HUMA CAPITA AN FAMIL RIS AN FAL Shu-Ling "Se Difference i th Proces o - PDF document

HUMA CAPITA AN FAMIL RIS AN FAL Shu-Ling "Se Difference i th Proces o Stratification. Ph.D disserta Universit o Wisconsin 1983 Jenn Bourne "Fertilit i America Historica Pattern an Wealt Effect th Quantit an Qualit o Children. Ph.D dissertation Universit o 1985 P de an va Slijpe A R D "Th Relatio betwee Income Intelli Educatio an Socia Background. 4 no 3 235-64 Shlomo "O th Relatio betwee Retur an Income. Mimeo Jerusalem Hebre University 1984 Glen C Transfer an th Distributio o Earnings. 49 no 4 (1981) 843-67 Benoit "Paretia Distribution an Incom Maximization. 76 no 1 (1962) 57-85 Thomas Berkeley Universit Californi Press 1972 J E Albany Stat Universit o Ne Yor Press 1976 Pau L "Inter-generationa Transmissio o Inequality A Empirica o Wealt Mobility. 46 no 18 (1979) 349-62 Jacob Ne York Columbi Universit (fo NBER) 1974 Marc Razin Assaf an Sadka Efraim "Som Welfar Theoreti Impli o Endogenou Fertility. 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Mimeographed Universit o Colorado 1985 F L "Simulatio o th Impac o Socia an Economi Institution o Siz Distributio o Incom an Wealth. 63 no (1973) 50-72 A D "Th Distributio o Earning an o Individua Output. 60 no 23 (1950) 489-505 Josep A translate b Hein Norden York Augustu M Kelley 1951 A F "O th Structur o Inter-Generationa Transfer betwee Fam 46 no 18 (1979) 415-25 Herbert "Rationalit i Psycholog an Economics. no 4 par 2 (Oct 1986) S209-24 Jame P "Rac an Huma Capital. 74 no 4 685-98 Lee Madison Universit o Wisconsi 1965 J E "Distributio o Incom an Wealt amon Individuals. no 3 (1969) 382-97 Jan " Positiv an a Normativ Theor o Incom Distribution. 16 no 3 (1970) 221-34 Nigel 'Th Family Inheritance an th Intergenerationa Transmissio 89 no 5 (1981) 928-58 "Inequalit withi th Famil an Regressio t th Mean. Mimeo London Universit o Wester Ontario Departmen o Econom 1984 HUMA CAPITA AN FAMIL RIS AN FAL Isaac an Ben-Zion Uri "Asse Management Allocatio o Time an t Saving. 14 no 4 (1976) 558—86 Davi L. an Hauser Rober M "Change i th Socioeconomi o th Races 1962-1973. 82 no 3 621-51 Richar B "Blac Economi Progres afte 1964 Wh Ha Gaine Why? I edite b Sherwi Rosen Chicago Uni o Chicag Pres (forNBER) 1981 Roger "Intra an Intergenerationa Incom Mobility Genev Surve Pape presente a th meetin o th Internationa Sociologi Associatio Researc Committe o Stratification Budapest Septembe Arthu S "Famil Dat Analysis Assortment Selection an Trans Proposa t th Nationa Scienc Foundation Washington D.C. "Modellin th Economi Family. Lecture An Arbor Uni o Michigan Institut o Publi Administration 1985 Claudia an Parsons Donal O "Industrialization Chil Labor an Economi Weil-Being. Mimeographed Philadelphia Universit o Departmen o Economics 1984 C D. an Hitchens D M W N London Alle & Unwin 1979 Rober M "Earning Trajectorie o Youn Men. I edite b D J Treima an K Tominaga I press Rober M. Sewell Willia H. an Lutterman Kennet G "Socioeco Background Ability an Achievement. I edite b Willia H Sewel an Rober M Hauser Ne York Aca Press 1975 Jame J. an Hotz V.Joseph "Th Labo Marke Earning o Pana Males. Mimeographed Chicago Universit o Chicago 1985 Richar J "I.Q. 228 no 3 (1971) 43-58 Nicholas "Alternativ Theorie o Distribution. 23 no 2 (1956) 83-100 Jonathan Robinson Rober U. an Klein Herber S " Theor o Socia wit Dat o Statu Attainmen i a Peasan Society. I vol 1 edite b Donal J Treima an Rober Robertson Greenwich Conn. JAI 1981 Laurenc J. Shoven John an Spivak Avia "Th Effec o Annuit o Saving an Inequality. I 4 no 3 J P "Househol Bequests Perfec Expectations an th Distri o Wealth. 47 no 5 (1979) 1175-93 H Gregg Chicago Universit o Chi Press 1986 Le A. an Willis Rober J "Dynami Aspect o Earnin Mobility. no 5 (1978) 985-1012 Gar S. an Tomes Nigel "Chil Endowment an th Quantit an o Children. 84 no 4 pt 2 (1976) "A Equilibriu Theor o th Distributio o Incom an Intergenera Mobility. 87 no 6 (1979) 1153-89 "Huma Capita an th Ris an Fal o Families. Discussio Pape no Chicago Economic Researc Center NORC Octobe 1984 Jere an Taubman Paul "Intergenerationa Transmissio o Incom Wealth. 66 no 2 (1976) 436-40 "Intergenerationa Mobilit i Earning i th U.S. Mimeographed Universit o Pennsylvania Cente fo Househol an Famil 1983 "Intergenerationa Earning an Mobilit i th Unite States Som an a Tes o Becker' Intergenerationa Endowment Model. 67 no 1 (1985) 144—51 D L "Inheritanc an th Distributio o Wealth. 46 no 18 381-402 D L. an Stiglitz J E "Intergenerationa Transfer an Inequality. 1 no 1 (1979) 6-26 Willia T. an Hauser Rober M "Respons Erro i Earning Func fo Nonblac Males. 6 no 2 (1977) Willia T Hauser Rober M. an Featherman Davi L "Respons Er o Blac an Nonblac Male i Model o th Intergenerationa Trans o Socioeconomi Status. 82 no 6 1242-88 Judith "Famil Siz an th Qualit o Children. 18 no 4 421-42 Pete M. an Duncan Oti Dudley York Wiley 1967 Ala S Cambridge MI Press 1974 "Inequalit an Mobilit i th Distributio o Wealth. 29 no 4 607-38 Benjami S Ne York 1976 Samuel "Schoolin an Inequalit fro Generatio t Generation. 80 no 3 pt 2 (1972) S219-S251 Joh A Washington D.C. Brooking 1977 John "Ca Equalizatio o Opportunit Reduc Socia Mobility? 64 no 1 (1974) 80-90 John "Galton' Statistica Methods. 1 no 7 (1889) 331-34 Allan "Governmen Debt Huma Capita an Bequest i a Life-Cycl 86 no 3 (1978) 505-16 CAPITA AN FAMIL RIS AN FAL deb an socia securit o th consumptio o differen genera o a family Barr (1974 use a mode o paren altruis tha i t th mode o altruis i thi paper whe fertilit i fixed t whethe socia securit an publi deb hav significan effect consumption Parent wh mak positiv bequest t childre d no thei consumptio whe the receiv socia securit o revenu th issu o publi debt Instead the rais thei bequest t offse effec o thes program o th consumptio o children However consumptio o altruisti parent wh ar constraine fro leavin t childre i raise b socia securit an publi debt an th o thei childre i lowere (se Draze 1978) avoi misunderstanding w haste t ad tha w d no clai al publi program ar neutralize throug compensator reduc withi families Thi i no tru fo poore familie i thi exampl fo al familie whe fertilit ca var (se Becke an Barr 1985) w hav show tha progressiv incom taxe reduc th in t inves i children W clai no neutralit bu tha ou analysi famil behavio i helpfu i understandin th effect o variou pub program o th ris an fal o families empirica evidenc i necessar befor thi an othe ca b evaluated W clos b reiteratin ou belie tha suc evi wil confir tha th analysi o famil behavio withi a utility framewor provide man insight int th ris an fal o i moder societies A B "O Intergenerationa Incom Mobilit i Britain. 3 no 2 (1981) 194-217 Cambridge Mass. MI Press 1983 Rober J "Ar Governmen Bond Ne Wealth no 6 (1974) 1096-1117 Gar S "Huma Capita an th Persona Distributio o Income A Approach. Woytinsk Lectur no 1 An Arbor Universit o Institut o Publi Administration 1967 " Theor o Socia Interactions. 82 no 6 1063-93 2 ed New York Columbi Universit Pres (fo NBER) Cambridge Mass. Harvar Universit Press 1981 Gar S. an Barro Robert " Reformulatio o th Economi Theor Fertility. Discussio Pape no 85-11 Chicago Economic Researc Cen NORC Octobe 1985 AN DISCUSSIO an Tome (1979 pp 1175-78 sho tha a progressiv in ta coul rais th long-ru relativ inequalit i after-ta income standar deviatio clearl falls bu averag income als fal eventu becaus parent reduc thei bequest t children Goldberger' use calculation (1985 pp 24-25 suppor ou analytica proo tha a i th degre o progressivit coul actuall lea t a increas after-ta inequality Hi calculation suggest however tha a coupl o woul elaps befor relativ inequalit migh eve begi t H overstate th dela befor whic inequalit migh begi t an h understate th likelihoo o a eventua ne increase no considerin th effec o greate progressivit o th contributio inequalit o th unsystemati componen o th ta syste (se an Tome 1979 pp 1177-78). ar no concerne wit inequalit i thi paper bu w believ tha mode develope her als implie tha after-ta inequalit migh whe th degre o progressivit increases Incom taxe alte i ou analysi partl b affectin th coefficient i equation a (11) (18) an (27) Empirica o regressiv model tha star suc equation o wit othe equation no derive fro a explici o behavio acros generation woul hav difficult i analyzin effect o incom taxe o th coefficient i thes equation be suc model usuall provid insufficien guidanc t ho thes ar determined conclusio applie t othe policie a wel an t variou i th environmen face b families Indeed th issue ar no t inequalit an intergenerationa mobilit bu appl t effort understan