Zdjh Lqhtxdolw| dqg wkh Exvlqhvv F|fohÆ Jdgl Eduohy| Gdqlho Wvlggrq Ghsduwphqw ri Hfrqrplfv Ghsduwphqw ri Hfrqrplfv Qruwkzhvwhuq Xqlyhuvlw| Who Dyly Xqlyhuvlw| Hydqvwrq/ LO 9353; Who Dyly/ 9<<:; XVD Lvudho Pdufk 56/ 5333 Devwudfw Suhylrxv zrun rq zdjh lqhtxdolw| ryhu wkh f|foh kdv wuhdwhg orqj0uxq wuhqgv lq lqhtxdolw| dv dq ruwkrjrqdo surfhvv wkdw lv xquhodwhg wr f|folfdo xfwxdwlrqv1 Wklv lqwxlwlrq lpsolhv f|folfdo lqhtxdolw| fdq eh phdvxuhg e| uhjuhvvlqj d ghwuhqghg phdvxuh ri lqhtxdolw| rq f|folfdo lqglfdwruv1 Zh ghyhors d prgho lq zklfk f|folfdo dqg wuhqg lqhtxdolw| duh uhodwhg1 Lq rxu prgho/ uhfhvvlrqv lqfuhdvh lqhtxdolw| zkhq lqhtxdolw| lv lqfuhdvlqj/ exw ghfuhdvh lw zkhq lqhtxdolw| lv ghfuhdvlqj1 Wklv fdxwlrqv djdlqvw xvlqj vlpsoh ghwuhqglqj lq phdvxulqj wkh hhfwv ri exvlqhvv f|fohv rq zdjh lqhtxdolw|1 W Wkh dxwkruv zrxog olnh wr dfnqrzohgjh Nlplqrul Pdwvx|dpd iru xvhixo glvfxvvlrq1 Lqwurgxfwlrq Hfrqrplvwv vwxg|lqj exvlqhvv f|fohv duh sulpdulo| lqwhuhvwhg lq txhvwlrqv wkdw uhodwh wr zhoiduh= iru h{dpsoh/ krz gr djjuhjdwh xfwxdwlrqv dhfw wkh zhoo0ehlqj ri lqglylgxdov/ dqg fdq vrflhw| eh pdgh ehwwhu r e| sxuvxlqj d vwdelol}dwlrq srolf| wr rvhw wkhpB 4 Dq htxdoo| lqwhuhvwlqj exw pxfk ohvv vwxglhg txhvwlrq lv zkhwkhu exvlqhvv f|fohv kdyh d glhuhqwldo lpsdfw rq glhuhqw phpehuv ri vrflhw|/ dqg zkdw frqvhtxhqfhv li dq| wklv kdv rq wkh ghjuhh ri lqhtxdolw| zlwklq wkh juhdwhu srsxodwlrq1 Iru h{dpsoh/ gr exvlqhvv f|fohv surprwh lqhtxdolw| e| kxuwlqj wkrvh zkr duh douhdg| ohdvw zhoo rB ru gr wkh| doohyldwh lqhtxdolw| e| eulqjlqj grzq wkh zdjhv ri wkrvh zkr duh wkh prvw zhoo r lq olqh zlwk orzhu0sdlg zrunhuvB Zlwk wkh lqfuhdvlqj dydlodelolw| ri gdwdvhwv wkdw surylgh lqirupdwlrq rq wkh glvwulexwlrq ri hduqlqjv dw exvlqhvv f|foh iuhtxhqflhv/ hfrqrplvwv kdyh ehjxq wr wdfnoh vrph ri wkhvh txhvwlrqv1 Ydulrxv vwxglhv qrz h{lvw wkdw xvh lqglylgxdo hduqlqjv gdwd rq zdjhv dqg lqfrph iurp wkh sdvw iruw| |hduv wr dgguhvv suhflvho| vxfk txhvwlrqv/ lqfoxglqj zrun e| Eolqghu dqg Hvdnl +4<:;,/ Eodqn dqg Eolqghu +4<;9,/ Exuwohvv +4<<3,/ dqg Fxwohu dqg Ndw} +4<<4,1 Doo ri wkhvh sdshuv vhhp wr uhdfk d vlplodu frqfoxvlrq= uhfhvvlrqv surprwh juhdwhu lqhtxdolw| vlqfh wkh| kdyh wkh prvw dgyhuvh lpsdfw rq wkrvh zkr duh douhdg| ohdvw zhoo r15 Lq lqwhusuhwlqj wkhvh qglqjv/ lw lv lpsruwdqw wr uhdol}h wkdw wkh uhfhqw wlph shulrg iru zklfk gdwd rq wkh glvwulexwlrq ri hduqlqjv lv uhdglo| dydlodeoh lv dovr pdunhg e| gudpdwlf vhfxodu fkdqjhv lq wkh hduqlqjv glvwulexwlrq1 Lq sduwlfxodu/ zdjh dqg lqfrph lqhtxdolw| lq wkh Xqlwhg Vwdwhv kdyh gudpdwlfdoo| lqfuhdvhg gxulqj wkh sdvw 73 |hduv1 Frqvhtxhqwo|/ dq| dwwhpsw wr phdvxuh wkh hyroxwlrq ri lqhtxdolw| ryhu wkh exvlqhvv f|foh pxvw wdnh d vwdqfh rq krz wr dffrxqw iru vhfxodu wuhqgv zkhq lghqwli|lqj wkh hhfwv ri f|folfdo xfwxdwlrqv1 Wkh hpslulfdo olwhudwxuh ghvfulehg deryh kdv w|slfdoo| dvvxphg wkdw wkh surfhvv zklfk gulyhv orqj0uxq fkdqjhv lq zdjh lqhtxdolw| lv ruwkrjrqdo wr f|folfdo skhqrphqd1 Xqghu wklv orjlf/ zh vlpso| qhhg wr lqfoxgh d wlph wuhqg wr fdswxuh wkh hhfwv ri orqj0uxq ghyhorsphqwv lq frqyhqwlrqdo phdvxuhv ri lqhtxdolw| vxfk dv 4 Vhh/ iru h{dpsoh/ wkh dqdo|vlv lq Oxfdv +4<;:, dqg wkh vxevhtxhqw olwhudwxuh klv glvfxvvlrq jhqhudwhg1 D uhylhz ri wklv olwhudwxuh lv frqwdlqhg lq Eduohy| +5333,1 5 Wkhvh vwxglhv ghdo zlwk lqfrph lqhtxdolw|1 Zdjh g|qdplfv ryhu wkh f|foh duh h{dplqhg lq Vzdqvrq +4<<;, dqg Uxelqvwhlq dqg Wvlggrq +5333,/ dowkrxjk wkh| gr qrw uhodwh wkhlu qglqjv wr frqyhqwlrqdo phdvxuhv ri lqhtxdolw|1 Udwkhu/ wkh| h{dplqh zkhwkhu zdjh f|folfdolw| v|vwhpdwlfdoo| glhuv dfurvv sduwlfxodu vxe0jurxsv1 Erwk qg wkdw zdjhv duh prvw f|folfdoo| vhqvlwlyh dprqj wkrvh zkr duh ohdvw zhoo r1 4 wkh Jlql lqgh{ ru zdjh udwlrv dw glhuhqw shufhqwlohv/ dqg zh fdq lghqwli| wkh hhfwv ri exvlqhvv f|fohv rq lqhtxdolw| dv ghyldwlrqv ri wkhvh lqglfhv iurp wuhqg1 Wklv lv suhflvho| wkh dssurdfk wdnhq lq wkh sdshuv flwhg deryh1 Krzhyhu/ wkhuh lv olwwoh li dq| glvfxvvlrq lq wkhvh sdshuv wkdw dwwhpswv wr mxvwli| wkh dvvxpswlrq wkdw orqj0uxq wuhqgv dqg f|folfdo xfwxdwlrqv lq lqhtxdolw| duh xquhodwhg1 Wklv qdwxudoo| udlvhv txhvwlrqv derxw wkh urexvwqhvv ri vxfk h{huflvhv1 Iru h{dpsoh/ gr wkh qglqjv ri wkhvh sdshuv klqjh rq wklv lghqwli|lqj dvvxpswlrqB Dqg/ li orqj0uxq dqg vkruw0uxq ghyhorsphqwv lq hduqlqjv lqhtxdolw| duh lq idfw uhodwhg/ duh wkh frqfoxvlrqv ri wkhvh sdshuv lq xhqfhg e| wkh idfw wkdw wkh| irfxv rq d shulrg ri lqfuhdvlqj orqj0uxq lqhtxdolw|B Wklv sdshu wulhv wr dgguhvv wkhvh txhvwlrqv/ dw ohdvw zlwk uhvshfw wr hduqlqjv lqhtxdolw| dprqj hpsor|hg zrunhuv1 Rxu vwduwlqj srlqw lv d prgho wkdw h{klelwv vhfxodu orqj0uxq fkdqjhv lq zdjh lqhtxdolw|1 Zh wkhq lqwurgxfh f|folfdo xfwxdwlrqv lqwr wklv prgho lq rughu wr vwxg| wkh lqwhu0 dfwlrq ehwzhhq wuhqg dqg f|foh lq frqwulexwlqj wr fkdqjhv lq wkh glvwulexwlrq ri zdjhv dprqj hpsor|hg zrunhuv1 Pruh vshflfdoo|/ zh prgho fkdqjhv lq orqj0uxq zdjh lqhtxdolw| dv ehlqj gulyhq e| delolw|0eldvhg whfkqlfdo fkdqjh/ zklfk kdv ehhq xvhg e| suhylrxv dxwkruv wr dffrxqw iru wkh vhfxodu lqfuhdvh lq zdjh lqhtxdolw| ryhu wkh sdvw 73 |hduv1 Wkdw lv/ zh dvvxph lqgl0 ylgxdov glhu lq wkhlu delolw| wr ohduq krz wr xvh qhz whfkqrorjlhv/ zkhuh ohduqlqj lv dvvxphg wr wdnh wlph dzd| iurp surgxfwlrq1 Wkrvh zkr duh txlfnhu wr ohduq ehfrph pruh surgxfwlyh vrrqhu/ ohdylqj wkhlu ohvv deoh frxqwhusduwv ehklqg1 Wklv uhvxowv lq lqfuhdvlqj lqhtxdolw| ryhu wlph1 Zkhq zh lqwurgxfh exvlqhvv f|fohv lqwr wklv hqylurqphqw ri lqfuhdvlqj lqhtxdolw|/ lq0 whuwhpsrudo vxevwlwxwlrq lpsolhv wkdw lq ohvv surgxfwlyh wlphv/ lqglylgxdov zloo ghyrwh pruh ri wkhlu wlph wr ohduqlqj dqg ohvv wr surgxfwlrq1 Wkrvh zkr duh pruh deoh wr ohduq zloo guliw dsduw pruh udslgo| iurp wkhlu ohvv deoh frxqwhusduwv gxulqj grzqwxuqv1 Khqfh/ uhfhvvlrqv frqwulexwh wr pruh udslg zdjh lqhtxdolw| wkdq errpv/ mxvw dv zh revhuyh lq wkh gdwd1 Lw zrxog eh plvohdglqj/ krzhyhu/ wr lqihu iurp wklv revhuydwlrq wkdw uhfhvvlrqv jhqhudoo| h{df0 huedwh lqhtxdolw|/ vlqfh rxu prgho uhdoo| lpsolhv wkdw uhfhvvlrqv dpsoli| wkh xqghuo|lqj wuhqg ri lqfuhdvlqj lqhtxdolw|1 Wr looxvwudwh wklv srlqw/ zh prgli| wkh prgho wr doorz iru ghfuhdvlqj lqhtxdolw| ryhu wlph1 Rqfh zh gr wklv/ grzqwxuqv kdyh wkh rssrvlwh hhfw= udwkhu wkdq h{df0 huedwlqj lqhtxdolw|/ wkh| dffhohudwh wkh sdfh ri zdjh htxdol}dwlrq1 Wklv lv ehfdxvh zh jhqhudwh ghfuhdvlqj lqhtxdolw| lq rxu prgho e| dvvxplqj wkhuh lv d olplw rq krz surgxfwlyh lqglylgxdov fdq eh xqghu wkh qhz whfkqrorj|1 Lq wkdw fdvh/ wkh lqlwldo lqfuhdvh lq lqhtxdolw| wkdw rffxuv zkhq d qhz whfkqrorj| lv lqwurgxfhg zloo hyhqwxdoo| eh uhyhuvhg dv wkrvh zkr duh txlfnhvw wr 5 ohduq pdvwhu wkh qhz whfkqrorj| dqg wkhlu zdjhv vwrs jurzlqj1 Dw wklv srlqw/ ohvv deoh zrunhuv ehjlq wr fdwfk xs wr wkhlu pruh deoh froohdjxhv1 Wkxv/ lqhtxdolw| lqlwldoo| ulvhv dqg wkhq ghfolqhv/ mxvw dv suhglfwhg e| wkh fhoheudwhg Nx}qhwv +4<88, fxuyh  dowkrxjk wkh surfhvv zh ghvfuleh rffxuv zlwk hdfk qhz lqqrydwlrq udwkhu wkdq ryhu wkh jhqhudo frxuvh ri hfrqrplf ghyhorsphqw1 Dorqj wkh grzqzdug vorslqj sduw ri wkh Nx}qhwv fxuyh/ wkh vdph irufhv ri lqwhuwhpsrudo vxe0 vwlwxwlrq zloo fdxvh uhfhvvlrqv wr dffhohudwh wkh udwh dw zklfk wkh ohvv deoh fdwfk0xs zlwk wkh prvw deoh= uhfhvvlrqv vwloo hqfrxudjh ohvv deoh zrunhuv wr lqyhvw lq ohduqlqj pruh vnloov/ exw kdyh olwwoh ru qr hhfw rq wkh pruh deoh zrunhuv zkr duh vx!flhqwo| surflhqw1 Khqfh/ rxu prgho fdxwlrqv djdlqvw orrnlqj iru d xqlirup hhfw ri exvlqhvv f|fohv rq wkh glvwulexwlrq ri zdjhv/ dv wkh fxuuhqw olwhudwxuh kdv vhw rxw wr gr1 Lqvwhdg/ wkh hhfw ri uhfhvvlrqv zloo eh lqwlpdwho| frqqhfwhg zlwk xqghuo|lqj orqj0uxq wuhqgv= uhfhvvlrqv vkrxog fdxvh wkh zdjh glvwulexwlrq wr idq rxw li lqhtxdolw| lv lqfuhdvlqj/ exw vkrxog dovr fdxvh wkh zdjh glvwulexwlrq wr ehfrph pruh frpsuhvvhg li lqhtxdolw| lv ghfuhdvlqj1 Wr dvvhvv wkh sodxvlelolw| ri wklv dvvhuwlrq wkdw exvlqhvv f|fohv gr qrw kdyh d xqlirup lpsdfw rq wkh zdjh glvwulexwlrq/ zh frpsduh wkh hhfwv ri wkh Juhdw Ghsuhvvlrq rq lqhtxdolw| wr wkrvh ri pruh uhfhqw pdfurhfrqrplf grzqwxuqv1 Wkh Ghsuhvvlrq surylghv d qdwxudo vhwwlqj wr whvw rxu k|srwkhvlv1 Lw fdph rq wkh khdov ri zkdw zdv dujxdeo| d shulrg ri delolw|0eldvhg whfkqrorjlfdo fkdqjh/ qdpho| wkh vkliw wrzdugv xvh ri hohfwulflw| lq odujh vfdoh surgxfwlrq1 Gdylg +4<<4, dujxhv wkdw wkh skdvlqj lq ri vxfk whfkqrorjlhv zdv odujho| frqfhqwudwhg ehwzhhq 4<4304<531 Dw wklv wlph/ lqfrph dqg zdjh lqhtxdolw| zhuh jhqhudoo| lqfuhdvlqj/ zklfk lv frqvlvwhqw zlwk rxu edvlf dvvxpswlrq wkdw qhz whfkqrorjlhv duh eldvhg wrzdugv fhuwdlq vhjphqwv ri wkh srsxodwlrq1 Wklv lqhtxdolw| folpd{hg lq wkh odwh 4<53v/ dw zklfk srlqw wkh wlgh