THE CASE FOR INTENSIVE SKILL-BIASED TECHNOLOGICAL CHANGE

Transcription

1 Page 67 THE CASE FOR INTENSIVE SKILL-BIASED TECHNOLOGICAL CHANGE Suar J. Fowler, Mddle Tennessee Sae Unversy Jennfer J. Fowler, Belmon Unversy ABSTRACT The skll-premum, defned as he relave wage of college o hgh-school graduaes, has seadly ncreased over he pas weny years. Though skll based echnologcal change (SBTC) s generally consdered o be he cause of he rse (Bound and Johnson 99), lle s known abou he processes ha have generaed he mprovemens n echnology. In hs paper, we consruc an nergeneraonal model of skll acquson for he purpose of evaluang wo heorecal alernave sources of SBTC. We fnd ha nensve SBTC s necessary for he complee characerzaon of he observed changes n he wage premum profle. An example of nensve SBTC ncludes echnologcal mprovemens n he acual acquson of sklls. In hs case, an neremporal subsuon effec generaes a reducon n he rae of skll acquson by he old hereby replcang an mporan fac found n he daa. INTRODUCTION The skll-premum, defned as he relave wage of college o hgh-school graduaes, has seadly and remarkably ncreased over he pas hry years. Roughly, he premum has rsen abou % per year mplyng ha he relave wage rae s hree mes as hgh as was n 980, he year he premum began o ncrease. Skll based echnologcal change (SBTC) s generally consdered o be he cause (e.g., Bound and Johnson, 99; Auor, Kaz, and Krueger, 998; Guvenen and Kuruscu, 00). In hs case, echnologcal advancemens n he producon of goods cause he relave margnal producs of sklled o unsklled labor o rse. Ths form of SBTC has been examned n a dynamc general equlbrum framework by Heckman, Lochner, and Taber (998) and has been found o explan he rsng average skll premum reasonably well. Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

2 Page 68 Recenly, however, he causaly of SBTC has been called no queson by Card and DNardo (00). Ther argumen can be found n Fgure. They ask, why hasn' he wage gap profle, ha represens he logged skll-premum by age, ncreased for every age group? Presumably, because SBTC necessarly predcs an equal change n he demand for all levels of sklled labor, Card and DNardo (00) label he behavor of he skll premum a cohor levels a puzzle. Though her emprcs rase quesons, a poenal explanaon can be heorzed when SBTC s combned wh lfe-cycle moves. For example, could be he case ha an ncrease n he reurn o sklled labor causes hose wh relavely more sklls (mddle o older aged workers) o economze on her skll acquson acves hereby recevng a small wage premum. The younger workers, and herefore he less sklled, neremporally subsue no he acquson of sklls and herefore receve a larger wage premum. The oal effecs of he combned lower skll acquson raes by he old and hgher skll acquson raes by he young are a seeper skll acquson profle and a flaer wage gap profle. The purpose of hs paper s wofold. Frs, we consruc an nergeneraonal model of skll acquson for he responses of lfe-cycle educaonal expendures from a SBTC. The heorecal analyss employs a dynamc general equlbrum overlappng generaons (OLG) model of skll acquson drawng from Heckman (976), Auerbach and Kolkoff (987), Heckman e al. (998), Fowler and Young (004), and Guvenen and Kuruscu (00). The model represens an exenson n one mporan way: he unsklled do no parcpae n rsky capal markes. Ths feaure replcaes he well-known fac ha equy ownershp and educaon Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

3 Page 69 aanmen are hghly correlaed (Halassos and Berau, 995; Berau and Sarr-McCluer, 00) and a large percenage of he populaon, roughly 43.%, never hold rsky equy asses (Mankw and Zeldes, 99; Guso, Halassos, and Jappell, 00). An neresng feaure ha resuls from he model's skll acquson secor and lmed parcpaon assumpon s ha based echnologcal mprovemens (n favor of sklled labor) can ener n wo mporan ways: he fnal goods secor and he skll acquson secor. If he relave producvy of sklled labor ncreases n he fnal goods secor, hen he demand for sklls s ndrecly affeced. Alernavely, f he labor's producvy n he acquson of sklls ncreases, hen he demand for sklls s drecly affeced. Technologcal change occurrng hrough he demand for labor va he producon of goods s labeled exensve SBTC and hrough he supply of labor va skll acquson s denoed nensve SBTC. Unl now, exensve SBTC has been he focus of sudy whn he leraure. We fnd ha he exensve margn alone canno accoun for a flaer wage gap profle. Insead, a combnaon of exensve and nensve SBTC s requred o replcae hs puzzlng emprcal fac. In hs case, he older aged workers economze on her skll acquson acves whle he younger workers subsue no he acquson of sklls. As predced, he skll acquson profle s seeper and he wage gap profle s flaer. Therefore, we make he case ha nensve SBTC, and he effecs has on he acquson of sklls, s also a key for our undersandng of he oal effecs of skll based echnologcal change. The dervaon of he heorecal hgher educaon consumpon profle also serves for a comparson o our second man purpose; o emprcally examne he neremporal subsuon effec heory. More specfcally, hs paper uses he Consumer Expendure Survey (CEX) daa se o esmae he lfe-cycle profles of he consumpon of hgher educaon. Changes n he educaon consumpon profle ha are conssen wh an neremporal subsuon effec would necessarly mply a seepenng of he skll acquson profle; he young and old respecvely ncrease and decrease spendng on he acquson of sklls. The esmaon echnque employs he Heckman (979) model of self-selecon. By esmang educaon lfe-cycle profles, and her subsequen changes over me, we documen a sgnfcan seepenng of he skll acquson profle over he years The organzaon of he paper s as follows. Secon develops he OLG model of skll acquson and of he skll premum. Secon 3 quanfes he dynamcs of he heorecal model. Secon 4 documens he emprcal mehodology and daa sources. Secon 5 quanfes he dynamcs of he emprcal model. Fnally, Secon 6 concludes. THE THEORETICAL MODEL OF HUMAN CAPITAL The heorecal analyss employs an overlappng generaons (OLG) model of producon and skll acquson by drawng from Ben-Porah (967), Heckman (976), Auerbach and Kolkoff (987), Heckman e al. (998), Fowler and Young (004), and Guvenen and Kuruscu Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

