchallenge is to markets.3 Similarly,we canexamine the prop- avoidrestricting the IMRS of theconsumer to a erties ofdifferent human capital returns by ex- speciŽc functionof the observed data. As in aminingthe differences in the mean-variance mostinvestment models, a commonimplication frontiersthat they span when a newhuman ofhuman capital investment models is that the capitalasset is introduced. equilibriumprice of future human capital pay- As GiorgioDe Santis(1993) and other au- offs canbe representedas theexpectation, con- thorshave shown, the hypothesis of mean- ditionedon current information, of the product variancespanning can be formulatedin termsof ofthe payoff and the IMRS ofthe consumer. thevolatility bounds on theIMRS introducedby Theexclusive approach taken in the human capitalliterature is to restrict the IMRS tobe a speciŽc parametricfunction of the observed characterizing classes ofutility functions suitable for ana- data.This restriction leads to a numberof lyzingthe uncertainty and risk elements inhuman capital difŽculties, the main one being that the results markets. 3 ofthe empirical estimations depend on the See JohnY. Campbell(1996), Ravi Jagannathan and ZhenyuWang (1996), and Jagannathan et al.(1998). These particularfeatures assumed about the utility papers,however, do not examine theincremental contribu- 2 function. tionto risk and return from investing in Ž nancialassets from theperspective of someone who owns human capital orvice versa. Previousto these papers,Eugene F. Fama andG. WilliamSchwert (1977) examined the Capital Asset Pricing 2 JohnC. Hause (1974)in his critique of Yoram Weiss Model(CAPM) with the nonmarketable income model of (1972)already points out the problems with calculations DavidMayers (1972)using the growth rate inper capita basedon arbitrary utility functions and the importance of laborincome. 950 THEAMERICANECONOMIC REVIEW JUNE 2003

Lars P.Hansenand Jagannathan (1991), and utedto differencesin the nature and markets of extendedin Hansen et al. (1995), without re- theseassets (e.g., liquidity, taxation). On the strictingthe IMRS tobeanyspeciŽ c parametric otherhand, differences across demographic functionof theobserveddata. Frans A. De Roon groups(sex and race) for givenhuman capital andTheo E. Nijman(2001), who offer athor- holdings(e.g., a collegeeducation) will be oughreview of theliterature on mean-variance associatedwith relative differencesin nonmon- spanning,describe in detailthe duality between etaryreturns, capital market difŽ culties, fric- mean-variancefrontiers and volatility bounds. tions,and other circumstances across these Inthis paper we studythe risk properties of demographicgroups. We oftenŽ ndsubstantial humancapital returns both in terms of mean- differencesacross some sex and race groups variancefrontiers using the test introduced by withidentical human capital holdings. Hubermanand Kandel (1987) and in terms of volatilitybounds on theIMRS using De Santis’ I.Measuresof Human CapitalReturns (1993)procedure. Itis important to remark that these method- Themeasurement of human capital returns ologiesfor comparingthe properties of invest- hasbeen subject to a greatdeal of attention in mentreturns allow us to overcome existing theliterature. David Card (2001) offers acom- shortcomingsin the human capital literature prehensivereview of theliterature, as wellas an since:(i) themeasure of marginal risk may be extendeddiscussion of various econometric is- derivedfrom ananalysis of utility maximiza- sues.Given the various procedures available in tion;(ii) differences in marginalrisk and returns theliterature for estimatingthe returns to canbe accounted for byestimating differences schooling,we willevaluate the robustness of inmean-variancefrontiers using the covariance theempirical Ž ndingsfor variousmeasures of structureof returns; and (iii) no particularform humancapital returns. The basic measure we oftheutility function needs to bespeciŽed and, considercan be describedas follows.Returns to asa result,risk-return differentials do not de- schoolingare typically calculated as thepropor- pendon the form oftheutility function and the tionalincrease in earnings per year associated degreeof risk aversion. withthe last unit of education (the marginal Inwhat follows we willexamine the proper- return).Thus, we shallconsider the marginal tiesof human capital returns at the level of payoffof the last unit of education over one aggregationof demographic groups character- period,from t to t 1 1. Let we,t denotethe real izedby sex, race, education, and experience. payoffat time t ofanindividual with e units of Theempirical analysis yields a numberof re- education.The marginal return can then be ap- sults.First, we candetermine the size of the proximatedas: gainor loss associated with different forms of w riskyhuman capital investments and Ž nancial h e,t 1 1 (1) Re,t 1 1 5 . investmentsfor thedifferent demographic w e 2 1,t groups.For theperiod 1964 –1996,we Žndthat thegains from acollege(or greater)education Thisapproximation accounts for boththe perunit of riskare from 5percentto more than one-periodgains obtained from owning e 2 1 20percent greater than from riskyŽ nancial unitsof human capital at t,aswell as the skill assets,whereas the lossesfrom ahighschool (or premiumfrom owningone more unit at agiven lower) educationper unit of riskrelative to risky time.To seethis, note that it canbe decomposed Žnancialassets are typically greater than 15 as: percentfor mostdemographic groups. Second, asBeckerremarks, these comparisons also help w w h e 2 1,t 1 1 e,t 1 1 todeterminehow serious human capital market (2) R e,t 1 1 5 z w e 2 t we 2 t 1 difŽculties, lack of knowledge, and liquidity 1, 1, 1 problemsmay be. In particular, we canseparate 5 re 2 1 z rt 1 1 . twodifferent sources of gains and losses from t,t 1 1 e 2 1,e investments.On the one hand, differences be- tweenhuman capital and Ž nancialassets in TheŽ rst fractioncaptures the gains associ- termsof returns per unit of risk may be attrib- ated with e 2 1unitsof education.These gains, VOL.93 NO. 3PALACIOS-HUERTA:RISK PROPERTIES OF HUMANCAPITAL RETURNS 951 whichon averageare around 2 percentper year, theresults, it is important to remark that we will aretypically ignored or, at best, indirectly ap- Žndextremely similar results across the differ- proximatedin other human capital measures entmeasures. (Card,2001). The second fraction captures the relativeextra wages that are obtained by owning II.Mean-VarianceSpanning Methodology onemore unit of education at a giventime. In h thissense, the measure Re,t1 1 capturesthe Thetypical optimization problem of anindi- trade-offassociated with the marginal produc- vidualconsists of choosing the consumption tivitiesof different levels of education ( e 2 1 andinvestments that maximize his expected ` t and e)overone period of time, as itcapturesthe lifetimediscounted utility t5 0 b Etu(ct), earningspremium obtained at t 1 1relativeto where u isa well-behavedutility function, 4 t obtainedfrom onemore unit of education. Et[ z ]denotesthe expectation conditional on Alternatively,this measure may be interpreted informationavailable at time t, b . 0 repre- asthe premium necessary to transfer a given sentsthe rate of time preference, and ct is con- i i individualfrom hiscurrent life-cycle wage pro- sumptionat date t. Let R t11 5 1 1 r t11, i 5 Žleto that of someone with one more unit of 1, ... , n,denotethe real return of asset i from educationfrom t to t 1 1whenforgone wages date t to date t 1 1, Rt1 1 the n-dimensional f representthe cost of schooling. vectorof thesereturns, and Rt1 1 thereal return Theempirical tests will be implemented us- earnedby arisklessasset. The equilibrium con- ingwages to construct this measure for the ditionsin these models are: differentdemographic groups, and will be ex- tendedto account for tuitionfees, as well as for (3) Et @m t 1 1Rt 1 1 # # 1, theeffects of abilityand selectivity biases in the f measurementof wages. In addition, we will Et @mt 1 1Rt 1 1# # 1, considerthe traditional Becker-Mincer ap- proachto estimate human capital returns, the wherethe IMRS is mt1 1 5 bu9(ct1 1)/u9(ct) measuresuggested in the endogenous labor 1 f 6 supplymodel of Moshe Buchinsky and Philip and Rt 1 1 5 . Theseconditions hold Et @mt 1 1 # Leslie(1997), and the growth rate in labor in- withequality if there are no market frictions and comeaccounting for theeffects of revisions in withinequality otherwise. 7 Moregenerally, de- futurelabor income and discount rates sug- Re 5 Ž ne t1 1 asthe difference between any two gestedin Campbell (1996). Inanticipation of assetreturns. Then, the equilibrium conditions e canbe written as Et(mt1 1Rt1 1) 5 0, which impliesthat 4 Iam indebtedto Kevin M. Murphyfor suggesting this approximation.This measure can alsobe interpretedas the s ~m! zE~Re!z grossincome less themaintenance costs thatmust be in- (4) $ . curredto keep a unitof humancapital inworking order (see E~m! s ~Re! Becker, 1971).Note also that if we deŽne wt1 j,e 5 wt 1 j,e2 1 1 dt1 j,e,thenthe usual present value expres- sionof the typical human capital investmentmodel is ob- ` j tained: wt,e 2 1 # E t j5 1 b [u9(ct 1 j)/u9(ct)]dt 1 j,e, (1996)consider only the growth rate inper capita labor j and limj# ` b u9(ct 1 j)w t 1 j,e 5 0.This expression indi- income,which is thestationary analogue of the per capita cates thatutils provided by net real wages today( t) with laborincome variable used in Mayers’ (1972) one-period education e 2 1,are equalto the expected discounted sum model. 6 ofutilsprovided by the additional wages dt 1 j,e (wages with Inutility-based models, m is simplythe IMRS of the education e minuswages witheducation e 2 1) that one consumer.This discount factor can beparametrized insev- more unitof education will provide in the future. This measure eral ways leadingto the typical models used in theŽ nance is alsouseful to help explain the size ofthe international literature,e.g., the CAPM and factor modelssuch as the diversiŽcation puzzle when human capital is considered part of ArbitragePricing Theory (APT) and the Chen-Roll-Ross thewealth portfolio of individuals (Palacios-Huerta, 2001a). model.No speciŽ c parametrizationneeds to be assumed 5 h Relative toCampbell’ s (1996)measure, Re,t1 1 adjusts here.As aresult,the implications are as generalas possible. thegrowth rate ofreal wages fora given educationlevel 7 See Hua He andDavid M. Modest(1995) and Erzo e2 1 t1 1 rt,t1 1 bythe education premium term re2 1,e, which is G.J.Luttmer(1996) for the equilibrium Euler inequalities typicallyimportant and sizable, butdoes not include the forthe cases ofshort-sale constraints, borrowing con- effects ofrevisionin future labor income and discount rates. straints,solvency constraints, and proportional transaction Fama andSchwert (1977) and Jagannathan and Wang costs. 952 THEAMERICANECONOMIC REVIEW JUNE 2003