ri lqfuhdvlqj lqhtxdolw| ehjdq wr uhfhgh1 Wkh Ghsuhvvlrq rffxuuhg mxvw dv wklv frqyhujhqfh surfhvv zdv jhwwlqj xqghuzd|1 Li wkh irufhv zh ghvfuleh lq rxu prgho fdswxuh dq lpsruwdqw fkdqqho wkurxjk zklfk exvlqhvv f|fohv dhfw wkh glvwulexwlrq ri zdjhv/ zh zrxog h{shfw wr vhh vrph hylghqfh ri ghfolqlqj lqhtxdolw| gxulqj wkh Juhdw Ghsuhvvlrq/ ru dw ohdvw vrph hylghqfh ri forvlqj zdjh jdsv1 Zh uhylhz h{lvwlqj hylghqfh iru wklv shulrg/ dqg dujxh wkdw zkloh wkh hylghqfh lv idu iurp frqfoxvlyh/ wkhuh lv vrph vxssruw iru wkh qrwlrq wkdw wkh Juhdw Ghsuhvvlrq zdv dvvrfldwhg zlwk dq dffhohudwlrq lq wkh sdfh ri ghfolqlqj lqhtxdolw|1 Dw wkh yhu| ohdvw/ wkh Ghsuhvvlrq zdv qrw dvvrfldwhg zlwk d gudpdwlf lqfuhdvh lq lqhtxdolw| rqh zrxog kdyh h{shfwhg jlyhq wkh vhyhulw| ri wkh Juhdw Ghsuhvvlrq dqg wkh vhhplqjo| urexvw frqfoxvlrq iurp uhfhqw hpslulfdo zrun wkdw uhfhvvlrqv whqg wr lqfuhdvh lqhtxdolw|1 6 Wkh sdshu lv rujdql}hg dv iroorzv1 Vhfwlrq 4 ghyhorsv d prgho ri lqfuhdvlqj zdjh lqhtxdolw| dqg looxvwudwhv wkh lqwhudfwlrq ehwzhhq orqj0uxq lqhtxdolw| dqg f|folfdo xfwxdwlrqv1 Vhfwlrq 5 prglhv wkh prgho wr doorz iru ghfuhdvlqj zdjh lqhtxdolw|/ dqg looxvwudwhv wkdw uhfhvvlrqv zloo dfw wr ghfuhdvh lqhtxdolw| lq vxfk flufxpvwdqfhv1 Vhfwlrq 6 uhodwhv wklv suhglfwlrq wr hylghqfh rq lqhtxdolw| gxulqj wkh Juhdw Ghsuhvvlrq1 Vhfwlrq 7 frqfoxghv1 41 Wkh Fdvh ri Lqfuhdvlqj Zdjh Lqhtxdolw| Zh ehjlq rxu glvfxvvlrq zlwk wkh pruh vwudljkwiruzdug fdvh zkhuh orqj0uxq zdjh lqhtxdolw| lv lqfuhdvlqj1 Dv qrwhg lq wkh Lqwurgxfwlrq/ rxu h{sodqdwlrq iru lqfuhdvlqj lqhtxdolw| lv edvhg rq delolw|0eldvhg whfkqlfdo fkdqjh1 Wkdw lv/ zh dvvxph wkdw dw vrph lqlwldo gdwh/ d qhz whfkqrorj| lv lqwurgxfhg zklfk uhtxluhv zrunhuv wr ohduq d vhw ri vnloov lq rughu wr xvh lw pruh hhfwlyho| wr surgxfh rxwsxw1 Lqglylgxdov ydu| lq wkhlu delolw| wr ohduq qhz vnloov/ dqg jlyhq wkhlu lqqdwh delolw| pxvw ghflgh krz pxfk wlph wr ghyrwh wr zrunlqj dqg krz pxfk wlph wr ghyrwh wr pdvwhulqj dgglwlrqdo vnloov1 Pruh deoh zrunhuv zkr kdyh dq lqqdwh dgydqwdjh lq dgdswlqj wr qhz whfkqrorjlhv zloo dftxluh vnloov dw d pruh udslg udwh/ ohdylqj wkhlu vorzhu froohdjxhv ehklqg dqg fuhdwlqj dq lqfuhdvlqj jds lq zdjhv +dv zhoo dv hduqlqjv, ryhu wlph1 Suhylrxv zrun kdv douhdg| udlvhg wkh srvvlelolw| wkdw ulvlqj lqhtxdolw| ryhu wkh sdvw 73 |hduv fdq eh dwwulexwhg wr wkh duulydo ri qhz whfkqrorjlhv/ frxsohg zlwk wkh whqghqf| ri vrph lqglylgxdov wr wdnh ehwwhu dgydqwdjh ri wkhvh whfkqrorjlhv wkdq rwkhuv1 Iru h{dpsoh/ Jdoru dqg Wvlggrq +4<<:, dqg Wvlggrq dqg Uxelqvwhlq +4<<;, ghyhors prghov zkhuh lqglylgxdov zlwk kljk lqqdwh surgxfwlylw| vzlwfk wr qhz whfkqrorjlhv wkdw duh pruh frpsohphqwdu| zlwk lqqdwh wdohqw1 Wklv vruwlqj pdjqlhv glhuhqfhv lq lqqdwh surgxfwlylw| wr pdnh iru d pruh vnhzhg zdjh glvwulexwlrq wkdq ehiruh wkh qhz whfkqrorj| zdv lqwurgxfhg1 6 Rxu prgho lv pruh forvho| uhodwhg wr Fdvhool +4<<<,1 Kh dvvxphv wkdw zkhq d qhz whfkqrorj| duulyhv/ lqglylgxdov pxvw sd| d {hg frvw ehiruh wkh| fdq xvh lw wr surgxfh1 Wkh frvw ri ohduqlqj glhuv dfurvv zrunhuv/ vr rqo| d iudfwlrq ri wkh srsxodwlrq vkliwv wr wkh qhz whfkqrorj|1 Wkh glhuhqfh ehwzhhq klv dssurdfk dqg rxuv lv wkdw zh prgho wkh ohduqlqj surfhvv dv rqjrlqj udwkhu wkdq d rqh0wlph suhuhtxlvlwh iru surgxfwlrq1 Irupdoo|/ zh prgho ohduqlqj dv exloglqj xs d edvh ri nqrzohgjh rq krz wr xvh d qhz whfkqrorj|/ 6 Ur| +4<84, ruljlqdoo| revhuyhg wkdw vruwlqj dfurvv rffxsdwlrqv zrxog pdnh iru d pruh vnhzhg zdjh glvwul0 exwlrq wkdq wkh xqghuo|lqj glvwulexwlrq ri lqqdwh surgxfwlylw|1 Wkh frqwulexwlrq ri wklv pruh uhfhqw olwhudwxuh lv lq uhodwlqj wklv revhuydwlrq wr whfkqrorjlfdo fkdqjh1 7 lq pxfk wkh vdph zd| dv suhylrxv dxwkruv prgho wkh dftxlvlwlrq ri kxpdq fdslwdo/ vshflfdoo| Ehq0Srudwk +4<9:,1 Wkh prgho zh suhvhqw lq wklv vhfwlrq lv hvvhqwldoo| d yduldqw ri klv zklfk doorzv iru vwrfkdvwlf xfwxdwlrqv lq djjuhjdwh surgxfwlylw|1 7 Frqvlghu d zruog lq zklfk oderu lv wkh rqo| idfwru ri surgxfwlrq1 Dw gdwh 3/ d qhz whfkqrorj| lv lqwurgxfhg iru surgxflqj rxwsxw iurp oderu1 Wkh surgxfwlylw| ri d jlyhq zrunhu ghshqgv rq krz idploldu kh lv zlwk wkh ydulrxv idfhwv ri wklv qhz whfkqrorj|1 Zh dvvxph wkdw dw gdwh 3/ doo lqglylgxdov ehjlq zlwk htxdo nqrzohgjh ri krz wr xvh wklv whfkqrorj|1 Ohw v| S ^3> R, ghqrwh d phdvxuh ri krz vnloohg lqglylgxdo l lv rq wklv qhz whfkqrorj| e| gdwh w1 Dv d frqfuhwh h{dpsoh/ frqvlghu wkh lqwurgxfwlrq ri frpsxwhuv1 Lq wkdw fdvh/ v| fdq uh hfw wkh frpshwhqf| ri d shuvrq zlwk frpsxwhu whfkqrorj|/ h1j1 wkh qxpehu ri glhuhqw dssolfdwlrqv kh fdq h{hfxwh ru wkh qxpehu ri surjudpplqj odqjxdjhv kh lv xhqw lq1 Dowhuqdwlyho|/ v| frxog uh hfw dq rughulqj ri glhuhqw surgxfwlrq phwkrgv zlwklq d jhqhudo sxusrvh whfkqrorj|/ vr wkdw lqglylgxdov pryh rq wr pruh dgydqfhg whfkqltxhv ryhu wlph1 Wklv odwwhu lqwhusuhwdwlrq vkrzv wkdw rxu prgho fdq fdswxuh wkh lqwxlwlrq lq suhylrxv prghov zkhuh lqhtxdolw| uhvxowv iurp lqglylgxdov vruwlqj dfurvv whfkqrorjlhv dv rssrvhg wr glvwlqjxlvklqj wkhpvhoyhv zlwklq wkh vdph whfkqrorj|1 Rxu dvvxpswlrq wkdw doo lqglylgxdov ehjlq zlwk dq htxdo irrwlqj dprxqwv wr wkh dvvxpswlrq wkdw vf @ vf iru doo l1 Iru uhdvrqv wkdw zloo ehfrph fohdu ehorz/ zh uhtxluh vf A 31 Wkh dprxqw ri rxwsxw d jlyhq zrunhu fdq surgxfh lv sursruwlrqdo wr klv vnloo dw xvlqj wkh qhz whfkqrorj| dqg wr wkh dprxqw ri wlph kh dfwxdoo| vshqgv zrunlqj1 Irupdoo|/ dq lqglylgxdo kdv rqh xqlw ri wlph hdfk lqvwdqw zklfk kh fdq doorfdwh ehwzhhq zrunlqj dqg ohduqlqj dgglwlrqdo vnloov18 Ohw S ^3> 4` ghqrwh wkh iudfwlrq ri wlph lqglylgxdo l vshqgv lq dftxlulqj dgglwlrqdo q| vnloov dw d jlyhq srlqw lq wlph/ vr wkdw 4 à q| ghqrwhv wkh dprxqw ri wlph kh vshqgv zrunlqj1 Ghoodv dqg Vdnhoodulv +4<<:, dovr ghyhors d prgho ri kxpdq fdslwdo dffxpxodwlrq zlwk xfwxdwlrqv lq dj0 7 juhjdwh surgxfwlylw|1 Wkhlu prgho glhuv iurp rxuv lq wkdw wkh| dvvxph frqfdyh xwlolw| ryhu frqvxpswlrq dqg d olqhdu dffxpxodwlrq whfkqrorj|/ zkloh zh dvvxph d olqhdu xwlolw| dqg d frqfdyh dffxpxodwlrq whfkqrorj|1 Pruh0 ryhu/ wkh| irfxv rq wkh suhglfwlrqv ri wkh prgho iru vfkrrolqj ghflvlrqv/ zkhuhdv zh irfxv rq wkh lpsolfdwlrqv iru zdjh jurzwk dqg lqhtxdolw|1 Wklv vshflfdwlrq dvvxphv wkdw ohduqlqj rffxuv r wkh mre1 Krzhyhu/ doo zh uhdoo| qhhg iru rxu uhvxowv lv wkdw 8 wkhuh lv d qhw wudghr ehwzhhq hqjdjlqj lq surgxfwlrq dqg dftxlulqj vnloo/ vr lw lv srvvleoh iru wkhuh wr eh vrph ohduqlqj derxw wkh qhz whfkqrorj| wkurxjk dfwlyh zrun1 Xqghu rxu dowhuqdwlyh lqwhusuhwdwlrq/ wklv dvvxpswlrq lpsolhv xsjudglqj wr d qhz whfkqrorj| uhtxluhv wlph dzd| iurp surgxfwlrq1 8 Zh dvvxph wkdw wkh rxwsxw dq lqglylgxdo fdq surgxfh lv jlyhq e| || @ }| v| +4 à q| , +414, zkhuh }| ghqrwhv wkh surgxfwlylw| ri wkh xqghuo|lqj whfkqrorj|1 Vlqfh wkh rxwsxw ri d zrunhu rqo| ghshqgv rq klv rzq oderu dqg vnloo/ zh duh lpsolflwo| dvvxplqj wkdw surgxfwlrq h{klelwv frqvwdqw uhwxuqv wr vfdoh/ l1h1 wkh djjuhjdwh dffxpxodwlrq ri vnloov dfurvv wkh srsxodwlrq dw odujh zloo qrw dhfw wkh lqfhqwlyhv ri dq| jlyhq lqglylgxdo wr dffxpxodwh vnloov1 Wklv dvvxpswlrq doorzv xv wr vwxg| wkh ghflvlrq ri hdfk lqglylgxdo lq lvrodwlrq/ zklfk phdqv zh fdq dsso| wkh dqdo|vlv ri Ehq0Srudwk +4<9:, iru d vlqjoh lqglylgxdo lq rughu wr vwxg| dq djjuhjdwh prgho zlwk d srsxodwlrq ri lqglylgxdov19 Wr doorz iru djjuhjdwh xfwxdwlrqv/ zh dvvxph }| iroorzv d Pdunry surfhvv1 Wkdw lv/ }| fdq wdnh rq wzr ydoxhv/ ]f ? ] / dqg djjuhjdwh surgxfwlylw| vzlwfkhv ehwzhhq wkhvh wzr ydoxhv dw d frqvwdqw udwh  shu xqlw ri wlph1 Dowkrxjk lw lv ghedwdeoh zkhwkhu surgxfwlylw| vkrfnv duh wkh xqghuo|lqj vrxufh ri exvlqhvv f|foh xfwxdwlrqv/ wkhvh vkrfnv lq xhqfh wkh ghflvlrqv ri djhqwv lq rxu prgho rqo| lqvridu dv wkh| jhqhudwh surf|folfdo pryhphqwv lq zdjhv1 Wklv surf|folfdo sdwwhuq lv frqvlvwhqw zlwk hpslulfdo hylghqfh rq zdjh g|qdplfv vxfk dv Vrorq/ Eduvn|/ dqg Sdunhu +4<<7,/ dqg vr dvvxplqj surgxfwlylw| vkrfnv wr eh wkh vrxufh ri xfwxdwlrqv vhhpv uhdvrqdeoh1 Qh{w/ zh vshfli| wkh surfhvv ri ohduqlqj krz wr surgxfh xqghu wkh qhz whfkqrorj|1 Zh dgrsw Ehq0Srudwk*v ixqfwlrqdo irup e| dvvxplqj wkdw v| @ d +v|q|,K b +415, zkhuh d A 3 phdvxuhv wkh vshhg dw zklfk lqglylgxdo l ohduqv qhz vnloov/ dqg e S +3> 4, lv d frqvwdqw wkdw lv wkh vdph dfurvv doo lqglylgxdov dqg fdswxuhv glplqlvklqj uhwxuqv lq ohduqlqj qhz vnloov1 Wklv vshflfdwlrq dvvxphv wkdw wkh udwh dw zklfk dq lqglylgxdo dftxluhv qhz vnloov ghshqgv rq krz pdq| vnloov kh douhdg| nqrzv/ dv zhoo dv rq wkh dprxqw ri wlph wkh| vshqg ohduqlqj1 Zh fkrrvh wklv ohduqlqj whfkqrorj| iru wzr uhdvrqv1 Iluvw/ lw lv rqh wkdw pdq| uhdghuv duh olnho| wr eh idploldu zlwk1 Vhfrqg/ lw lv rqh ri wkh ihz ixqfwlrqdo irupv iru zklfk zh fdq jhw forvhg irup vroxwlrqv1 D nh| dvvxpswlrq lq zkdw iroorzv lv wkdw zkloh doo lqglylgxdov vwduw 9 Doorzlqj iru ghfuhdvlqj uhwxuqv lq wkh djjuhjdwh dprxqw ri vnloo frxog jhqhudwh lqwhuhvwlqj vslooryhuv> iru h{0 dpsoh/ dv deoh lqglylgxdov dffxpxodwh vnloo/ wkh| zrxog ghfuhdvh wkh uhwxuqv wr vnloo iru wkh uhvw ri wkh srsxodwlrq1 Wklv zrxog suhvxpdeo| dpsoli| lqhtxdolw|1 Krzhyhu/ vroylqj vxfk d g|qdplfdo v|vwhp zrxog eh frpsolfdwhg/ dqg lv eh|rqg wkh vfrsh ri wklv sdshu1 9 rxw dw wkh vdph vnloo ohyho/ wkh| glhu lq d 1 Wkdw lv/ vrph lqglylgxdov duh lqkhuhqwo| txlfn wr ohduq krz wr xvh wkh qhz whfkqrorj|= jlyhq wkh vdph ohyho ri vnloov dqg wkh vdph dprxqw ri wlph dv rwkhuv/ wkh| fdq ehfrph pruh surflhqw lq xvlqj wkh qhz whfkqrorj|1 Fohduo|/ xqohvv lqglylgxdov vwduw rxw zlwk d srvlwlyh dprxqw ri vnloov rq wkh qhz whfkqrorj|/ qr ohduqlqj fdq hyhu eh lqlwldwhg1 Wklv zduudqwv rxu hduolhu uhvwulfwlrq wkdw vf A 31 Ilqdoo|/ dvvxplqj lqglylgxdov kdyh olqhdu suhihuhqfhv ryhu frqvxpswlrq dqg glvfrxqw wkh ixwxuh dw udwh  dqg rplwwlqj wkh lqglylgxdo vxevfulsw/ zh fdq h{suhvv wkh sureohp ri hdfk lqglylgxdo lq wklv hfrqrp| dv #“ $ }| v| +4 à q| , h " pd{ Hf 3 4| gw +416, ?