al socia behavior illustrat wit a differen publi program conside th effect o Althoug Goldberge admit tha w onl clai a possibl long-ru increas i in h criticize th statemen tha "perhap thi conflic betwee initia an equilib effect explain wh th larg growt i redistributio durin th las fift year ha onl modes effect o after-ta inequality (Becke [1981 p 156] a simila statemen i Becke an Tome [1979 p 1178] Goldberge omit th "perhaps i ou statemen say w "conjecture") H asks "I i tru tha ove th pas fift years th mea an o disposabl incom bot fell I not wha explanatio ha hi mode [i.e. provided? (1985 pp 26—27) Thes ar strang questions W not enoug t conten tha onl th ta syste affecte th growt o income durin pas 5 year no di w tr t asses ho othe force affecte inequality Sinc w prov wit ou mode tha a progressiv incom ta nee not lowe i th run an sinc inequalit apparentl di not declin significantl durin th pas 5 w speculate abou whethe progressiv incom taxe di lowe ove thi Surely tha speculatio coul b ver relevan i forcin a reassessmen o th belie tha progressiv taxe lowe inequality O course othe change durin perio coul hav maske a negativ effec o taxe o inequality bu thi ha b prove rathe tha simpl assumed CAPITA AN FAMIL RIS AN FAL o endowment an th capita constraint o investment i ar no large Presumably thes constraint becam les im a fertilit decline ove tim an a income an subsidie t gre ove time thi pape an i previou wor w clai tha a theor o famil i necessar t understan inequalit an th ris an fal o I makin th claim however w hav no intende t down th importanc o empiricall oriente studies Indeed w hav viewe the a a necessar complemen t theoretica analysis apologiz i ou claim fo maximizin theor coul b interprete denyin th valu o empirica an statistica wor tha i no explicitl o a mode o maximizin behavior stil claim however tha ou mode o famil behavio i usefu i th effec o publi policie an othe event o inequal an th ris an fal o families Her w par compan wit Gold (1985) wh denie whethe ou theor add muc t formula no base o a mode o maximizin behavior H claim (se esp 30-33 tha ou theor ha fe implication tha diffe fro simpl model o th earning o income o differen generation o family Perhap som perspectiv abou th validit o hi clai ca b throug a brie summar o a fe implication o ou analysis Earning regres mor rapidl t th mea i riche tha i poore Moreover eve thoug endowment o childre an earning parent ar positivel related a smal redistributio o investmen i capita fro riche t poore familie woul ten t rais th efficienc o investments Th reaso i tha investment b familie ar constraine b limite acces t funds Unlik earnings, consumptio woul regres mor rapidl t th i poore tha i riche familie i fertilit i no relate t par wealth Indeed consumptio the woul no ten t regres a al ric familie wh leav gift an bequest t thei children However ou analysi als implie tha fertilit i positivel relate th wealt o parents Thi dilute th wealt tha ca b lef t eac an induce a regressio t th mea amon ric familie i th betwee consumptio pe chil an th consumptio o d no kno o an othe analysi o th famil tha ha thes impli regardles o th approac used Th implication hav no teste empirically bu Goldberge (1985 mainl question th o th implication o ou analysis no it empirica validity Addi implication ar obtaine b considerin th effec o publi pro AN DISCUSSIO o endowments Indeed i al parent ca readil borro t th optima investment i children th degre o intergenera mobilit i earning essentiall woul equa th inheritabilit o poo familie ofte hav difficult financin investment i becaus loan t supplemen thei limite resource ar no availabl whe huma capita i th collateral Suc capita mar restriction lowe investment i childre fro poore families In mobilit i earning the depend no onl o th in o endowment bu als o th willingnes o poo familie self-financ investment i thei children degre o intergenerationa mobilit i earning i als deter b th numbe o childre i differen families Additiona chil i a famil reduc th amoun investe i eac on whe invest mus b finance b th family Consequently a negativ relatio famil siz an th earning o parent als reduce th inter mobilit o earnings ac a a buffe t offse regressio t th mea i th endow and hence i th earning o children I particular successfu bequeat asset t childre t offse th expecte downwar i earnings wit goo acces t capita market ca transfe asset o deb nullif an effec o regressio t th mea i earning o th con o children Thi effectivel separate th relatio betwee th b parent an childre fro inheritabilit o endowment regressio t th mea i earnings Consumptio i poore an familie wh d no wan t leav bequest tend t regres becaus equilibriu margina rate o retur o investment i huma capita o childre ten t b highe i familie wit lo Consumptio an tota resource i riche familie tha d bequest t childre regres dow t th mean mainl becaus i positivel relate t parents wealth I thi way large familie th wealt bequeathe t eac child Imperfec assortativ matin tend t caus consumptio an wealt t regres t th mean hav examine abou a doze empirica studie relatin th earn income an asset o parent an children Asid fro familie b discrimination regressio t th mea i earning i th State an othe ric countrie appear t b rapid an th re i asset i sizable Almos al earning advantage an disadvan o ancestor ar wipe ou i thre generations Povert woul no t b a "culture tha persist fo severa generations regressio t th mea i earning implie tha bot th inher HUMA CAPITA AN FAMIL RIS AN FAL whethe wealt o earning regres les rapidl t th mean al wealt appear t regres les rapidly Wealt woul regres i parent bequeat asset t childre t buffe th tota wealt consumptio o childre agains regressio i thei earnings How wealt woul regres rapidl i wealthie parent hav sufficientl childre tha d poore parents Wah (1985 doe fin a stron relatio i th nineteent centur betwee th fertilit an th o parents constraint o investment i childre probabl decline dur thi centur i th Unite State an i man othe countrie be fertilit declined income rose an governmen subsidie t edu an t socia securit gre rapidly Evidenc i Goldi an (1984 i consisten capita constraint o poo fami i th Unite State durin th latte par o th nineteent century familie withdre thei childre fro schoo a earl age i orde rais th contributio o teenag childre t famil earnings A weak o capita constraint i th Unite State i als indicate b th ove tim i th inequalit i year o schoolin an b th de influenc o famil backgroun o educatio attainment o (Featherma an Hause 1976) i evidenc tha th influenc o famil backgroun o th o childre i greate i les develope countrie tha i i th Unite States Fo example father' educatio ha a greater effec son' educatio i bot Bolivi an Panam tha i th Unite Moreover th influenc o father' educatio apparentl de ove tim i Panam a wel a i th Unite State (se Kelley an Klei 1981 pp 27-66 Heckma an Hot 1985) pape develop a mode o th transmissio o assets an fro parent t childre an late descendants Th i base o utilit maximizatio b parent concerne abou th o thei children Th degre o intergenerationa mobility o ris an fal o families i determine b th interactio o utility behavio wit investmen an consumptio opportunitie differen generation an wit differen kind o luck assum tha cultura an geneti endowment ar automaticall fro parent t children wit th relatio betwee th en o parent an childre determine b th degre o "inherit Th intergenerationa mobilit o earning depend o th in c aV4 4 4aX0'e1tC~TCOr-mto-0O"toT—OT—mttooI-CPOH4.rto MW0O6S•2momoo0m© © ©o0ot0oG©©0©0©0 STUDIE raise th regressio towar th mea i earning (se th theoreti discussio i Sec 2) point ou (1985 pp 29-30 tha ou earlie wor use highe illustrativ value fo ( tha th value o 3 suggeste b empirica evidenc i thi section Bu B an B ar different t B refer t th propensit t bequeat wealt t childre b fami wh ar no capita constrained Therefore lo B*' ar no inconsis wit hig B's A lo B combine wit a lo doe impl sizabl mobilit i earnings, wherea a hig B implie lo in mobilit i wealt an consumptio amon familie bequeat wealt t thei childre (w ignor th distinctio be th wealt an consumptio o childre an th wealt an con pe child se Sees 3 an 4) readil admi (se Sec 1 tha th distinctio i th presen pape earnings wealth an consumptio a wel a ou attentio t capita constraint an fertilit behavio hav greatl ou thinkin abou intergenerationa mobility However sinc lo B i no inconsisten wit a hig B w se n reaso wh th evidenc o a lo B "woul occasio th tearin o [our hai th gnashin o [our teeth (Goldberge 1985 pp 29-30) More asid fro fertilit an marriage w stil expec hig value fo B Sec 3) 2 present evidenc fro thre