Thismeans that the lower bound on thestan- boundson the IMRS impliedby Ri and R are darddeviation of theIMRS isdeterminedby the statisticallyidentical. familiarmean-variance frontier for assetreturns Inour empirical analysis we evaluaterisk- from theasset with the greatest Sharpe ratio. adjusteddifferences in ratesof returnfollowing Hansenand Jagannathan (1991) show how this twodifferent methodologies. First we consider dualitybetween the frontiers for theIMRS and De Santis’(1993) x2 testof comparison of for assetreturns allows us both to construct frontiers.This test uses the covariance structure minimumvariance random variables mv from ofreturnsin measuring the extent of risk-return theset of returns and to analyze the mean- differentialsacross different sets of investment varianceimplications of investment returns. In returns,and is implemented using the General particular,we areinterested in comparing the Methodof Moments (GMM). Second,as indi- propertiesof the human capital returns of two catedearlier, we alsotest the hypotheses of mean- differentdemographic groups, as well as the variancespanning using the test developed in propertiesof the human capital returns of a theseminal paper of Huberman and Kandel givendemographic group with those of Ž nan- (1987).These authors propose a likelihoodratio cialreturns. test.Although this test involves additional re- Ingeneral, these comparisons can be imple- strictions,the exact distribution of the test sta- mentedfollowing an intuitive procedure which tisticunder the null hypothesis is known. 9 A canbe described as follows. Let RA and RB comparisonof the small sample properties of denotetwo different vectors of asset returns. theseand other test procedures can be foundin Considerthe variables mA 5 R9A z g 9A, mB 5 GeertBeckaert and Michael S. Urias (1996). R9B z g 9B,andthe variable m 5 R9 z b 9 5 Thesmall sample results suggest that the [R9A R9B] z [b A b B]9,for givenrisk-free rate likelihoodratio test for spanningproposed by f 8 Rt1 1 5 v. We wantto examine the effects of Hubermanand Kandel (1987) has better power addingthe vector RB tothe benchmark set of propertiesthan the GMM-based tests in the returns RA andvice versa. That is, we consider literature.A detaileddescription of thetests can thecomparison between Ri and R for both i 5 befoundin thesurvey on testingmethodologies A, B.Followingthe procedure in De Santis for mean-variancespanning by De Roonand (1993),it is then possible to develop a testof Nijman(2001). over-identifyingrestrictions to evaluate the hy- Lastly,in addition to evaluating whether the pothesisof coincidence of the mean-variance changein frontiers is statistically signiŽ cant frontierassociated with Ri andthe frontier as- usingthese two testing procedures, it is also sociatedwith R, for i 5 A, B. The test is importantto measure how much thefrontiers equivalentto a testof the coincidence of the changewhen the different human capital and volatilitybounds on mi andthe bounds on m, Žnancialreturns are compared. We willcon- for i 5 A, B.Underthe null hypothesis that the siderthe distance between the frontiers at the returns RA and RB havethe same stochastic value of E(m)thatcorresponds to the minimum properties,then Ri spans R, for both i 5 A, B. ofthefrontier of m.Thisstatistic is equalto the Interms of volatility bounds on the IMRS, the changein the Sharpe ratio divided by the risk- hypothesisof mean-variance spanning means free returnthat corresponds to that value of thata comparisonbetween mi and m will yield E(m).Sincethe minimum is typically very that the b j coefŽcients, i Þ j,inthevector b 5 closeto one, the change in the frontiers is ap- [b A b B]arezero; that is, that the volatility

9 Hubermanand Kandel (1987) show how the regression methodologycan beused to test thehypothesis of mean- 8 Hansen andJagannathan (1991) show that the sto- variance spanning.Their hypothesis of spanningmeans that v v v chastic discountfactor m 5 R 9 b 9 5 [R9A R9B each returnof theassets thatare addedto a benchmarkset v v v 2 1 1/v][b A b B w]9 5 R 9[E(R R 9)] 1 has thesame mean ofassets can bewrittenas thereturn on theportfolio of the as the true m,andhas theminimum variance amongall the benchmarkassets plusan error term. Thetest, therefore, possiblevariables that satisfy Et[mt1 1Rt 1 1] 5 1. This involveslinear restrictions on the regression coefŽ cients. randomvariable can beevaluated from the vector of asset Clearly,under the null hypothesis of spanning, since such returnsas longas E(RvRv9)isnonsingular. They also show anadditional asset can onlyadd to the variance ofthe thatall feasible m must obey s (m) $ b 9 b , where is the originalportfolio, individuals would not like to include variance-covariance matrixof therisky asset returns. them intheir portfolio. VOL.93 NO. 3PALACIOS-HUERTA:RISK PROPERTIES OF HUMANCAPITAL RETURNS 953 proximatelyequal to the increase in the ex- theseassets, their markets, frictions, and taxa- pectedreturn per unit of risk that is obtained tion.Likewise, differences in mean-variance whenadditional returns are included in theorig- frontiersacross demographic groups with iden- inal set: ticalhuman capital assets (e.g., a collegeedu- cation)will be associated with differences in zE~Re!z frictions,circumstances, nonmonetary gains, or (5) Ds ~m! $ D e z E~m! marketstructures where the different individu- s ~R ! alsoperate. 12 Thecomparisons we implement