4 Page 70 (00). The OLG model allows for he replcaon of heerogeney n households wh respec o her age and hgher educaon ype. Whn he model, here are wo ypes of agens ha make economc decsons: households and frms. In conras o he prevous leraure, access o he producon and skll acquson secor s assumed o be lmed: hs furher dsngushes wo subgroups of sklled and unsklled households. The unsklled do no o have access o capal, eher human or physcal, because of cred consrans; he cred consrans do no perm he acquson of sklls and hus allow us o label he cred consraned as he unsklled. As a resul, skll-based echnologcal change may ener he model n boh he skll acquson secor and he producon secor. Technologcal change n he producon secor alers he relave producvy of good producon. Technologcal change n he skll secor alers he relave producvy of skll aanmen. Sklled based echnologcal change occurrng hrough he demand for labor va he producon of goods s labeled exensve SBTC and hrough he supply of labor va skll acquson s denoed nensve SBTC. A any gven me he household secor comprses several generaons ha are overlappng. For analyss purposes, aduls are defned as hose ndvduals of college age - 8 years of age and older. Each perod, one generaon des and anoher akes s place. Agens from generaon lve for I perods, rere afer I R I perods, and hen de. Therefore, a any pon n me here s a se of agens ndexed by I = { 0,,, K, I }. For smplcy, no bequess or nherances are consdered n hs model. Whn each age cohor, ndvdual ases and nal capal socks are assumed o be dencal. Thus, he use of a represenave agen for each generaon enables one o descrbe he aggregae behavor of a generaon by he behavor of a sngle member Sklled Households Sklled agens n he model make lfeme decsons abou consumpon, savng, and lesure over her lves. Le u ( c +, l + ) be he flow of uly from consumpon, c, and lesure, l, a me + of an agen born a me. Le lfeme expeced uly of an agen born a me be represened by I E β Ψ u( c +, l + ), 0 () = where β s a me preference dscoun facor such ha 0 < β < and Ψ = j=0 ψ j denoes he uncondonal probably of survvng up o age wh each ψ j represenng he condonal probably of survvng from age j o j. Assume ha u ( ) s real valued, dfferenable, srcly ncreasng, and srcly concave. The me endowmen s normalzed such ha Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

5 Page 7 n, +, = + n l, () where n s me devoed o labor, n s me devoed o human capal accumulaon or skll acquson (me spen sudyng). Each ndvdual s born wh an nal level of human capal or nnae ably and chooses wheher or no o add o he endowmen, h + > 0. The budge consrans of a ypcal consumer born a me a any me +, sasfyng I 0, are gven n equaon (3): c ( + k + + +, k + r δ ) k + ( τ ) w h n ss, (3) where k represens physcal capal accumulaon, r s he reurn o physcal capal, δ K denoes he deprecaon rae assocaed wh physcal capal, τ s a labor ax o fund socal secury benefs ss o he old, and wh s he real effecve wage rae of sklled workers. Snce here are no bequess and nherances, agens nves n physcal capal by consumng less n her workng years han hey earn n wages. Accordngly, he nal level of physcal capal, k, s se equal o zero. Addonally, he old consume all goods and savng n her fnal perod of lfe mplyng ha k + I = 0. Human capal accumulaon s consraned by he followng: h + + h, + + n, +, + h + q h + q n + ( δ ) h, (4) where δ h denoes he deprecaon rae assocaed wh human capal. The q funcons represen he margnal producs for he facor npus o human capal producon. They are aken as gven by each agen and defned as: q q h, + n, + θ exp( a θ exp( a + + )( h )( h + ) θ ) θ + ( n ( n, + ) ) θ, + θ, where θ represens he prvae reurn on he exsng sock of human capal, θ measures he prvae reurn o sudy hours, h denoes exsng human capal used n he producon of fuure human capal, or he ably o earn, and a s an ably o learn parameer and represens an exogenous shf n oal effcency of human capal formaon for all I (For smplcy, he npu of physcal capal no he producon of human capal s gnored. Alhough hs assumpon seems resrcve, one can argue ha may no be a serous problem snce human Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

6 Page 7 capal producon s lkely o be relavely labor-nensve (Heckman e al., 998; and Fowler and Young, 004)). Because he margnal producs wh respec o exsng human capal and skll acquson hours of he rgh-hand sde of equaon (4) wll defne he reurns o human capal producon, we noe ha θ, θ, a, and h all affec he reurns o human capal producon. The oal produc s defned as he sum of he margnal producs and s gven by he funcon: Unsklled Households q + +, , + θ θ ( a, h, n ) = ( θ θ )exp( a )( h ) ( n ). For he agen who s unsklled, all earned wages are consumed and no savng akes place; he agen s assumed cred consraned and hus canno nves n human or physcal capal. The general model of equaons () (4) s modfed by: subjec o: I ~ max ( ~ E, ), { ~, ~ Ψ + +, } 0 0 β u c l I c + n + = = ~ ~ ) ~ ( ~ τ w h n su, (5) c + +, ~ ~ and h + + = ( δ h) h + where w ~ h ~ s he real effecve labor wage rae for unsklled workers. Also, τ s a socal secury ax rae used o fund paymens su o he old households. Agan, he ndvdual has no ably o accumulae human capal beyond her nal endowmen gven he cred consrans; hus, unsklled human capal merely deprecaes over me. The Frm The represenave frm s assumed o be nfnely lved, behaves compevely, and maxmzes he curren value of he frm by renng physcal capal from he old and hrng labor hours -- human capal -- from he sklled and unsklled young. Physcal capal s assumed homogeneous, whle labor dffers n s producve ably. The frm ulzes capal and labor, boh sklled and unsklled, subjec o a consan elascy of subsuon (CES) producon echnology. More specfcally, he aggregae oupu from a frm s produced accordng o: Y ~ F( K,, ) = N N αk σ + ( α)( λn σ + ~ σ ( ) ) σ σ σ λ N, (6) Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