| f vxemhfw wr 4= 3 # q| # 4 5= v @ d +vq, K b 6= }| iroorzv d Pdunry surfhvv 7= Lqlwldo frqglwlrqv }f > vf Qrwh wkdw zh kdyh vshflhg wkh pd{lpl}dwlrq sureohp dv wkrxjk djhqwv frqvxph wkhlu hqwluh lqfrph dw hdfk lqvwdqw1 Wklv lv ehfdxvh xqghu rxu dvvxpswlrq ri ulvn0qhxwudolw|/ lqglylgxdov zloo eh lqglhuhqw derxw wkh wlplqj ri frqvxpswlrq zkhqhyhu wkh lqwhuhvw udwh lv htxdo wr wkhlu glvfrxqw udwh1 Vlqfh doo lqglylgxdov vkduh d frpprq glvfrxqw udwh/ wkh rqo| htxloleulxp lv rqh zkhuh wkh lqwhuhvw udwh rq erqgv lv wkh vdph dv wkh glvfrxqw udwh1 Khqfh/ lq htxloleulxp/ qr lqglylgxdo zloo zlvk wr eruurz ru ohqg hyhq li fuhglw pdunhwv zhuh dydlodeoh/ dqg rxu ghvfulswlrq ri wkh lqglylgxdo pd{lpl}dwlrq sureohp +416, dffrugv zlwk wkh surshu qrwlrq ri dq htxloleulxp1 Zh fdq vroyh wkh deryh pd{lpl}dwlrq sureohp xvlqj vwdqgdug whfkqltxhv lq vwrfkdvwlf g|qdplf surjudpplqj1 Ohw Y +v, ghqrwh wkh h{shfwhg glvfrxqwhg xwlolw| ri wkh lqglylgxdo zkhq kh dfwv rswlpdoo|/ jlyhq wkdw klv vnloo ohyho wklv lqvwdqw lv htxdo wr v dqg wkdw wkh ohyho ri surgxfwlylw| dw wklv lqvwdqw lv htxdo wr ] 1 Wklv sdlu ri ixqfwlrqv iru m S i3> 4j pxvw vdwlvi| wkh v|vwhp ri dvvhw htxdwlrqv q r Y +v, @ pd{ ] v +4 à q, . Y +v, d +vq,K .  ^Y ?  3 v + , à Y +v,` +417, : zkhuh Y + , 3 v lv wkh ydoxh ixqfwlrq hydoxdwhg dw wkh vdph vnloo ohyho dw wkh frpsohphqwdu| ohyho ri surgxfwlylw|1 Wdnlqj wkh uvw rughu frqglwlrq zlwk uhvshfw wr q/ zh kdyh # deY +v, $    3K vq @ +418, ] Vxevwlwxwlqj wklv uvw rughu frqglwlrq lqwr +417, |lhogv d v|vwhp ri wzr glhuhqwldo htxdwlrqv/ rqh iru hdfk m = 7 8  7 8  deY +v,  3 K deY +v,  3 K Y +v, @ ] v à à Y +v,` 4 . .  ^Y + , v ]K e ]K 3 Wr vroyh wklv v|vwhp ri htxdwlrqv/ zh xvh wkh phwkrg ri xqghwhuplqhg frh!flhqwv1 Zh jxhvv wkdw wkh vroxwlrq ri wklv v|vwhp lv d olqhdu ixqfwlrq ri v/ l1h1 Y +v, @  .   v Lw fdq eh vkrzq wkdw wklv vroxwlrq lv lq idfw xqltxh1 : Xvlqj wkh vroxwlrq iru  dqg vxevwlwxwlqj lw lqwr wkh uvw rughu frqglwlrq +418, |lhogv wkh iroorzlqj h{suhvvlrq iru wkh jurzwk udwh ri vnloov lq whupv ri wkh sulplwlyhv iru hdfk lqglylgxdo= # $ K gv  e + . , ] . ]  3 K @ d +419, 3 3K gw  + . , ] . ] D ihz uhpdunv derxw +419, duh lq rughu1 Iluvw/ lw lpsolhv wkdw zlwklq d jlyhq uhjlph ri djjuhjdwh gv surgxfwlylw|/ vnloov duh dffxpxodwhg dw d frqvwdqw olqhdu udwh/ l1h1 lv htxdo wr d frqvwdqw1 gw Wkxv/ wkh lqglylgxdo dftxluh d frqvwdqw dprxqw ri qhz vnloov hdfk lqvwdqw/ zkhuh wkh qxpehu ri dgglwlrqdo vnloov ghshqgv rq wkh ohyho ri djjuhjdwh surgxfwlylw|1 Zh vkrxog qrwh wkdw vlqfh dffxpxodwlrq rffxuv dw d olqhdu udwh/ d zrunhu frqwulexwhv wr klv h{lvwlqj vnloo edvh dw dq hyhu glplqlvklqj udwh lq shufhqwdjh whupv1 Wklv kdv vrph frqvhtxhqfhv iru wkh h{whqw ri lqhtxdolw| zh frxog hyhu revhuyh lq wklv hfrqrp|/ exw grhv qrw dsshdu wr eh lpsruwdqw iru dq| ri rxu txdolwdwlyh uhvxowv1 Vhfrqg/ wkh udwh dw zklfk dq lqglylgxdo dffxpxodwhv qhz vnloov ulvhv zlwk : Wr suryh xqltxhqhvv/ zh fdq xvh wkh skdvh gldjudp gldjudp lq Iljxuh D41 Wklv gldjudp vkrzv wkdw wkh ydoxh ri ohduqlqj lv srvlwlyh dqg qlwh rqo| li lw lv frqvwdqw +l1h1 % Er pxvw dozd|v vwd| dw wkh vwhdg| vwdwh,1 Wklv ~r lpsolhv wkdw T Er 3 lv d frqvwdqw/ vr wkdw T Er lv xqltxho| olqhdu1 4 ; wkh delolw| sdudphwhu d1 Zrunhuv zkr duh ehwwhu deoh wr ohduq fkrrvh wr devrue vnloov dw d idvwhu udwh wkdq wkrvh zkr duh ohvv deoh/ zklfk zrxog ohdg wr d jurzlqj glyhujhqfh lq vnloo ohyhov dfurvv zrunhuv ri glhuhqw delolw|1 Ilqdoo|/ vlqfh ] A ] f / +419, lpsolhv lqglylgxdov ohduq qhz vnloov dw d idvwhu udwh zkhq djjuhjdwh surgxfwlylw| lv orz1 Wklv uhvxow uh hfwv rswlpdo lqwhuwhpsrudo vxevwlwxwlrq rq wkh sduw ri wkh djhqwv1 Lqwxlwlyho|/ lqglylgxdov wdnh dgydqwdjh ri wkh idfw wkdw wkh| duh uhodwlyho| ohvv surgxfwlyh gxulqj uhfhvvlrqv wr dffxpxodwh vnloov dqg ehwwhu suhsduh wkhpvhoyhv iru wkh ixwxuh/ zkhq wkh| h{shfw wkh| zloo eh pruh surgxfwlyh rq dyhudjh1 Wkh fodlp wkdw lqyhvwphqw lq vnloov vkrxog eh frxqwhuf|folfdo kdv ehhq dgydqfhg hovhzkhuh lq wkh olwhudwxuh/ dowkrxjk zlwk olwwoh ru qr hpskdvlv rq wkh lpsolfdwlrqv ri wklv uhvxow rq lqhtxdolw|1 ; Wr uhodwh wklv prgho wr zdjh lqhtxdolw|/ ghqh wkh zdjh ri dq lqglylgxdo dv klv lqfrph hdfk lqvwdqw glylghg e| wkh dprxqw ri wlph kh vshqgv zrunlqj1 Wkxv/ wkh zdjh ri lqglylgxdo l lv jlyhq e| z| @ }|v| +41:, Wklv zdjh lv sursruwlrqdo wr wkh lqglylgxdo*v vnloo ohyho/ zkhuh wkh frqvwdqw ri sursruwlrqdolw| lv wkh ohyho ri djjuhjdwh surgxfwlylw| dqg lv wkxv wkh vdph iru doo lqglylgxdov1 Khqfh/ wkh zdjh udwlr ri lqglylgxdov dw glhuhqw shufhqwlohv zloo eh wkh vdph dv wkh udwlr ri wkhlu vnloo ohyhov1 Vlqfh lqglylgxdov zlwk d ehwwhu delolw| fkrrvh wr dffxpxodwh vnloov pruh udslgo|/ wkh glvwulexwlrq ri vnloov idqv rxw ryhu wlph1 Wklv lv looxvwudwhg judsklfdoo| lq Iljxuh 4/ zklfk wudfhv wkh wlph sdwk ri wkh vnloo ohyho ri ydulrxv lqglylgxdov zlwk glhuhqw delolwlhv wr ohduq d 1 Vlqfh doo lqglylgxdov gv vwduw rxw dw wkh vdph vnloo ohyho dqg wkh fkdqjh lq vnloov lv vwulfwo| lqfuhdvlqj lq d uhjdugohvv gw ri djjuhjdwh frqglwlrqv/ wkh udqnlqj ri vnloov dfurvv lqglylgxdov lv suhvhuyhg ryhu wlph1 Khqfh/ zh fdq wklqn ri hdfk sdwk lq Iljxuh 4 dv wkh vnloo ohyho ri d sduwlfxodu shufhqwloh zlwklq wkh vnloo glvwulexwlrq +dqg frqvhtxhqwo| wkh zdjh glvwulexwlrq,1 Dv fdq eh vhhq lq wkh jxuh/ wkh vnloo ohyho dw kljkhu shufhqwlohv guliwv dsduw iurp wkh vnloo ohyho dw orzhu shufhqwlohv1 Wkxv/ frqyhqwlrqdo phdvxuhv ri zdjh lqhtxdolw| vxfk dv lqwhushufhqwloh zdjh udwlrv +h1j1 wkh udwlr ri ; Vhh/ iru h{dpsoh/ Kdoo +4<<4,/ Frrshu dqg Kdowlzdqjhu +4<<6,/ Ghoodv dqg Vdnhoodulv +4<<:,/ Djklrq dqg Vdlqw Sdxo +4<<;,/ dqg Fdqwrq dqg Xkolj +4<<<,1 Lq pxfk hduolhu zrun/ Ehfnhu +4<:8, glvfxvvhv wkh uroh ri lqwhuwhpsrudo vxevwlwxwlrq iru kxpdq fdslwdo dffxpxodwlrq/ dowkrxjk kh grhv qrw uhodwh klv uhvxowv wr djjuhjdwh xfwxdwlrqv1 Lqvwhdg/ kh dujxhv orz zdjhv hduo| lq olih surylgh lqfhqwlyh wr dffxpxodwh kxpdq fdslwdo hduo| lq olih1 Vwloo/ wkh dqdorj| wr orz zdjhv gxulqj uhfhvvlrqv lv vwudljkwiruzdug1 Ehfnhu grhv h{dplqh wkh lpsolfdwlrqv ri wklv fkdqqho iru lqhtxdolw| ryhu wkh olih f|foh1 Kh dujxhv orz zdjhv dw d |rxqj djh jhqhudwh juhdwhu lqhtxdolw| dprqj zrunhuv zkhq rog vlqfh wkh| kdyh vruwhg wkhpvhoyhv dffruglqj wr wkhlu kxpdq fdslwdo1 Wklv pluuruv vrph ri rxu glvfxvvlrq ehorz iru zk| uhfhvvlrqv irvwhu lqhtxdolw| zkhq lqhtxdolw| lv lqfuhdvlqj1 Krzhyhu/ wkh hhfw ri uhfhvvlrqv zkhq lqhtxdolw| lv ghfuhdvlqj grhv qrw kdyh d sdudooho lq Ehfnhu*v glvfxvvlrq ri wkh olih f|foh1 < s s0 boom recession boom t Figure 1: Skill Distribution Over Time Note: Each path represents the evolution of skills for an individual at a given percentile in the ability (and consequently skill) distribution. wkh zdjh ri wkh <3wk shufhqwloh wr wkh zdjh ri wkh 43wk shufhqwloh, zloo lqfuhdvh ryhu wlph dv wkh vnloo glvwulexwlrq ehfrphv pruh idqqhg rxw1 Pruhryhu/ wkh glvwulexwlrq ri vnloov idqv rxw pruh udslgo| gxulqj uhfhvvlrqv dv doo lqglylgxdov vkliw wr dftxlulqj pruh vnloov/ dqg vr frqyhqwlrqdo phdvxuhv ri lqhtxdolw| zloo whqg wr lqfuhdvh dw d idvwhu udwh gxulqj grzqwxuqv1 Zh fdq irupdol}h wkhvh revhuydwlrqv zlwk wkh iroorzlqj Sursrvlwlrq/ zkrvh surri lv frqwdlqhg lq dq Dsshqgl{1 Sursrvlwlrq 4= Frqvlghu wzr lqglylgxdov l dqg m zkhuh d A d  1 z| 41 Wkh zdjh udwlr z| @ 4 dw w @ 31 Iru dq| uhdol}dwlrq ri } ghqhg iru  S ^3> R,/ wkh z| udwlr lv lqfuhdvlqj dqg frqwlqxrxv lq w/ dqg frqyhujhv dv|pswrwlfdoo| wr d qlwh xsshu z| erxqg/ ! "  z| d 3 K olp @ A4 |<" z| d z 51 Iru dq| uhdol}dwlrq ri } zkhuh  S ^3> w,/ wkh fkdqjh lq z| lv ghfuhdvlqj lq }| / l1h1 | ! " ! " g z|  g z|    A   A3 gw z| 5 '~f | gw z| ' 5 | ~ Rxu prgho wkhuhiruh ghvfulehv rqh sduwlfxodu fkdqqho wkdw fdxvhv uhfhvvlrqv wr h{dfhuedwh zdjh lqhtxdolw|1 Krzhyhu/ wklv hhfw ghshqgv rq wkh idfw wkdw lqhtxdolw| lv lqfuhdvlqj ryhu wkh orqj uxq= grzqwxuqv surylgh juhdwhu lqfhqwlyh iru djhqwv wr vruw wkhpvhoyhv lqwr glhuhqw vnloo ohyhov/ exw vruwlqj lqwr vnloo ohyhov lv wkh vrxufh ri lqhtxdolw| wr ehjlq zlwk1 Lq rwkhu zrugv/ uhfhvvlrqv dpsoli| wkh xqghuo|lqj lqfuhdvh lq lqhtxdolw| udwkhu wkdq fuhdwh lw1 Euhdnlqj grzq lqhtxdolw| lqwr ruwkrjrqdo wuhqg dqg f|foh frpsrqhqwv lv hqwluho| duwlfldo lq rxu iudphzrun1 Ri frxuvh/ wkhuh pd| yhu| zhoo eh rwkhu fkdqqhov wkurxjk zklfk djjuhjdwh xfwxdwlrqv dhfw lqhtxdolw| ryhu wkh f|foh dqg zklfk duh ruwkrjrqdo wr orqj0uxq wuhqgv lq wkh glvwulexwlrq ri zdjhv/ dqg wkhvh pd| yhu| zhoo kdyh prwlydwhg suhylrxv uhvhdufkhuv wr wuhdw orqj0uxq wuhqg dqg f|foh dv glvwlqfw1 Exw wklv grhv qrw ghq| wkh phfkdqlvp zh kdyh ghvfulehg khuh1 Ilqdoo|/ zh vkrxog srlqw wkdw rxu glvfxvvlrq vr idu kdv rqo| irfxvhg rq zdjh lqhtxdolw|1 Zh fdq vlploduo| lqyhvwljdwh wkh hyroxwlrq ri lqfrph lqhtxdolw| lq rxu prgho/ zkhuh lqfrph lv 43 ghqhg e| || @ }| v| +4 à q| ,1 Khuh/ wzr revhuydwlrqv duh lq rughu1 Iluvw/ rxu prgho devwudfwv iurp xqhpsor|phqw/ zklfk suhvxpdeo| sod|v dq lpsruwdqw uroh lq fkdqjhv lq wkh glvwulexwlrq ri lqfrph ryhu wkh f|foh1 Wkxv/ dq| suhglfwlrqv rxu prgho pdnhv iru lqfrph lqhtxdolw| duh rqo| dssursuldwh dv vwdwhphqwv derxw lqhtxdolw| dprqj wkrvh zkr uhpdlq hpsor|hg gxulqj uhfhvvlrqv1 Wkdw vdlg/ li zh h{dplqh lqwhushufhqwloh lqfrph udwlrv lq rxu prgho/ zh fdq hvwdeolvk wkdw wkh vhfrqg sduw ri Sursrvlwlrq 4 zloo frqwlqxh wr krog1 Wkdw lv/ lqfrph lqhtxdolw| dprqj hpsor|hg zrunhuv ulvhv pruh udslgo| gxulqj uhfhvvlrqv wkdq gxulqj errpv1 Krzhyhu/ lq frqwudvw zlwk wkh uvw sduw ri wkh Sursrvlwlrq/ lqfrph udwlrv duh qrw frqwlqxrxv/ vlqfh zrun krxuv q| duh qrw frqwlqxrxv ryhu wlph1 Lqvwhdg/ d qhjdwlyh surgxfwlylw| vkrfn zloo fdxvh lqfrph udwlrv wr mxps xszdugv rq lpsdfw1 Wkh uhdvrq iru wklv lv wkdw zkhq d qhjdwlyh surgxfwlylw| vkrfn klwv/ zrunhuv zlwk kljk delolw| zloo uhgxfh wkh wlph wkh| vshqg zrunlqj e| d juhdwhu sursruwlrq wkdq ohvv deoh zrunhuv1 Khqfh/ rq lpsdfw/ wkh lqfrph ri pruh deoh zrunhuv zloo idoo uhodwlyh wr ohvv deoh zrunhuv zkhq wkh hfrqrp| hqwhuv d grzqwxuq/ uhgxflqj lqhtxdolw|1 Exw iurp wkdw srlqw rq/ lqwhushufhqwloh lqfrph udwlrv zloo lqfuhdvh dw d pruh udslg udwh dv wkh hduqlqjv ri pruh deoh zrunhuv jurz dsduw iurp wkrvh ri ohvv deoh zrunhuv1 Dv orqj dv vxfk glvfrqwlqxrxv mxpsv duh vpdoo dqg revhuydwlrqv duh vx!flhqwo| idu dsduw vr wkdw mxpsv duh qrw hdvlo| glvfhuqleoh/ lqfrph lqhtxdolw| zloo dsshdu wr iroorz wkh vdph sdwwhuq dv zdjh lqhtxdolw|1 51 Wkh Fdvh ri Ghfuhdvlqj Zdjh Lqhtxdolw| Lq wkh suhylrxv vhfwlrq/ zh dujxhg wkdw uhfhvvlrqv fdxvh wkh zdjh glvwulexwlrq wr idq rxw pruh udslgo|1 Krzhyhu/ lw lv lpsruwdqw wr uhfrjql}h wkdw wklv grhv qrw lqglfdwh uhfhvvlrqv lqkhuhqwo| frqwulexwh wr juhdwhu lqhtxdolw|1 Udwkhu/ wkh deryh prgho lpsolhv uhfhvvlrqv dpsoli| dq xqghu0 o|lqj wuhqg wrzdugv lqfuhdvlqj lqhtxdolw|1 Wklv vhfwlrq xqghuvfruhv wklv srlqw e| looxvwudwlqj wkdw uhfhvvlrqv zloo eh dvvrfldwhg zlwk idvwhu zdjh htxdol}dwlrq zkhq zdjh lqhtxdolw| h{klelwv d ghfolqlqj wuhqg1 Wr doorz iru d ghfuhdvlqj wuhqg lq zdjh lqhtxdolw|/ zh prgli| wkh prgho deryh wr lqfoxgh glplqlvklqj uhwxuqv wr vnloo dw wkh lqglylgxdo ohyho1 Zlwk wklv dvvxpswlrq/ pruh deoh lqglylgxdov hyhqwxdoo| vorz grzq lq dftxlulqj vnloov/ zklfk doorzv wkhlu ohvv deoh frxqwhusduwv wr fdwfk xs dqg forvh wkh zdjh jds1 Wkh vdph fkdqqho ri lqwhuwhpsrudo vxevwlwxwlrq zloo qrz fdxvh uhfhvvlrqv wr kdvwhq wkh ghfolqh lq lqhtxdolw|= grzqwxuqv surylgh juhdwhu lqfhqwlyh wr frqfhq0 wudwh rq vnloo dffxpxodwlrq iru ohvv deoh zrunhuv wkdq iru pruh deoh zrunhuv/ dqg vr uhfhvvlrqv dffhohudwh wkh udwh dw zklfk orzhu sdlg zrunhuv fdwfk xs zlwk wkhlu kljkhu sdlg froohdjxhv1 44 Zh vkrxog djdlq srlqw rxw wkdw rxu revhuydwlrq wkdw delolw|0eldvhg whfkqlfdo fkdqjh jhqhudwhv rqo| whpsrudu| lqfuhdvhv lq lqhtxdolw| kdv ehhq qrwhg e| suhylrxv dxwkruv1 Jdoru dqg Wvlggrq +4<<:, dujxh wkdw lqhtxdolw| zloo hyhqwxdoo| ghfolqh dv plqru lqqrydwlrqv rq qhz whfkqrorjlhv duh lqwurgxfhg wkdw doorz dffhvv wr qhz whfkqrorjlhv wr ohvv lqqdwho| surgxfwlyh zrunhuv1 Krzhyhu/ wkh| prgho wkh duulydo ri lqqrydwlrqv dv h{rjhqrxv/ dqg vr wkhlu iudphzrun lv lqdghtxdwh iru vwxg|lqj krz wklv surfhvv ri forvlqj zdjh jdsv zrxog eh dhfwhg e| djjuhjdwh xfwxdwlrqv1 Fdvhool +4<<<, dovr suhvhqwv d vfhqdulr lq zklfk lqfrph dqg zdjh jdsv pljkw glvdsshdu lq wkh orqj uxq1 Lq klv prgho/ rqjrlqj fdslwdo dffxpxodwlrq lqfuhdvhv wkh lqhtxdolw| lq zdjhv ehwzhhq qhz dqg rog whfkqrorjlhv/ gudzlqj lqfuhdvlqjo| pruh zrunhuv lqwr wkh qhz whfkqrorj|1 Iru fhuwdlq sdudphwhu uhvwulfwlrqv/ wklv surfhvv fxoplqdwhv zlwk doo zrunhuv lq wkh srsxodwlrq vzlwfklqj wr wkh qhz whfkqrorj|/ dw zklfk srlqw wkhuh lv d glvfuhwh mxps wr frpsohwh htxdolw|1 Lq frqwudvw zlwk klv prgho/ rxu dssurdfk doorzv iru d judgxdo frqyhujhqfh wrzdugv htxdolw| wkdw ghshqgv rq wkh hqgrjhqrxv ghflvlrqv ri zrunhuv zklfk fdq eh lq xhqfhg e| djjuhjdwh xfwxdwlrqv1 Wkxv/ rxu prgho lv pruh vxlwdeoh iru vwxg|lqj wkh hhfwv ri exvlqhvv f|fohv rq lqhtxdolw| zkhq orqj0uxq lqhtxdolw| lv rq wkh ghfolqh1 Lw lv suhflvho| wkh dssolfdwlrq wr djjuhjdwh xfwxdwlrqv wkdw pdnhv rxu prgho lqwuljxlqj= li rxu dujxphqw lv fruuhfw/ lw zrxog iroorz wkdw wkh pdlq uhdvrq hfrqrplvwv kdyh irxqg vxfk fohdu hylghqfh wkdw uhfhvvlrqv surprwh lqhtxdolw| ryhu wkh sdvw 73 |hduv lv ehfdxvh wklv zdv d shulrg ri ulvlqj lqhtxdolw|> kdg wkh| lqyhvwljdwhg wkh vdph txhvwlrqv xqghu d glhuhqw odpssrvw/ wkh| zrxog olnho| kdyh ehhq ohg wr yhu| glhuhqw frqfoxvlrqv1< Wr lqwurgxfh glplqlvklqj uhwxuqv wr vnloo dw wkh lqglylgxdo ohyho/ zh lpsrvh dq xsshu erxqg rq wkh vnloo ohyho/ l1h1 v| # v1 Wkxv/ dw vrph srlqw/ dffxpxodwlqj dgglwlrqdo vnloov qr orqjhu frqwulexwhv wr surgxfwlylw|/ dq h{wuhph irup ri glplqlvklqj uhwxuqv1 Lqwxlwlyho|/ rxu dvvxps0 wlrq lpsolhv wkhuh lv rqo| vr pxfk wr ohduq derxw d qhz whfkqrorj| ehiruh rqh ehfrphv ixoo| surflhqw lq lw1 Dowhuqdwlyho|/ li zh lqwhusuhw v| dv dq rughulqj ri surgxfwlrq surfhvvhv zlwklq d jhqhudo sxusrvh whfkqrorj|/ rxu dvvxpswlrq zrxog uh hfw wkh idfw wkdw wkhuh lv vrph xsshu erxqg rq krz surgxfwlyh dq| sduwlfxodu surgxfwlrq surfhvv fdq eh iru d jlyhq jhqhudo sxusrvh < Juhhqzrrg dqg \ruxnrjox +4<<:, rhu d uhodwhg h{sodqdwlrq iru zk| wkh wuhqg wrzdugv lqfuhdvlqj lqhtxdolw| dw wkh rqvhw ri d qhz whfkqrorj| lv hyhqwxdoo| uhyhuvhg1 Lq wkhlu prgho/ qhz whfkqrorjlhv fdq rqo| eh lpsuryhg e| vnloohg zrunhuv1 Zrunhuv fdq ehfrph vnloohg e| sd|lqj d {hg frvw zklfk ydulhv dfurvv wkh srsxodwlrq1 Wkh lqlwldo lqfuhdvh lq lqhtxdolw| lv gxh wr lqfuhdvhg ghpdqg iru kljk vnloo zrunhuv1 Ryhu wlph/ wkh whfkqrorjlhv duh vx!flhqwo| surgxfwlyh/ ghpdqg iru vnloohg zrunhuv ghfolqhv/ dqg lqhtxdolw| zloo eh uhyhuvhg1 Wkhlu vwru| dovr kdv wkh ihdwxuh wkdw wkh wudqvlwlrq lqwr d qhz whfkqrorj| idyruv zrunhuv zkr kdyh dq hdvlhu wlph ehfrplqj vnloohg/ dowkrxjk lqwurgxflqj djjuhjdwh xfwxdwlrqv lqwr wkhlu iudphzrun dsshduv wr eh d pruh frpsolfdwhg xqghuwdnlqj1 45 whfkqrorj|1 Dgglqj hyhq vxfk d plqru prglfdwlrq pdnhv wkh pdwkhpdwlfdo dqdo|vlv vxevwdq0 wldoo| pruh frpsolfdwhg1 Zh ehjlq rxu glvfxvvlrq ri wklv vfhqdulr e| devwudfwlqj iurp djjuhjdwh xfwxdwlrqv> wkdw lv/ zh frqvlghu wkh fdvh zkhuh djjuhjdwh surgxfwlylw| lv frqvwdqw1 Wklv fdvh wxuqv rxw wr lqyroyh d glhuhqwldo htxdwlrq wkdw fdq vwloo eh vroyhg lq forvhg irup1 Zh wkhq lqwur0 gxfh exvlqhvv f|fohv lqwr wklv iudphzrun/ zklfk lqyroyhv d wzr0glphqvlrqdo g|qdplfdo v|vwhp wkdw kdv qr forvhg irup vroxwlrq/ dw ohdvw dv idu dv zh nqrz1 Krzhyhu/ zh fdq vwloo fkdudfwhul}h lwv pdlq surshuwlhv/ zklfk doorzv xv wr glvfxvv wkh hyroxwlrq ri hduqlqjv lqhtxdolw| ryhu wkh f|foh zkhq orqj0uxq wuhqg lqhtxdolw| lv ghfolqlqj1 Lqwurgxflqj dq xsshu erxqg dqg dvvxplqj d frqvwdqw ohyho ri surgxfwlylw| ] fkdqjhv +416, lqwr wkh iroorzlqj pd{lpl}dwlrq sureohp= “ ]v| +4 à q|, h " pd{ 3 4| gw +514, ?| f vxemhfw wr 4 = 3 # )| # 4 q 5 = v@ b li v ? v d +vq,K li v @ v 3 6 = Lqlwldo frqglwlrq vf Zkhq v| @ v/ wkhuh lv qr srlqw wr ohduqlqj/ dqg vr lqglylgxdov zloo vhw q| @ 31 Wkxv/ dq lqglylgxdo zloo hduq d frqvwdqw rz ]v shu xqlw ri wlph rqfh kh kdv uhdfkhg v/ zklfk glvfrxqwhg dw d udwh  hvwdeolvkhv wkdw ]v Y +v, @ +515,  Iruv ? v/ zh djdlq xvh whfkqltxhv ri frqwlqxrxv wlph g|qdplf surjudpplqj wr vroyh iru hdfk zrunhu*v pd{lpl}dwlrq sureohp11 Iru v ? v/ wkh dvvhw htxdwlrq iru Y +v, lv jlyhq e| q r Y +v, @ pd{ ]v +4 à q, . Y +v, d +vq,K ?  