e inthenext section, therefore, may be interpreted zE~R !z 1 inthis sense. 5 D e z f . s ~R ! Rt 1 1 III.Dataand EmpiricalEvidence Inconcluding this brief description of the testingmethodology, it is important to remark A. Data thefollowing aspects: First,the methodology allows us to compare Yearlydata on theU.S. equityindex and the thestochastic properties ofdifferent human capi- U.S. Treasurybill for theperiod March 1963– taland Ž nancialreturns accounting for risk,with- March1996 were obtainedfrom theCenter for outimposing or assuming that a speciŽc parametric Researchin Security Prices (CRSP) Žles.Eq- modelfor theIMRS is generating the returns. uityreturns include both capital gains and div- Second,it is possible to take explicit account of idendyields. The wage data come from the thedifferential riskiness of investments in educa- MarchCurrent Population Survey (CPS) for tionby using the covariance structure of returns in surveyyears 1964 to 1996. The CPS provides measuringdifferences in mean-variance frontiers. informationon earnings and weeks worked in Lastly,the comparison of risk-adjusted rates thecalendar year preceding the March survey, ofreturn across different human capital assets for approximately1.4 million workers. The data andŽ nancialassets does not and cannot test for areinitially divided into 2,880 distinct groups, speciŽ c frictionsin humancapital markets. This distinguishedby sex, race (white, black), years wouldrequire testing whether speciŽ c m’s and ofeducation (1 to 18), and potential years of speciŽc Eulerinequalities are consistent with experience(from 0to40), deŽ ned as humancapital returns under different speciŽ ca- min{age 2 yearsof schooling 2 7, age 2 17}. tionsof preferences. 10 Thisis likely the reason Theaverage real weekly wage of full-time whyBecker (1993) considers that these com- workersis then computed within each gender- parisons help determiningwhether capital mar- race-education-experiencecell as total annual ketdifŽ culties, the lack of knowledge, liquidity earningsde ated by the personal consumption problems,or other frictions, may impede the expenditurede ator from thenational income owof resources into education. 11 For instance, andproduct accounts divided by total weeks ifhumancapital assets were asliquidas Žnan- worked.13 Wetestthe properties of human cap- cialassets and if they were subjectto identical italreturns at this level of aggregation. taxation,lack of arbitrage opportunities would implythat they span the same returnspace. Any 12 Because humancapital is illiquidand it is generally differencesin mean-variance frontiers that we impossiblefor individuals to hold more thanone type of mayŽ ndwillthen indicate the gains and losses humancapital asset (exceptperhaps through marriage, al- associatedwith differences in the nature of truism,and other arrangements withinthe family), differ- ences inrates ofreturn cannot typically be arbitraged out. 13 See Lawrence Katz andKevin M. Murphy(1992), for example,for a detaileddescription of themain features of 10 See Palacios-Huerta (2001b)for an analysis of the thewage data andfor how top-coding and bracketing are extentto whichdifferent frictions may reconcile consump- typicallydealt with. The same proceduresare followedhere. tionwith human capital returnsunder plausible preference Thechanges in educational attainment questions that oc- parameters. curredin 1992 in the CPS are reconciledwith the previous 11 Thereason is thatdifferences inmean-variance fron- questionsusing the procedure followed by DavidA. Jaeger tiers implydifferences inthe set offeasible m’s, which may (1997).See Murphyand Finis Welch (1992) and Chinhui beattributedto differences inhuman capital frictions(e.g., Juhnet al.(1993) for analyses ofthe structure of wages and borrowingconstraints, transaction costs). wage differentialsduring most of ourperiod of analysis. 954 THEAMERICANECONOMIC REVIEW JUNE 2003

TABLE 1—MEAN REAL HUMAN CAPITAL RETURNS AND U.S. EQUITY INDEX RETURN FOR 1964–1996

Males Females White Black White Black Nohigh school Experience:1– 5 5.9 (6.2) 25.1(8.2) 2.0 (5.7) 25.5 (10.5) 6–15 5.4 (4.7) 24.0(8.3) 1.4 (4.9) 23.9 (10.0) .15 5.2 (5.3) 23.1(10.6) 3.5 (6.3) 20.6 (9.9) High school Experience:1– 5 13.6(9.7) 21.9 (16.5) 18.8 (9.3) 20.3 (14.0) 6–15 8.1(5.9) 15.8 (11.2) 13.7 (10.2) 22.9 (14.3) .15 5.2(7.6) 12.3 (8.7) 7.2 (6.7) 12.2 (10.2) Somecollege Experience:1– 5 6.0(6.0) 15.0 (9.9) 11.0 (4.7) 10.2 (14.0) 6–15 7.1 (5.4) 9.6(8.2) 11.2 (5.1) 8.5 (12.3) .15 7.3 (4.2) 8.8(8.1) 10.0 (7.5) 9.0 (11.7) College Experience:1– 5 14.2(11.3) 18.1 (10.1) 16.8 (8.4) 11.1 (8.2) 6–15 9.0(7.6) 12.6 (9.3) 14.2 (10.4) 13.6 (9.7) .15 10.2(9.1) 14.0 (12.3) 9.2 (8.7) 6.0 (9.9) Morethan college Experience:1– 5 10.5(4.7) 12.3 (10.5) 12.1 (6.6) 14.2 (8.9) 6–15 10.0(5.0) 10.4 (8.6) 10.3 (9.4) 20.6 (11.2) .15 8.7 (8.1) 7.0(12.0) 11.0 (8.9) 18.3 (12.8) U.S.equity index return 7.0 (12.7)

Note: Standarddeviations are inparentheses.

B. EmpiricalEvidence attemptto justify these claims, economists and policymakers often indicate that there may be Table1 reportsthe basic descriptive statistics importantexternal effects from increased h ofhumancapital returns Re,t1 1 for thedifferent schoolingand school spending. Empirically, demographicgroups and the U.S. equityindex however,human capital externalities are either during1964 –1996. hardto Ž ndor negligible [see, e.g., James Theaverage rates of return are broadly con- J.Heckmanand Peter J. Klenow(1997) and sistentwith previous estimates in the literature DaronAcemoglu and Joshua Angrist (2000)]. A for mostgroups. It is important to note, how- morenatural resolution, at least in part, to this ever,that when compared to the return on the problemcan be offeredby simplylooking at the U.S. equityindex, mean human capital returns reward tovariability ratio of the investment; arerelatively high and the standard deviation of thatis, not just at thelevel of returnsbut at the returnsrelatively low for mostdemographic Sharperatios. There are large differences be- groups.Thus, human capital Sharpe ratios tweenhuman capital Sharpe ratios and Ž nancial zE(Re)z/s (Re)areoften much larger than the Sharperatios in many instances. The former Sharperatio of the U.S. equityindex. onesclearly dominate the latter ones for many Thisaspect is importantsince the information demographicgroups at different education and on the relative variabilityof humancapital rates experiencelevels. Note, however, that although ofreturn can help to explain a subtlebut long broaddifferences in Sharpe ratios are clearly standingproblem in theliterature. This problem informative,the covariance structure of returns arisesfrom thefact that “ theprivate returns to alsoplays a keyrole in determiningdifferences schoolingare not nearly large enough to justify inrisk-adjustedreturns. We turnnext to testing theclaims of importance made for schooling,” for thesedifferences in investment returns. asMarkBils (2000, pp. 59 –60)indicates. This As indicatedearlier, we considerthe GMM- iscertainly true for the level ofreturns on basedtest of spanning in terms of volatility schoolingin many areas of economics where boundson the IMRS proposed by De Santis humancapital plays an important role. In an (1993)and the likelihood ratio test proposed by VOL.93 NO. 3PALACIOS-HUERTA:RISK PROPERTIES OF HUMANCAPITAL RETURNS 955