7 Page 73 I I where K = = 0 k represens aggregae physcal capal, N = = 0 h n, s aggregae sklled ~ I ~ labor, and N = = h n~ 0, s aggregae unsklled labor. The parameer α s he ncome share parameer of physcal capal n oal ncome. The parameer λ represens he ncome share of sklled labor n oal labor ncome. The parameers σ and σ govern he elascy of subsuon beween physcal capal, sklled labor and unsklled labor. Specfcally, /( σ ) s he elascy of subsuon beween sklled and unsklled labor, /( σ ) represens he elascy of subsuon beween physcal capal and labor - sklled and unsklled. Profs of he frm, ha are o be maxmzed, are: ~ π = F K, N, N ) r K ~ w~ N. ( w N Compeve behavor by he frms ensures ha facors are pad her margnal producvy. The margnal producvy condons are gven by: ~ ~ ~ F K, N, N ) = r, F ( K, N, N ) = w, F ( K, N, N ) = w~, ( 3 where ~ F ( ) = F( K, N, N ) / K, for example. Characerzaon of he Saonary Equlbrum Opmal behavor by he households ensures ha he followng Euler equaons, n addon o he budge consrans, hold for each agen n each me perod. Every sklled agen wll have hree Euler equaons: () nvesmen n physcal capal; () amoun of sklled work n producon; and () nvesmen n human capal - he amoun of skll acquson. The Euler equaons are derved by comparng he margnal coss and margnal benefs assocaed wh each ype of consumpon and savng acvy. Frs, he Euler equaon for nvesmen n physcal capal s derved by consderng he rade-off beween consumpon and savng. Suppose he household from generaon nvess n a un of me physcal capal. The margnal cos s he los me un of consumpon; n uly hs s defned as he margnal uly of a un of consumpon: u u( c, l, ) =. c, Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

8 Page 74 In erms of margnal benef, he agen receves he dscouned gross reurn on capal ( + r + δ k ) ; dscouned by βψ τ + and he margnal uly of one more un of consumpon: u u( c+, l = c, +, + + Equang margnal benefs and coss gves he Euler equaon n (9): ). u { u, + ( + r δ )}., = Eβψ τ + + k (9) Second, he Euler equaon for a sklled worker s derved by consderng he rade-off beween work and lesure. Suppose ha he agen works one exra hour a me. Then he margnal cos s he me los lesure; n uly hs s defned as he margnal dsuly of a un of labor: u u( c =, n n,,, n, ). In erms of margnal benef, he agen receves an exra hour of effecve wages mes he margnal uly assocaed wh an exra un of consumpon, w h u,. Equang he margnal benefs o he margnal coss gves anoher Euler equaon (0): u = u ( τ ) w h. (0) Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0,, Thrd, he Euler equaon for nvesmen n human capal s derved by consderng he rade-off beween obanng an addonal un of human capal and lesure. Suppose ha he agen nvess n one un of me human capal. The margnal cos s he ou-of-pocke and opporuny cos assocaed wh purchasng one more un of human capal and he me los lesure; n uly hs s defned as he margnal uly of a un of human capal, u3, / qn,. In erms of margnal benef, he agen receves he dscouned gross reurn on human capal from work w qn, n, dscouned by βψ τ + and he margnal uly of one more un of human capal. Addonally, gven he nvesmen n human capal, s now easer for he household o oban fuure human capal - mplyng learnng beges learnng or ha sklls acqured early faclae laer learnng by ncreasng he margnal produc of n. The benef of learnng beges learnng s he margnal produc of he human capal producon funcon, q h,. Equang he margnal benefs and coss gves ():

9 Page 75 u q 3, n, u 3, + = Eβψ + u, + ( τ ) w + n, + + ( [ q + + ]) h, δ h () qn, + By he same logc, one could derve he Euler equaon for he unsklled worker. Snce ha se of workers canno nves n eher human or physcal capal, here wll be only one Euler equaon and s found by consderng he rade-off beween work and lesure: u~ ~ ~ ) ~, = u, ( τ w h () Exensve versus Inensve SBTC The parameer λ s sklled labor's share n oal labor. Alernavely, we can renerpre λ as sklled labor's share mes a echnologcal parameer ha deermnes he producvy of he sklled. The rao λ /( λ ) s sklled labor's relave echnologcal progress ha occurs n he producon of fnal goods. Snce frms pay labor her margnal producs, he relave wage of sklled o unsklled s drecly deermned by λ /( λ ). Therefore, an ncrease n λ s a SBTC. We denoe hs ype of echnologcal change as exensve SBTC. An neresng feaure ha resuls from he model's skll acquson secor and lmed parcpaon assumpon s ha based echnologcal mprovemens (n favor of sklled labor) can ener n anoher mporan way: he skll acquson secor. If he labor's producvy n he acquson of sklls ncreases, hen he demand for sklls s affeced causng he skll premum o change. Technologcal change occurrng hrough he supply of labor va skll acquson s denoed nensve SBTC. Inensve SBTC can occur from changes n he se of parameers { h, θ, θ, a}. An example of he exensve ype of echnologcal change may be he nroducon of compuers; he producvy of sklled-workers, who mos lkely use he echnology, ncreases relave o he unsklled (Johnson 997). Inensve skll-based echnologcal change arses n he skll acquson secor and occurs when he margnal produc of sklled workers ncreases whou necessarly decreasng he margnal produc of unsklled workers. An example of hs ype of echnologcal change may be he nroducon of he Inerne a campus lbrares. The acual acquson and, poenally, he reenon of sklls become more effcen. Calbraon Calbraon of he model requres he lengh of he lfe-cycle, a funconal form for uly, and a varey of parameers o be se. The parameers form four groups: preferences, producon, Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