studie fo th Unite State Grea Britai o th relatio betwee th wealt o parent an Harbur an Hitchen (1979 an Menchi (1979 us pro o wealth estates whil Wah (1985 use dat o wealt fro th an 187 censuses Th estimate elasticit betwee th asset o an son i abou . i th Unite State fo probate asset i year bu i les bot fo asset o livin person i th nineteent an fo probate asset i Britain find a smal negativ coefficien fo grandparents wealt whe ar use fo bot parents an grandparents wealt bu a coefficien fo grandparents wealt whe thei actua wealt i Th theoretica analysi incorporate int equatio (18 doe im a smal negativ coefficien fo grandparents wealt whe th effec parents wealt i no large a i th cas i he study However Behr an Taubma (1985 usuall fin smal positiv (bu no statisticall coefficient o grandparents schoolin i thei stud o o schoolin fo thre generations Thei finding ma b inconsis wit ou theory althoug equatio (18 doe impl a negligibl fo grandfathers schoolin whe th coefficien o parents i small—i i les tha .2 i thei study dat i table 2 an 2 ar to limite t determin wit conn CAPITA AN FAMIL RIS AN FAL b les tha .2 i (3* moreover < . i P = 0 an < 0 i > . (se n 4) constraint completel disappeared woul th sam familie th best-pai an mos prestigiou occupations (Fo thi fear th often-cite articl b Herrnstei [1971]. Th answe i no fami i th bes occupation woul chang frequentl eve i "meritocra becaus endowment relevan t earning ar no highl inherit i les tha . an ma b muc less Anothe wa t se thi i notin that i th relatio betwee th lifetim earning o father son i n large tha .4 practicall al th advantage o disadvan o ancestor ten t disappea i onl thre generations "fro t shirtsleeve i thre generations. Parent i suc "open hav littl effec o th earning o grandchildre an late Therefore the hav littl incentiv t tr t affec th o descendant throug famil reputatio an othe means particular an lifetim "cultur o poverty tend t disappea be generation becaus characteristic tha determin earning ar betwee generations Fo example childre o parent wh onl hal th mea ca expec t ear abov 80 o th mea i generation an thei ow childre ca expec t ear onl slightl th mean famil backgroun i stil important Fo example eve i th de o regressio t th mea i 80% o parent whos earn ar twic th mea ten t ear 30 mor tha th childre o whos earning ar onl 50 o th mean A 30 premiu i relativ t th 10%-15 premiu fro unio membershi (se 1986 o t th 16 premiu fro tw additiona year o school (se Mince 1974) Childre fro successfu familie d hav a sig economi advantage wh ar poo partl becaus o discriminatio agains thei caste o othe "permanent characteristic ma advanc mor Clearly black i th Unite State hav advance muc mor tha hav immigrants partl becaus o publi an privat dis agains blacks Althoug man hav studie change ove i th averag positio o black relativ t white (see e.g. th recen stud b Smit [1984]) fe hav studie th relatio earning o son an father i blac families Th evidenc i 2 suggest tha olde black regres mor rapidl t th mea tha olde whites althoug th evidenc ma b spuriou becaus re error ar highe an apparentl mor complicate fo black Bielby Hauser an Featherma 1977) Opportunitie fo younge clearl hav improve durin th las 2 years Th evidenc i 2 tha younge black regres mor slowl suggest discrimina r- ^0 0O Ot t. .o Oo"oC/"So m mO ^" "^ ^ *^ »~^ i i©GC©GCO0I—OCO©.0r-H©T—co o1b b0 0b0b bObo-o oa0ca aoCai©irvr« H STUDIE e al (1975 reduc respons error an th transitor compo b usin a four-yea averag o parents incom an a three-yea o son' earnings whil Hause (i press use a four-yea aver o parents incom an a five-yea averag o son' earning durin initia perio o labor-forc participation Tsa (1983 no onl aver income o parent ove severa year bu als use a retrospectiv o thei incom i 1957 A Hauser' suggestion w hav cor fo th respons error i father' earning b usin th analysi Bielb an Hause (1977) Behrma an Taubma (1983 exclud wh hav les tha fou year o wor experienc becaus thei d no represen wel thei lifetim earnings D Wolf an va (1973 an Freema (1981 reduc th importanc o th transi componen b usin th averag incom i father' occupatio a estimat o hi lifetim earnings thes adjustment fo respons error an transitor incomes estimate o th regressio coefficient fo earning an income rathe lo i al th studie (excep fo larg income i Sweden) a stud i progres b Elizabet Peter (1985 tha use dat th Nationa Longitudina Surve (th sam surve use b Free [1981] als find a smal coefficien (belo .2 whe a simpl aver o fou year o son' earning i regresse o a simpl averag o year o father' earnings indirec evidenc o sizabl regressio towar th mea i life earning i provide b life-cycl variation i earnings B defini endowment ar fixe ove a lifetime Therefore earning shoul mor closel relate ove th lif cycl tha acros generation be endowment ar imperfectl transmitte fro paren t chil (en ar no a "fixe effect acros generations) State differently t othe member o hi cohort a perso i usuall muc mor t himsel a differen age tha i a fathe simila t hi so the ar o th sam age Th correlatio coefficien betwee th componen o mal earning a differen age ha bee fro a seven-yea pane t b abou . i th Unite State Lillar an Willi 1978 tabl 1) Th inheritabilit o endowment father t son i surel less probabl muc less tha i th correla betwee th permanen componen o earning a differen ages evidenc i tabl 2 suggest tha neithe th inheritabilit o b son no th propensit t inves i children' hu capita becaus o capita constraint (P* i large Fo example i regressio coefficien betwee th lifetim earning o father an i ^. an i th transitor varianc i lifetim earning i les o th varianc i tota lifetim earnings the bot an P HUMA CAPITA AN FAMIL RIS AN FAL a fe empirica studie lin earning o wealt o differen gen becaus o difficultie i gatherin suc informatio an be o insufficien interes b socia scientists Table 2 an 2 presen fro severa studie o th degre o regressio t th mea i income an wealth wit coefficient o determinatio (whe th numbe o observations an note abou othe variable any include i eac regression 2 ha evidenc o th earning o income o son an father thre studie base o separat dat set fo th Unite State an stud eac fo England Sweden Switzerland an Norway. Al th averag ag o father an son i quit differen excep i Genev study bot Atkinso (1981 an Behrma an Taubma presen evidenc tha suc difference i ag d no greatl af th estimate degre o regressio t th mean poin estimate fo mos o th studie indicat tha a 10 in i father' earning (o income raise son' earning b les tha Th highes poin estimat i fo York England wher son' hourl appea t b raise b 4.4% However th confidenc interval sizabl i al studie excep Malm becaus fathers earning "ex a smal fractio o th variatio i th earning o sons Moreover error an th transitor componen i father' earning (o ma severel bia thes regressio coefficients. Furthermore analysi i Sectio 2 indicate tha transitor variation i lifetim an th omissio o th earning o grandparent biase thes coefficient downward However th erro fro omittin earning woul b smal i parents earning d no hav larg effec (se eq [18] an i th transitor i lifetim earning i large W ar indebte t Rober Hause fo bringin t ou attentio severa studie o inter mobilit tha us th dat o Wisconsi hig schoo graduate an fo guid u throug variou adjustment tha correc fo respons an measuremen error i studies Thes studie hav variou limitations Hause e al (1975 sampl familie i onl on (Wisconsin an onl includ son wh graduate fro hig school al father i Behrma an Taubma (1983 sampl ar twins father i th Atkinso (1981 sam ha modes earning i th cit o York father i th d Wolf an va Slijp (1973 ar fro th cit o Malmo Solto (1965 use a ver smal sampl fro on cit i an Giro (1984 survey student i th canto o Geneva Thes estimate ma als b biase (th directio i no clear becaus informatio no availabl o hour worke an nonpecuniar incom fro employmen (se th i Becke an Tome [1984 n 13]) AN MARRIAG 1976 Becke 1981 chap 6 Tome 1981 o response t differ betwee children Thi analysi implie tha riche familie inves huma capita i better-endowe childre an tha the compen othe childre wit large gift an bequests Poore familie wh inves i huma capita fac a conflic betwee th efficienc greate investment i better-endowe childre an th equit o investment i les wel endowe children th clai tha observe difference betwee sibling i i helpfu i determinin th degre o intergenerationa i earning (see e.g. Brittai 1977 pp 36-37) ther i n connectio betwee th relatio amon sibling an th o intergenerationa mobility Th reaso i tha difference i betwee sibling i determine b characteristic withi a generation suc a th substitutio betwee sibling i