Hubermanand Kandel (1987). In addition to ningcannot be rejected at conventional signiŽ - thesetests, we alsoreport the increase in the cancelevels when considering the human expectedreturn per unit of riskthat is obtained capitalreturns of any demographic group ex- whenadditio nalreturns are included in the ceptwhite females with some college. Interest- originalset: Ds (m).14 Inour case, we con- ingly,the hypothesis is rejectedin allthe cases siderthe hypothesis of mean-variance spanning ofa graduateeducation and, at the level of whenadding just one asset to a benchmarkset of collegeeducation, for allblack females. 15 returns. BLACK MALES.—Thepattern of rejections of Table2 showsthe p-valuesof the results of thehypothesis of mean-variance spanning is thetests for differenthuman capital returns, for quitedifferent for thisgroup. When considering giveneducation and experience groups, across thehuman capital returns of white males, the sexand race characteristics. The null hypothesis hypothesisis rejected in all cases except at the ofspanning is that the frontier associated with levelof graduate education and up to 15 years thehuman capital returns of a givendemo- ofexperience.In the case of whitefemales, the graphicgroup (benchmark returns) coincides hypothesisis always rejectedat conventional withthe frontier associated with the returns of signiŽcance levels. With respect to black fe- thatdemographic group plus the human capital males,the hypothesis is onlyrejected at college returnsof a differentdemographic group. andmore than college education levels with Beforediscussing speciŽ c Žndings,it is fewer than15 years of experience. worthnoticing the following general patterns. WHITE FEMALES.—Inthis case, it is very dif- First,the results of the GMM andlikelihood Žcultto reject the hypothesis of mean-variance ratio(LR) testsare very similar. In virtually all spanning.In fact, no testindicates the rejection casesconsidered, these two tests agree on ofthe hypothesis at the 5-percent level. Only whetheror not the null hypothesis of mean- whitemales at lower education levels appear to variancespanning should be rejectedat conven- becloser to induce a rejectionat the usual tionalsigniŽ cance levels. Second, there is a conŽdence levels, as well as somemales at the robustrelationship between the indicator of the levelof graduate education. estimatedincrease in expected returns per unit BLACK FEMALES.—Thehypothesis is never of risk Ds (m) and the p-valueof thetests. As rejectedwhen considering the human capital ageneralpattern, when p-valuesare greater returnsof black males. Interestingly, the hy- than0.40 the indicator ranges from 1to3 per- pothesisis almost never rejected when consid- cent, when p-valuesare between 0.30 and 0.10 eringwhite individuals with at least a college theindicator ranges from 4to9 percent.More education,but it is strongly rejected for educa- importantly,when the null hypothesis of coin- tionlevels below college. cidenceof frontiers is rejected at conventional We concludefrom theseŽ ndingsthat there levels,the indicator ranges from 9to14percent arenontrivial differences across some demo- for p-valuesbetween 0.10 and 0.05, and from graphicgroups with identical human capital 14to29percentfor p-valuesbetween 0.05 and holdings.For instance,net gains for whiteand 0.00.The following features can be observedin blackfemales with respect to other groups tend thespeciŽ c comparisonsacross groups: toariseat highlevels of education,whereas for WHITE MALES.—For educationlevels below whitemales they arise at education levels up to college,the hypothesis of mean-variance span- college.Net losses arise for blackindividuals, typicallyat lower levels of education and, es- pecially,for highschool and college dropouts, 14 Thisindicator can alsobe usedto compute the net gain andrelative to their white counterparts. of asset A over asset B as theincrease inexpected return per InTable 3 we reportthe results of mean- unitof riskobtained when adding asset A to asset B minus theincrease inexpected return per unit of risk that is variancespanning tests for humancapital and obtainedwhen adding asset B to asset A. Žnancialreturns. 15 Underthe null hypothesis of coincidence of bound- InPanel A, we testthe hypothesis of span- aries, DeSantis’GMM-based test statistic isdistributedas ningwhen the returns on the U.S. equityindex a x2 with2 degrees offreedom. The likelihood ratio test proposedby Hubermanand Kandel (1987) is distributedas areadded to a benchmarkof human capital an F distributionwith 2 N and 2(T 2 K 2 N) degrees of assetsfor eachof the different demographic freedom.In our case K 5 N 5 1 and T 5 33. groups.The results show that the null hypothesis 956 THEAMERICANECONOMIC REVIEW JUNE 2003

TABLE 2—MEAN-VARIANCE SPANNING TESTS FOR HUMAN CAPITAL RETURNS ACROSS DEMOGRAPHIC GROUPS

PanelA— BenchmarkHuman Capital Returns: White Males AdditionalHuman Capital Returns Black Males WhiteFemales Black Females GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) Nohighschool Experience:1– 5 0.370.48 3.17 0.25 0.32 6.55 0.42 0.55 3.26 6–15 0.27 0.42 4.11 0.28 0.23 5.15 0.39 0.46 3.00 .150.21 0.28 6.32 0.24 0.19 6.29 0.53 0.44 1.86 High school Experience:1– 5 0.140.28 8.88 0.12 0.20 8.80 0.36 0.42 3.60 6–15 0.10 0.18 9.00 0.21 0.26 7.77 0.23 0.33 6.61 .150.09 0.14 8.73 0.08 0.11 12.80 0.12 0.17 8.50 Somecollege Experience:1– 5 0.360.53 3.07 0.01 0.00 21.39 0.24 0.26 5.50 6–15 0.21 0.20 6.55 0.02 0.00 19.98 0.22 0.30 4.52 .150.13 0.17 7.90 0.12 0.17 8.30 0.09 0.18 8.88 College Experience:1– 5 0.120.16 8.66 0.12 0.16 8.01 0.03 0.02 16.40 6–15 0.06 0.12 12.50 0.09 0.12 10.40 0.04 0.05 15.31 .150.19 0.22 7.20 0.04 0.02 16.88 0.01 0.00 20.57 Morethan college Experience:1– 5 0.040.04 15.91 0.04 0.03 15.90 0.00 0.00 26.03 6–15 0.03 0.02 15.86 0.02 0.01 17.46 0.00 0.00 23.40 .150.02 0.00 18.22 0.04 0.01 14.52 0.07 0.05 12.70

PanelB— BenchmarkHuman Capital Returns: Black Males AdditionalHuman Capital Returns White Males WhiteFemales Black Females GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) Nohighschool Experience:1– 5 0.010.00 25.20 0.03 0.00 18.11 0.11 0.13 9.33 6–15 0.03 0.00 19.31 0.04 0.00 16.32 0.20 0.30 7.80 .150.10 0.08 10.60 0.05 0.02 15.24 0.09 0.12 12.64 High school Experience:1– 5 0.010.02 22.22 0.03 0.01 17.70 0.09 0.12 11.21 6–15 0.04 0.00 17.17 0.04 0.00 15.18 0.15 0.18 8.23 .150.06 0.05 14.83 0.07 0.05 12.59 0.10 0.14 10.00 Somecollege Experience:1– 5 0.000.04 23.00 0.03 0.00 17.24 0.11 0.14 12.36 6–15 0.03 0.00 15.31 0.06 0.05 14.98 0.18 0.23 10.41 .150.07 0.04 12.72 0.02 0.01 17.67 0.06 0.07 14.54 College Experience:1– 5 0.010.03 20.64 0.03 0.01 16.76 0.05 0.01 14.79 6–15 0.05 0.01 14.32 0.07 0.05 12.49 0.04 0.00 16.86 .150.11 0.15 10.55 0.06 0.04 13.85 0.14 0.12 8.90 Morethan college Experience:1– 5 0.110.10 9.29 0.06 0.02 13.51 0.00 0.00 28.45 6–15 0.17 0.22 8.39 0.03 0.00 15.79 0.17 0.16 8.60 .150.06 0.02 12.47 0.04 0.01 14.90 0.12 0.14 9.66 VOL.93 NO. 3PALACIOS-HUERTA:RISK PROPERTIES OF HUMANCAPITAL RETURNS 957

TABLE 2—Continued.