10 Page 76 skll acquson, and polcy. Table below provdes a lsng of he nal model parameers, descrpons, and values. Frs, he lengh of he lfe-cycle, I, mus be deermned. In he OLG leraure, agens ypcally make economc decsons over a 63-year perod wh reremen begnnng a age 66. For hs analyss, economc lfe sars a age 8, whch mples ha he ermnal age s 80. To keep compuaon of he equlbra manageable, however, he lfe-cycle s condensed. Because few people graduae from college n less han 5 years, each perod n he model chosen represens a 5-year me span. As such, he lengh of he lfe-cycle becomes I = perods. Each agen des a age 77 or a he end of perod. For he sklled, reremen s assumed o begn a age 63, or a he end of perod 9. Reremen represens he hree perods where sklled labor 0 hours are exogenously se o zero, n, = n, = n, = 0. As a resul of he exogenously se reremen age, skll acquson hours sop afer perod egh snce workers would no have enough me o be n he labor force o make skll acquson worhwhle; hus, 9 0 n, = n, = n, = n, = 0. These assumpons are also made for he unsklled; he unsklled are requred o rere a he end of perod 9. Table : Baselne Model Parameers, Descrpons, and Values Parameer Descrpon Preferences μ = Arrow-Pra measure of rsk averson μ = = Deermnes he neremporal labor supply elascy φ =.5 Wegh parameer on lesure β = Dscoun facor for me preferences Producon σ = Deermnes demand elascy of subsuon beween sklled and unsklled labor σ = Deermnes demand elascy of subsuon beween physcal capal and labor α = 0.34 Share of physcal capal o oal labor λ = 0.5 Share of sklled labor o oal labor δ K = 0.66 Deprecaon rae of physcal capal, 6% per year = 0 Inal level of physcal capal Skll Acquson θ = 0.5 Prvae reurn on exsng human capal sock θ = 0.5 Prvae reurn on sudy hours = 3.6 Inal level of human capal of sklled = 9.53 Inal level human capal of unsklled = 0 Ably o learn δ h = Deprecaon rae of human capal Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

11 Page 77 Parameer Polcy τ = 0.4 Table : Baselne Model Parameers, Descrpons, and Values Descrpon Socal Secury ax rae Preferences ulzng he convenonal power uly specfcaon are chosen: u ( c, n, n ) μ c = + ϕ μ ( n n ) μ μ. The separable form of uly s chosen for wo man reasons: () perms one o separae he neremporal elasces of consumpon and lesure; and () s commonly used n he dynamc macroeconomc leraure (e.g., Heahcoe, Soresleen, Volane, 004). The parameer μ represens he Arrow-Pra coeffcen of relave rsk averson. The parameer's value s resrced o he lmng case where μ = so ha preferences wll be conssen wh balanced growh. As μ approaches, he consumpon poron of he uly funcon collapses o he log of consumpon. The parameer μ deermnes he neremporal labor supply elascy; seng μ = falls whn he range of exsng esmaes found n he mcro and macro leraure (Brownng e al. 999). Followng Heahcoe e al. (004), he parameer ϕ denoes he wegh parameer on lesure and s se such ha he average fracon of me devoed o work s roughly 0.33; hs resuls n a value of ϕ =. 5. A value s needed o dscoun preferences over me; β = /(.03) 5 = s chosen o be compable wh a yearly psychologcal rae of hree percen. The survval probables are esmaed by converng he annual moraly probables from he U.S. Lfe Tables of he Naonal Cener for Healh Sascs (99) o he I = lfecycle. The values for survval probables are presened n Table. Table :Calbraons for Survval Probables Ψ 0 = Ψ = Ψ = Ψ 3 = Ψ 4 = Ψ 5 = Ψ 6 = Ψ 7 = Ψ 8 = Ψ 9 = Ψ 0 = Ψ = Ψ = As ndcaed n equaon (6), producon has fve man parameers o calbrae, σ, σ, δ k, α, and λ. The parameer σ represens he demand elascy of subsuon beween sklled and unsklled labor. Ths value s se a σ = gvng an elascy of.5, conssen wh esmaes found n he leraure (e.g., Brownng e al., 999; Auor, Kaz, and Kearney, 008). Krusell, Ohanan, Ros-Rull, and Volane (000) esmae he parameer governng he Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

12 Page 78 demand elascy of subsuon beween capal and labor a σ = 0. 05, resulng n an elascy of subsuon close o ha s no oo dfferen han he Cobb-Douglas specfcaon beween capal and labor ( σ = 0 ) found by Heckman, e al. (998). As a consequence, α s roughly capal's share of oupu whch Heckman e al. (998) repor a α = Nex, he value 5 for deprecaon of physcal capal s needed; δ k = ( 0.06) whch mples a sx percen annual deprecaon rae, an average of he esmaes mos commonly found n he dynamc macroeconomc leraure. The remanng parameer of he producon funcon λ s se o mach he wage premum for he begnnng of he 980's decade of approxmaely.30 (Card and DNardo, 00) whch gves a share of sklled labor n oal labor of λ = A fnal group of parameers s needed for skll acquson. As saed prevously, he parameer θ represens he prvae reurn on he exsng sock of human capal whle he parameer θ measures he prvae reurns o sudy hours. There s a wde range of esmaes found n he leraure (e.g., Ben-Porah, 967; Heckman, 976; Rosen, 976; Brownng e al., 999). The wo parameers are resrced by 0 θ < and 0 θ so as o guaranee ha he human capal producon funcon s concave n he conrol varables. Because we conduc comparave sacs on hese parameers, we ulze he lower end of he parameer esmaes lsed n Brownng e al. (999): θ = θ = The nal levels of sklled and unsklled human capal mus be se. The skll levels are se accordng o hose denfed by Heckman e al. (998). Inal sklled human capal s se o h = 3. 6 and unsklled human capal s se o ~ h = Esmaes for a and δ h are needed o complee he calbraon of skll acquson. The ably o learn parameer s nally se o a = 0. The level of human capal deprecaon s nally se very close o zero, δ h = o allow for some loss n skll f human capal s no developed. The curren U.S. socal secury payroll ax s.4% mplyng τ = Though he program s pay-as-you-go, benefs are ed o conrbuons so as o guaranee a specfc replacemen rae of reurn. We ake hs o mply ha he socal secury conrbuons of he sklled are used o fund he rered sklled work force; hey are equally spl beween he hree oldes generaons of sklled rerees. Lkewse, he conrbuons of he unsklled are used o fund he reremen of he unsklled workers; hey are equally spl beween he hree oldes groups of unsklled rerees. MODELING RESULTS Usng he nal calbraons denfed n Table, he baselne model s solved. Because he baselne resuls wll be used as comparson for he forhcomng expermens, s mporan o assess he model's performance. Frs, Table 3 shows ha he model s able o replcae, Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