th functio o parents wherea intergenerationa mobilit i earn i determine b difference acros generations suc a th re towar th mea o endowment (fo a furthe discussion Tome [1984]) t th mea i marriage—calle imperfec positiv as mating—als increase th degre o regressio t th mea earnings, consumption an assets However th effec o marriag i obviou tha i ma appea becaus parent ofte ca anticipat th sortin o children Fo example wealth parent woul us gift bequest t offse som o th effect o th well-bein o thei chil o th tendenc fo ric childre t marr down jus a the us an bequest t offse th effec o th regressio downwar i en Althoug a ful analysi o th interactio betwee th behav o parent an expectation abou th marriage o childre i com b bargainin betwee in-law o th gift t b mad t thei (som issue ar discusse i Becke [1981 chap 7 an an Tome [1984]) on canno b satisfie wit th man mod tha simpl ignor expectation abou children' marriage (see e.g. 1969 Pryo 1973 Blinde 1976 Atkinso 1983) an marriag hav no bee full integrate int ou analysi intergenerationa mobility—w onl woul inser "fully int Gold statemen tha "it' fai t sa tha [fertilit an marriag are integrate int hi intergenerationa system (1985 p 13) However discussio i thi section th discussio o fertilit i Becke an (1985) an tha o marriag i Becke an Tome (1984 indicat u tha a utility-maximizin approac ca integrat fertility marriage intergenerationa mobilit int a commo framewor wit usefu CAPITA AN FAMIL RIS AN FAL towar th mea i marriag an th positiv effec o o fertilit hel explai wh difference i consumptio an tota amon riche familie d no persis indefinitel int futur Her w onl sketc ou a analysis Th implication o an marriag fo consumptio an bequest ar als discusse Becke an Tome (1984 an Becke an Barr (1985) u firs dro th assumptio tha al parent hav onl on chil generaliz th utilit functio i equatio (20 t 0 wher i th utilit o eac o th identica childre an i th degre o altruis pe child Th first-orde conditio fo optima numbe o childre i tha th margina utilit an margina o childre ar equal Th margina cos o childre t parent ne expenditure o children includin an bequest an othe Th margina cost ar determine b th circumstance an deci o parents previou sectio showe tha th consumptio an tota re o wealth familie ma no regres dow becaus thes familie offse th downwar regressio i th earning o thei childre b larg gift an bequests Fortunately thi unrealisti implica doe no hol whe th numbe o childre ca vary Riche fami ten t spen som o thei greate resource o additiona chil Thi reduce th beques t eac chil belo wha i woul b i di no increas th numbe o childre (se th proof i Becke Barro [1985]) A positiv respons o fertilit t increase i wealt consumptio an wealt pe chil t regres down perhap an middle-incom familie withou asset wh ar prevente leavin deb t thei childre mus trad of betwee earning eac child numbe o children an paren consumption Th capita investe i eac chil and hence th earning o eac woul the b negativel relate t th numbe o children a i man studie (see e.g. Blak 1981) Th degre o regres t th mea i earning amon thes familie woul b lowe fertilit an parents earning ar negativel relate tha i the unrelated d no hav muc t ad t ou previou analysi (se Becke an AN CONSUMPTIO th exponentia function thi first-orde conditio become il ( + (27 ci a positiv constan an wher th distributio o fluctua- i Z, 1 aroun doe no depen o I th capita marke al familie t financ th wealth-maximizin investment i children i al families wher i th asse rate The (27 implie tha th growt i consumptio follow a rando wit drif (Kotlikoff Shoven an Spiva [1986 deriv a simila whe th lengt o lif i uncertain) Mor generally equatio show that i th utilit functio i exponential uncertaint add a ter t consumptio bu doe no basicall chang th implica o ou analysi concernin th degre o regressio t th mea i second-orde approximatio t th left-han sid o equatio (26 show tha th effec o uncertaint o th degre o regressio th mea wit mor genera utilit function tha th exponen depend o th sign an magnitude o second an higher-orde o th utilit function. Uncertaint coul induc regressio th mea i consumptio eve whe ther woul b non wit However uncertaint coul als induc regressio awa fro mean o greate rate o regressio towar th mea a highe tha a lowe level o consumption wit utilit function tha see a empiricall relevan a thos havin opposit implica Consequently w canno mak an stron statemen concernin effec o uncertaint o th degre o regressio towar th mea th consumptio o parent an children I i constant a second-orde approximatio t i eq (26 give i th thir derivative w'"' i th fourt derivativ o utilit fro consumptio th + 1 firs generation an i th give varianc o aroun Z Th ter o left-han sid i mor likel t b les tha on (regressio towar th mean whe i larg relativ t CAPITA AN FAMIL RIS AN FAL an upwar regressio i th endowment an earning o thei Parent woul fac a complicate maximizatio proble be capita constraint ma b bindin onl fo som descendants Th o utilit maximizatio ca b summarize b endogenousl de subjectiv discoun rate an margina rate o retur fo eac o a famil tha guid a wel a reflec th decision fo tha Thes shado price excee th rat o asset wheneve o acces t deb preven borrowin fro children Discoun o (richer parent wit sufficien asset t rais o lowe thei be t childre woul equa th rat o assets argu i Sectio 2 tha equilibriu margina rate o retur o parent ten t declin a thei earning becom larger equatio (23 o equatio (25 implie tha th relativ o abso growt i consumptio betwee generation woul als declin a earning o parent rose However th relativ o absolut growt consumptio betwee generation woul b constan amon riche wh receiv a margina rat o retur equa t th rat o assets th consumptio o childre woul regres mor rapidl up t th mea i poo familie tha downwar t th mea i ric Thi produce a conve relatio betwee th consumptio o an children A th sam time earning regres mor slowl i poo familie tha the regres downwar i ric families bequeathe t childre i riche familie ac a a buffe t off an regressio t th mea i th earning o children Th riches coul maintai thei consumptio ove tim compare t les familie onl b increasin thei bequest sufficientl t offse th downwar regressio i th earning o th riches children a result bequest coul regres awa fro th mean analysi o consumptio ha assume perfec certainty althoug abou muc o th luc o futur generation i no full o diversifiable I eac generatio know th yield o invest i th huma capita o an i bequest t children bu no hav perfec certaint abou th earning o childre an i mor uncertai abou subsequen generations the th first-orde fo maximizatio o expecte utilit i refer t expectation take a generatio befor an ne in abou earning an othe wealt o descendant i acquire an 1 AN CONSUMPTIO ] = *l ( + Vl + parent coul financ expenditure o thei childre wit deb tha th obligatio o children th margina cos o fund woul th rat o asset i al families The equatio (23 o equatio implie tha th relativ o absolut chang i consumptio be generation woul b th sam i al familie tha ar equall al (8 an tha hav equa degree o substitutio (c o Eac woul maintai it relativ o absolut consumptio positio ove an consumptio woul no regres t th mean State an degre o relativ o absolut inequalit i consumptio th parents generatio woul the b full transmitte t th chil generation th earning o childre woul stil regres t th mean o th altruis o parents a lon a endowment ar full b childre (se Sec 2) Consumptio doe no automaticall t th mea whe earning d becaus parent ca anticipat thei childre woul ten t ear les o mor tha the do The us deb an asset t offse th effec o wealt o th expecte i earnings althoug earning ma regres t th mean well-bein a b consumptio woul no regres a al i parent hav ful t capita market t financ investment i thei children' hu capital Th asset bequeathe t childre woul ris an th deb woul fal a parents earning rose Thi crucia distinctio regressio acros generation i earning an consumptio ap t hav bee ignore i th extensiv literatur o th mobilit families th mai implicatio o equation suc a (23 an (25 i disqui namely tha al initia difference amon familie i consumptio tota resource ar full transmitte t futur descendants. Surely resource o th curren generatio ar essentiall independen o resource o thei distan ancestors Severa force ar responsibl th deca ove tim i th influenc o th pas o consumptio tota resources Thes includ difficultie i transmittin deb t uncertaint abou th future th effec o parents wealt o an imperfec assortativ mating W conside thes variable turn i full separate fro earning onl whe childre ca obligate fo debt create b parents I deb canno b create