PanelC— BenchmarkHuman Capital Returns: White Females AdditionalHuman Capital Returns White Males Black Males Black Females GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) Nohighschool Experience:1– 5 0.110.09 8.70 0.19 0.15 6.66 0.29 0.36 5.42 6–15 0.08 0.09 11.02 0.12 0.15 8.49 0.32 0.28 6.15 .150.12 0.07 8.22 0.09 0.11 9.15 0.21 0.23 7.34 High school Experience:1– 5 0.070.06 13.64 0.13 0.19 9.63 0.30 0.48 7.10 6–15 0.09 0.08 11.29 0.12 0.16 8.90 0.37 0.29 4.66 .150.15 0.16 7.51 0.12 0.10 8.27 0.32 0.40 4.83 Somecollege Experience:1– 5 0.110.15 8.50 0.23 0.30 4.46 0.39 0.40 5.72 6–15 0.08 0.07 11.77 0.09 0.19 10.61 0.25 0.30 4.94 .150.06 0.09 13.12 0.12 0.14 10.07 0.21 0.18 7.60 College Experience:1– 5 0.070.09 12.91 0.07 0.06 12.85 0.24 0.32 7.65 6–15 0.12 0.17 8.28 0.12 0.10 8.34 0.16 0.36 8.50 .150.23 0.20 5.43 0.10 0.10 9.24 0.38 0.50 3.02 Morethan college Experience:1– 5 0.140.20 8.28 0.08 0.11 12.59 0.32 0.44 4.33 6–15 0.11 0.26 8.80 0.07 0.12 14.00 0.12 0.26 9.07 .150.07 0.12 12.02 0.11 0.15 9.21 0.25 0.21 10.12

PanelD— BenchmarkHuman Capital Returns: Black Females AdditionalHuman Capital Returns White Males Black Males WhiteFemales GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) Nohighschool Experience:1– 5 0.000.00 29.71 0.24 0.28 5.75 0.01 0.00 26.39 6–15 0.00 0.00 26.15 0.12 0.18 8.92 0.02 0.00 24.50 .150.00 0.00 25.67 0.23 0.30 5.20 0.04 0.00 24.61 High school Experience:1– 5 0.000.00 25.51 0.15 0.11 8.29 0.03 0.00 20.90 6–15 0.02 0.01 18.60 0.09 0.15 9.56 0.05 0.02 18.31 .150.02 0.00 17.93 0.07 0.10 12.03 0.12 0.14 10.10 Somecollege Experience:1– 5 0.020.03 17.34 0.17 0.22 10.50 0.02 0.01 24.99 6–15 0.03 0.01 16.62 0.10 0.11 14.15 0.04 0.01 19.96 .150.06 0.00 13.43 0.23 0.18 5.69 0.02 0.00 28.82 College Experience:1– 5 0.120.15 8.60 0.11 0.19 9.00 0.03 0.03 16.53 6–15 0.13 0.11 8.39 0.22 0.20 6.33 0.08 0.03 15.76 .150.16 0.20 7.82 0.07 0.07 12.12 0.12 0.08 10.88 Morethan college Experience:1– 5 0.120.15 8.57 0.34 0.48 3.26 0.02 0.00 20.44 6–15 0.21 0.28 6.11 0.10 0.12 9.28 0.23 0.18 7.97 .150.12 0.12 8.39 0.07 0.12 14.79 0.10 0.10 14.85

Note: Thistable reports the p-valuesof the GMM andLR tests inthe GMM andLR columns,respectively, and the estimated increase perunit of riskunder column Ds(m). isrejectedat the5-percent level for all individ- males)with a highschool education or with ualswho have not completed high school, and somecollege education (typically college drop- allmales (but, interestingly enough, not fe- outs)and less than 15 years of experience. 958 THEAMERICANECONOMIC REVIEW JUNE 2003

TABLE 3—MEAN-VARIANCE SPANNING TESTS FOR HUMAN CAPITAL AND FINANCIAL RETURNS

PanelA— Benchmark:Human Capital Assets White Males Black Males WhiteFemales Black Females GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) Nohigh school Experience:1– 5 0.030.00 17.55 0.00 0.02 23.58 0.03 0.02 17.55 0.02 0.00 18.41 6–15 0.01 0.00 26.66 0.00 0.00 18.64 0.03 0.01 20.92 0.00 0.00 26.90 .150.00 0.01 23.47 0.04 0.03 18.37 0.04 0.04 15.38 0.01 0.03 22.28 High school Experience:1– 5 0.040.02 16.70 0.04 0.01 14.92 0.17 0.22 8.04 0.57 0.71 1.33 6–15 0.04 0.00 18.89 0.04 0.03 20.18 0.27 0.23 6.56 0.77 0.88 0.42 .150.09 0.05 9.98 0.21 0.12 7.90 0.33 0.30 3.62 0.41 0.52 2.82 Somecollege Experience:1– 5 0.000.03 23.21 0.01 0.03 20.70 0.11 0.17 8.66 0.37 0.41 3.26 6–15 0.01 0.00 20.09 0.03 0.04 15.61 0.21 0.30 7.02 0.05 0.05 14.66 .150.23 0.19 5.18 0.17 0.18 8.52 0.09 0.14 9.11 0.28 0.36 4.07 College Experience:1– 5 0.480.52 2.34 0.73 0.96 0.51 0.47 0.37 2.30 0.80 0.96 0.03 6–15 0.40 0.50 3.32 0.77 0.92 0.40 0.50 0.60 1.82 0.37 0.32 3.76 .150.35 0.41 3.51 0.81 0.88 0.26 0.31 0.26 4.00 0.61 0.79 0.92 Morethan college Experience:1– 5 0.430.60 2.21 0.30 0.44 4.08 0.67 0.77 0.82 0.66 0.89 0.08 6–15 0.56 0.70 1.09 0.81 0.80 0.11 0.60 0.70 1.17 0.57 0.77 1.21 .150.37 0.33 3.08 0.63 0.93 0.92 0.31 0.40 3.89 0.05 0.02 14.88

PanelB— Benchmark:Financial Assets White Males Black Males WhiteFemales Black Females GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) Nohigh school Experience:1– 5 0.810.97 0.40 0.87 0.98 0.02 0.85 0.98 0.02 0.84 0.93 0.01 6–15 0.60 0.78 1.20 0.84 0.99 0.00 0.75 0.82 0.32 0.81 0.90 0.02 .150.63 0.80 1.08 0.83 0.99 0.00 0.74 0.80 0.40 0.55 0.62 1.60 High school Experience:1– 5 0.350.45 3.56 0.60 0.73 0.91 0.22 0.18 6.59 0.14 0.10 8.31 6–15 0.33 0.40 3.89 0.59 0.60 1.10 0.14 0.11 8.17 0.14 0.12 7.02 .150.14 0.19 8.23 0.16 0.15 8.22 0.06 0.05 12.26 0.06 0.04 13.19 Somecollege Experience:1– 5 0.810.98 0.01 0.76 0.88 0.42 0.10 0.08 10.27 0.14 0.12 9.08 6–15 0.55 0.79 1.19 0.82 0.93 0.09 0.11 0.10 9.26 0.14 0.16 6.74 .150.55 0.86 0.56 0.50 0.46 2.00 0.11 0.12 8.39 0.32 0.28 3.56 College Experience:1– 5 0.100.14 9.09 0.05 0.04 14.26 0.13 0.16 8.86 0.07 0.06 12.63 6–15 0.06 0.05 13.26 0.06 0.03 13.82 0.14 0.20 7.29 0.09 0.08 10.28 .150.05 0.05 14.17 0.06 0.02 14.11 0.09 0.12 10.73 0.10 0.05 9.94 Morethan college Experience:1– 5 0.060.05 10.26 0.11 0.14 8.23 0.05 0.04 14.07 0.06 0.05 13.28 6–15 0.05 0.04 16.82 0.07 0.06 12.00 0.02 0.01 17.53 0.16 0.12 8.26 .150.04 0.03 15.26 0.20 0.21 7.10 0.02 0.01 17.17 0.31 0.25 4.00

Note: Thistable reports the p-valuesof the GMM andLR tests inthe GMM andLR columns,respectively, and the estimated increase perunit of riskunder column Ds(m).