13 Page 79 roughly, aggregae labor hours. Though sklled workers do no work as many hours as unsklled workers (her human capal s more valuable and brngs a hgher wage rae), he average me spen n goods producon s ( ) / = 33.04%. Consumpon s raher unequal; he mpled Gn coeffcen for sklled o unsklled consumpon s 6%. In he daa, he U.S. consumpon Gn s n he range of 5-9% (Blundell 006). Gven ha he sklled nvesmen n human capal s abou 3.8% of oal consumpon (0.047 / ( ) = 0.038), human capal non-rvally ncreases wh age o from he nal sarng pon - he acquson of sklls s an mporan margn of choce for he sklled. Fnally, he average skll premum of.308 s conssen wh ha repored by Card and DNardo (00). Recall ha skll-specfc wages are gven by: w, = w h, and w, = w h,. The wage gap, or he logged skll premum, s defned as: log(w, /w ĩ, Table 3: Seleced Seady Sae Allocaons Baselne Measure Mean Sklled Labor Hours Unsklled Labor Hours Sklled Consumpon of Goods.83 Unsklled Consumpon of Goods Skll Acquson Expendures Human Capal Skll Premum.3088 Fgure llusraes he seady-sae profles of he baselne model. Fgure (a) shows ha consumpon exhbs he ypcal hump shape conssenly found n he lfe-cycle leraure. The mplcaon s ha households do no perfecly smooh consumpon by age. Ths s a drec resul of he assumpon of no ncome nsurance markes. Skll acquson expendures, Fgure (b), appear o be conssen wh economc logc and wh hose found hroughou he leraure as well. For example, as one ages here s less me o recoup he benefs of addonal years of schoolng. As such, makes sense ha spendng on hgher educaon servces (.e., skll acquson expendures) should fall wh age. Gven ha he young are relavely poor n human capal, s no surprsng o see human capal, Fgure (c), rse wh age as well as he logged skll premum, panel (d). The wage gap corresponds ncely o Fgure ha s aken from Card and DNardo (00). The nex sep s o evaluae he effec of changes n skll-based echnology; he followng several paragraphs accomplsh hs ask. The frs expermen adjuss he baselne model by ncreasng λ from 0.5 o 0.56; roughly a 0% ncrease. Fgure 3(a) plos he effecs of hs exensve SBTC on he wage premum. As expeced, he relave margnal produc of sklled Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

14 Page 80 workers ncreases for all ages. As a resul, he wage gap ncreases unformly across age. The mpac on he average wage gap s abou 8%, ncreasng from o Alhough he ncrease n λ s relavely small, he mpac on he wage premum s large bu conssenly whn he range of skll premums n he leraure (Card & DNardo, 00; Krueger, 003). Fgure 4(a) plos he effec of ncreasng λ by 0% on skll acquson expendures. We see for he young, skll acquson expendures rse; hs s a subsuon effec. Apparenly, he hgher relave wages from havng sklls nduces he young o subsue no he acquson of sklls. Fgure : Seady Sae Profles for he Baselne Model Fgure 3(b) plos he effec on he wage gap of a 0% ncrease n he nal sock of sklled human capal (he ably o earn). The hgher level of human capal ncreases he wage gap evenly across all age groups. However, he average ncrease n he wage premum s abou 3% mplyng ha he exra supply of human capal somewha dmnshes he sklled-o-unsklled wage. Presumably, he combnaon of ncreased supply of sklled labor and ncreased producvy of he unsklled (snce hey are complemens) causes log( w / ~, w, ) o fall. Fgure 4(b) shows he effec on human capal expendures; here s lle o no change n expendures Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

15 Page 8 on hgher educaon. Ths oal effec s due wo compeng nermedae effecs cancellng. In he frs case, he exra nal human capal ncreases he wage reurn of an addonal human capal un and, as a resul, he household demands more human capal. Alernavely, he margnal produc of he acual reurn o skll producon falls snce q h / h < 0. As a resul, boh effecs cancel hus leavng consumpon of hgher educaon unchanged. Now consder he effecs of a 0% ncrease o he prvae reurn on he exsng sock of human capal θ. Fgure 3(c) plos he effecs of hs ype of nensve SBTC; we see ha he wage gap sars below and hen rses above he exsng profle. The ncrease n he prvae rae of reurn on exsng human capal ncreases he acquson of human capal; hs s confrmed n Fgure 4(c). The ncrease n sklled human capal has hree compeng effecs. Frs, he ncrease n human capal ncreases he wage for he unsklled, w ~ h ~, as hey are relave complemens o he sklled. Second, because he sklled wage rae, w, s a decreasng funcon of sklled human capal, he wage for he sklled falls. Alernavely, for a gven sklled wage rae, he effecve sklled wage rae, w h, ncreases. In oal, he young sklled - who are relavely human capal poor - see her relave wage fall snce hey have no accumulaed enough human capal o offse he negave effecs on her relave wage rae. Fgure 3(d) plos he effecs of a 0% ncrease o he prvae reurn on sudy hours θ. The wage gap sars above and falls below he exsng profle. Because sudy hours are more effecve, he household can shf more me no lesure acves; hs s an ncome effec. The shf no lesure acves s evden n Fgure 4(d) where nvesmen n human capal falls for all age groups. As a resul, he sklled enjoy he ncrease n sudy hour producvy when hey are young. Those wh relavely more sklls (mddle o older aged workers) see a lower skll premum snce hey economzed on her skll acquson acves when hey were young. Fgure 3(e) plos he effecs on he wage gap of a 0% ncrease o he ably o learn a. Jus lke he ncrease n he prvae reurn on he exsng sock of human capal n Fgure 3(c), he wage gap sars below and rses above he exsng profle. Agan, he ncrease n he producvy of human capal acquson has hree compeng effecs. The resulng effec s ha he young see her relave wage fall snce hey have no accumulaed enough human capal o offse he negave effecs on her relave wage rae. Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

16 Page 8 Fgure 3: The Effecs of Dfferen Types of SBTC on he Wage Premum (a) Exensve SBTC: % λ=.0 (b) Inensve SBTC: % h = Wage Gap Baselne % λ= Baselne % h= Age Group Age Group (c) Inensve SBTC: % θ =.0 (d) Inensve SBTC: % θ = Wage Gap Baselne % θ = Baselne % θ = Age Group Age Group (e) Inensve SBTC: % a=.0 Wage Gap Age Group Baselne % a=.0 Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

17 Page 83 Fgure 4: The Effecs of Dfferen Types of SBTC on Skll Acquson Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

18 Page 84 Fgure 5: The Effecs of Combned Types of SBTC on he Wage Premum & Skll Acquson Now consder Fgure 5 ha plos he effecs of a combnaon of dfferen ypes of SBTC. More specfcally, we ncrease λ by 5% and ncrease θ and a by 0%. Fgure 5(a) shows ha he wage gap profle shfs up a an unequal rae. More specfcally, he ncrease n relave wages s larger for he young han he old. Fgure 5(b) shows ha he unequal shf n he wage gap s arbued o he fac ha each household neremporally subsues her consumpon of hgher educaon more owards her younger years. The fac ha he rae of reurn o human capal s hgher causes he young he ncrease hours of sudy me. Alernavely, he old subsue away from sudy hours and presumably no consumpon and lesure. Graphcally, s apparen ha he exensve SBTC parameer has he greaes mpac on he skll premum and s assocaed wage gap. Bu, n erms of he emprcal facs of he wage gap, exensve and nensve SBTC alone do no provde an answer o Card and DNardo's (00) crque of he SBTC hypohess found n Fgure ; namely ha he wage gap changes very lle n older age groups. Insead, a combnaon of boh exensve and nensve SBTC s needed o accoun for he flaenng of he wage gap profle. THE EMPIRICAL MODEL OF HUMAN CAPITAL ACQUISITION The heorecal resuls show ha household spendng on hgher educaon servces shfs when SBTC occurs. Though a varey of macroeconomc sudes have esmaed lfe-cycle consumpon profles (Gournchas and Parker 00; and Fernandez-Vllarverde and Krueger Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

19 Page 85 00), none have specfcally focused on hgher educaon expendures and, f hey exs, shfs across he lfe-cycle. Thus, our sudy bulds upon he work of Gournchas and Parker (00) and Fernandez-Vllarverde and Krueger (00) - who esmae reduced form demands for consumpon excludng hgher educaon servces - and exends her framework o he consumpon of hgher educaon. The Daa To develop and esmae he hgher educaon consumpon profles and subsequen changes over me, a varey of daa sources are ulzed. Frs, and foremos, U.S. Bureau of Labor Sascs' (BLS) Consumer Expendure Survey (CES) s ulzed o gaher spendng and demographc daa on households. The CES has he bes avalable daa on household consumpon. Approxmaely 5,500 households are nervewed quarerly across he Uned Saes. Each household remans n he survey for four consecuve quarers afer whch hey are roaed ou and replaced by a new household - also called a roang panel. The daa used cover he me perod of 98:-00:4; a me frame conssen wh Card and DNardo (00). Nex, he BLS average U.S. regonal unemploymen raes are used o proxy busness cycle effecs. Fnally, he BLS's regonal Consumer Prce Index - All Urban Consumers base year - s used o deflae all dollar denomnaed daa. We make several modfcaons o he daa. Frs, we drop he households ha do no complee all four quarerly nervews. Ths reduces he sample o abou 78,43 households. Second, he CES asks each member of he household f hey are enrolled n college and an accepable mssng response s repored f he famly member s no qualfed for college. For example, a mssng response s repored for a wo year old as well as a 70 year old who has no compleed hgh school. Households who do no have a leas one qualfed member for each quarer are dropped from he sample leavng 67,76 households. A plo of real hgher educaon expendures by age of he head of household would no necessarly gve he skll acquson profle of an ndvdual - an emprcal profle would presumably be upward slopng for ceran age groups. There are wo man reasons why spendng on hgher educaon may be upward slopng. Frs, spendng by households mos lkely ncludes spendng on oher famly members who would be of college age furher no he head's lfe-cycle. Second, par-me suden enrollmens have a clear humped shaped paern wh a dsnc peak; he peak occurs n he lae wenes. Therefore, for denfcaon of he ndvdual and full-me skll acquson profle, we jonly pursue wo denfcaon sraeges. In he frs, we denfy he members of he famly who are n college. Though he CES only gves famly expendures on hgher educaon (aggregaed), he ncol varable allows us o model he aggregaon of he ndvdual o he famly level. Specfcally, because he famly members enrolled are denfed, we are able o compue he average age of famly members enrolled (age) so ha may be relaed o he average real Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

20 Page 86 spendng, relave o hose enrolled, on hgher educaon (hed). Real spendng on hgher educaon s defned as uon for college plus school books, supples and equpmen for college all deflaed by he prce ndex. In he second par of he sraegy, we denfy hose ndvduals who are par-me sudens (par) from he ncol varable. Then, he par varable s neraced wh he age of he enrolled member, age, so as o compue he average age, relave o hose enrolled, of par me sudens (agepar). The nex secon more formally descrbes he esmaon model. Fgure 6 llusraes he average real hgher educaon expendures of enrolled sudens, hed, by he average age of enrolled sudens age for he me perods of 98: o 00:4. The daa used for Fgure 6 were spl no age cohors, meaned by decade, by spenders (hose households who spend on hgher educaon), and by full-me sudens. The daa anecdoally verfy ha real spendng has conssenly ncreased over he perods 98:-99: o 99:3-00:4 for mos, bu no all, age groups. In fac, he old have appeared o decrease her spendng. Fgure 6: Mean Household Hgher Educaon Expendures 99:3-00:4 98:-99: Average Age Table 4 lss he oher varables ha are exraced from he daa ses for he purpose of denfcaon of he skll acquson profle. Mos varable descrpons are self-explanaory bu some may need furher explanaon. The varable chldeq0 represens a scale of he number of chldren age 8 and under n each household. Employng a mehodology smlar o Fernandez- Vllaverde and Krueger (00) and Brownng and Ejrnæ s' (00), a household equvalence scale, chldeq0, s esmaed for famly j of sze famsze as follows: j Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

21 Page 87 chldeq0 famsze = j age μ 0 + μ 8 age + μ 8 age + μ3 8 3 ( d ) = where age s equal o he maxmum of he 'h famly member's age or 8, { μ 0, μ, μ, μ3} s he se of chld response parameers used o approxmae he age effecs of chldren, and d s a zero-one dummy represenng an adul when age s greaer han 8. Noe ha f he ndvdual age s greaer han 8 years old, hen d =. The resrcon μ3 = μ0 μ μ s mposed so ha he funcon s connuous. Employng esmaes from Brownng and Ejrnæ s (00), he chld response parameers have he followng values: μ 0 = 0. 09, μ =. 469, and μ 5. = 73. Varable Dependen Varables: Table 4:Descrpve and Summary Sascs of Daa Descrpon Mean: All HHS Mean: Spenders hed0 0/: hgher educaon parcpaon hed Real average household spendng on hgher educaon Famly Varables: age0 Age of head of household age0 Squared age of head of household mws0 0/: lve n urban Md-Wes sh0 0/: lve n urban Souh wes0 0/: lve n urban Wes rural0 0/: rural resdence blk0 0/: black head of household ohrc0 0/: oher han Caucasan or black race head of household fem0 0/: female head of household mar0 0/: marred head of household nohs0 0/: no hgh school dploma for head of household hs0 0/: only hgh school dploma for head of household chldeq0 Number of equvalen chldren n household colage0 Number of college-age people n household, excl. head dyr0 0/: ndcaor of me: 99:3-00: age0dyr0 Ineracon: age of head of household and me age0dyr0 Ineracon: squared age of head of household and me Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

22 Page 88 Varable Member Varables: Table 4:Descrpve and Summary Sascs of Daa Descrpon Mean: All HHS Mean: Spenders age Average age of household members enrolled n college age age3 Average squared age of household members enrolled n college Average cubed age of household members enrolled n college par Fracon of members enrolled n par-me college agepar agepar Ineracon: age of member and enrolled n par-me college Ineracon: squared age of member and enrolled n parme college agedyr0 Ineracon: age of enrolled member and me agedyr0 Ineracon: squared age of enrolled member and me age3dyr0 Ineracon: cubed age of enrolled member and me Regonal B.C.Varables uer Average regonal unemploymen rae Wegh Varable: enroll3 Average number of members enrolled n college Households: 67,76. Toal observaons: 70,904. Spendng on hgher educaon observaons: 3,97. METHODOLOGY In order o generae hgher educaon consumpon profles, hs emprcal analyss ceners on a herarchcal applcaon o he sample selecon model of Heckman (976). By ulzng a sample selecon model (Heck), wo ypes of parameers are esmaed. For he frs ype, a prob model - usng all households - esmaes he probably of household hgher educaon parcpaon. For he second ype of parameers, a lnear model s ulzed o fnd he margnal effecs of demographc and descrpve varables on he consumpon of hgher educaon. Consumpon profles are hen generaed from he lnear model resuls. More specfcally, he j 'h famly's choce o parcpae s gven by he followng dscree choce model: y j, = [ w θ + z θ + ε > 0] (3) Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

23 where y, s one f he household spends on college (hed0), j Page 89 w ncludes he age of he head of household (age0), no hgh school dploma for he head (nohs0), o name jus a few, and he z s a vecor of exogenous varables used o proxy busness cycle effecs ha ncludes a regonal unemploymen rae (uer). Le c j, be defned as real hgher educaon consumpon by ndvdual from famly j a me. Then, for an ndvdual who s enrolled n college and spendng on college, we specfy an equaon ha relaes consumpon of hgher educaon o age by: c = β β β par age + β 5 + β par ( age age ) + β + β 6 3 ( age par ) 3 + ( age ) + u, where j age, s he me age of ndvdual (less 8) from famly j who s enrolled n college, j par, s a dscree varable equal o f he ndvdual has ndcaed enrollmen s par-me, and u, s an unobserved ransory shock ha s ndependenly, dencally (across famles), j and normally dsrbued: u N(0, σ ). In marx form, we wre he above equaon as: u c = x β + u. (4) Addonally, followng a ypcal herarchcal approach, he parameers n famly characerscs by he followng relaonshp: β are relaed o β j, = w γ + ε where ε N(0, σ ) and γ are fxed coeffcens o be esmaed. ε Unforunaely, he CEX does no gve c,. Insead, n any me perod, he CEX provdes j oal household spendng on hgher educaon. Gven ha he ncol varable gves he oal number of members of famly j enrolled n college ( n j, ), we dvde equaon (4) by n j, o yeld: c / n = x / n β + u / n. Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

24 Page 90 Or, alernavely, c = β + u x (5) where he bars ndcae ha he varable has been meaned across hose enrolled n college. Equaons (3) and (5) form he base lkelhood model for our regressons. The number of members enrolled n college s used o wegh he regresson snce he varance of he error s a funcon of n. Also, he sandard errors are robus and clusered on he household. Noce ha we nclude he busness cycle varable n equaon (3) bu no n (5). Alhough he sae of he busness-cycle s mporan n he nal parcpaon sage, one can argue ha once he decson o parcpae n hgher educaon s made he sae of he economy s no longer an mporan deermnae of spendng. Whle many people have he opon of purchasng as few as one class per semeser, sgnfcan enrollmen coss n mos U.S. unverses place a floor on he dollar cos of aendng. Addonally, due o me and course load consrans, sudens can ake no more han a maxmum of 8 o 4 cred hours per semeser, hus placng a celng on he number of cred hours and cos of aendance. Gven he exsence of boh a uon floor and celng, he mpac of busness-cycle varables a he second sage - how much o acually spend - becomes less mporan. Our selecon of he famly varables n β j, s deermned by he resrcons placed on γ. Mos of he famly varables are assumed o nerac wh he consan (a level shf) makng mos of he columns, excep for he frs, of γ zero. However, s ofen he case ha he head of he household s also he hgher educaon spender. In hs case, he coeffcens on age and age0 are no able o be denfed. To sharpen he dfferences beween age0 and he member varable age, we nerac age0 wh age (denoed age0age). Nex, he fracon of households ha spend on hgher educaon and have a head whou a hgh school educaon s small. To ncrease he varaon n nohs0, s added o hs0 (denoed nohs0+hs0) o form a new dummy for households headed by an ndvdual wh an educaon a or below he hgh school level. Fnally, all ages- for boh he head of household and enrolled sudens - are normalzed o zero on age 8. EMPIRICAL RESULTS Table 5 presens he resuls of he prob model. The age varables and he neracon erms ha nclude age are, overall, no ha sgnfcan. The mos noable esmaon resuls for he prob are he educaon saus of he head; he varables nohs0 and hs0 are each negave and sgnfcan a any reasonable crcal level mplyng ha an ncrease n hese varables leads o an decrease n he probably of spendng for he famly on hgher educaon. Also noable s he age composon of he famly. For example, when he number of chldren, chldeq0, ncreases n he household, he probably of spendng on hgher educaon falls presumably due o he need o subsue oward oher goods and servces such as food and clohng. Fnally, as he number of Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

25 Page 9 people n he household who are of college age rses, he probably of spendng on hgher educaon rses, he coeffcen on colage0 s posve and sgnfcan a any reasonable crcal level. Table 5: Heck Model Par Prob Selecon Probably ha hed0 = hed0 Coeffcen Robus Sd. Error z Pr> z age age mws sh wes rural blk ohrc fem mar nohs hs chldeq colage dyr age0dyr age0dyr uer consan Number of Observaons: 70,904 Table 6 presens he resuls for he second par of he Heck Model. Unlke before, he age varables and he neracon erms ha nclude age are mosly sgnfcan a he.05-level. For he mos par, hgher educaon consumpon s downward slopng (age's coeffcen s ) wh some slgh curvaure; he hgher order coeffcens for age are margnally sgnfcan. Oher resuls ndcae, for example, ha relave o hose n he norheas survey parcpans n he mdwes, souh, wes, and rural areas spen less on hgher educaon. The race varable, blk0, s negave and sgnfcan a he.0-level bu oher races show no sgnfcan dfference from whes. Because he esmaon s n reduced form, however, he causaly of varables lke regon and race are dffcul o asceran. I may be he case ha race and regon are rackng ncome. In any even, he majory of he esmaes n Table 6 appear conssen wh economc nuon. Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

26 Page 9 Real Spendng on Hgher Educaon Table 6: Heck Model Par : Weghed Lnear Regresson hed Coeffcen Robus Sd. Error z Pr> z age age age dyr agedyr agedyr age3dyr par agepar agepar mws sh wes rural blk ohrc fem mar chldeq colage nohs0+hs age0age age0dyr0age consan Mlls: ρ σ λ Goodness of f: Null: H 0 : β = 0 Wald Pr > χ 6 : 54.9 χ 6 : Number of Observaons: 3,97 Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

27 Page 93 We see n Table 6 ha he majory of he ndvdual me coeffcens are sgnfcan (age3dyr s no sgnfcan). The es of he consans, dyr0, presened n Table 7 shows, ha for he younges consumers, real consumpon ncreases by 0.6 real dollars n he 990's. The jon es on he slopes rejecs he null hypohess ha slopes, wh respec o age, are he same across me perods; he es resuls n a χ ( 6) = 6. 6 wh a probably value equal o The jon es on he consans and slopes furher confrms ha srucural change n real hgher educaon consumpon has occurred beween he 980s and he 990s; he es resuls n a χ wh a probably value equal o zero. ( 8) = Tes : Consans H 0 : dyr0 = 0 χ : 6.0 Pr> χ : Tes : Slopes Table 7: Tess of Coeffcens H 0 : age0dyr0 = age0dyr0 = agedyr0 = agedyr0 = age3dyr0 = age0dyr0age = 0 χ 6 : 6.6 Pr> χ 6 : 0.09 Tes 3: Jon H 0 : dyr0 = agedyr0 = agedyr0 = age3dyr0 = age0dyr0age = 0 χ 8 : Pr> χ 8 : Parameer esmaes from Table 6 and age are used o creae he household hgher educaon consumpon profles. The ypcal household ha generaes he profle s assumed o be: a sngle, whe, male who lves n he norheas, has some college educaon, does no have any chldren, and s he head of hs household. Fgure 7 depcs he resuls. The emprcal profle appears o be conssen wh he heorecal lfe-cycle profles. In addon, he lfe-cycle profle dsplays srucural change. Each have sascally changed beween he 980s and he 990s - he young consume more hgher educaon servces whle he old consume less n he 990s. In erms of our heory, he poson n he lfe-cycle appears o deermne he relave mporance of he ncome and subsuon effecs ha arse from he ncreasng college skll premum. Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0

28 Page 94 Fgure 7: Esmaed Skll Acquson Profle 99:3-00:4 98:-99: Average Age CONCLUSION Theorecally, he followng conclusons can be drawn from he quanave expermens presened. Frs, alhough pure subsuon effecs resulng from exensve SBTC are conssen wh he wdenng skll premum over me, hey do no explan why he skll premum has leveled off for he older age groups. When nensve SBTC parameers are nvesgaed separaely, hey can lead o ncome effecs - specfcally changes n θ. A combnaon of exensve and nensve SBTC parameers s able o provde a flaer wage gap va a change n skll acquson expendures. Ths fnal quanave resul provdes an explanaon for one of he problems ha Card and DNardo (00) ce regardng SBTC, namely, by showng ha SBTC can lead o a flaer wage gap profle va an neremporal subsuon of skll acquson. Emprcally, he major fndng s ha he hgher educaon lfe-cycle consumpon profles have sascally changed beween he 980s and he 990s mplyng ha he poson n he lfecycle appears o be an mporan deermnae o how households respond from, presumably, an ncreasng skll premum. The seeper hgher educaon consumpon profle s mporan because s exacly wha he heory predced from boh an exensve and an nensve SBTC; a subsuon effec for he young accompaned by an ncome effec for he old. Several neresng conclusons flow from our analyss. Frs, he nnovaons generaed by echnologcal advancemens n he goods producon secor have been also ncorporaed n he Journal of Economcs and Economc Educaon Research, Volume 3, Number, 0