fo (se th discussio i Sec 2) parent withou asset coul no HUMA CAPITA AN FAMIL RIS AN FAL However w ca simplif th relatio betwee th consumptio parent an childre b assumin tha utilit depend o th o childre a i i th consumptio o parent an 8 i a constan tha measure altruis o parents th preferenc functio give b equatio (20 i th sam fo al an i consumptio durin childhoo i ignored the th o th paren indirectl woul equa th discounte su o th fro th consumptio o al descendants = |> utilit o parent depend directl onl o th utilit o children bu depend indirectl o al descendant becaus childre ar concerne thei descendants assum tha parent succee i maximizin thei "dynastic utility represente b equatio (21) Thi rule ou bargainin b childre obtai large transfer tha thos tha maximiz parents utility A genera assumptio i tha parent maximiz a weighte averag thei ow an thei children' utility wit weight determine b bar powe (se th normativ us o thi assumptio i Nerlove an Sadk [1984]) however thi generalizatio woul no an majo conclusions perfec certaint abou rate o retur an income i al genera th first-orde condition t maximiz utilit ar th usua ones example wit a constan elasticit o substitutio i consumption c > 0 an 1 =^ln( + r, + I Z, measure th margina rat o retur t investment i chil i perio Wit a exponentia utilit function AN CONSUMPTIO ar foun i a relativel smal numbe o riche familie an th ratio o asset t huma capita o childre woul ris a wealt rose Th empirica evidenc clearl indicate tha an incom fro nonhuma capita ar muc mor importan riche tha i poore families studie als indicat tha th proportio o incom save reasonabl constan o tha i rise a income includin "perma income increase (se th studie reviewe i Maye [1972]) thes studie provid flawe measure o saving becaus in i huma capita an "capita gain o losses fro intergener increase o decrease i endowment ar no considere sav Lower an middle-incom familie inves primaril i thei huma capital Endowment ten t increas fro parent t a lowe level an t decreas fro parent t childre highe level becaus o regressio t th mea i endowments empirica studie understat relativ saving b lower an familie becaus bot intergenerationa capita gain investment i huma capita ar relativel large i thes families believ tha a appropriat concep o saving ma wel sho tha fractio save decline a permanen incom rises Afte all thi b expecte i equilibriu margina rate o retur o invest i childre declin a incom increases conclusio tha mos bequest o asset ar foun i a relativel numbe o riche familie doe no presuppos "class difference altruis o othe clas difference i th propensit t save a i (1956 an Pasinett (1962) o a use i Atkinso (1983) I analysis al familie hav th sam intrinsi tendenc t sav an estate becaus the ar assume t hav th sam altruis towar Still apparen "class difference i saving woul exis be poore familie sav mainl i th huma capita o children ar no recorde a saving o bequests asset o a perso ar determine b bequest fro parent an hi ow life-cycl accumulations W assum tha parent choos be b maximizin expecte utility subjec t th expecte earn an life-cycl asse accumulatio o children T develo furthe analysi o bequests w mus tur t a explici treatmen o utilit b parents W continu t assume unti th nex section eac adul ha on chil withou marriage tha th utilit functio o parent i additivel separabl i ow consumptio an i variou characteristic o children Mos ou analysi doe no depen o a specifi measur o thes character a lon a the ar positivel relate t th tota resource o chil HUMA CAPITA AN FAMIL RIS AN FAL man programs—includin Hea Star programs welfare ai t women an socia security—becaus th redistribution effect clear whil substitutio effect ar no clear eve i direction Fo wha i th substitutio effec o a socia securit program O ther evidenc tha Hea Star program rais rathe tha lowe mar rate o retur o parents expenditures (Se Becke 1981 p Althoug tuitio subsidie t educatio ma appea t rais rate retur o parents expenditure o education actuall the migh margina rate o retur whe combine wit rationin o place Peltzma 1973) o expenditure withi familie induce b govern subsidie ca explai wh man program appea t hav wea o participant (se th discussio i Becke [1981 pp 125-26 O course wea effect o participants d no impl tha sub effect ar negligibl o tha the reinforc redistribution ef bu wea effect d impl tha thes program d no hav stron substitutio effects constraine parent coul financ expenditure o childre reducin thei life-cycl saving i childre coul b counte o t fo elderl parents I man societies poore an middle-income parent ar supporte durin ol ag b childre instea o b th o gold jewelry rugs land houses o othe asset tha coul b b parent a younge ages Ou analysi suggest tha thes choos t rel o childre instea o o asset becaus rate o o investment i childre ar highe tha the ar o othe effect poore an middle-leve parent an childre ofte hav a contract enforce imperfectl b socia sanctions tha parent i childre i retur fo suppor durin ol age Bot parent childre woul b mad bette of b suc contract i investment childre yiel a hig return wher include i th yiel i an insur provide b childre agains a unusuall lon ol age analysi implie tha bequest an gift o asset t childre d ris rapidl unti margina rate o retur o investment i chil ar reduce t th rat o assets Furthe increase i contribu fro parent the mainl tak th for o asset rathe tha o capita becaus return o asset ar les sensitiv t th accumulated Thes conclusion impl tha mos bequest t AN HUMA CAPITA margina rate ar lowe i riche families a smal redistribution o capita awa fro thes familie an towar childre fro familie woul rais th averag margina rat o retur acros families Thi woul rais efficienc eve thoug endowment th averag productivit o investment i childre ar greate i familie (se als Becke 1967 1975) Th usua conflic betwee a measure b inequality an efficienc i absen becaus a o investment towar les advantage childre i equiva t a improvemen i th efficienc o capita markets publi expenditure o th huma capita o childre i fami subjec t capita constraint rais th tota amoun investe i thes eve whe publi an privat expenditure ar perfec substi Th reaso i tha publi expenditure increas th tota resource a famil i taxe ar impose o othe families A increas i famil i capita constraine familie i share betwee parent an i childre i a rati determine b th margina propen t inves ((3*) I publi an privat expenditure ar perfec substi th fractio 1 — (3 o governmen expenditure o childre i b compensator response o thei parents Tha is t furthe towar othe famil members eve constraine parent redistrib som tim an expenditure awa fro childre wh benefi fro expenditure t sibling an themselves Compensator re o parent apparentl greatl weake th effect o publi healt foo supplement t poore pregnan women som Hea programs an socia securit program (se th discussio i [1981 pp 125-26 251-53]) sa earlie i Sectio 2 tha th tota investmen i childre i wit positiv bequest t childre i unaffecte b publi expen o childre tha ar perfec substitute fo parents expendi Parent reduc thei ow expenditure t offse full suc publi However publi an privat expenditure ma no b per substitutes If fo example publi expenditure rais rate o retur famil expenditures increase publi expenditure coul eve rais expenditure becaus a "substitutio effect work agains th "re effect. criticize u (1985 pp 9-10 Simo [i press repeat criticism becaus w emphasiz redistributio o incom a th expens o substitutio effect whe discussin variou pub programs Sinc ou firs join pape w hav explicitl note tha program ma hav substitutio effect b changin rate retur o parenta investment i childre (se Becke an Tome p S156) However w hav emphasize th redistribution effect CAPITA AN FAMIL RIS AN FAL motivate th assumptio i ou earlie wor tha ( > assumptio use t identif ( an fro th coefficient i a equa suc a (18) (1985 pp 19-20 correctl state tha w di no provid independen wa t evaluat thi assumption Th presen pape progres towar th goa o identificatio becaus ca b deter fro knowledg o th coefficient i th equatio fo th earn o parent an childre i (richer familie wh leav positiv be t children Give 3 (o a mor genera relatio betwee 3 parents earnings ca b determine fro knowledg o th coef o parents o o grandparents earning i th earning equa fo poore familie wh ar capita constrained Eve 3—th mar propensit o parent t bequeat wealt t children—migh b fro informatio o th relatio betwee th consumptio parent an childre i riche familie (se th nex section) familie ca mor readil self-financ a give investmen i chil tha ca poo an middle-leve families Riche familie als hav tha averag endowments whic raise th wealth-maximizin in i huma capita b riche familie abov tha b poore fami Empirica observation strongl indicat tha riche familie com t financin th optima investmen i th huma capita o chil tha d poore families Thi indicate tha th wealt effec o i childre dominate th endowmen effect Th wealt woul dominat i endowment regres strongl t th mean fo th endowment o riche childre woul b muc belo thos o parent an th endowment o poore childre woul b muc thos o thei parents Th evidenc considere i Sectio 6 doe tha endowment relevan t earning d regres strongl t mean return o asset ar no highl sensitiv t earning an endow th greate resource availabl t ric familie t financ wealth investment i childre impl tha equilibriu margina o retur o investment i childre ar lowe i riche familie the ar i mor capita constraine poo an middle-leve familie thoug endowment an averag rate o retur ar highe i families Equilibriu margina rate the ten t decline per no monotonically a earning o parent rise Eventually margina o huma capita woul equa th rat o retur o assets an margina rate woul b relativel constan a parents earning Poore childre ar a a disadvantag bot becaus the inheri endowment an becaus capita constraint o thei parent limi marke valu o th endowment tha the d inherit AN HUMA CAPITA us o instrument fo th lifetim earning o parents suc a th earning o uncle o o great-grandparent (se Goldberge Behrma an Taubma 1985) direc relatio betwee th earning o parent an childre i (14 i likel t b concav rathe tha linea becaus obstacle th self-financin investment i childre declin a parents earning Whe investment i th huma capita o childre ar suffi t lowe margina rate o retur t th marke rat o assets fur increase i parents earning rais th asset bequeathe t chil bu hav n effec o th amoun investe i th huma capita childre (i rate o asset ar independen o parents earnings) "contacts o parent an th direc utilit t parent fro huma capita o childre ar mor importan i riche families capita constraint hav differen implication fo th curvatur th relatio betwee th earning o parent an childre tha d alternativ explanations an Tomes' (1979 discussio implie that becaus 3 an symmetrically eve knowledg o th tru value o th coeffi attache t parents an grandparents income i a equatio a (18 coul no identif 3 withou othe information suc whic coefficien i larger Earning i ric familie no subjec t constraint ar relate b th simpl equatio (11) whic doe includ 3* Therefore woul b know i th coefficien o par earning i ric familie i known The 3 an coul b distin i equatio (18 b usin thi informatio o earlie draft o th presen pape w unwisel denot 3 b 3 3 i Becke an Tome (1979 refer t a differen concept th coefficien 3 measure th margina propensit t inves i huma capita o childre b capita constraine parent wh ar fro makin th wealth-maximizin investmen i thei chil 3 doe no ente th earnings-generatin equatio fo riche fam (eq [11] wh ar no s constrained Pu differently 3 i zer i families Ther i n genera presumptio abou th siz o 3 t eve i low-incom familie becaus 3 depend o publi t children incomes an othe variables coefficien 3 m ou earlie wor (see e.g. Becke an Tome measure th margina propensit t bequeat wealt t childre parent ca leav deb t childre an whe huma wealt i no fro othe wealth Ou earlie wor an Sectio 3 o th pape sho tha thi propensit depend o th generosit o towar childre an ma no b sensitiv t th leve o income i i likel t b larg i mos familie (se Sec 3) Suc a HUMA CAPITA AN FAMIL RIS AN FAL an rais th positiv effec o parents earning o chil earnings. F wer approximatel linearl relate t an then = + (p + wit B = <}>; (18 coefficien o parents earning exceed th degre o inheritabilit th margina propensit t inves i th huma capita o childre A i equatio (12) OL estimate o th coefficien o ar downwar b th transitor componen o lifetim earnings Or leas square estimate o th relatio betwee an ten < A = M-I-<- < min R + i th partia regressio coefficien betwee an bot partia an simpl regressio cofficient betwee th earning o parent an childre provid uppe limit o th o capita marke constraint o th propensit t inves i chil Th biase i thes OL estimate ca sometime b overcom b Goldberge (1985 pp 16-17 perhap properl take u t tas fo expressin to "surprise i ou earlie wor abou a negativ coefficien o grandparents wealt income becaus thi i implie b ou mode (Becke an Tome [1979 sa tha a coefficien "ma see surprising [p 1171] Becke [1981 say "i i surprising 148]) However w neve claime tha a increas i grandparents wealt woul th wealt o grandchildre (Goldberger' discussio [1985 p 2 i misleadin ou claims) W hav aske ho person wh star wit a presume relatio amon wealt o grandchildren parents an grandparent woul interpre a negativ coeffi o grandparents wealt suc a i foun i Wahl' stud (1985 reporte i tabl 23 A simila equatio i derive i Becke an Tome (1979 eq 25) However th coeffi calle B ther refer t th propensit t bequeat al capital includin debt t not t th propensit t inves i th huma capita o childre b parent wh leav debt Th approximatio i eq (18 woul b linea i th log o th earn o children parents an grandparent i th endowmen an earnings-generatin ar linea i logs The B woul giv th percentag increas i th earn o childre pe 1 increas i th earning o fathers an similarl fo — B*/j Equatio (18 implie tha + Ap*6; th econom i i long-ru equilibriu (se Becke an Tome 1979) the an th equalit i eq (19 follows Th relatio betwee th right-han sid o eq (19 i derive i Becke an Tome (1979 app E) AN HUMA CAPITAt,Yt_vkt_,),st_A,E} +€t (14)=CAPITA 4*(£, Y_V kt_x) + e,where kt_l include an Earning o childre no depen o th earning o parent a wel a indirectl throug th trans o endowments Som author (e.g. Bowle 1972 Mead 1976 1983 argu fo a direc effec becaus "contacts o parent sai t rais th opportunitie o children other argu fo a direc becaus parent ar sai t receiv utilit directl fro th huma o children Fortunately th effect o paren earning o acces capita ca b distinguishe analyticall fro it effect o "contacts "utility. indirec effec o parents earning o th earning o childre throug th transmissio o endowment an ca b foun b fo an the usin equatio (14 fo su o bot th direc an th indirec effect o parents earn i indirec effec o grandparents earnings, holdin earning i o grandparent an grandchildre ar indirectl linke th constraint o financin investment i children Tha is earning o parent ar no sufficien t describ th effect o chil o bot th resource an th endowment o parents Equatio show tha a increas i th earning o grandparent lower th o grandchildre whe parents earning an grandchildren' ar hel constant Constraint o financin investment i childre a negativ relatio betwee th earning o grandparent an CAPITA AN FAMIL RIS AN FAL ar expecte t b riche becaus tha lower th margina utilit parent o additiona expenditure o children deman curve fo expenditure i char 1 ar simila t thos char 1 an ar highe i familie wit better-endowe children Th o fund t a famil i n longe constan o th sam t al families expenditure o childre lowe th consumptio b parents raise thei subjectiv discoun rate (th shado cos o funds) discoun rate ar smalle t parent wit highe earning o mor endowe children Expenditure o childre i eac famil ar b th intersectio o suppl an deman curves A in i parenta earning shift th suppl curv t th righ an in greate expenditure o childre (compar 5 an 5' i char Th distributio o intersectio point determine th distributio investment an rate o retur and hence a show i Becke (1967 th inequalit an skewnes i th distributio o earnings substitutin equatio (13 int th earnings-generatin equation an (4) w ge 13 expenditure o children wit capita constraints AN HUMA CAPITA hazard fro th privat natur o informatio abou wor effor employmen opportunitie ca greatl affec th earning realize huma capital Moreover mos societie ar reluctan t collec fro childre tha wer contracte b thei parents perhap be th minorit o parent wh d no car muc abou th welfar thei childre woul rais thei ow consumptio b leavin larg t children brin ou sharpl th effec o imperfec acces t deb contracte children w assum tha parent mus financ investment i chil eithe b sellin assets b reducin thei ow consumption b re th consumptio b children o b raisin th labor-forc activi o children Conside parent withou assets wh woul hav t th efficien investmen i huma capita (say CWi char 12 b reducin thei ow consumptio becaus the canno contrac fo thei children A reductio i thei ow consumptio woul it margina utilit relativ t th margina utilit o resource in i children Thi woul discourag som expenditur o chil Consequently bot th amoun investe i childre an parenta ar reduce b limitation o th deb tha