Wkh uvw0rughu frqglwlrq lv jlyhq e| # $  deY +v,  3 K vq @ ] 46 zklfk zkhq vxevwlwxwhg edfn lqwr wkh dvvhw htxdwlrq |lhogv wkh glhuhqwldo htxdwlrq Y +v, @ ]v . 4 à e # de $   ÃY +v,Ä   3K  3K +516, e ]K zlwk +515, dv lwv erxqgdu| frqglwlrq1 Htxdwlrq +516, lv reylrxvo| uhodwhg wr wkh qrq0olqhdu glhuhqwldo htxdwlrq lq wkh suhylrxv vhfwlrq1 Krzhyhu/ e| lpsrvlqj d erxqgdu| frqglwlrq dw v @ v/ zh uxoh rxw d olqhdu ixqfwlrqdo irup iru Y +v,1 Vwloo/ wklv glhuhqwldo htxdwlrq fdq eh uhdglo| dqdo|}hg e| xvlqj d wudqvirupdwlrq ri Y +v,1 Ghqh d qhz yduldeoh { +v, dv ]v { +v, @ Y +v, à  Wklv yduldeoh { +v, kdv d uhdg| hfrqrplf lqwhusuhwdwlrq= lw lv wkh ydoxh ri wkh rswlrq wr ohduq dgglwlrqdo vnloov zkhq wkh fxuuhqw vnloo ohyho lv v= Wklv lv ehfdxvh li wkh djhqw zdv suhyhqwhg iurp ohduqlqj dq| dgglwlrqdo vnloov/ kh zrxog doorfdwh doo ri klv wlph hqgrzphqw wr zrunlqj/ jlylqj ]v klp d glvfrxqwhg xwlolw| ri 1 Wkh glhuhqfh ehwzhhq wklv dqg Y +v, uh hfwv krz pxfk wkh  zrunhu zrxog eh zloolqj wr sd| iru wkh rswlrq ri ohduqlqj dgglwlrqdo vnloov eh|rqg klv fxuuhqw ohyho1 Diwhu vrph dojheudlf pdqlsxodwlrq/ zh fdq uhzulwh +516, dv d glhuhqwldo htxdwlrq lq whupv ri { +v,= { +v,  ! " g{ +v, Ã] 3 K @ +517, gv n  zkhuh n@ 4 à e # de $   3K 1 Wkh skdvh gldjudp iru { +v, lv looxvwudwhg lq Iljxuh 5/ zklfk sorwv e ] K g{+v, {+v, djdlqvw 1 Wklv v|vwhp kdv d xqltxh vwhdg| vwdwh dw gv ! "  n ]  3K { @ W +518,   D vlpsoh fdofxodwlrq frqupv wkdw { W deryh lv htxdo wr wkh ydoxh ri ohduqlqj zkhq v lv xq0 erxqghg1 Vlqfh wkh ydoxh ri ohduqlqj zloo eh zhdno| orzhu zkhq v lv erxqghg deryh wkdq zkhq lw lv xqerxqghg/ zh nqrz wkdw zkhq vnloo lv erxqghg deryh/ lw pxvw eh wkh fdvh wkdw { +vf, # { 1 W Pruhryhu/ lw lv hdv| wr vkrz e| frqwudglfwlrq wkdw { +vf , W@ { 1 Lq whupv ri Iljxuh 5/ wklv lp0 W g{ +v, solhv { +vf, zloo olh wr wkh ohiw ri wklv vwhdg| vwdwh { 1 Lq wklv uhjlrq/W ? 31 Wr dvfhuwdlq gv ghwhuplqh krz { +v|, fkdqjhv ryhu wlph/ zh qhhg wr ghwhuplqh wkh odzv ri prwlrq iru v1 Dv 47 dx ds ρx 1-b Z 1 k ρ k Z 1-b ρ ρ x Z ρ Figure 2: Phase Diagram for the Option Value of Learning (Bounded Skill) looxvwudwhg lq wkh Dsshqgl{/ zh fdq h{suhvv wkh g|qdplfv ri v gluhfwo| lq whupv ri wkh ydoxh ri ohduqlqj { +v,= # $ K ! "K gv  e 3 K { +v, @ d 3K gw ] n Wkh deryh htxdwlrq kdv dq dsshdolqj lqwhusuhwdwlrq/ qdpho| wkdw lqglylgxdov dffxpxodwh vnloov pruh udslgo| zkhq wkh rswlrq wr dftxluh dgglwlrqdo vnloov lv sduwlfxoduo| ydoxdeoh/ l1h1 zkhq { +v, lv odujh143 v ? v/ wkh lqglylgxdo zloo fkrrvh Vlqfh wkh ydoxh ri wklv rswlrq lv srvlwlyh iru gv wr dffxpxodwh pruh vnloov li kh kdv qrw |hw pdvwhuhg wkh qhz whfkqrorj|/ l1h1 A 31 Wkxv/ gw wkh lqglylgxdo zloo dffxpxodwh pruh vnloov dqg pryh forvhu wrzdugv v ryhu wlph1 Krzhyhu/ vlqfh g{ +v, ? 3/ wkh rswlrq wr ohduq ehfrphv ohvv ydoxdeoh ryhu wlph/ dqg wkh lqglylgxdo dffxpxodwhv gv dgglwlrqdo vnloov dw d surjuhvvlyho| vorzhu udwh1 Lqwxlwlyho|/ wklv lv ehfdxvh rxu dvvxpswlrqv rq wkh dffxpxodwlrq whfkqrorj| lpso| wkhuh dffxpxodwlqj vnloov idflolwdwhv vxevhtxhqw dffxpxodwlrq odwhu rq1 Dv wkh lqglylgxdo hgjhv forvhu wr v dqg wkhuh duh rqo| d ihz dgglwlrqdo vnloov ohiw wr ohduq/ wklv hhfw ehfrphv lqfuhdvlqjo| ohvv lpsruwdqw/ jlylqj wkh zrunhu ohvv lqfhqwlyh wr dffxpxodwh vnloov ryhu wlph1 Wkh wlph suroh ri wkh vnloo ohyho ri dq lqglylgxdo zloo orrn olnh rqh ri wkh sdwkv looxvwudwhg lq sdqho +d, ri Iljxuh 6/ zklfk wudfhv wkh hyroxwlrq ri vnloo iru lqglylgxdov zlwk glhuhqw delolw| sdudphwhuv d/ mxvw dv lq Iljxuh 4 deryh1 Wkh jxuh lv gudzq vr wkdw wkh udqnlqj ri lqglylgxdov e| vnloo uhpdlqv frqvwdqw ryhu wlph/ l1h1 zrunhuv zkr duh pruh deoh wr ohduq zloo dozd|v udqn kljkhu wkdq zrunhuv zkr duh ohvv deoh wr ohduq/ dqg zkhuh lqglylgxdov uhdfk wkh xsshu erxqg v lq qlwh wlph1 Zh frqup wkdw wklv lv lq idfw wkh fdvh lq wkh iroorzlqj Sursrvlwlrq1 Sursrvlwlrq 5= Iru dq lqglylgxdo zlwk duelwudu| ohduqlqj sdudphwhu d A 3/ zh kdyh 41 Wkh wlph sdwk ri wkh vnloo ohyho v| lv frqfdyh lq w/ dqg olp| <" v| @ v1 51 Wkhuh h{lvwv d W ? R vxfk wkdw v| @ v iru doo w $ W / l1h1 wkh xsshu erxqg rq v lv dwwdlqhg lq qlwh wlph1 61 Iru dq| wzr lqglylgxdov l dqg m zkhuh d A d  / zh kdyh v| $ v| iru doo w/ zlwk vwulfw lqhtxdolw| iru vf ? v| ? v1 43 Zkloh wklv uhvxow lv lqwxlwlyh/ lw fdq eh plvohdglqj1 Zkhq zh doorz iru exvlqhvv f|fohv/ zh fdq vkrz wkdw iru r vx!flhqwo| forvh wr r/ wkh lqglylgxdo zloo dffxpxodwh pruh vnloov gxulqj uhfhvvlrqv hyhq zkhq wkh rswlrq wr ohduq lv pruh ydoxdeoh gxulqj errpv1 Zh uhwxuq wr wklv srlqw ehorz1 48 s si/s s s0 t 1 t (a) (b) Figure 3: Skill Levels and Ratios with Bounded Skills Note: Each path in panel (a) represents the evolution of skills for an individual at a given percentile in the ability (and consequently skill) distribution. Each path in panel (b) represents the ratio of skill between a given percentile in the ability distribution and the skill level of the least able individual in the population. Vlqfh wkh odvw sduw ri Sursrvlwlrq 5 lpsolhv vnloo ohyhov fdq eh rughuhg e| delolw|/ zh fdq wuhdw hdfk sdwk lq Iljxuh 6+d, dv wkh sdwk ri vnloo iru d sduwlfxodu shufhqwloh zlwklq wkh vnloo glvwul0 exwlrq1 Pruhryhu/ vlqfh wkh zdjhv ri doo zrunhuv duh htxdoo| sursruwlrqdo wr vnloo dw doo wlphv/ Iljxuh 6+d, fdswxuhv xs wr d vfdolqj idfwru wkh sdwkv ri zdjhv dfurvv wkh srsxodwlrq ryhu wlph1 Dv lv fohdu iurp wkh jxuh/ doorzlqj iru dq xsshu erxqg jhqhudwhv d sdwwhuq ri zdjh lqhtxdolw| wkdw lv frqvlvwhqw zlwk Nx}qhwv* +4<88, glvfxvvlrq ri wkh uhodwlrqvkls ehwzhhq jurzwk dqg wkh glvwulexwlrq ri hduqlqjv= dv surgxfwlylw| jurzv ryhu wlph/ lqhtxdolw| uvw ulvhv dqg wkhq idoov1 Wkh uhdvrq wklv rffxuv lq rxu iudphzrun lv wkdw zkhq wkh qhz whfkqrorj| uvw duulyhv/ lqglylg0 xdov ohduq dw glhuhqw udwhv krz wr xvh lw/ fdxvlqj wkh glvwulexwlrq ri vnloov dfurvv lqglylgxdov wr idq rxw1 Exw hyhqwxdoo|/ zrunhuv zkr duh pruh deoh wr ohduq vorz grzq dv wkh| pryh forvhu wr wkh pd{lpxp vnloo ohyho v1 Surgxfwlylw| frqwlqxhv wr jurz/ doehlw dw d vorzhu udwh wkdq ehiruh/ exw zdjh lqhtxdolw| ghfolqhv dv ohvv deoh zrunhuv ehjlq wr fdwfk xs wr wkhlu shhuv1 Dw wklv srlqw/ wkh zdjh glvwulexwlrq ehfrphv pruh frpsuhvvhg1 Dq dowhuqdwlyh zd| ri looxvwudwlqj wklv uhgxfwlrq lq lqhtxdolw| lv e| orrnlqj dw vnloo udwlrv udwkhu wkdq vnloo ohyhov/ dv looxvwudwhg lq sdqho +e, ri Iljxuh 61 Wklv jxuh vkrzv wkh udwlr ri wkh vnloo ohyho ri d jlyhq lqglylgxdo uhodwlyh wr wkh vnloo ohyho ri wkh lqglylgxdo zlwk wkh orzhvw delolw| sdudphwhu d1 Iru hdfk shufhqwloh/ wkh udwlr ehjlqv dw 4/ ulvhv xs wr vrph pd{lpxp ohyho/ dqg wkhq ghfolqhv judgxdoo| edfn wr 4 dv hyhq wkh vorzhvw lqglylgxdo lq wkh hfrqrp| uhdfkhv v144 Qrwh wkdw rxu prgho suhglfwv wkh glvwulexwlrq ri zdjhv ehfrphv frpsuhvvhg iurp wkh wrs ri wkh glvwulexwlrq grzq1 Lq sduwlfxodu/ uhodwlyh zdjhv ehjlq wr ghfolqh uvw dw wkh wrs ri wkh glvwulexwlrq dv lqglylgxdov wkhuh vorz grzq lq wkhlu dffxpxodwlrq ri vnloov1 Dw wkh vdph wlph/ wkh uhodwlyh zdjhv ri zrunhuv lq wkh plggoh ri wkh glvwulexwlrq frqwlqxhv wr ulvh/ lqfuhdvlqj wkh jds ehwzhhq wkh plggoh dqg wkh erwwrp ri wkh glvwulexwlrq zkloh ghfuhdvlqj wkh jds ehwzhhq wkh plggoh dqg wkh wrs ri wkh glvwulexwlrq1 Wr vwxg| wkh hhfw ri exvlqhvv f|fohv zkhq wkh zdjh glvwulexwlrq lv ehfrplqj frpsuhvvhg/ zh lqwurgxfh xfwxdwlrqv lq djjuhjdwh surgxfwlylw| lqwr wklv prgho1 Zkloh rxu fodlp wkdw uhfhvvlrqv vkrxog dffhohudwh wkh surfhvv ri zdjh frqyhujhqfh pd| dsshdu wr eh d vwudljkwiruzdug h{whqvlrq ri rxu suhylrxv dujxphqwv/ hvwdeolvklqj lw irupdoo| lv qrw wulyldo1 Wkh uhpdlqghu ri wklv vhfwlrq wudfhv rxu vwhsv lq hvwdeolvklqj wklv fodlp/ dorqj zlwk vrph revhuydwlrqv derxw wkh qdwxuh ri 44 Wkh idfw wkdw doo lqglylgxdov hyhqwxdoo| uhdfk wkh vdph vnloo ohyho lv fohduo| xquhdolvwlf1 Wklv uhvxow lv gxh wr rxu dvvxpswlrq wkdw doo lqglylgxdov kdyh d frpprq fhlolqj r1 Rxu dqdo|vlv zrxog frqwlqxh wr jr wkurxjk li hdfk lqglylgxdo kdg klv rzq fhlolqj r / surylghg wkdw wkhvh fhlolqjv vwloo jhqhudwh vrph hyhqwxdo frpsuhvvlrq lq wkh glvwulexwlrq ri zdjhv dfurvv lqglylgxdov +l1h1 lqglylgxdov zlwk d ehwwhu fdsdflw| wr ohduq pxvw uhdfk wkhlu fhlolqjv uvw wr doorz ohvv deoh lqglylgxdov wr fdwfk xs/ dw ohdvw lq sduw,1 49 rxu uhvxow wkdw zloo eh xvhixo lq lqwhusuhwlqj hpslulfdo hylghqfh odwhu rq1 Zh ehjlq zlwk wkh fodlp wkdw mxvw dv lq wkh fdvh ri xqerxqghg vnloo dffxpxodwlrq/ zrunhuv zloo dftxluh vnloov dw d pruh udslg udwh gxulqj uhfhvvlrqv wkdq gxulqj errpv1 Sursrvlwlrq 6= Frqvlghu dq lqglylgxdo zlwk d vnloo ohyho v ? v1 Iru dq| uhdol}dwlrq } ghqhg iru  S ^3> w,/ wkh lqglylgxdo zloo dffxpxodwh vnloov pruh udslgo| li djjuhjdwh surgxfwlylw| dw gdwh w lv orz/ l1h1   gv|  