Virtuallythe opposite resultsare obtained in U.S. equityindex. In this case, the hypothesis is PanelB. Inthis panel, we testthe hypothesis of typicallyrejected at theusual conŽ dence levels mean-variancespanning when the human capi- inboth the GMM testsand the likelihood ratio talreturns of the different demographic groups testsfor collegeand more than college educa- areadded to a benchmarkof asset returns on the tionlevels but, interestingly, never for educa- VOL.93 NO. 3PALACIOS-HUERTA:RISK PROPERTIES OF HUMANCAPITAL RETURNS 959 tionlevels below college. 16 Notethat, as in ingsin terms of education and experience Table2, theGMM andLR testsare very simi- groups,and between human capital and Ž nan- lar,and that the relationship between the indi- cialreturns. For manypurposes, however, we cator Ds (m) and the p-valuesof the tests maywant to examine differences across educa- followsthe general pattern described above. tionand experience levels for givendemo- Theseresults are important. They indicate graphiccharacteristics. Using the evidence thatat the level of aggregation of these demo- presentedin thesetables, these comparisons can graphicgroups the “ losses”from a“low”in- bereadilymade. For instance,risk-adjusted dif- vestmentin education relative to risky Ž nancial ferencesbetween college and high school re- assetscan be substantial.The net increasein the turnscan be obtained by looking at how a Sharperatio (computed as indicatedin footnote collegeeducation compares with Ž nancialas- 14)for highschool dropouts goes from 15to26 setsand by then looking at how Ž nancialassets percentacross the different groups, whereas for comparewith a highschool education for each maleswith a highschool degree and some col- demographicgroup. The net estimates of the legeit goes from about13 to 19 percent. Note correspondingrisk-adjusted differences in the alsothat these losses appear to be reducedwith rateof returnper unitof riskcan thus be broadly theaccumulation of experience.Conversely, the inferredfrom thetables. Consistent with the “gains”from investmentsin education relative Žndingsof alargeliterature on thecollege– high toŽ nancialassets typically come from college schoolpremium, they conclusively indicate a andgraduate education levels. The net increase superiorityof greater levels of education over inthe Sharpe ratio is about 7 to14 percent for lowerlevels of education. maleswith at least a collegedegree, 14 to 17 Thecomparisons in theprevious section also percentfor whitefemales with more than a showthat differences in risk-adjusted rates of collegedegree, and 7 to13 percent for black returnper unit of risk between human capital femalesother than the very experienced ones. andŽ nancialassets can be substantial. For in- Lastly,the tests were alsoimplemented at the stance,the private gains from acollegeeduca- aggregatelevel for variousaggregate measures tionfor awhitemale per unit of riskare about ofhuman capital returns. 17 Thehypothesis of 7to10 percentgreater than from investmentsin mean-variancespanning cannot be rejected Žnancialassets, whereas the losses for most whenŽ nancialreturns are added to the set of whitehigh school males are about 15 percent humancapital returns, but it isstronglyrejected relativeto Ž nancialassets. These results are whenhuman capital returns are added to Žnan- consistentwith Becker’ s (1993,p. 207) intu- cialreturns. The maximum Sharpe ratio is about itionthat “ whileeducation seems to yield a 15percentgreater with both sets of returnsthan moneygain to the typical whitemale college withŽ nancialreturns alone, and only about graduate,it may not to the typical white male 1.5–3 percentgreater than with human capital high-schoolgraduate” (italics added). Interest- returnsalone. Thus, the net gainsfor aggregate ingly,similar evidence is foundfor femalesand humancapital assets are about 12 to 13.5 per- for blacksas well. centin terms of expected returns per unit of risk. TheseŽ ndingscorrespond to the period 1964–1996and can help explain why education C. Discussionand Interpretation andall other skills were accumulatedvery rap- idlyduring this period. The results also appear Thecomparisons in the previous subsection tosuggestthat investments in college(or more) were implementedacross demographic (sex, educationwill continue growing in the future. race) groupswith identical human capital hold- As indicatedearlier, however, the comparisons cannotidentify the causes of these risk-adjusted differences.This would require evaluating 16 Theonly exception is females witha highschool whetherdifferent parametric models for the educationand more than15 years ofexperience.Note also IMRSaregenerating the different human capi- that the p-valuesof thetests forfemales witha highschool taland Ž nancialreturns. In principle, human educationor some collegeare substantiallylower than the p-valuesfor males inthe same group. capitalassets are not only risky but illiquid as 17 These resultsare availablefrom the author in an well—they cannot be sold and are rather poor Appendixupon request. collateralon loans— so a positiveliquidity 960 THEAMERICANECONOMIC REVIEW JUNE 2003 premiumwould be associatedwith human cap- productionis supplied inelastically. 19 Using ev- ital.Despite this liquidity premium, however, idencefrom compulsoryschooling laws, Ace- individualsat lower levels of education typi- mogluand Angrist (2000) Ž ndthat externalities callyexperience “ losses”relative to liquid as- arevery small, typically not signiŽ cantly differ- sets.Differences in taxation may also explain entfrom zero.As aresult,the risk-adjusted partof these differences. However, “ although estimatesobtained in this analysis may re ect thedifferences might be explained by compen- bothprivate and social total gains and losses satingdifferences in liquidity and taxation, a from humancapital investments. Thus, they can morereasonable inference would be that the providereliable estimates for variouspublic privatemoney gain from collegeto the typical policymatters. graduateis greater than what could have been obtainedby investing elsewhere” (Becker, D. AdditionalEmpirical Evidence 1993,p. 206). Differences in nonmonetary re- wards acrossgenders (perhaps because of the Therobustness of the empirical Ž ndingshas divisionof labor within the family) could also beenevaluated by examining a numberof ex- bea sourceof differences in monetary returns. tensionsincluding the role of tuition costs and Withregard to the interpretation of theresults theeffects of abilityand selectivity biases, and for the“ typical”individual discussed above, it byconsidering other approximations to human isimportant to note that when examining dif- capitalreturns that account for othersources of ferencesin risk-returntrade-offs at any level of riskand heterogeneity, including the typical aggregation,some idiosyncratic risk is left out Becker-Mincerapproach and the measures sug- ofthe calculations. This is commonly done in gestedby Buchinsky and Leslie (1997) and Žnancialresearch in the analysis of theproper- Campbell(1996). We foundvery few differ- tiesof indexes of Ž nancialreturns. However, enceswith respect to the previous estimates. 20 unlikeŽ nancialasset returns which yield the Theresults are available in an Appendix upon samereturn to all individuals, human capital request. returnsvary across individuals. Interestingly, KennethL. Judd’s (2000)theoretical analysis showshow when idiosyncratic risk is endoge- 19 See thediscussion in Becker (1993). nousthe risk premium for humancapital may 20 Rates ofreturn were estimated fromthe classical dependon systematic components of risk, not Becker-Mincer log-wageregressions using a set ofregres- onidiosyncraticrisk. In the analysis we control sorsthat includes education, experience, sex, race, nine for sex,race, education, and experience lev- geographicdummies, metropolitan area, individualand 18 familynonearned income, and marital status.These returns els. We thusrefer tothe typical individualat h tendto have lower means andlower variances than Re,t1 1, thislevel of aggregation. In the next subsection buthighly similar Sharperatios. The results of the tests we alsodiscuss the results of thetests once we ofdifferences inrisk-adjuste dreturnsare verysimilar. accountfor othersources of heterogeneity,and Buchinskyand Leslie (1997)develop a dynamicmodel with endogenouslabor supply that accounts for evolving percep- we Žndvery few differences. tionsabout future wages. Thehuman capital measures in Lastly,for somespeciŽ c publicpolicy impli- theirmodel are obtainedusing a quantileregression ap- h cations,the relevantmeasure is thesocialrate of proach.Mean returns are similar to Re,t1 1,butthey tend to returnrather than the private rate of returnfrom havelower variability, especially forgreater educationlev- els. As aresult,human capital Sharperatios are slightly educationand other forms ofhuman capital. h greater thanthose corresponding to Re,t1 1.However,the Thesemay be different because of differences p-valuesof both the GMM tests andthe likelihood ratio betweensocial and private costs and returns, tests are similar. Onlyminor differences were foundfor dueto human capital externalities from amore collegedropouts when comparing human capital andŽ nan- educatedlabor force, because schooling may cial returns.The measure suggestedin Campbell(1996) also inducesslightly greater Sharperatios than those induced by havea signalingvalue in addition to raising h Re,t1 1.Whencomparing human capital returnsacross de- productivity,or because some other factor of mographicgroups, the p-valuesof the GMM and likelihood ratiotests are essentiallyidentical to thosein Table 2. When comparinghuman capital andŽ nancialreturns, however, it 18 Interestingly,when the comparisons in Table2 and3 isslightlyeasier toreject (accept) thehypothesis that Ž nan- are implementedcontrolling for occupation and industry in cial (humancapital) returnsspan the same mean-variance h thecomputation of Re,t1 1,theresults are virtuallyidentical space thanŽ nancialplus human capital returnsfor educa- tothosereported in these tables. tionlevels abovehigh school. VOL.93 NO. 3PALACIOS-HUERTA:RISK PROPERTIES OF HUMANCAPITAL RETURNS 961

We havealso considered an aspect that is noveltyof this work is as a contributionto concernedwith the measures of Ž nancialre- economicscenters on its attempt to provide an turns.It might be argued that an appropriate analysisof the risk-return properties of human comparisonbetween human capital and Ž nan- capitalreturns and a comparisonwith other cialreturns should involve the year to year investmentsovercoming the difŽ culties that changesin corporate dividends alone, that is havepersisted in the literature for thelast few withoutconsidering capital gains. If allŽ nancial decades. capitalgains could be explained by changing Theempirical analysis has yielded a number expectationsof future dividends, then the two ofresults. In particular, the variation in the measureswould be equivalent.But this need not stochasticproperties of differenthuman capital bethe case. We thusconsider the procedure in returnsis substantial, especially when compar- CaseyB. Mulligan(2002) to measure physical inghuman capital and liquid assets. These dif- capitalreturns from thenational accounts ferencesindicate how much is gainedor lostby which,as withthe labor market data, have only individualsand society from investmentsin hu- the“ dividend”portion of thereturn [see Mulli- mancapital assets relative to Ž nancialinvest- gan(2002) for detailsof the computation of ments.The analysis cannot identify the sources thesereturns]. This idea has also been followed ofthese risk-adjusted differences, but it does byanumberof authors,including Zvi Griliches suggestthat some “ difŽculties,” “frictions,” or andDale W. Jorgenson(1966), Martin S. Feld- costsof trading claims on the present dis- steinand Lawrence Summers (1979),Feldstein countedvalue of future wages may be present etal.(1983), and others. The results of thetests for someindividuals, especially at low educa- ofmean-variancespanning between human and tionlevels and for someminorities. The empir- physicalcapital returns are shown in Table 4. icalanalysis can also explain the superiority of Twointeresting features are worth noticing. humancapital, at least at college levels, over First, the p-valuesof the tests are very similar to liquidinvestments. While the level of private thosein Table 3. This result is consistent with returnsto schooling in the literature is not suf- theidea (but does not imply) that Ž nancialcap- Žcientto justify the claims of importancemade italgains are largely associated with changing for educationin many areas of economics, the expectationsof futuredividends. Second, when analysisshows how it is possible to justify thenull hypothesis of coincidence of bound- thesuperiori tyof investme ntsin schoolin g ariesis rejected, the indicator Ds (m) of the bysimply accounting for theriskiness of the gainsper unit of risk is consistently lower (on investments. averageabout 20 percent lower) thanthe indi- Theanalysis can also be useful in other areas. catorobtained for Žnancialreturns, although For instance,to the extent that marriage and stillsizable. familiesserve to hedgesome risks and to diver- We concludefrom theseŽ ndingsthat the sifyhuman capital investments through altruism resultsobtained above are largely consistent orimplicitcontracts, the analysis may be useful withthose obtained using other approximations tothe understanding of marriage and divorce ofhuman capital returns and with those ob- markets,the structure of thefamily, and invest- tainedfor physicalcapital returns. mentsin the human capital of children. It may alsoshed light on the behavior of individuals IV.Concluding Remarks regardingtheir allocations among risky Ž nan- cialassets (bonds and stocks) and nontraded Theanalysis of capital returns, both human assetssuch as human capital. 21 Theempirical andŽ nancial,provides a backdropfor, and the subjectmatter of, several important areas of economics(human capital, labor economics, Ž - 21 See, forinstance, Niko Canner et al.(1997) and Luis nance).They are also important in manypublic Viceira (2001).Steven Davis andPaul Willen (2000) eval- policyareas, and in models of economicgrowth uate theportfolio choice and welfare implicationsof hedg- anddevelopment, macroeconomics, and busi- inglabor income risks with Ž nancialassets. Theresults in ouranalysis indicate that the less educatedindividuals nesscycles where microestimates of human wouldbe the ones that could beneŽ t themost from access to capitalreturns play a fundamentalrole in cali- Žnancialmarkets perhaps,for instance, through 401k and brationsand empirical analyses. The principal similar plans. 962 THEAMERICANECONOMIC REVIEW JUNE 2003

TABLE 4—MEAN-VARIANCE SPANNING TESTS FOR HUMAN AND PHYSICAL CAPITAL RETURNS

PanelA— Benchmark:Human Capital Assets White Males Black Males WhiteFemales Black Females GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) Nohighschool Experience:1– 5 0.020.02 14.81 0.00 0.00 18.90 0.01 0.01 15.22 0.03 0.00 15.06 6–15 0.00 0.01 22.70 0.00 0.00 16.02 0.00 0.01 15.33 0.02 0.00 21.88 .150.03 0.02 19.69 0.02 0.03 15.17 0.03 0.04 11.77 0.03 0.00 17.93 High school Experience:1– 5 0.040.00 14.02 0.00 0.02 13.18 0.21 0.32 6.33 0.71 0.75 0.83 6–15 0.03 0.01 15.21 0.04 0.04 15.88 0.25 0.30 5.06 0.63 0.56 1.32 .150.07 0.03 8.13 0.26 0.10 7.07 0.39 0.40 3.12 0.52 0.64 0.91 Somecollege Experience:1– 5 0.030.03 19.07 0.02 0.01 18.11 0.10 0.29 6.16 0.21 0.46 2.66 6–15 0.02 0.05 17.30 0.02 0.05 12.88 0.17 0.25 5.17 0.07 0.08 11.50 .150.27 0.22 4.61 0.22 0.17 7.23 0.07 0.17 6.07 0.31 0.52 3.21 College Experience:1– 5 0.380.42 1.89 0.60 0.76 0.67 0.58 0.47 1.57 0.84 0.72 0.03 6–15 0.51 0.39 2.84 0.57 0.90 0.30 0.41 0.54 0.92 0.69 0.48 2.90 .150.37 0.51 3.31 0.72 0.92 0.11 0.60 0.38 2.33 0.82 0.91 0.08 Morethan college Experience:1– 5 0.440.62 2.01 0.21 0.34 3.71 0.81 0.70 0.09 0.71 0.74 0.08 6–15 0.50 0.57 0.88 0.83 0.82 0.20 0.72 0.60 0.60 0.82 0.64 0.55 .150.41 0.40 2.53 0.89 0.77 0.63 0.28 0.41 1.28 0.04 0.01 12.12

PanelB— Benchmark:Physical Capital Assets White Males Black Males WhiteFemales Black Females GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) GMM LR Ds (m) Nohigh school Experience:1– 5 0.650.73 0.63 0.63 0.80 0.00 0.85 0.88 0.02 0.90 0.99 0.00 6–15 0.47 0.82 0.92 0.90 0.87 0.00 0.75 0.95 0.00 0.89 0.70 0.03 .150.58 0.71 0.81 0.98 0.96 0.00 0.74 0.99 0.09 0.77 0.77 0.87 High school Experience:1– 5 0.460.55 2.34 0.78 0.88 0.28 0.22 0.18 5.40 0.16 0.10 6.80 6–15 0.43 0.74 1.20 0.84 0.75 0.83 0.14 0.21 6.53 0.08 0.17 5.53 .150.21 0.21 6.50 0.22 0.11 6.82 0.06 0.10 11.22 0.08 0.03 9.82 Somecollege Experience:1– 5 0.720.83 0.09 0.92 0.64 0.41 0.10 0.10 8.23 0.21 0.20 6.60 6–15 0.64 0.92 0.12 0.63 0.76 0.50 0.11 0.15 6.66 0.16 0.17 5.40 .150.41 0.64 0.40 0.21 0.85 0.90 0.11 0.08 6.82 0.44 0.41 3.22 College Experience:1– 5 0.080.12 7.50 0.04 0.09 12.06 0.13 0.11 7.44 0.03 0.15 9.90 6–15 0.08 0.05 11.02 0.09 0.06 11.12 0.14 0.19 5.94 0.11 0.16 8.02 .150.03 0.06 11.60 0.08 0.07 11.02 0.09 0.08 8.66 0.02 0.09 9.03 Morethan college Experience:1– 5 0.050.11 9.12 0.12 0.08 7.82 0.05 0.00 11.40 0.07 0.04 10.44 6–15 0.03 0.07 13.66 0.03 0.03 9.50 0.02 0.01 14.04 0.10 0.10 7.06 .150.02 0.06 12.08 0.08 0.05 5.92 0.02 0.00 13.55 0.62 0.40 2.12

Note: Thistable reports the p-valuesof the GMM andLR tests inthe GMM andLR columns,respectively, and the estimated increase perunit of riskunder column Ds(m). resultsmay also be relevant to determine the sumption[Robert E. Hall(1988); Mulligan optimalsocial rate of discount to use in evalu- (2002)]. atingbeneŽ t andcost streams from publicin- Lastly,to the extent that the restrictions im- vestment(e.g., public education), and for the posedon the IMRS aredifferent for different analysisof intertemporal substitution in con- humancapital assets, and given that all individ- VOL.93 NO. 3PALACIOS-HUERTA:RISK PROPERTIES OF HUMANCAPITAL RETURNS 963 ualshold human capital assets, the analysis has Canner,Niko; Mankiw, N.Gregoryand Weil, implicationsfor theproperties of valid IMRS David N. “AnAsset Allocation Puzzle.” for modelsof dynamic economies and for some AmericanEconomic Review ,March1997, compellingquestions in these Ž elds:What are 87(1),pp. 181– 91. thefundamental sources of individual and ag- Card,David. “Estimatingthe Return to School- gregaterisk? How doesrisk affect the allocation ing:Progress on Some Persistent Economet- ofthe different classes of capital? After all, ricProblems.” Econometrica , September “ultimately,a satisfyingmodel of risk and re- 2001, 69(5),pp. 1127– 60. turnmust explain the magnitudes of therewards Davis,Steven and Willen,Paul. “RiskyLabor thatinvestors receive for bearing differentkinds Incomeand Portfolio Choice.” Mimeo, Uni- of risk”(Campbell,1996, p. 342). An open, versityof Chicago, 2000. importantquestionfor futureresearch is that DeRoon, Frans A. and Nijman,Theo E. “Testing ofŽndingthe classes of models,preferenc es, for Mean-VarianceSpanning: A Survey.” andmarket structure sthatmay be consiste nt Journalof Empirical Finance , May 2001, withhuman capital returns. The different 8(2),pp. 111– 55. restrictionsimposed on the IMRS bydiffer- DeSantis, Giorgio. “VolatilityBounds for Sto- enthuman capital assets suggest that they chasticDiscount Factors: Tests and Implica- maygreatly vary across educatio nlevelsand tionsfor InternationalFinancial Markets.” individuals. Ph.D.dissertation, University of Chicago, 1993. Fama,Eugene F. and Schwert,G. William. “Hu- REFERENCES manCapital and the Capital Market Equilib- rium.” Journalof Financial Economics , Acemoglu,Daron and Angrist,Joshua. “How January1977, 4(1),pp. 95– 125. LargeAre Human-CapitalExternalities? Ev- Feldstein,Martin S.; Dicks-Mireaux, Louis and idencefrom CompulsorySchooling Laws,” Poterba,James. “TheEffective Tax Rate and inBen S. Bernankeand Kenneth Rogoff, thePretax Rate of Return.” Journalof Public eds., NBERmacroeconomicsannual 2000. Economics, July 1983, 21(2),pp. 129 – 58. Cambridge,MA: MITPress, 2000,pp. 9 –59. Feldstein,Martin S. and Summers,Lawrence. Beckaert,Geert and Urias,Michael S. “Diversi- “Ination and the Taxation of Capital Income Žcation,Integration, and Emerging Market intheCorporate Sector.” NationalTax Jour- Close-EndFunds.” Journalof Finance , July nal,December1979, 32(4),pp. 445– 70. 1996, 51(3),pp. 835– 70. Griliches,Zvi and Jorgenson,Dale W. “Sources Becker,Gary S. Economictheory . New York: ofMeasured Productivity Change: Capital Alfred A.Knopf,1971. Input.” AmericanEconomic Review , March . Humancapital: A theoreticaland em- 1966, 56(1),pp. 50 –61. piricalanalysis with special reference to ed- Hall,Robert E. “IntertemporalSubstitution in ucation.Chicago:University of Chicago Consumption.” Journalof Political Econ- Press, 1993. omy,April1988, 96(2),pp. 339 – 57. Bils, Mark. “Commentto How LargeAre Hansen,Lars P.; Heaton, John and Luttmer,Erzo Human-CapitalExternalities? Evidence from G. J. “EconometricEvaluation of AssetPric- CompulsorySchooling Laws,” in Ben S. Ber- ingModels.” Reviewof Financial Studies , nankeand Kenneth Rogoff, eds., NBER mac- Summer 1995, 8(2),pp. 237– 74. roeconomicsannual 2000 .Cambridge,MA: Hansen,Lars P. and Jagannathan,Ravi. “Impli- MITPress, 2000,pp. 59 –68. cationsof Security Market Data for Models Buchinsky, Mosheand Leslie,Philip. “Educa- ofDynamicEconomies.” Journalof Political tionalAttainment and the Changing U.S. Economy,April1991, 99(2),pp. 225– 62. WageStructure: Some Dynamic Implica- Hause,John C. “TheRisk Element in Occupa- tions.”Working Paper No. 97-13, Brown tionaland Educational Choices: Comment.” University,1997. Journalof Political Economy , July 1974, Campbell,John Y. “UnderstandingRisk and Re- 82(4),pp. 803– 07. turn.” Journalof Political Economy , April He,Hua and Modest,David M. “MarketFrictions 1996, 104(2),pp. 298 –345. andConsumption-Based Asset Pricing.” 964 THEAMERICANECONOMIC REVIEW JUNE 2003

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