ca b lef t Clearly riche parent woul ten t hav bot highe con an greate investment i children expenditure o childre b parent withou asset depen onl o endowment o childre an publi expenditures a i (7) bu als o earning o parent (K,_,) thei generosit to childre an perhap no o th uncertaint (e,^ abou luc o childre an late descendants a i withg*>0 an privat expenditure woul no b perfec substitute i pub expenditure affecte rate o retur o privat expenditures a tuitio i subsidized However i the ar perfec substitutes g depen simpl o th su o s,_ an F,_, a increas i publi i the equivalen t a equa increas i parenta earn Th effec o children' endowment o investment i no ambig 0 becaus a increas i thei endowment raise th re o childre a wel a th productivit o investment i thei capital Expenditure o childre ar discourage whe chil Eve parent wh accumulat asset ove thei lifetim ma lac asset whil investin children CAPITA AN FAMIL RIS AN FAL +€ € = €, r,_ intercep woul diffe amon familie i governmen expenditure V2 differe amon them Th stochasti ter €, i negativel t th marke luc o parents th luc o adult an childre (€* i hel constant th earning childre woul regres t th mea a th rat o 1 — However th i biase downwar b th "transitory componen o lifetim o parent i OL regression o th actua lifetim earn o childre o th actua lifetim earning o parent o i th sam fo al families th expecte valu o th regressio woul equa cr an ar th variance o € an Thi coefficien i close th degre o inheritabilit whe th inequalit i th transitor com o lifetim earning i a smalle fractio o th tota inequalit lifetim earnings o particula races religions castes o othe characteristic suffe fro marke discriminatio ear les tha d familie with thes characteristics Person wit characteristic tha ar subjec t ear les tha d person no subjec t discriminatio whe thei parents earning ar equal Person subjec t discrimi woul ear less—give th degre o inheritability—a lon a reduce th earning fro give endowments fo dis the reduce th intercep i th equatio tha relate th o parent an childre i eq [11]) t capita market t financ investment i childre separate transmissio o earning fro th generosit an resource o par Economist hav argue fo a lon time however tha huma capi i poo collatera t lenders Childre ca "default o th marke contracte fo the b workin les energeticall o b enterin wit lowe earning an highe psychi income Suc AN HUMA CAPITA a increas i th rat o interes reduce th investmen i capita and hence earnings Compar O an char 12 effec o a increas i publi expenditure i les clear I publi ar perfec substitute dolla fo dolla fo privat expendi th productio o huma capita woul b determine b thei an b a increas i publi expenditure woul the a equa decreas i privat (parental expenditures an th o huma capita woul b unchanged Eve then a suf larg increas i publi expenditure woul rais th accumula o huma capita becaus privat expenditure canno b negative tha th huma capita an earning o childre woul no o thei parents asset an earning becaus poo parent borro wha i neede t financ th optima investmen i thei However th incom o childre woul depen o parent gift an bequest o asset an deb woul b sensitiv t th an wealt o parents Indeed wealth parent woul ten t th whol accumulatio o huma capita an t ad a siz gif o asset a well th earning an huma capita o childre woul no b relate t parents earning an wealth the woul b indirectl throug th inheritabilit o endowments Th greater th de o inheritability th mor closel relate woul b th huma capi an earning o parent an children T deriv th relatio betwee earning o parent an children substitut th optima leve o b equatio (7 int th earnings-generatin equatio (3 t ge Vl £ (£, V: (9 , thi equatio relate t an ca b replace b (2 an the ca b relate t an othe variables surprisingly th earning o parent an childre ar mor relate whe endowment ar mor inheritabl However relatio betwee thei earning als depend o th tota effec o o earning I thi effec i independen o th leve endowment the CAPITA AN FAMIL RIS AN FAL publi an privat expenditure ar substitutes Parent ca separat i childre (a exampl o th separatio theorem fro ow resource an altruis towar childre becaus borrowe ca b mad th children' obligation optima investmen i give i char 1 b th intersectio o th "suppl curv o funds, wit a negativel incline deman Thi figur clearl show tha better-endowe chil accumulat mor huma capital thos wit th endowmen ac unit o expenditure whil thos wit £ accumulat Therefore better-endowe childre woul hav highe ex earning becaus equatio (3 convert huma capita int ex adul earnings Th tota effec o endowment o earnings an inequalit an skewnes i earning relativ t tha i endowments raise b th positiv relatio betwee endowment expenditures 12 o retur o parenta expenditure o children AN HUMA CAPITA ill rr > 0 b inequalit (5) th huma capita o differen person ma b clos substi i production eac perso form a separate human-capita "mar Rate o retur t hi depen o th amoun investe i hi a a o aggregat stock o huma capital Margina rate o retur declin a mor i investe i a perso becaus investmen eventuall ris a hi forgon earning rise Also benefit declin rapidl a hi remainin workin lif shorten (se th mor discussio i Becke [1975]) capita o asset ca usuall b purchase an sol i rela efficien markets Presumably therefore return o asset ar les t th amoun owne b an perso tha ar o huma Littl i know abou th effec o abilities othe endowments wealt o return fro differen assets althoug som theor sug a positiv relatio (se Ehrlic an Ben-Zio [1976] se als th i Yitzhak [1984]) Ou analysi onl require th reasonabl tha return o asset ar muc les sensitiv t endowment accumulation b an perso tha ar return o huma capita ( assumptio i mad i Becke [1967 1975]) A simpl specia o thi assumptio i tha th rat o retur o asset i th sam t persons o th endowe luc o childre i reveale t parent prio mos o thei investmen i children Therefore w assum tha rate retur o thes investment ar full know t parent (a lon a socia environmen [ct an publi expenditure [5,_ ar known) mus decid ho t allocat thei tota "bequest t childre huma capita an assets W assum initiall tha parent ca a th asse interes rat t financ expenditure o childre an thi deb ca becom th obligatio o childre whe the ar ar assume t maximiz th welfar o childre whe n i thei ow consumptio o leisur i entailed The parent whateve i necessar t maximiz th ne incom (earning mi debt o thei children whic require tha expenditure o th capita o childre equat th margina rat o retur t th in rate o *,- Vi 0 (b eq [6]) 0 an als wit 0 (8 HUMA CAPITA AN FAMIL RIS AN FAL a wel a th publi expenditure o educatio an othe huma o childre an othe variables Sinc earning ar practicall th incom fo mos persons parent influenc th economi welfar thei childre primaril b influencin thei potentia earnings analyz thes influence i a simpl way assum tw period o life an adulthood an tha adul earning depen o huma partl perhap a a measur o credentials an marke (€) earning o on uni o huma capita (7 i determine b equilib i facto markets I depend positivel o technologica knowl ( an negativel o th ratio o th amoun o huma capita t capita i th econom Sinc w ar concerne wit amon families th exac valu o 7 i no usuall importan tha i commo t al families Therefore w assum tha th o i s tha 7 = 1 huma capita take man forms includin skill an abili personality appearance reputation an appropriat credentials furthe simplif b assumin tha i i homogeneou an th sam i differen families Sinc muc researc demonstrate tha in durin childhoo ar crucia t late developmen (see e.g. 1976) w assum als tha th tota amoun o huma capita includin on-the-jo training i proportiona t th accumulate durin childhood The adul huma capita an earning ar determine b endowment inherite fro par an b parenta (x an publi expenditure o hi o he devel = wit > 0 (4 earl an othe aspect o a family' cultura an ge "infrastructure usuall rais th margina effec o famil an pub expenditure o th productio o huma capital tha is margina rat o retur o parenta expenditure i define b equatio AN HUMA CAPITA endowments an w wil no tr t specif th exac mechanis cultura transmission W follo ou previou pape (Becke an 1979 se also e.g. Beva 1979 i assumin a a firs approxima tha bot ar transmitte b a stochastic-linea o Marko equation (2)where Et i th endowmen (o vecto o endowments o th it famil th rth generation i th degre (o vecto o degrees o "inherit o thes endowments an measure unsystemati component luc i th transmissio process W assum tha parent canno in i thei children' endowment prior restriction o th magnitud o eve o th sig o th in o endowment ar unnecessar sinc th degre o inherit