gv   A | gw 5 '~f gw 5 '~  | | Wkh deryh Sursrvlwlrq vwdwhv wkdw uhjdugohvv ri klvwru| ri djjuhjdwh surgxfwlylw|/ dv orqj dv d zrunhu lv vwloo dffxpxodwlqj vnloov +l1h1 klv vnloo ohyho lv ehorz wkh erxqg v,/ kh zloo ohduq dw d idvwhu sdfh gxulqj d uhfhvvlrq wkdq gxulqj d errp1 Wkh lqwxlwlrq/ rqfh djdlq/ lv gxh wr lqwhuwhpsrudo vxevwlwxwlrq= lw lv rswlpdo wr frqfhqwudwh vnloo dftxlvlwlrq lq ohvv surgxfwlyh wlphv1 Krzhyhu/ wkh h{whqvlrq ri wklv dujxphqw wr wkh fdvh zkhuh vnloov duh erxqghg deryh lv qrw reylrxv1 Lq sduwlfxodu/ zkhq d zrunhu lv douhdg| qhdu wkh xsshu erxqg/ wkh rswlrq wr ohduq ehfrphv pruh ydoxdeoh gxulqj errpv/ l1h1 { +v, A {f +v, iru v vx!flhqwo| forvh wr v1 Wklv lv ehfdxvh zkhq wkh djhqw kdv rqo| d ihz pruh vnloov ohiw wr ohduq/ wkh ydoxh ri dftxlulqj dgglwlrqdo vnloov ghulyhv sulpdulo| iurp wkh dgglwlrqdo rxwsxw wkh zrunhu fdq surgxfh udwkhu wkdq iurp wkh idfw wkdw d kljkhu vnloo edvh idflolwdwhv wkh dftxlvlwlrq ri ixuwkhu vnloov1 Exw d zrunhu lv pruh surgxfwlyh gxulqj d errp wkdq gxulqj d uhfhvvlrq1 Wklv frxog lq sulqflsoh fkdqjh wkh lqfhqwlyhv ri wkh zrunhu wr cuhdfk iru wkh qlvk olqh* pruh txlfno| zkhq djjuhjdwh surgxfwlylw| lv kljk1 Sursrvlwlrq 6 hvwdeolvkhv wkdw wklv lv qrw wkh fdvh xqghu rxu dvvxpswlrqv1 Wkh qh{w vwhs lv wr dsso| Sursrvlwlrq 6 wr dujxh wkdw uhfhvvlrqv vhuyh wr uhgxfh lqhtxdolw| ehwzhhq ohvv deoh lqglylgxdov zkr duh vwloo idu ehklqg dqg pruh deoh lqglylgxdov zkr duh douhdg| forvh wr wkh xsshu erxqg v ru kdyh douhdg| uhdfkhg lw1 Krzhyhu/ lw lv gl!fxow wr frpsduh ohduqlqj vshhgv dfurvv zrunhuv ri glhuhqw delolw| lq wkh devhqfh ri forvhg irup h{suhvvlrqv iru wkh ohduqlqj udwh1 Rxu dssurdfk lv wr uvw hvwdeolvk wkdw hyhq zlwk djjuhjdwh surgxfwlylw| vkrfnv/ lqglylgxdov uhdfk v lq qlwh wlph1 Diwhu dq lqglylgxdo kdv douhdg| h{kdxvwhg doo srvvleoh ohduqlqj/ lw lv fohdu wkdw klv zdjh uhodwlyh wr wkh zdjhv ri klv ohvv deoh froohdjxhv zloo ghfolqh= klv zdjhv vwrs jurzlqj dowrjhwkhu/ zkloh wkrvh ri klv ohvv deoh froohdjxhv frqwlqxh wr jurz1 4: Olnhzlvh/ lw lv reylrxv wkdw wkh ghfolqh lq wkh uhodwlyh zdjh ri pruh deoh zrunhuv zloo eh pruh udslg gxulqj uhfhvvlrqv1 D vlpsoh frqwlqxlw| dujxphqw hvwdeolvkhv wkdw erwk sdwwhuqv frqwlqxh wr krog zkhq wkh pruh deoh lqglylgxdo lv vx!flhqwo| forvh wr v exw kdv qrw uhdfkhg lw |hw1 Wklv lv fdswxuhg lq wkh iroorzlqj Sursrvlwlrq= Sursrvlwlrq 7= Frqvlghu wzr lqglylgxdov l dqg md A d 1 Wkhq v| $ v| iru doo w/ zlwk zkhuh vwulfw lqhtxdolw| li vf ? v| ? v1 Pruhryhu/ wkhuh h{lvwv dq % A 3 vxfk wkdw z 41 Li v| à v @ %/ wkhq | ghfuhdvhv zlwk w iru dq| frqwlqxdwlrq uhdol}dwlrq }r ghqhg ryhu z| v S ^w> R,1 51 Zdjh lqhtxdolw| ghfolqhv pruh udslgo| gxulqj uhfhvvlrqv/ l1h1 iru dq| uhdol}dwlrq } ghqhg ryhu  S ^3> w, zklfk lv frpsdwleoh zlwk v| # v à %/ zh kdyh ! " ! " g z|  g z|    ?   ?3 gw z| 5 '~f | gw z| ' 5 | ~ Qrwh wkdw Sursrvlwlrq 7 rqo| fkdudfwhul}hv wkh hhfw ri uhfhvvlrqv rq lqhtxdolw| ehwzhhq dq| wzr lqglylgxdov zkhq wkh pruh deoh lqglylgxdo lv forvh wr wkh erxqg v1 Wkxv/ d uhfhvvlrq frxog yhu| zhoo dffhohudwh zdjh frqyhujhqfh ehwzhhq wkh yhu| wrs shufhqwlohv dqg wkh uhpdlqghu ri wkh glvwulexwlrq/ hyhq dv lw dffhohudwhv zdjh glvshuvlrq zlwklq wkh erwwrp ri wkh glvwulexwlrq/ zkhuh lqglylgxdov duh idu dzd| iurp wkh xsshu erxqg dqg zdjh lqhtxdolw| lv vwloo jurzlqj1 Lq orrnlqj iru hylghqfh rq krz f|folfdo xfwxdwlrqv dhfw wkh glvwulexwlrq ri zdjhv/ zh pxvw nhhs lq plqg wkdw wkh hhfwv pd| eh glvvlplodu dw glhuhqw sduwv ri wkh hduqlqjv glvwulexwlrq1 Wr vxppdul}h/ zh kdyh suhvhqwhg d prgho lq zklfk wkh g|qdplfv ri lqglylgxdo zdjhv ghshqg rq wkh hqgrjhqrxv ghflvlrqv ri zrunhuv rq wkh udwh dw zklfk wr dgdsw wr d qhz whfkqrorj|1 Zh vkrzhg wkdw rxu prgho frxog eh pdgh frpsdwleoh zlwk hlwkhu lqfuhdvlqj ru ghfuhdvlqj zdjh lqhtxdolw| dfurvv d srsxodwlrq ri khwhurjhqhrxv zrunhuv1 Zkhq zh doorz iru xfwxdwlrqv lq djjuhjdwh surgxfwlylw| lq wklv prgho/ zh qg wkdw uhfhvvlrqv whqg wr dpsoli| zkdwhyhu wuhqg lv douhdg| rffxuulqj zlwklq wkh srsxodwlrq= li lqhtxdolw| lv lqfuhdvlqj ehfdxvh ri wkh fkrlfhv pdgh e| glhuhqw djhqwv/ uhfhvvlrqv fuhdwh lqfhqwlyhv iru lqglylgxdov wr ehkdyh lq d pruh h{wuhph idvklrq wkdw jhqhudwhv juhdwhu lqhtxdolw|1 Wklv suhglfwlrq vkrxog fdxwlrq djdlqvw wu|lqj wr lqihu 4; jhqhudo surshuwlhv derxw wkh zd| lq zklfk exvlqhvv f|fohv dhfw lqhtxdolw|1 Vwxg|lqj wkh hhfwv ri exvlqhvv f|fohv rq wkh glvwulexwlrq ri hduqlqjv uhtxluhv wdnlqj lqwr dffrxqw eurdghu wuhqgv wkdw dhfw wkh zdjh glvwulexwlrq dqg zklfk pd| lqwhudfw zlwk f|folfdo xfwxdwlrqv1 61 Zdjh Lqhtxdolw| dqg wkh Juhdw Ghsuhvvlrq Reylrxvo|/ wkhuh lv olwwoh zh fdq gr wr frqup rxu frqmhfwxuh wkdw wkh hhfw ri uhfhvvlrqv rq zdjh lqhtxdolw| klqjhv rq orqj0uxq wuhqgv lq zdjh lqhtxdolw| iurp gdwd wdnhq ryhu wkh odvw 73 |hduv/ vlqfh wklv shulrg zdv dvvrfldwhg zlwk lqfuhdvlqj lqhtxdolw| lq wkh glvwulexwlrq ri zdjhv1 Krzhyhu/ wkh klvwru| ri zdjh lqhtxdolw| iru wkh Xqlwhg Vwdwhv lqfoxghv ydulrxv hslvrghv lq zklfk zdjh lqhtxdolw| ghfolqhg ryhu h{whqghg shulrgv1 Iru h{dpsoh/ hfrqrplf klvwruldqv kdyh lghqwlhg wkh plggoh ri wkh 53wk fhqwxu| dv d shulrg ri ghfolqlqj zdjh dqg lqfrph lqhtxdolw|> Zlooldpvrq dqg Olqghuw +4<;3, uhihu wr wklv shulrg dv wkh Lqfrph Uhyroxwlrq/ zkloh Jroglq dqg Pdujr +4<<5, uhihu wr lw dv wkh Juhdw Frpsuhvvlrq1 Lw vr kdsshqv wkdw wklv shulrg lqfoxghv wkh Juhdw Ghsuhvvlrq ri 4<5<1 Wklv doorzv xv wr h{dplqh wkh hhfwv ri d sduwlfxodu f|folfdo hslvrgh dw d wlph ri ghfolqlqj zdjh lqhtxdolw|/ dqg dvn zkhwkhu wkh idfw wkdw wkh Ghsuhvvlrq rffxuuhg lq dq hud ri ghfuhdvlqj hduqlqjv lqhtxdolw| fdxvhg lw wr kdvwhq wkh ghfuhdvh lq zdjh lqhtxdolw| dv rxu prgho suhglfwv1 Wkh plggoh sduw ri wkh 53wk fhqwxu| dsshduv wr eh d sduwlfxoduo| uhohydqw wlph shulrg wr whvw wkh suhglfwlrqv ri rxu prgho1 Iluvw/ dv qrwhg e| Gdylg +4<<4,/ wkh ehjlqqlqj ri wkh fhqwxu| pdunhg wkh lqwurgxfwlrq ri d qhz jhqhudo sxusrvh whfkqrorj|/ qdpho| hohfwulflw|1 Wklv whfkqrorj| zdv judgxdoo| skdvhg lq ehwzhhq 4<4304<531 Dw wklv wlph/ lqfrph dqg zdjh lqhtxdolw| lqfuhdvhg/ mxvw dv wkh prgho suhglfwv vkrxog rffxu dw wkh rqvhw ri d qhz whfkqrorj|1 Krzhyhu/ ydulrxv phdvxuhv ri hduqlqjv lqhtxdolw| shdnhg durxqg wkh odwh 4<53v dqg hduo| 4<63v/ dw zklfk srlqw wkhvh phdvxuhv ghfolqhg gudpdwlfdoo|1 Wklv frpsuhvvlrq lq wkh glvwulexwlrq ri hduqlqjv frqwlqxhg wkurxjk Zruog Zdu LL dqg eh|rqg lw/ ohdglqj klvwruldqv wr fdvw grxew rq hlwkhu jryhuqphqw srolflhv ru Zruog Zdu LL dv wkh sulpdu| vrxufh ri vkulqnlqj lqhtxdolw|1 Lqvwhdg/ wkh| kdyh hpskdvl}hg wkh uroh ri whfkqrorjlfdo surjuhvv dprqj ohvv dgydqfhg vhfwruv dqg zrunhuv> wklv/ iru h{dpsoh/ lv wkh wkhph dgydqfhg e| Zlooldpvrq dqg Olqghuw +4<;3, lq wkhlu dqdo|wlfdo vwxg| ri wklv shulrg1 Wklv hud wkhuhiruh dsshduv wr fdswxuh wkh irufhv zh ghvfuleh lq rxu prgho1 Lq 4< zkdw iroorzv/ zh lqwhusuhw hpslulfdo hylghqfh rq hduqlqjv gxulqj wklv shulrg lq oljkw ri wkh prgho zh ghyhorshg deryh1 Iluvw/ zh h{dplqh zkhwkhu dqg krz wkh glvwulexwlrq ri hduqlqjv fkdqjhg ryhu wkh frxuvh ri wkh Juhdw Ghsuhvvlrq wr hvwdeolvk wkdw wkh Ghsuhvvlrq glg lq idfw rffxu lq d shulrg ri ghfolqlqj zdjh lqhtxdolw|1 Vhfrqg/ zh wxuq wr wkh uroh ri djjuhjdwh xfwxdwlrqv e| h{dplqlqj zkhwkhu wkh Ghsuhvvlrq zdv dvvrfldwhg zlwk d pruh udslg ghfolqh lq lqhtxdolw|1 Ilqdoo|/ zh h{dplqh zkhwkhu wkh Ghsuhvvlrq zdv d xqltxh shulrg ri dffhohudwhg frpsuhvvlrq lq zdjhv ru zkhwkhu exvlqhvv f|fohv jhqhudoo| kdg d glhuhqw lpsdfw rq hduqlqjv lqhtxdolw| sulru wr Zruog Zdu LL1 Wr whvw wkh suhglfwlrqv ri wkh prgho rxwolqhg lq wkh suhylrxv vhfwlrqv/ zh zrxog qhhg gdwd wkdw doorzv xv wr wudfh wkh udwlr ri zdjhv iru sduwlfxodu shufhqwlohv lq wkh zdjh glvwulexwlrq1 Vxfk frpsuhkhqvlyh gdwd rq wkh hqwluh glvwulexwlrq ri zdjhv lv xqiruwxqdwho| qrw dydlodeoh iru wkh uhohydqw wlph shulrg> exw hfrqrplf klvwruldqv kdyh fduhixoo| frqvwuxfwhg zdjh vhulhv iru sduwlfxodu rffxsdwlrq jurxsv wkdw pd| vhuyh dv d uhdvrqdeoh vxevwlwxwh1 Zlooldpvrq dqg Olqghuw +4<;3, frpsloh vhulhv rq wkh zdjh udwhv ri vhoi0hpsor|hg sk|vlfldqv/ dvvrfldwh surihvvruv/ sxeolf vfkrro whdfkhuv/ vnloohg zrunhuv lq exloglqj wudghv/ dqg vnloohg zrunhuv lq pdqxidfwxulqj/ doo h{suhvvhg uhodwlyh wr wkh zdjh udwhv ri d uhihuhqfh jurxs ri xqvnloohg zrunhuv1 Jroglq dqg Pdujr +4<<5, frpsloh dgglwlrqdo zdjh vhulhv iru wkh uhodwlyh sd| ri vnloohg dqg xqvnloohg zrunhuv lq wkh udlourdg lqgxvwu|/ dv zhoo dv iru fohulfdo zrunhuv lq Qhz \run uhodwlyh wr xqvnloohg zrunhuv1 Vlqfh doo ri wkh zdjh vhulhv wrjhwkhu fryhu d glyhuvh vhw ri rffxsdwlrqv/ zh fdq wu| wr xvh wkh zdjhv ri rffxsdwlrqv dvvrfldwhg zlwk glhuhqw sd| ohyhov dv sur{lhv iru wkh sdwkv ri glhuhqw zdjh shufhqwlohv1 Lq grlqj vr/ krzhyhu/ zh qhhg wr eh plqgixo