ca b estimate fro accurat informatio o th earning o an childre (an perhap als grandparents) Ye th assump tha endowment ar onl partiall inherited tha i les tha unit greate tha zero i a plausibl generalizatio t cultura endow o wha i know abou th inheritanc o geneti traits Thi as implie tha endowment regres t th mean childre wit parent ten als t hav above-averag endowment bu relativ t th mea tha thei parents' wherea childre wit endowe parent ten als t hav below-averag endowment large relativ t th mea tha thei parents' ter a ca b interprete a th socia endowmen commo t member o a give cohor i th sam society I th socia endow wer constan ove time an i 1 th averag endowmen eventuall equa 1/( — time th socia endowmen (i.e. li a/[ — However a ma no b constan because fo example inves i th socia endowment al forma model o th distributio o incom tha con wage an abilitie assum tha abilitie automaticall translat int mediate sometime b demand fo differen kind o abili (see e.g. Ro 1950 Mandelbro 1962 Tinberge 1970 Beva an 1979) Thi i usefu i understandin certai gros feature o distributio o earnings suc a it skewness bu i hardl satisfac fo analyzin th effec o parent o thei children' earnings Par no onl pas o som o thei endowment t children bu the influenc th adul earning o thei childre b expenditure o skills health learning motivation "credentials, an man othe Thes ar determine no onl b th abili o childre bu als b th incomes preferences an fertilit o par HUMA CAPITA AN FAMIL RIS AN FAL i a considerabl improvement W no distinguis huma an earning fro othe wealth an w incorporat restriction th intergenerationa transfe o debt W assum no tha parents depend o th utilit o childre instea o o th permanen o children W als conside th effec o endogenou fertilit th relatio betwee th wealt an consumptio o parent an Thes improvement explai wh th implication o th pres pape ar sometime quit differen fro thos o th earlie paper a essa devote t critiquin part o Becke (1981) Becke an (1984) an a earlie draf o thi paper Goldberge (1985 fail t se thes difference betwee th curren pape an earlie work W commen furthe o hi critiqu elsewher i thi inequalit ove generation an inequalit betwee familie ar relate (a implie b eq [1]) an adequat analysi o inequal mus als conside marita patterns fertility expectation abou fu generations an investment i huma capital Therefore i i surprisin tha a growin literatur durin th las 1 year ha t integrat mor realisti model o famil behavio int model th distributio o incom an wealth. Althoug thi literatur an wor hav man similarities th presen pape i almos alon i th ris an fal o familie t investment i huma capita tha wit th accumulatio o assets th evolutio o consumption th deman fo children Huma childre hav a advantag becaus the ar bor int familie greate ability greate emphasi o childhoo learning an othe cultura an geneti attributes Bot biolog an cultur ar fro parent t children on encode i DN an th i a family' culture Muc les know abou th transmissio o attribute tha o biologica ones an eve les i know abou relativ contribution o biolog an culture t th distinctiv en o eac family W d no nee t separat cultura fro ge Amon th importan contributor t thi literatur ar Stiglit (1969) Blinde (1974) (1974) Behrma an Taubma (1976) Mead (1976) Beva (1979) Laitne Menchi (1979) Shorrock (1979) Lour (1981) an Atkinso (1983) o mode t interpre thei findings W tr t remed thi an t fil a mor genera lacun i th literatur b developin systemati mode tha relie o utility-maximizin behavio b al parti equilibriu i differen markets an stochasti force wit un incidenc amon participants analysi tha i adequat t cop wit th man aspect o th ris fal o familie mus incorporat concer b parent fo childre a i altruis towar children investment i th huma capita children assortativ matin i marriag markets th deman fo chil th treatmen b parent o exceptionall abl o handicappe an expectation abou event i th nex o i eve late gen Althoug thes an othe aspect o behavio ar incorporate a consisten framewor base o maximizin behavior w d no t handl the al i a satisfactor manner However ou ap indicate ho a mor complet analysi ca b develope i future nex sectio ha a length o investment i th huma o children Th discussio i length becaus th relatio be th earning o parent an childre i th majo determinan o ris an fal o mos families Sectio 3 move o t conside th betwee investment i huma capital transfer o materia (gift an bequests fro parent t children an th evolutio consumptio ove generations 4 consider th effec o th numbe o childre o intergen mobilit o consumptio an wealt an als th effec o mo o assortativ matin i marriag markets 5 assemble abou a doze studie o th degre o regressio th mea betwee parent an childre i income earnings an Availabl studie ar fe an ar base o limite data bu th o som basi parameter o ou mode ar suggeste b th fo th Unite State an othe countries o ou analysi o huma capita i base o th mode devel i Becker' Woytinsk Lectur (1967 t explai differen invest amon families However tha lectur i mainl concerne wit skewnes earning an wealt an doe no deriv rela betwee th earning an asset o parent an children Th ap i thi pape i als base o a serie o paper b u i th las tha analyze marriage fertility altruis o parents an long equilibriu relation betwee parent an childre (se esp Becke 1981 Becke an Tome 1976 1979 Tome 1981) presen pape i closes i spiri t Becke an Tome (1979) thes paper diffe i importan ways W believ tha th presen CAPITA AN FAMIL RIS AN FAL considerabl empirica evidenc o th occupations education othe characteristic o childre an parents Bla an Dunca i th influentia boo con th effec o famil backgroun o th achievement o children lon ag a 1889 Joh Dewe wrote "[U]po th average childre parent wh ar exceptional o wh deviat fro th mean wil deviat fro th mea onl on thir o thei parents devia .. I i no likel tha childre o th poo woul b bette off an o th wealthie poore i anythin lik th rati o 2/3 [1889 pp 333-34] thi statemen wa brough t ou attentio O D Duncan) discussion o inequalit amon familie hav bee almos separat fro discussion o inequalit betwee generation o sam family thes inequalitie ar analyticall closel related I par regressio awa fro th mea i th relatio between say th o parent an childre implie larg an growin inequalit o ove time whil regressio towar th mea implie a smalle mor stabl degre o inequality Thes statement ar obviou i a Marko mode o th relatio betwee parent an children i th incom o parents I + , i th incom o children an ar constants an th stochasti force affectin th incom o chil (e j ar assume t b independen o th incom o parents i incom wil continu t gro ove tim i i greate o equa t unity whil inequalit i incom wil approac a con leve i i smalle tha unit i absolut value Clearly th siz o als measure whethe childre o riche parent ten t b les ric thei parent an whethe childre o poore parent ten t b of tha thei parents Thi exampl implie that eve i rigi caste-dominate societies man o th elit an underprivilege woul chang place ove generation unles inequalit contin t gro ove tim 1) degre o regressio towar o awa fro th mea i th o childre compare t thos o thei parent i a meas o th degre o equalit o opportunit i a society Th purpos thi pape i t analyz th determinant o unequa opportunities calle "intergenerationa mobility, or a i th titl o ou "th ris an fal o families. W us al thes term inter man empirica studie o mobilit b sociologist hav lacke a X S Becke an Nige Tome sinc Paret discovere tha th distributio o large income an i reasonabl wel approximate b a particula skewe distribu sinc the calle th "Paret distribution, economist hav contin t discus inequalit i th distributio o earnings, income an amon individual an families However the hav pai littl t th inequalit withi familie ove generation a deter b th relatio betwee th income o wealt o parents chil an late descendants Schumpete i th onl majo economis systematicall considere intergenerationa mobilit wit empirica a wel a wit theoretica analysi (se Schumpete 1951) an othe socia scientists o th othe hand hav pre researc ha bee supporte b Nationa Scienc Foundatio Gran no SE W receive valuabl assistanc fro Gal Mostelle an Michae Gibbs W ap th usefu comment a th Conferenc o th Famil an th Distributio o Reward an a seminar a Bar-Ila University Brigha Youn University th o Chicago th Hebre University Institut de Etude Politiques th Univer o Pennsylvania Purdu University Stanfor University an th Universit o Wester W especiall than Rober Willi fo hi helpfu discussio a th Conferenc th Famil an th Distributio o Economi Rewards W hav als benefite fro b Arthu Goldberge an Sherwi Rosen