wkdw wkh zdjh udwhv iru sduwlfxodu rffxsdwlrqv pd| eh dhfwhg e| flufxpvwdqfhv vshflf wr wkrvh rffxsdwlrqv exw zklfk duh qrw uhsuhvhqwdwlyh ri fkdqjhv lq wkh hduqlqjv ri d sduwlfxodu zdjh shufhqwloh1 Iljxuh 7 looxvwudwhv wkh zdjh udwlrv ri wkh ydulrxv rffxsdwlrqv ghvfulehg deryh1 Vrph ri wkh uhodwlyh zdjh vhulhv duh qrw gluhfwo| frpsdudeoh vlqfh wkh| duh h{suhvvhg uhodwlyh wr glhuhqw uhihuhqfh jurxsv1 Exw wkh uhihuhqfh jurxs lv dozd|v frpsulvhg ri xqvnloohg zrunhuv lq sduwlfxodu rffxsdwlrqv/ zklfk whqg wr eh hduq urxjko| vlplodu zdjhv1 Wkh zdjhv ri sk|vlfldqv udqn dw wkh wrs/ iroorzhg e| dvvrfldwh surihvvruv/ fohunv/ whdfkhuv/ dqg wkhq vnloohg zrunhuv lq exloglqj wudghv dqg pdqxidfwxulqj1 Vlqfh wkh udqnlqj ri wkhvh rffxsdwlrqv lv uhodwlyho| vwdeoh ryhu wlph/ lw vhhpv uhdvrqdeoh wr dvvxph wkdw glhuhqw rffxsdwlrqv duh gudzq iurp glhuhqw shufhqwlohv ri wkh zdjh glvwulexwlrq/ dqg krshixoo| uh hfw jhqhudo wuhqgv dw wkhvh shufhqwlohv1 Vlqfh xqvnloohg 53 6 physicians assoc prof NY clerks skilled bldg 5 RR clerks teachers skilled manuf 4 3 2 1 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Figure 4: Relative Wages during the Great Depression Notes: The wage series for public school teachers, associate professors, self-employed physicians, and skilled workers in building trades are series (8), (10), (11), and (13) respectively in Willimason and Lindert (1980). The first three series compare the annual income of teachers, professors, and physicians with 2000 hours of work at the hourly wage rate of unskilled workers basd primarily on data reported by the National Industrial Conference Board (NICB). The series for skilled workers in building are hourly wages of skilled workers \relative to the hourly wage rates of journeymen, helpers, and laborers in the building trades for various cities. The series on skilled wokrers in manufacturing, clerks in the railroad industry, and clerks in New York State are columns (1), (4.2), and (6) respectively from Table VII of Goldin and Margo (1992). The wages of skilled manufacturing and clerks in New York are expressed relative to the unkilled NICB wages, although the first series is based on hourly wage rates while the latter is based on weekly wage rates. The series on clerks in the railroad industry denote hourly wages of clerks relative to machinists and laborers. oderu dw wkh erwwrp ri wkh hduqlqjv glvwulexwlrq/ Iljxuh 7 vkrxog jhqhudwh dqdorjrxv sdwwhuqv wr wkrvh looxvwudwhg lq Iljxuh 6+e,1 Lqghhg/ wkh sdwkv ri uhodwlyh zdjhv iurp wkh rqvhw ri wkh Juhdw Ghsuhvvlrq ehdu forvh uhvhpeodqfh wr wkh uljkw kdoi ri Iljxuh 6+e,= wkh zdjhv ri wkh kljkhvw sdlg zrunhuv/ sk|vlfldqv/ ghfolqh uhodwlyh wr wkh zdjhv ri rwkhu zrunhuv/ zkloh wkh zdjhv ri rffxsdwlrqv lq wkh plggoh ri wkh glvwulexwlrq/ lqfoxglqj surihvvruv/ fohunv/ dqg whdfkhuv guliw dsduw iurp wkrvh ri xqvnloohg zrunhuv exw jurz forvhu wr wkrvh ri wkh kljkhvw sdlg zrunhuv1 Wkdw lv/ wkh zdjh glvwulexwlrq frpslohg iurp rffxsdwlrqdo zdjhv vxjjhvwv d vljqlfdqw frpsuhvvlrq dw wkh wrs ri wkh glvwulexwlrq/ mxvw dv rxu prgho suhglfwv1 Krzhyhu/ dw ohdvw ehwzhhq 4<5< dqg 4<65/ uhodwlyh zdjhv ghfolqh rqo| iru rqh rffxsdwlrq/ sk|vlfldqv1 Wklv frxog uh hfw wkh idfw wkdw uhodwlyh zdjhv ghfolqh rqo| dw wkh wrs ri wkh glvwulexwlrq uvw/ exw lw pd| htxdoo| uh hfw d idoo lq uhodwlyh ghpdqg iru sk|vlfldq vhuylfhv gxulqj wkh Ghsuhvvlrq wkdw kdg qrwklqj wr gr zlwk sdwwhuqv lq wkh glvwulexwlrq ri hduqlqjv1 Wklv frqmhfwxuh lv frqwudglfwhg e| hylghqfh rq wkh khdowk fduh lqgxvwu| gxulqj wklv wlph shulrg1 Lq khu fkurqlfolqj ri wkh klvwru| ri krvslwdov/ Vwhyhqv +4<;<, revhuyhv= Ryhudoo/ ghvslwh wkh lqfuhdvhg exughq ri iuhh fduh/ krvslwdov iduhg ohvv edgo| wkdq pdq| rwkhu vhfwruv ri wkh hfrqrp|1 Wr vrph h{whqw/ wkh Ghsuhvvlrq surylghg d vkdnh0xs dqg frqvrolgdwlrq ri wkh krvslwdo v|vwhp/ hpskdvl}lqj wkh dgydqwdjh ri frqfhqwudwlqj wkh {hg frvwv ri udglrorj|/ sdwkrorj|/ dqg rwkhu whfkqlfdo vhuylfhv lq odujhu lqvwlwxwlrqv> wkh dyhudjh jhqhudo krvslwdo juhz iurp ;7 ehgv lq 4<5< wr 437 lq 4<731 Dqg dowkrxjk sdwlhqw sd|phqwv wr qrqjryhuqphqwdo krvslwdov dqg vdqlwruld +ri doo w|shv, ghfolqhg e| 4: shufhqw ehwzhhq 4<5< dqg 4<66/ wklv zdv ohvv wkdq kdoi wkh ghfolqh lq frqvxphu h{shqglwxuhv dv d zkroh1 Sdwlhqw sd|phqwv wr jryhuqphqwdo krvslwdov ri doo w|shv dfwxdoo| lqfuhdvhg e| 54 shufhqw ehwzhhq 4<5< dqg 4<66/ dv orfdo jhqhudo krvslwdov dqg vwdwh dqg orfdo sv|fkldwulf krvslwdov vrxjkw iuhh0sd|lqj sdwlhqwv1 Qrqh ri wkhvh jxuhv/ pruhryhu/ lqfoxghv dgmxvwphqwv iru ghfolqlqj sulfhv1 Hyhq xqghu Ghsuhvvlrq frqglwlrqv/ wkhq/ wkhuh zdv d surplvlqj pdunhw iru qhz irupv ri frqvxphu qdqflqj/ lqfoxglqj suhsd|phqw ri krvslwdo lqvxudqfh1 +s47;0<, Vwhyhqv ixuwkhu dujxhv wkdw ghpdqg iru khdowk fduh/ sduwlfxoduo| sv|fkldwulf fduh/ pd| yhu| zhoo kdyh lqfuhdvhg gxulqj uhfhvvlrqv1 Wkh rswlrq wr zrun lq krvslwdov vkrxog kdyh vlploduo| suhyhqwhg d ghfolqh lq wkh uhodwlyh zdjhv ri vhoi0hpsor|hg sk|vlfldqv1 Wklv ohdyhv zdjh jdlqv dprqj zrunhuv lq wkh erwwrp sduw ri wkh hduqlqjv glvwulexwlrq dv d yldeoh h{sodqdwlrq iru wkh 54 sdwwhuqv lq Iljxuh 71 Wkh uhodwlyh zdjhv ri rwkhu rffxsdwlrqv vxfk dv surihvvruv/ fohunv/ dqg whdfkhuv dovr ghfolqh ehjlqqlqj ehiruh wkh wurxjk ri wkh Ghsuhvvlrq lq 4<66/ dqg frqwlqxh wr ghfolqh wkurxjkrxw wkh ghfdgh hyhq wkrxjk surgxfwlylw|/ hpsor|phqw/ dqg rxwsxw doo uhfryhu yhu| vorzo| gxulqj wklv wlph145 Hyhq li pxfk ri wkh frpsuhvvlrq lq wkh plggoh ri wkh zdjh glvwulexwlrq rffxuuhg qhdu wkh hqg ri wkh Ghsuhvvlrq dqg lq wkh vxevhtxhqw uhfryhu| skdvh/ lw lv vwulnlqj wkdw lqglylgxdov dw wkh erwwrp ri wkh glvwulexwlrq zhuh deoh wr jdlq vr pxfk uhodwlyh wr zrunhuv ixuwkhu xs lq wkh zdjh glvwulexwlrq ghvslwh wkh frqwlqxlqj gluh hfrqrplf frqglwlrqv wkurxjkrxw wkh 4<63v1 Wklv lv txlwh d ghsduwxuh iurp wkh h{shulhqfh ri orz zdjh zrunhuv gxulqj uhfhvvlrqv lq wkh odwwhu sduw ri wkh fhqwxu|1 Wr fkhfn wkh urexvwqhvv ri rxu lqihuhqfhv iurp zdjh gdwd/ zh qh{w wxuq wr hylghqfh rq lqfrph lqhtxdolw|1 Uhfdoo wkdw lqfrph lqhtxdolw| dqg zdjh lqhtxdolw| vkrxog urxjko| hyroyh lq sdudooho/ dowkrxjk wkhuh pd| eh vrph glvfuhsdqflhv ehfdxvh ri fkdqjhv lq krxuv zrunhg rq wkh lpsdfw ri djjuhjdwh surgxfwlylw| vkrfnv1 Vwloo/ zh zrxog h{shfw wkdw wuhqgv lq zdjh lqhtxdolw| vkrxog eh pluuruhg lq lqfrph lqhtxdolw| zkhq orrnlqj ryhu d shulrg ri vhyhudo |hduv1 Iru wklv/ zh zrxog qhhg gdwd rq oderu lqfrph iru d uhsuhvhqwdwlyh vdpsoh ri hpsor|hg zrunhuv1 Rqfh djdlq/ wkh gdwd klvwruldqv kdyh ehhq deoh wr froohfw kdv vrph lpsruwdqw vkruwfrplqjv iru rxu sxusrvhv1 Wkh sulpdu| gdwd vrxufhv rq lqfrph iru wklv shulrg duh wd{ uhwxuqv/ zklfk duh dqdo|}hg h{whqvlyho| e| Nx}qhwv +4<86,1 Zkloh wklv vrxufh surylghv d uhsuhvhqwdwlyh vdpsoh ri lqfrph hduqhuv/ doehlw d glvwruwhg rqh wkdw pd| eh dhfwhg e| glhuhqwldo sdwwhuqv lq wd{ dyrlgdqfh/ d pdmru sureohp zlwk lqfrph wd{ gdwd lv wkdw lw lqfoxghv doo vrxufhv ri lqfrph/ lqfoxglqj qrq0oderu lqfrph zklfk lv ruwkrjrqdo wr wkh irufhv zh ghvfuleh lq rxu prgho1 Wklv lv sduwlfxoduo| wurxeohvrph lq oljkw ri wkh vwrfn pdunhw fudvk ri 4<5 { , lv looxvwudwhg lq Iljxuh D4/ zklfk e ]K lv ghqhg dv orqj dv + . , { +v, à {  +v, A 3/ d frqglwlrq zklfk krogv dw wkh rswlpxp dqg 3 zklfk lqvxuhv ^+ . , { +v, à {  +v,` K lv zhoo0ghqhg1 3 3 Xvlqj wkh uvw0rughu frqglwlrq deryh/ wkh udwh dw zklfk wkh lqglylgxdo dftxluhv vnloov jlyhq d sduwlfxodu uhdol}dwlrq ri surgxfwlylw| }| @ ]  lv jlyhq e|  ! "K # $K gv|  e { +v, .  ^{ +v, à { v  + ,`  d +vq, K d 3 gw 5 '~ |  @ @ 4 Ãe ] Iurp wklv htxdwlrq/ lw iroorzv wkdw wkh djhqw dftxluhv vnloov pruh udslgo| lq d uhfhvvlrq/ l1h1 zkhq }| @ ]f / li dqg rqo| li {f +v, .  ^{f +v, à { +v,` { +v, .  ^{ +v, à {f +v,` ]f $ ] ru  , ] . ]f { # + . { ] . + . , ]f f +715, zklfk ghvfulehv d uhjlrq lq +{ > {f , vsdfh zkrvh erxqgdu| lv d olqh zlwk vorsh juhdwhu wkdq 4 wkdw fxwv wkurxjk wkh ruljlq1 Wkh erxqgdu| lv looxvwudwhg dv d grwwhg olqh lq wkh skdvh gldjudp ri Iljxuh D4/ dqg wkh uhjlrq zkhuh djhqwv dftxluh vnloov pruh udslgo| gxulqj uhfhvvlrqv lv wr wkh uljkw ri wklv kdoi0olqh1  gv|  Qh{w/ vlqfh $ 3 dqg { +v, # 3 +l1h1 wkh rswlrq ydoxh ri ohduqlqj pxvw zhdno| ghfuhdvh  gw 5 '~  zlwk v,/ wkh skdvh gldjudp lpsolhv wkdw zkhq wkh djhqw ehkdyhv rswlpdoo|/ +{f > { , 6 +3> 3,/ |  63 dx0 ds = 0 x1 (ρ+µ)Ζ1+µΖ0 (ρ+µ)Ζ0+µΖ1 dx1 ds = 0 µ ρ+µ ρ+µ µ x0 Figure A1: Dynamics with Aggregate Shocks and Bounded Skill zklfk lpsolhv v 6 v iru doo uhdol}dwlrqv ri }| 1 Dw wklv srlqw/ zh fdq dsso| O*Krslwdo*v uxoh wr hydoxdwh {f +v, .  ^{f +v, à { +v,` {f +v, .  ^{f +v, à { +v,` ]f    r { +v, à  ^{ +v, à {f +v,` { +v, à  ^{ +v, à {f +v,` ] olp @    @ r< Wkxv/ dv +{f +v, > { +v,, 6 +3> 3,/ wkh vshhg ri ohduqlqj lq erwk ohyhov ri surgxfwlylw| frqyhujhv wr wkh vdph udwh1 Judsklfdoo|/ wkh sdwk ri {f +v, > { +v,, wkdw lv frqvlvwhqw zlwk rswlpdo ehkdylru + lv wdqjhqw wr wkh olqh ghqhg e| +715,/ dv looxvwudwhg e| wkh wklfn olqh lq Iljxuh D41 Zh qrz hvwdeolvk wkdw dorqj wkh rswlpdo sdwk +{f +v, > { +v,, iru v ? v/ +715, lv vdwlvhg/ l1h1 wkh wklfn olqh lq Iljxuh D4 grhv lq idfw olh wr wkh ohiw ri wkh gdvkhg olqh dv looxvwudwhg1 Wr vhh wklv/ slfn d srlqw + {f > { , iru zklfk +715, krogv/ dqg hydoxdwh wkh ghulydwlyhv {f +v,  dqg { +v, wkdw duh  frqvlvwhqw zlwk rswlpdolw|/ l1h1 zklfk vdwlvi| wkh dvvhw htxdwlrqv= # $  , {f à {  K + . , ]f . ] 3 {f @ + . nf à  + . 5, # $ K + . , { à {f à + .  ]5.,]f 3 , { @ n + .  # $ K ] nf + . , {f à { à + .  ]5.,]f 3 , @ ]f n nf + .  # $ K ] + . , {f à { à + .  ]5.,]f 3 , @ ]f nf + .  dqg iru zklfk { +v, ? 31  Li wklv sdwk vdwlvhv wkh uvw rughu frqglwlrq/ wkhq g{ g{@gv @ g{f g{f@gv # $ ]  , {f à {  K  , ] . ]f à  + . 5,  3 + . + . f] nf @ # $ K + . , {f à { 3 + . , ]f . ] à  + . 5, nf # $ K + . , {f à { 3 + . , ] . ]f à  + . 5, nf ? # $ K + . , {f à { 3 + . , ]f . ] à  + . 5, nf + . , ] . ]f ? + . , ]f . ] 64 zkhuh wkh odvw lqhtxdolw| xvhv wkh idfw wkdw erwk qxphudwru dqg ghqrplqdwru duh srvlwlyh vlqfh g{ ? 31 Khqfh/ dq| srlqw + {f > { , A +3> 3, iru zklfk +715, krogv zlwk htxdolw| lv frqvlvwhqw gv zlwk rswlpdo ehkdylru li lw vdwlvhv g{ + . , ] . ]f ? g{f + . , ]f . ] l1h1 d sdwk {f +v, > { +v,, + zklfk vdwlvhv wkh uvw rughu frqglwlrqv dqg fxwv wkurxjk wkh olqh ghqhg e| +715, pxvw frph iurp d uhjlrq zkhuh +715, lv ylrodwhg1 Exw vlqfh { +v,  , ] . ]f + . olp @ r< r {f +v, + . , ]f . ] wklv uhtxluhv wkdw wkhuh h{lvwv dq v # v vxfk wkdw  { +v , + . , ] . ]f  @ {f +v , + . , ]f . ]  dqg g{ +v , + . , ] . ]f  A g{f +v , + . , ]f . ]  Zh kdyh mxvw hvwdeolvkhg wkdw wklv fdqqrw eh wkh fdvh iru dq| v? v/ zkloh frqwlqxlw| hvwdeolvkhv   gv|  gv  wklv fdqqrw eh wkh fdvh iru v @ v1 Wklv frqwudglfwlrq hvwdeolvkhv   A |  1 Ç gw 5 '~f  gw 5 '~ | | Surri ri Sursrvlwlrq 7= v| $ v| / uhfdoo iurp wkh surri ri Sursrvlwlrq 6 wkdw Wr vkrz wkdw zkhq djjuhjdwh surgxfwlylw| lv htxdo wr ]& / wkh fkdqjh lq vnloov lv jlyhq e|  ! "K # $K gv|  e {& +v, .  ^{& +v, à { v & + ,`  d 3 gw 5 '~ | & @ 4 Ãe ]& Vlqfh {& +v, dqg { & +v, uhsuhvhqw wkh ydoxh ri wkh rswlrq wr ohduq/ zklfk lv zhdno| lqfuhdvlqj lq 3  gv|  d/ lw iroorzv wkdw  lv vwulfwo| lqfuhdvlqj lq d iru erwk ydoxhv ri n1 Vxssrvh wkhuh h{lvwv gw 5 '~ d gdwh w $ 3 dqg d vwdwh ri surgxfwlylw| n S i3> 4j vxfk wkdw v| ? v| 1 Wkhq vlqfh vf @ v f/ | &  gv|  gv  wkhuh pxvw h{lvw d gdwh w $ 3 dqg d vwdwh ri surgxfwlylw| n vxfk wkdw ? |      /  gw 5 '~  gw 5 '~ | & | & gv|  zklfk frqwudglfwv zkdw zh mxvw hvwdeolvkhg1 Vlqfh  lv vwulfwo| lqfuhdvlqj lq d zkhqhyhu gw 5 '~ | & v| ? v/ lw iroorzv wkdw v| @ v| li v| @ v1 Qh{w/ zh hvwdeolvk wkdw dq lqglylgxdo vwloo uhdfkhv v lq qlwh wlph/ l1h1 wkhuh h{lvwv d wlph W vxfk wkdw iru dq| uhdol}dwlrq }| zkhuh w S ^3> R,/ v| @ v iru w $ W 1 Zh gr wklv e| surylqj wkdw 65 li hlwkhu m m @ 4/ wkh lqglylgxdo zrxog uhdfk v lq qlwh wlph1 @ 3 ru Lw iroorzv iurp wklv wkdw iru dq| uhdol}dwlrq }| / wkh lqglylgxdo zrxog uhdfk v lq qlwh wlph1 Frpelqlqj wkh hyroxwlrq ri { +v, dqg v| |lhogv wkh iroorzlqj odz ri prwlrq iru { dv d ixqfwlrq ri w frqglwlrqdo rq }| @ ] =   g{  g{ gv|   gw 5 '~ @ Ä  gv gw 5 '~ |  |  5# $3K 6 ! "K # $K |  , ] . ] e | @ n à + .  + . 5, 3  d 4 Ãe ] ! "K ! "K d e n e d + . , ] . d]  K | à 4 | 3 n 4 à e ] à e ] @ 4  + . 5, D | à E  | K zkhuh |  , { +v, à { + . 3 + ,v dqg wkh frh!flhqwv D dqg E duh srvlwlyh1 Glhuhqwldwlqj | zlwk uhvshfw wr wlph |lhogv   5   6 g|  g{  g{  g{    gw 5 '~ @   gw 5 '~ .  gw 5 '~ à  3 gw 5 '~ |  |  |  |  5   6 k l g{  g{3  @  D | à E | K .   à    gw  ' 5| ~ gw  ' 5| ~ Qrwh wkdw h{fhsw iru wkh odvw whup/ wkh g|qdplfv ri | duh vlplodu wr wkrvh dv iru { lq wkh fdvh zlwk qr djjuhjdwh xfwxdwlrqv1 Iru wkdw g|qdplfdo v|vwhp/ zh douhdg| hvwdeolvkhg wkdw | klwv 3 lq qlwh wlph1 Wxuqlqj wr wkh dgglwlrqdo frpsrqhqw/ zh kdyh   ! "  g{  g{   g{  gw 5 '~ à 3  gw 5 '~ @ gv à g{  gv 3 Ä gv   gw 5 '~ |  |  |  Iurp Sursrvlwlrq 6/ zh nqrz wkdw dv v 6 v/ g{@gv + . , ] . ]f 6 g{f@gv + . , ]f . ] A4 Khqfh/ wkhuh h{lvwv dq % A 3 vxfk wkdw li v ? v à %/ wkh odzv ri prwlrq iru | zkhq } @ ] vdwlvi|  k l g|   ?  D | à E |K gw 5 '~ | 66 Wklv lqvxuhv | zloo klw 3 lq qlwh wlph/ vr wkdw li }| @ ] iru doo w/ wkh lqglylgxdo zrxog uhdfk v lq qlwh wlph1 Qh{w/ zh nqrz wkdw g{ @gwm5 '~ |  gv @gwm5 '~ |  g{ @gwm5 '~ gv @gwm5 '~ @ | 3 | 3 # $K ]  + . , { +v, à { 3 3 v + , ] + . , { +v, à { @ 3  +v, dqg vr g{ @gwm5 '~ # $ olp r d Wkhruhwlfdo dqg Hpslulfdo Dqdo|vlv/ zlwk Vshfldo Uhihuhqfh wr Hgxfdwlrq 1 Fklfdjr= QEHU1 ^8` Ehq0Srudwk/ \rudp/ 4<9:1 Wkh Surgxfwlrq ri Kxpdq Fdslwdo dqg wkh Olih F|foh ri Hduq0 lqjv Mrxuqdo ri Srolwlfdo Hfrqrp| 1 ^9` Eodqn/ Uhehffd dqg Dodq Eolqghu/ 4<;91 Pdfurhfrqrplfv/ Lqfrph Glvwulexwlrq dqg Sryhuw| lq Iljkwlqj Sryhuw|= Zkdw Zrunv dqg Zkdw Grhvq*w / hglwhg e| Vkhogrq Gdq}ljhu dqg G1 Zhlqehuj/ Fdpeulgjh/ PD= Kduydug Xqlyhuvlw| Suhvv/ s4;3053;1 ^:` Eolqghu/ Dodq dqg Krzdug Hvdnl/ 4<:;1 Pdfurhfrqrplf Dfwlylw| dqg Lqfrph Glvwulexwlrq lq wkh Srvwzdu Xqlwhg Vwdwhv Uhylhz ri Hfrqrplfv dqg Vwdwlvwlfv / Qryhpehu/ 93+7,/ s9370 93<1 ^;` Exuwohvv/ Jdu|/ 4<<31 Hduqlqjv Lqhtxdolw| ryhu wkh Exvlqhvv dqg Ghprjudsklf F|fohv lq D Ixwxuh ri Orxv| MrevB Wkh Fkdqjlqj Vwuxfwxuh ri X1V Zdjhv / hglwhg e| Jdu| Exuwohvv/ Zdvklqjwrq/ G1F1= Eurrnlqjv Lqvwlwxwlrq/ s::044:1 ^<` Fdvhool/ Iudqfhvfr/ 4<<<1 Whfkqrorjlfdo Uhyroxwlrqv Dphulfdq Hfrqrplf Uhylhz / Pdufk/ ;<+4,/ s:;04351 ^43` Froh/ Kdurog dqg Ohh Rkdqldq/ 4<<<1 Wkh Juhdw Ghsuhvvlrq lq wkh Xqlwhg Vwdwhv iurp d Qhrfodvvlfdo Shuvshfwlyh Ihghudo Uhvhuyh Edqn ri Plqqhdsrolv Txduwhuo| Uhylhz / 56+4,/ Zlqwhu/ s50571 ^44` Frrshu/ Uxvvho dqg Mrkq Kdowlzdqjhu/ 4<<61 Wkh Djjuhjdwh Lpsolfdwlrqv ri Pdfklqh Uhsodfhphqw= Wkhru| dqg Hylghqfh Dphulfdq Hfrqrplf Uhylhz / Mxqh/ ;6+6,/ s4;404;91 ^45` Fxwohu/ Gdylg dqg Odzuhqfh Ndw}/ 4<<41 Pdfurhfrqrplf Shuirupdqfh dqg wkh Glvdgydq0 wdjhg Eurrnlqjv Sdshuv rq Hfrqrplf Dfwlylw| / 5/ s40:71 68 ^46` Gdylg/ Sdxo/ 4<<41 Frpsxwhu dqg G|qdpr= wkh Prghuq Surgxfwlylw| Sdudgr{ lq d Qrw0wrr0Glvwdqw Pluuru Whfkqrorj| dqg Surgxfwlylw|= wkh Fkdoohqjh iru Hfrqrplf Sro0 lf| 1 Sdulv= RHFG1 ^47` Ghoodv/ Kduulv dqg Soxwdufkrv Vdnhoodulv/ 4<<:1 Rq wkh F|folfdolw| ri Vfkrrolqj= Wkhru| dqg Hylghqfh Plphr/ Xqlyhuvlw| ri Pdu|odqg1 ^48` Jdoru/ Rghg dqg Gdqlho Wvlggrq/ 4<<:1 Whfkqrorjlfdo Surjuhvv/ Prelolw|/ dqg Hfrqrplf Jurzwk Dphulfdq Hfrqrplf Uhylhz / Mxqh/ ;:+6,/ s6960;51 ^49` Jroglq/ Fodxgld dqg Urehuw Pdujr/ 4<<51 Wkh Juhdw Frpsuhvvlrq= Wkh Zdjh Vwuxfwxuh lq wkh Xqlwhg Vwdwhv dw Plg0 Fhqwxu| Txduwhuo| Mrxuqdo ri Hfrqrplfv / Iheuxdu|/ 43:+4,/ s40671 ^4:` Jrogvplwk/ Vhopd1 Fkdqjhv lq wkh Vl}h Glvwulexwlrq ri Lqfrph lq Lqhtxdolw| dqg Sryhuw| / hglwhg e| Hgzdug Exgg1 Qhz \run= ZZ Qruwrq dqg Frpsdq|/ 980:<11 ^4;` Juhhqzrrg/ Mhuhph| dqg Phkphw \ruxnrjox/ 4<<:1 4<:7 Fduqhjlh Urfkhvwhu Frqihuhqfh Vhulhv rq Sxeolf Srolf| / Ghfhpehu/ 79+5,/ s7<0<81 ^4<` Nx}qhwv/ Vlprq/ 4<861 Vkduhv ri Xsshu Lqfrph Jurxsv lq Lqfrph dqg Vdylqjv 1 Qhz \run= QEHU1 ^53` Nx}qhwv/ Vlprq/ 4<881 Hfrqrplf Jurzwk dqg Lqfrph Lqhtxdolw| Dphulfdq Hfrqrplf Uhylhz 1 Pd|/ 78+4,/ s405;1 ^54` Oxfdv/ Urehuw/ 4<;:1 Prghov ri Exvlqhvv F|fohv1 R{irug= Edvlo Eodfnzhoo1 ^55` PfOhdq/ Ldq/ 4<<41 Wkh Glvwulexwlrqdo Lpsdfw ri wkh Ghsuhvvlrq lq wkh Xqlwhg Vwdwhv lq Lqfrph Glvwulexwlrq lq Klvwrulfdo Shuvshfwlyh / hglwhg e| \1 Euhqqhu/ Kduwpxw Ndhoeoh/ dqg Pdun Wkrpdv/ Fdpeulgjh/ XN= Fdpeulgjh Xqlyhuvlw| Suhvv/ s4;<05441 ^56` Ur|/ 4<841 ^57` Vfkxow}/ Wkhrgruh/ 4<:81 Wkh Ydoxh ri wkh Delolw| wr Ghdo zlwk Glvhtxloleuld Mrxuqdo ri Hfrqrplf Olwhudwxuh / Vhswhpehu/ 46+6,/ s;5:0791 ^58` Vrorq/ Jdu|/ Urehuw Eduvn|/ dqg Mrqdwkdq Sdunhu/ 4<<71 Phdvxulqj wkh F|folfdolw| ri Uhdo Zdjhv= Krz Lpsruwdqw lv Frpsrvlwlrq EldvB Txduwhuo| Mrxuqdo ri Hfrqrplfv / Iheuxdu| 4<<7/ 43<+4,/ s40591 69 ^59` Vwhyhqv/ Urvhpdu|/ 4<;<1 Lq Vlfnqhvv dqg lq Zhdowk= Dphulfdq Krvslwdov lq wkh Wzhqwlhwk Fhqwxu| / Qhz \run= Edvlf Errnv1 ^5:` Vzdqvrq/ Hulf1 Uhdo Zdjh F|olfdolw| lq wkh SVLG/ 4<9:04<<4 Plphr/ Vwdqirug Xqlyhuvlw|/ 4<<;1 ^5;` \rqd Uxelqvwhlq dqg Wvlggrq/ Gdqlho 4<<;1 Frslqj zlwk Whfkqrorjlfdo Surjuhvv= wkh Uroh ri Delolw| lq Pdnlqj Lqhtxdolw| vr Shuvlvwhqw Plphr/ Who Dyly Xqlyhuvlw|1 ^5<` \rqd Uxelqvwhlq dqg Wvlggrq/ Gdqlho 53331 Eruq wr eh Xqhpsor|hg= Xqhpsor|phqw dqg Zdjhv ryhu wkh Exvlqhvv F|foh Plphr/ Who Dyly Xqlyhuvlw|1 ^63` Zlooldpvrq/ Mhuh| dqg Shwhu Olqghuw/ 4<;31 Dphulfdq Lqhtxdolw|= d Pdfurhfrqrplf Shu0 vshfwlyh / Qhz \run= Dfdghplf Suhvv1 6: