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ØØ ),Ȭ ›Aˆ"’ Æ}× Ųoc‡ ļŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś12Ś  ŚóóŻ Ź ŻņņTables€of€regressions€backing€up€each€statement€in€this€paragraph€areŠ ° Šavailable€at€http://www.econ.duke.edu/~kelley/ack.homepage.html.óóVV ’’8Document[1]Document StyleĢŌ  Ōą@ģ..ģąņņņ ņŌ  ŌŌ2ŌŌ3  Ō€Ō  ŌŌ  ŌŌ  ԈĢóóó óV-’’8Document[2]Document StyleĢņ ņŌ2ŌŌ3  Ō€ņņŌ  ŌŌ  ŌĢó óóóV=’’8Document[3]Document StyleĢą..ąņ ņŌ2ŌŌ3  Ō€Ō  ŌŌ  Ōó óV ’’8Document[4]Document Styleą..ąņ ņņņ.óó€€ó óV ’’8Document[5]Document Styleą0..ąĢV ’’8Document[6]Document Styleą8..ąĢV& ’’8Document[7]Document Styleą0..ąą0` ..` ąĢV& ’’8Document[8]Document Styleą0..ąą8` ..` ąĢ<+ ’’:Technical[1]Ō2ŌŌ3  Ōą0..ąX ,Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś8Ś  ŚóóŻ Ź ŻņņThe€aggregate„saving€literature€is€about€evenly€divided€between€the€useŠ ° Šof€domestic€versus€national€saving€and€output€measures.€€We€employ€GDP€in€theĻdenominator€of€either€saving€ratio€since€most€studies€of€aggregate€growth€(asĻdistinct€from€saving)€focus€on€GDP.€€However,€at€least€conceptually,€there€areĻsome€advantages€to€the€GNS€measure€which€focuses€on€broader€aspects€of€wealthĻaccumulation€and€takes€into€account,€at€least€implicitly,€relevant€trade„offsĻbetween€foreign€and€domestic€sources€of€accumulation.€€Operationally€we€haveĻundertaken€most€of€our€empirical€work€using€the€ratio€GNS/GDP,€but€have€testedĻthe€sensitivity€of€the€results€to€a€measure€that€excludes€foreign€capitalĻflows,€GDS/GDP.óó(D|«$””Ń7€XXdČ7ŃŃ s Ń<> ’’:Technical[2]ą0..ąŌ2ŌŌ3  Ōą0..ąHP LaserJet IIIr’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’HP3.PRSP F2|,\,\,,š’HĄQȉ- 0<Q ’’:Technical[3]ą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą<Ō6X9`+Courier<d ’’:Technical[4]ą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą<w ’’:Technical[5]ą0..ąą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą<Š ’’:Technical[6]ą0..ąą0..ąą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą< ’’:Technical[7]ą0..ąą0..ąą0..ąą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą<° ’’:Technical[8]ą0..ąą0..ąą0..ąą0..ąą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ąBV ’’$1Document StyleĢŌ  Ōą@ģ..ģąņņņ ņŌ  ŌŌ2ŌŌ3  Ō€Ō  ŌŌ  ŌŌ  ԈĢóóó óB-’’$2Document StyleĢņ ņŌ2ŌŌ3  Ō€ņņŌ  ŌŌ  ŌĢó óóóB=’’$3Document StyleĢą..ąņ ņŌ2ŌŌ3  Ō€Ō  ŌŌ  Ōó óB ’’$4Document Styleą..ąņ ņņņ.óó€€ó óB ’’$5Document Styleą0..ąĢB ’’$6Document Styleą8..ąĢB& ’’$7Document Styleą0..ąą0` ..` ąĢB& ’’$8Document Styleą0..ąą8` ..` ąĢ&+ ’’$9Ō2ŌŌ3  Ōą0..ą(> ’’&10ą0..ąŌ2ŌŌ3  Ōą0..ą(Q ’’&11ą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą(d ’’&12ą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą(w ’’&13ą0..ąą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą(Š ’’&14ą0..ąą0..ąą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą( ’’&15ą0..ąą0..ąą0..ąą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ą(° ’’&16ą0..ąą0..ąą0..ąą0..ąą0..ąą0..ąą0..ąŌ2ŌŌ3  Ōą0..ąR& ’’8BibliogrphyBibliographyą0..ąą°..°ąĢzS ’’:Right Par[1]Right-Aligned Paragraph NumbersąŠ..ąŌ2ŌŌ3  Ō€ˆą°..°ąą0..ąĢzf ’’:Right Par[2]Right-Aligned Paragraph Numbersą..ąąŠ` ..` ąŌ2ŌŌ3  Ō€ˆą..ąą0` ..` ąĢzy ’’:Right Par[3]Right-Aligned Paragraph Numbersą..ąą` ..` ąąŠø ..ø ąŌ2ŌŌ3  Ō€ˆą` ..` ąą0ø ..ø ąĢzŒ ’’:Right Par[4]Right-Aligned Paragraph Numbersą..ąą` ..` ąąø ..ø ąąŠ..ąŌ2ŌŌ3  Ō€ˆąø ..ø ąą0..ąĢzŸ ’’:Right Par[5]Right-Aligned Paragraph Numbersą..ąą` ..` ąąø ..ø ąą..ąąŠh..hąŌ2ŌŌ3  Ō€ˆą..ąą0h..hąĢz² ’’:Right Par[6]Right-Aligned Paragraph Numbersą..ąą` ..` ąąø ..ø ąą..ąąh..hąąŠĄ..ĄąŌ2ŌŌ3  Ō€ˆąh..hąą0Ą..ĄąĢzÅ ’’:Right Par[7]Right-Aligned Paragraph Numbersą..ąą` ..` ąąø ..ø ąą..ąąh..hąąĄ..ĄąąŠ..ąŌ2ŌŌ3  Ō€ˆąĄ..Ąąą0..ąĢzŲ ’’:Right Par[8]Right-Aligned Paragraph Numbersą..ąą` ..` ąąø ..ø ąą..ąąh..hąąĄ..Ąąą..ąąŠp..pąŌ2ŌŌ3  Ō€ˆą..ąą0p..pąĢfp’’2Doc InitInitialize Document StyleÓ€2ÓÓ  ÓĒÓS€ 3   I. 1. A. a.(1)(a) i) a)SÓŲŲ456 ’’A_ekqw‡DocumentDocument StyleI.1.A.a.(1)(a)i)a)(’’$˜˜Ģą0 ąą ą(’’$™™ą0 ąą0 ąą ą((’’$ššą0 ąą0 ąą0 ąą ąjo’’4Tech InitInitialize Technical StyleÓS€ 8   1 .1 .1 .1 .1 .1 .1 .1 žSÓŲŲ  ’’CEIQ]m™µTechnical11.11.1.11.1.1.11.1.1.1.11.1.1.1.1.11.1.1.1.1.1.11.1.1.1.1.1.1.1xF–ö2PleadingHeader for numbered pleading paperÓČÓŃ °ŃŃč°ŃÖ€:’’CI:;Ö @Ż ƒ;’’(ŻŻ  ŻÓČÓŅX°ŅҰ°ŅÓ’’Ą°›XÓß>€<='ü°ų*d>ßß>€<='°ų*d>ßĢĢąHĄą1ˆĢĢąHĄą2ˆĢĢąHĄą3ˆĢĢąHĄą4ˆĢĢąHĄą5ˆĢĢąHĄą6ˆĢĢąHĄą7ˆĢĢąHĄą8ˆĢĢąHĄą9ˆĢĢąŠĄą10ˆĢĢąŠĄą11ˆĢĢąŠĄą12ˆĢĢąŠĄą13ˆĢĢąŠĄą14ˆĢĢąŠĄą15ˆĢĢąŠĄą16ˆĢĢąŠĄą17ˆĢĢąŠĄą18ˆĢĢąŠĄą19ˆĢĢąŠĄą20ˆĢĢąŠĄą21ˆĢĢąŠĄą22ˆĢĢąŠĄą23ˆĢĢąŠĄą24ˆĢĢąŠĄą25ˆĢĢąŠĄą26ˆĢĢąŠĄą27ˆĢĢąŠĄą28Ō"  ą.Ą+ Ų'Ą+Ą+"Ō(_2v $ØØŻ ƒ|«!ŻŃ7€XXdČ7ŃŃ s ŃŻ W Ż d(Eˆ$ņņŚ  Ś18Ś  Śóó(q!2’W$¤¤Ż ƒ|«!ŻŃ7€XXdČ7ŃŃ s ŃŻ W ŻÓӀ€€€€ņņŚ  Ś0Ś  Śóó$j aZ.LinePrinter Regular(`3qš$„„Ż ƒ|«!ŻŃ7€XXdČ7ŃŃ s ŃŻ W ŻŚ  Ś0Ś  Ś.($Ó$‘‘ņņŚ  Ś0Ś  Śóó<ž6X9`(Courier’’ČcLEFF Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś2Ś  ŚóóŻ Ź ŻņņKelley€and€Schmidt€1994;€see€also€Brander€and€Dowrick€1994.óó€ #Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś3Ś  ŚóóŻ Ź ŻņņLeff€observes€that€Ygr€represents€a€more€appropriate€variableŠ ° Štheoretically,€but€he€uses€Y/Ngr€(as€did€Modigliani€and€Ando€1957)€on€theĻbasis€of€improved€fit€and€statistical€significance.óó Ń ° Ń3üŖHa`' Line Printer Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś1Ś  ŚóóŻ Ź ŻŌ €E ŌņņLeff's€results€were€not€robust€with€respect€to€the€country€sample,Š ° Šmeasurement€of€variables,€or€estimation€techniques.€€Additionally,€theĻlogarithmic€transformation€designed€to€attenuate€heteroscedasticity€provedĻtroublesome€in€the€face€of€zero€or€negative€growth€rates€of€per€capita€income.€ĻIn€retort,€Leff€notes€that€alternative€sample€selections€are€also€arbitrary,€andĻthat€the€estimated€dependency€impacts€are€little€affected€by€the€problem€of€usingĻlogarithmic€transformations.€€For€a€detailed€literature€review€of€thisĻcontroversy,€see€Kelley€(1988b).ĢĢ€€€€€€*Kelley€is€James€B.€Duke€Professor€of€Economics,€and€Associate€Director,ĻCenter€for€Demographic€Studies,€Duke€University;€Schmidt€is€Associate€ProfessorĻof€Economics,€University€of€Richmond.€€The€editorial€assistance€of€Gail€McKinnis;Ļthe€financial€support€of€the€National€Institutes€for€Child€Health€and€HumanĻŃCIOaŃŃ C ŃDevelopment;€feedback€at€seminars€(Monash€University,€Melbourne;€University€ofĻŃCIOaŃŃ C ŃIndonesia,€Jakarta;€and€East„West€Center,€Honolulu);€and€comments€by€Mark€An,ĻŃCIOaŃŃ C ŃRobert€L.€Clark,€Nathaniel€H.€Leff,€Andrew€Mason,€George€Tauchen,€and€twoĻanonymous€referees€are€gratefully€acknowledged.€€The€usual€caveats€apply.€€MarchĻŃCIOaŃŃ C Ń1996.ŃCIOaŃŃ C ŃŃCIOaŃŃ C ŃóóŃCIOaŃŃ C ŃŃCIOaŃŃ C ŃŃCIOaŃŃ C Ń $Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś6Ś  ŚóóŻ Ź ŻņņBoth€an€F„test€for€the€joint€significance€of€the€country€and€periodŠ ° Šbinaries€as€well€as€a€likelihood€ratio€Chi„squared€test€were€employed€toĻassess€the€FEM€versus€the€Pooled€specification.óó’’ČY’’HY ńŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś4Ś  ŚóóŻ Ź ŻņņThe€extent€of€interaction€between€domestic€capital€markets€andŠ ° Šinternational€capital€flows€is€unsettled€in€the€debates.€€Compare€TaylorĻ(1995)€and€Taylor€and€Williamson€(1994)€for€extensive€integration€versusĻFeldstein€and€Bacchetta€(1991)€for€limited€integration.€€We€remain€agnostic€onĻthis€issue,€especially€since€variables€ideal€to€untangling€these€relationshipsĻare€not€readily€available.óó$j aZ.LinePrinter Regular ’’’d&’’0 d d Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś2Ś  ŚóóŻ Ź ŻņņKelley€and€Schmidt€1994;€see€also€Brander€and€Dowrick€1994.óó€ #Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś3Ś  ŚóóŻ Ź ŻņņLeff€observes€that€Ygr€represents€a€more€appropriate€variableŠ ° Štheoretically,€but€he€uses€Y/Ngr€(as€did€Modigliani€and€Ando€1957)€on€the€basisĻof€improved€fit€and€statistical€significance.óó$j aZ.LinePrinter Regular |Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś13Ś  ŚóóŻ Ź ŻņņOne€must€be€cautious€not€to€extrapolate€too€far€from€these€pointŠ ° Šelasticities€because€of€the€interdependent€nature€of€economic€growth.€€TheseĻelasticities€hold€Ygr€constant€when€our€two„stage€estimation€technique€alreadyĻacknowledges€that€S/Y€and€Ygr€are€jointly€determined.óó€/é„$j aZ.LinePrinter Regular KńńŠ ° ŠńńŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś8Ś  ŚóóŻ Ź ŻņņThe€aggregate„saving€literature€is€about€evenly€divided€between€the€use€ofŠ ° Šdomestic€versus€national€saving€and€output€measures.€€We€employ€GDP€in€theĻdenominator€of€either€saving€ratio€since€most€studies€of€aggregate€growth€(asĻdistinct€from€saving)€focus€on€GDP.€€However,€at€least€conceptually,€there€areĻsome€advantages€to€the€GNS€measure€which€focuses€on€broader€aspects€of€wealthĻaccumulation€and€takes€into€account,€at€least€implicitly,€relevant€trade„offsĻbetween€foreign€and€domestic€sources€of€accumulation.€€Operationally€we€haveĻundertaken€most€of€our€empirical€work€using€the€ratio€GNS/GDP,€but€have€testedĻthe€sensitivity€of€the€results€to€a€measure€that€excludes€foreign€capital€flows,ĻGDS/GDP.óó FŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś1Ś  ŚóóŻ Ź ŻŌ €E ŌņņLeff's€results€were€not€robust€with€respect€to€the€country€sample,Š ° Šmeasurement€of€variables,€or€estimation€techniques.€€Additionally,€theĻlogarithmic€transformation€designed€to€attenuate€heteroscedasticity€provedĻtroublesome€in€the€face€of€zero€or€negative€growth€rates€of€per€capita€income.€ĻIn€retort,€Leff€notes€that€alternative€sample€selections€are€also€arbitrary,Ļand€that€the€estimated€dependency€impacts€are€little€affected€by€the€problemĻof€using€logarithmic€transformations.€€For€a€detailed€literature€review€ofĻthis€controversy,€see€Kelley€(1988b).ĢĢ€€€€€€*Kelley€is€James€B.€Duke€Professor€of€Economics,€and€Associate€Director,ĻCenter€for€Demographic€Studies,€Duke€University;€Schmidt€is€AssociateĻProfessor€of€Economics,€University€of€Richmond.€€The€editorial€assistance€ofĻGail€McKinnis;€the€financial€support€of€the€National€Institutes€for€ChildĻHealth€and€Human€ŃCIOaŃŃ C ŃDevelopment;€feedback€at€seminars€(Monash€University,ĻMelbourne;€University€of€ŃCIOaŃŃ C ŃIndonesia,€Jakarta;€and€East„West€Center,€Honolulu);Ļand€comments€by€Mark€An,€ŃCIOaŃŃ C ŃRobert€L.€Clark,€Nathaniel€H.€Leff,€Andrew€Mason,ĻGeorge€Tauchen,€and€two€anonymous€referees€are€gratefully€acknowledged.€€TheŠ A‘  ŠŃCIOaŃŃ C Ńusual€caveats€apply.€€March€ŃCIOaŃŃ C Ń1996.ŃCIOaŃŃ C ŃŃCIOaŃŃ C ŃóóŃCIOaŃŃ C ŃŃCIOaŃŃ C ŃŃCIOaŃŃ C Ń öŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś5Ś  ŚóóŻ Ź ŻņņWith€the€exception€of€Rawanda,€absent€terms€of€trade€data,€the€countryŠ ° Šlisting€(65€LDCs€and€23€DCs)€is€the€same€as€in€Kelley€and€Schmidt€1994.óó  ’BD’ (’multicolinearity’($’Expositionally’$&’computationally’& ’gr’ ’Modigliani’’Horioka’’Bacchetta’ ’uncorrelated’ ’MacKinnon’’Davidson’’Hasuman’ ’i’ ’t’ ’’ ’’ ’ it’&’autocorrelation’&’Lagrange’’Limdep’*’multicollinearity’* ’Sq’ ’Std’’Obs’’DFFITS’ ’childrearing’ ’durables’’monotonic’’Decadal’,’disproportionately’, ’Ay’  öŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś5Ś  ŚóóŻ Ź ŻņņWith€the€exception€of€Rawanda,€absent€terms€of€trade€data,€the€countryŠ ° Šlisting€(65€LDCs€and€23€DCs)€is€the€same€as€in€Kelley€and€Schmidt€1994.óó$j aZLinePrinter $Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś6Ś  ŚóóŻ Ź ŻņņBoth€an€F„test€for€the€joint€significance€of€the€country€and€periodŠ ° Šbinaries€as€well€as€a€likelihood€ratio€Chi„squared€test€were€employed€to€assessĻthe€FEM€versus€the€Pooled€specification.óó$j aZ.LinePrinter Regular<Ō6X9`+Courier ńŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś4Ś  ŚóóŻ Ź ŻņņThe€extent€of€interaction€between€domestic€capital€markets€andŠ ° Šinternational€capital€flows€is€unsettled€in€the€debates.€€Compare€Taylor€(1995)Ļand€Taylor€and€Williamson€(1994)€for€extensive€integration€versus€Feldstein€andĻBacchetta€(1991)€for€limited€integration.€€We€remain€agnostic€on€this€issue,Ļespecially€since€variables€ideal€to€untangling€these€relationships€are€notĻreadily€available.óó3j aZ.LinePrinter Regular "ńńŠ ° ŠŠ ° ŠńńŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś7Ś  ŚóóŻ Ź ŻņņTables€of€regressions€backing€up€each€statement€in€this€paragraph€areŠ ° Šavailable€at€http://www.econ.duke.edu/~kelley/ack.homepage.html.óóŌ »Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś9Ś  ŚóóŻ Ź ŻņņMason€(1981)€demonstrates€that€a€necessary€and€sufficient€condition€for€aŠ ° Špositive€rate„of„growth€effect€is€that€the€mean€age€of€consumption€exceeds€theĻmean€age€of€earning.€€This€empirical€relationship€is€most€plausible€for€the€LDCs,Ļand€is€assumed€in€our€analysis€although,€should€it€not€prevail,€the€model€wouldĻadmit€a€negative€sign€on€Ygr.€€Hammer€(1986)€observes€that€the€theory€is€weakenedĻwhen:€€(1)€the€model€is€based€on€households€(rather€than€individuals)€whereĻchildren€are€considered€as€"consumer€durables";€(2)€the€distribution€of€incomeĻacross€age€groups€changes€over€time,€and€depends€in€part€on€population€growth;Ļ(3)€other€saving€motivations€(e.g.,€for€bequests)€figure€prominently;€and€(4)Ļcapital€markets€(which€facilitate€consumption€smoothing)€are€weak,€and€childrenĻcontribute€to€household€income„„situations€common€to€the€LDCs.óóTABLE A »Ż ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś9Ś  ŚóóŻ Ź ŻņņMason€(1981)€demonstrates€that€a€necessary€and€sufficient€condition€forŠ ° Ša€positive€rate„of„growth€effect€is€that€the€mean€age€of€consumption€exceedsĻthe€mean€age€of€earning.€€This€empirical€relationship€is€most€plausible€forĻthe€LDCs,€and€is€assumed€in€our€analysis€although,€should€it€not€prevail,€theĻmodel€would€admit€a€negative€sign€on€Ygr.€€Hammer€(1986)€observes€that€theĻtheory€is€weakened€when:€€(1)€the€model€is€based€on€households€(rather€thanĻindividuals)€where€children€are€considered€as€"consumer€durables";€(2)€theĻdistribution€of€income€across€age€groups€changes€over€time,€and€depends€inĻpart€on€population€growth;€(3)€other€saving€motivations€(e.g.,€for€bequests)Ļfigure€prominently;€and€(4)€capital€markets€(which€facilitate€consumptionĻsmoothing)€are€weak,€and€children€contribute€to€household€income„„situationsĻcommon€to€the€LDCs.óó *ńńŠ ° ŠŠ ° ŠńńŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś7Ś  ŚóóŻ Ź ŻņņTables€of€regressions€backing€up€each€statement€in€this€paragraph€areŠ ° Šavailable€at€http://www.econ.duke.edu/~kelley/ack.homepage.html.óó •ńńŠ ° ŠŠ ° ŠńńŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś10Ś  ŚóóŻ Ź ŻņņThat€growth€in€population€and€in€per€capita€income€have€the€sameŠ ° Šimpact€was€first€derived€by€Modigliani,€although€his€empirical€analysisĻrejected€this€implication.€€Mason's€theoretical€extension€of€the€life„cycleĻmodel€utilizes€this€assumption.óóŚ’Modigliani’’nonmarket’’Bhalla’&’computationally’&’lnC’ ’’ ’’ ’ ’ ’gr’ ’Shumaker’ ’i’ ’t’ ’ln’’ it’’Hausman’&’autocorrelation’&’DFFITS’’GDPgr’’foonote’ ’childrearing’ ,’heteroskedasticity’, ’wu’ ’Sq’ ’Std’’Obs’’Tms’’Chg’’the’’DEFITS’(’heteroskedasticy’(’Horioka’’decadal’ ’BD’ ’paragraphs’’endogeniety’’Bacchetta’’Lagrange’(’multicolinearity’(’xx.xx’’yy.yy’’durables’’monotonic’(’heteroscedasticy’(’UNMODELED’’LINDEP’,’disproportionately’, ’Ay’ ’Nassau’<Ō6X9`+Courier ‘ńńŠ ° ŠŠ ° ŠńńŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś10Ś  ŚóóŻ Ź ŻņņThat€growth€in€population€and€in€per€capita€income€have€the€same€impactŠ ° Šwas€first€derived€by€Modigliani,€although€his€empirical€analysis€rejected€thisĻimplication.€€Mason's€theoretical€extension€of€the€life„cycle€model€utilizes€thisĻassumption.óó õŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś11Ś  ŚóóŻ Ź ŻņņExpositionally,€we€term€"life„cycle"€effects€as€those€pertaining€toŠ ° ŠYgr.€€This€is€appropriate€in€the€simple€model€where€Y€=€C.€€In€contrast,€weĻ(and€others)€interpret€D1€as€associated€with€bequests,€which€are€not€a€part€ofĻthe€simple€life„cycle€model.€€Of€course,€in€more€complex€modeling,€bequestsĻpartake€of€life€time€planning€as€well.€€Our€expositional€distinction€is€thusĻsomewhat€arbitrary.Ģóó õŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś11Ś  ŚóóŻ Ź ŻņņExpositionally,€we€term€"life„cycle"€effects€as€those€pertaining€to€Ygr.€Š ° ŠThis€is€appropriate€in€the€simple€model€where€Y€=€C.€€In€contrast,€we€(andĻothers)€interpret€D1€as€associated€with€bequests,€which€are€not€a€part€of€theĻsimple€life„cycle€model.€€Of€course,€in€more€complex€modeling,€bequests€partakeĻof€life€time€planning€as€well.€€Our€expositional€distinction€is€thus€somewhatĻarbitrary.Ģóó ļŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś12Ś  ŚóóŻ Ź ŻņņTables€of€regressions€backing€up€each€statement€in€this€paragraph€areŠ ° Šavailable€at€http://www.econ.duke.edu/~kelley/ack.homepage.html.óó’’ČY ›ńńŠ ° ŠńńŻ ƒ?’W$ŻÓӀ€€€€ņņŚ  Ś13Ś  ŚóóŻ Ź ŻņņOne€must€be€cautious€not€to€extrapolate€too€far€from€these€pointŠ ° Šelasticities€because€of€the€interdependent€nature€of€economic€growth.€€TheseĻelasticities€hold€Ygr€constant€when€our€two„stage€estimation€technique€alreadyĻacknowledges€that€S/Y€and€Ygr€are€jointly€determined.óó€ P{QRESTEUVEWXEY”݉?xxx,,Xxąßž’ˆ 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?k+HHH,,Ÿ©HŽYž’ž’ž’ž’ž’ž’ž’’’’’’’’’’’’’’’’’ž’’’’’’’’’’’ž’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’”żk#GGG,,ā©GŒIž’ž’ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’Tžk#K/K,,©KĪŁž’ž’ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’’k#?/?,,X©?żž’ž’ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’Tńa-GGGXXƒ©G]ó’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’”ó—1ddd,,āXdŒIž’ ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’Ōō‰?xxx,,ĢXxąßž’ž’ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’’’ž’’’ž’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’”ņ;SCS,,XSŖž’ž’ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’T 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,)”qž’ž’ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ԁa+TTT,,<¤TIœž’ž’ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’ž’’’ž’ž’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’Ōr5ddd,,‡ōdŽ×ž’ž’ž’ž’ž’ž’ž’’’’’’’’’’’’’’’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’’’’’ŌXb,UUU,,<©UIœž’ž’ž’Īž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’ž’’’ž’ž’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’ŌN#DDD,,<TDIœž’ž’ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’ž’’’ž’ž’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ž’ž’ž’ž’ž’ž’TnV5&5,,¾T5\ž’ž’ž’ž’ž’ž’ž’’’ž’’’’’’’ž’’’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’Ō€\)PPP,,<PIœž’ž’ŗž’ž’ž’ž’’’ž’’’’’’’?’’’’ž’’’’’ž’’’ž’ž’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’°?+¦! œ 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"’’/’’6’’=’’’’’’’’’’D’’’’’’zŽ’’õ’’’õ’’ą/)@.€"‚u«Ü,ŁĄ‡a’’’’e’’’’’’^;C]dd²œCCCd²CCCCddddddddddCCȲČY²~‰”~v”CN~µ”s…k~”½‚CCCddCYdYdYCdd88d8œddddJN8ddddYYdYČńddddddCdddddddddYYYYY²…‰Y~Y~Y~Y~YC8C8C8C8”ddddd”d”d”d”ddY”dddd”dsdYYY‰Y‰Y‰Y‰Y”d~Y~Y~Y~Ydddddd”d”dC8C8C8C8’oNd~8~8~8|8|8”d”t”d”ddd²…J…J…JkNlLkNkN~8~8~8”d”d”d”d”d”d½d‚Y€X‚Y”d~8”d…JkN~8dd”dd”d~YC88d4CCddCC/ČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČČNdddCYQQdd°ddd²²dFdddd²FCChhd²44ČČddxx˜ČdČddv¤¤oo²Chd½ńF«ČČČdČČh²²ČČČdČČČČå²²ČČȲdCCČČČČȐxȲCČddod²ČČ…dCdYdsœ‚ČȐČČČČČ]ȐČČČČČČČČČČČČČČČČČČȐČČČČČȤ…xœČČČČUvČČČČČČՐdČČČȐYYCCCCŲx~oxo…Y~N‚Y”dYC8Y…oµo”Y…dYxsdxdd~YY…xoœxxxx~N”dC88YYYxxYxxxxCCCdddddddxxxxxxxxxxxxxxxxxxxxxxNNNNNNNdddddddddddddddddddddd888888888888YYYYYYYYYYYYYYYYYYYxxxxxxxxxxxxxxxxxxxxxxsdYCČ"‚u«Ü,ŁĄ‡a’’’’e’’’’’’^!.22YN!!!2Y!!!!2222222222!!dYd,YH?EJ?;HJ!'F?[JH9HC6?JH^HHA!!!22!,2,2,!222N2222%'22H22,,2,dń222222!222222222H,H,H,H,H,YCE,?,?,?,?,!!!!J2H2H2H2H2J2J2J2J2H2H,J2H2H2H2J292H,H,H,E,E,E,E,J2?,?,?,?,H2H2H2H2H2H2J2J2!!!!I8'F2???>>J2J:J2J2H2H2YHC%C%C%6'6&6'6'???J2J2J2J2J2J2^HH2A,@,A,J2?J2C%6'?H2H2J2H2J2?,!H24!!22!!/ddddddddddddddddddddddddddddddddddddddddddddddddNHHH222!,))22X222YY2#2222Y#!!442Ydd22<E’’’’’’ę’’’’’’^!+,fC}m!33Co!,!$CCCCCCCCCC$$oooAƒf[^l]Rlm3:cU~flPlfIXmfƒff_,$,…CCAG:IB,AI$$E$mIHIH33+IX+X+mImImImImImIƒZf;_:_:_:lIU$fIf3I3X+f;f;~\lHmI]B3$$lH/CCCC/……………………………………………………………………………………………………………………N\ZNCC+ACCCYiC16jjC,7IIPj,!>>C…))h…CCmh…RpsKL……!>jjjjjj“…,«mmuuuG`~tWCoo……ƒƒƒƒhoooooCoooooooo……CC…CPPPP,Ioo,,CdoEOOOU…ŸMJOX@:MfALZHX=fVfM:Mf7MMMMMMMMMMMMMMMMMMMMMM:::::::MMMMMMMMMMMMMMMMMMMMMM.j"‚u¦×'Ō>E’’’’’’ę’’’’’’^!+.fCih!33Co!,!$CCCCCCCCCC$$ooo@ƒVX]bXPdh4AeT~bhSh^MTaUy]TX9$9…CCDH:I<*AL')G(nLCIH99-JT(vIU(bLbbbLbLhChC‰`^9^9^9M9M9M9M9TDT-T-aJaJaJaJaJaJyVTEˆŻņņŚ  Ś1Ś  ŚóóŻ  Ż×  ׀€Additionally,€studies€by€several€scholars€foundŠ `"°& ŠŃIOaŃѰHŃŃ  чthat€(youth)€demographic€dependency€had€little€or€no€impact€onĻthe€national€saving€rate,€although€this€result€is€not€withoutĻchallenge,€especially€in€models€exposing€variable€rate„of„growthĻeffects€(Fry€and€Mason€1982).€€Still,€the€possibility€of€weakĻobserved€overall€linkages€is€now€better€understood.ĢĢĢą  ąņņFinancing€the€Consumption€of€DependentsóóĢĢą  ąFirst,€at€the€household€level,€the€traditional€dependency„¼ńYń¼ńYńrate€formulation€was€too€narrow.€€In€third„world€countries,Ļfamilies€may€be€so€poor€that€they€accumulate€little€or€nothing;Ļthe€options€for€financing€additional€children€are€thereforeĻseverely€constrained„„children€must€be€financed€out€of€householdĻconsumption.€€Moreover,€the€impact€of€children€on€householdĻspending€can€be€complex€because€children€may€(1)€substitute€forĻother€forms€of€consumption;€(2)€contribute€directly€to€householdĻmarket€and€nonmarket€income;€(3)€encourage€parents€to€work€moreĻ(or€less);€(4)€stimulate€the€amassing€(or€reduction)€of€estates;Ļand€(5)€encourage€(or€discourage)€the€accumulation€of€certainĻtypes€of€assets€(e.g.,€education,€or€farm€implements).€€TheĻimpact€of€expanded€family€size€on€household€saving€can€thereforeĻbe€negative,€negligible,€or€positive;€the€issue€is€an€empiricalĻone€(Kelley€1988a,€Hammer€1986).€€ĢĢą  ąSecond,€the€analysis€of€the€impact€of€population€pressuresĻon€public„sector€spending€has€also€been€narrow.€€As€withĻhouseholds,€there€are€several€options€for€financingĻdemographically€sensitive€spending.€€In€addition€to€reducingĻsaving,€trade„offs€are€possible€within€the€government€budget€inĻgeneral€and€within€the€demographically€sensitive€education€sectorĻin€particular.€€For€example,€taxes€can€be€raised,€and€theĻefficiency€of€providing€government€services€may€be€increased.€ĻThe€impacts€of€youth€dependency€on€government€expenditureĻallocations€are€complex€and€poorly€understood€(Kelley€1995,€SimonĻand€Pilarski€1979,€and€Schultz€1987).ĢĢ€€€€€Third,€in€LDCs,€measured€economy„wide€financial€savingĻunderstates€true€household€saving,€especially€in€subsistenceĻagricultural€settings€where€in„kind€saving€and€investment€areĻundertaken€simultaneously.€€Finally,€as€capital€markets€develop,Ļany€downward€pressures€on€saving€due€to€dependency€can€be€offsetĻby€other€forms€of€domestic€and€foreign€saving,€a€process€inducedĻby€changing€interest€rates€(Giovannini€1983).€€Such€an€inducedĻcompensating€feedback€via€interest„rate€changes€would€plausiblyĻbe€only€partial.€€ĢĢą  ąOn€analytical€grounds,€then,€it€should€not€be€surprising€toĻobserve€little€or€no€impact€of€dependency€on€aggregate€saving.€Š 0*€%0 ŠNote€that€such€a€finding€does€not€necessarily€imply€thatĻdependency€effects€are€absent€or€even€unimportant€at€theĻhousehold€level.€€It€could€mean€that€the€effects€of€dependencyĻare€offset€through€market€responses€elsewhere.€€However,€if€theyĻare€important€quantitatively,€then€the€saving„dependencyĻhypothesis€based€mainly€on€household€behavior€may€well€beĻobserved€in€aggregate€data.€ĢĢą  ąņņSaving€and€Dependency,€and€the€"Population€Debate"ó󀀀€€€ĢĢą  ąOn€empirical€grounds,€most€of€the€studies€that€haveĻevaluated€the€impact€of€dependency€rates€on€aggregate€saving€showĻlittle€or€no€impacts€of€demography.€€This€finding€has€had€aĻprofound€impact€on€the€"population€debate"€in€general,€since€inĻthe€1960s€and€1970s€physical€capital€formation€was€considered€toĻbe€a€particularly€important€determinant€of€economic€growth.€€AndĻwhile€in€the€1980s€somewhat€greater€emphasis€has€been€placed€onĻhuman€capital€accumulation,€a€recent€outpouring€of€research€onĻconvergence€and€endogenous€growth€has€elevated€again€theĻpotential€importance€of€saving/investment€and€growth€linkages.€ĻIf€rapid€population€growth€(through€high€dependency€rates)€hadĻlittle€impact€on€investment€and€saving,€then€the€impact€ofĻpopulation€growth€might€be€assessed€as€weak„„at€least€by€theĻsaving„dependency€mechanism.€€Such€an€interpretation€obtainedĻapparent€corroboration€by€yet€another€empirical€finding€which,Ļmore€than€any€other,€conditioned€the€population€debates:€€namely,Ļthere€did€not€appear€to€be€a€correlation€in€aggregate€cross„¼ńYń¼ńYńcountry€data€between€the€rate€of€per€capita€output€growth€and€theĻrate€of€population€growth€(reviews€of€this€literature€areĻprovided€by€Kelley€1988b,€and€Lee€1983).€€For€some,€the€lack€ofĻempirical€evidence€showing€a€strong€dependency€impact€on€savingĻwas€considered€a€(the)€reason€accounting€for€the€surprisingĻabsence€of€economy„wide€correlations€between€population€andĻeconomic€growth.€ĢĢą  ąRecently,€the€population€debate€has€changed.€€Based€on€dataĻfor€the€1980s,€a€fairly€strong€ņņnegativeóó€relationship€betweenĻpopulation€growth€and€per€capita€output€growth€is€revealed€inĻcross„country€correlations,€including€our€own€which€evaluates€andĻextends€the€literature€and€provides€calculations€useful€forĻappraising€the€results€of€the€present€study.ńYń׃S×ńYńńYń׃G×ńYńŻ ƒ>EˆŻņņŚ  Ś2Ś  ŚóóŻ  Ż×  ׀€While€theseŠ š#@( Šstudies,€like€those€for€the€earlier€decades,€should€beĻinterpreted€with€caution,€they€will€predictably€have€a€notableĻimpact€on€the€debates.€€Whether€such€correlations€represent€anĻ"emerging€trend"€or€whether€they€will€in€the€future€revert€to€theĻno„association€pattern€of€the€earlier€decades€depends€on€theirĻcause,€yet€to€be€determined.€€An€important€component€of€suchĻanalysis€will€be€a€reassessment€of€the€saving€results.€€Could€itĻbe€that€the€impacts€of€dependency€on€saving€have€also€changed€inŠ 0*€%0 Šthe€1980s?€€That€and€related€questions€will€be€addressed€in€theĻpresent€inquiry.ĢĢą  ąņņThe€Plan€and€GoalsóóĢĢą  ąTo€assess€the€impacts€of€dependency€on€saving,€we€considerĻthe€two€demographically€augmented€saving€models€that€haveĻattracted€the€most€attention€in€the€literature:€€the€LeffĻ"eclectic"€model€and€the€Mason€life„cycle€framework.€€While€moreĻelaborate€modeling€is€possible,€these€two€paradigms€possess€theĻattribute€of€simplicity;€they€provide€historical€continuity€withĻa€large€literature;€and€they€incorporate,€albeit€imperfectly,Ļmost€of€the€leading€saving€hypotheses.€€ĢĢą  ąIn€addition€to€updating€the€saving€inquiry€to€1990,€weĻextend€the€analysis€in€several€directions.€€First,€we€use€up„to„¼ńYń¼ńYńdate€data€based€on€more€appropriate€conversion€indexes€to€accountĻfor€differential€living€standards€between€countries.€€Second,€weĻaugment€the€usual€OLS€cross„section€estimation€by€decade€withĻpanel€data€over€three€decades,€thereby€providing€a€broader€andĻlonger€sweep€of€experience.€€Third,€we€explore€panel€estimatesĻusing€two€alternative€econometric€procedures„„pooled€and€Ģfixed„effects€models.€€Fourth,€we€test€for€parameter€changes€overĻtime€in€an€attempt€to€expose€sources€of€variations€in€theĻaggregate€growth„rate€changes€noted€above.€€Fifth,€we€employĻinstrumental€variables€to€account€for€theoretically€plausibleĻendogeneity€of€right„hand„side€variables.€€ĢĢą  ąFinally,€and€importantly,€our€empirical€results€areĻsubjected€to€extensive€robustness€tests,€and€for€good€reason.€ĻThe€literature€on€saving€is€replete€with€studies€that€provideĻseemingly€small€embellishments€to€empirical€models€andĻestimation,€and€yet€obtain€quite€different€results.€€While€thisĻevolutionary€format€of€literature€building€is€useful,€it€is€timeĻconsuming.€€To€collapse€time€and€to€provide€more€confidence€inĻour€results,€we€have€employed€a€methodology€whereby€we€focus€onĻour€theoretically€preferred€estimation€results,€but€alsoĻsummarize€the€findings€of€a€large€number€of€sensitivity€tests.€ĻThese€sensitivity€tests€employ€alternative:€€(1)€estimationĻtechniques€(OLS€vs.€2SLS),€(2)€treatment€for€possibleĻheteroscedasticity€(White„corrected€standard€errors),€(3)Ļaggregation€periods€(10„€vs.€5„years),€(4)€definitions€of€savingĻ(GDS€vs.€GNS),€(5)€samples€(excluding€countries€identifiedĻstatistically€as€exerting€unusual€influence),€and€(6)€definitionsĻof€dependency€in€the€Mason€model€(combined€youth€plus€aged€vs.Ļyouth€only).ĢĢą  ąWe€turn,€then,€to€updating€and€extending€the€two€most€widelyĻā āinvestigated€models€of€saving€and€dependency.Š 0*€%0 ŠŌ  Ōā ā‡Ō  Ō2.0€€€ņņThe€Leff€Model:€Theory€and€Empirical€SpecificationóóĢĢą  ąOur€variant€of€Leff's€model,€including€anticipatedĻcoefficient€signs,€is€as€follows:ĢĢ(1)€ņņlnóó(1/{1„S/Y})€=€f(ņņlnóóY/N,€Y/Nņņgróó,€ņņlnóóD1,€ņņlnóóD2)Š ˜č Š€€€€€€€€€€€€€€€€€€€€€€€(+)€€€(+)€€€(?)€€€(?)ĢĢ€€€€S/Y€=€percentage€share€of€gross€national€saving€in€GDPĢ€€€€Y/N€=€per€capita€gross€domestic€product€(1985€US€$1,000)Ģ€€€€€D1€=€youth€dependency€(100€x€{population€0„14/15„64})Ģ€€€€€D2€=€aged€dependency€(100€x€{population€65+/15„64})Ģ€€€€ņņ€gróó€=€continuous€growth€rate€(percent).Š `  ŠĢThe€left„hand„side€saving€transformation,€increasingly€used€inĻthe€saving„demographic€literature,€serves€two€purposes.€€(1)ĻMathematically€equivalent€to€ņņlnóó(1/{C/Y})€=€„ņņlnóó(C/Y),€it€overcomesŠ 0€  Šproblems€of€taking€logs€of€near„zero€or€negative€saving€rates.€Ļ(2)€It€simplifies€interpretation€of€estimated€coefficients„„aĻpositive€coefficient€implies€a€direct€relationship€between€theĻsaving€rate€and€the€variable.€€With€respect€to€coefficient€signs,Ļsaving€is€posited€to€increase€at€higher€levels€of€income.€€TheĻgrowth€of€per€capita€income€captures€the€impact€of€life„cycleĻconsumption€smoothing€whereby€upward€adjustments€in€income€areĻconsidered€transitory€and€are€largely€saved.ńYń׃T×ńYńńYń׃H×ńYńŻ ƒ>EˆŻņņŚ  Ś3Ś  ŚóóŻ  Ż×  ׀€€Finally,€higherŠ pĄ Šdependency€is€hypothesized€by€Leff€to€deter€saving,€although,Ļbased€on€our€argumentation€above,€we€remain€eclectic€on€thisĻmatter.€€Functional€form€and€variable€definitions€are€chosen€toĻapproximate€Leff's€original€model.ĢĢą  ąThis€formulation€incorporates€pitfalls:€€(1)€dependency€isĻimperfectly€measured€by€a€fixed€age€cohort€since€the€ages€ofĻdependency€vary€across€countries€and€by€stage€of€development;Ģ(2)€potential€simultaneity€problems€exist€between€saving€andĻoutput€growth,€although€some€researchers€use€techniques€toĻovercome€this;€and€(3)€there€are€interrelationships€betweenĻdomestic€saving€and€international€capital€movements.€€OurĻempirical€estimates€do€address€the€second€concern,€but€not€theĻfirst€and€third€which€have€been€considered€in€various€studies.€ĻThe€major€finding€showing€weak€dependency€impacts€in€the€1960sĻand€1970s€is,€for€the€most€part,€invariant€to€refinements.€€WhileĻthis€is€not€a€satisfying€defense,€we€observe€that€the€simplicityĻā āof€the€widely€examined€Leff€framework€and,€important€for€ourŠ €%Š * Špurposes,€its€impact€on€the€demographic€debates€justify€anĻinquiry€into€its€applicability€to€the€1980s.€ńYń׃c×ńYńńYń׃O×ńYńŻ ƒ>EˆŻņņŚ  Ś4Ś  ŚóóŻ  Ż×  ׀Š xČ Šā āĢą  ąņņData€and€Country€SelectionĢóóĢ€ą  ąOur€data€set€is€comprised€of€panels€of€six€growth€periodsŠ ˜č Š(1960„65,...,1985„90)€and€88€countries€with€populations€exceedingĻ1€million€in€1960€that€Summers€and€Heston€(1995)€classify€asĻmarket„oriented,€and€for€which€they€provide€data€on€grossĻdomestic€product.€€We€exclude€countries€with€missing€data,Ļextensive€resource€dependency,€and€problems€with€dataĻdefinitions.ńYń׃^x×ńYńńYń׃\›×ńYńŻ ƒ>EˆŻņņŚ  Ś5Ś  ŚóóŻ  Ż×  ׀(Kelley€and€Schmidt€1994).€€Summers€and€Heston€useŠ H ˜  Šprice€indexes€that€convert€each€country's€national„accountsĻaggregates€from€nominal€into€purchasing„power€values.€€ThisĻattenuates€problems€in€the€use€of€exchange€rates,€which€deviateĻsystematically€by€level€of€development€from€a€"true"€index€ofĻpurchasing€power.€€Since€most€savings€studies€have€used€exchangeĻrates,€our€results€will€test€indirectly€whether€the€previousĻfindings€are€modified€using€the€new€deflators.€€Data€sources€andĻdefinitions€are€provided€in€Appendix€A.ĢĢŌ  Ōą  ąņņEconometric€and€Modeling€ConsiderationsĢóóĢą  ąThe€first€modeling€issue€that€merits€attention€relates€toĻthe€theoretically€plausible€bi„directional€causation€between€S/YĻand€Yņņgróó.€€To€evaluate€this€possibility,€both€the€Leff€and€(below)Š 8ˆ Šthe€Mason€S/Y€models€have€been€estimated€with€instrumentalĻvariables€(IV)€through€2SLQ.€€The€methodology€for€selectingĻinstruments,€presented€in€Appendix€A,€is€based€on€this€paper'sĻperspective€that€the€saving€models€are€as€given€by€Leff€andĻMason;€we€are€not€seeking€additional€explanatory€variables€orĻtheoretical€embellishments€ņņper€seóó.€€2SLS€results€which€attenuateŠ č8 Šsimultaneity€bias€are€presented€in€the€text;€the€instrument€setĻwas€selected€to€improve€estimation€efficiency.€€The€Davidson„¼ńYń¼ńYńMacKinnon€overidentification€test€indicates,€for€both€models,Ļthat€the€saving€equation€is€correctly€specified€(with€respect€toĻendogeneity)€and€that€the€instruments€are€uncorrelated€with€S/YĻresiduals.€€A€joint€test€on€the€identifying€instruments€in€theĻfirst„stage€regressions€indicate€that€they€are€well€correlatedĻwith€Y/Nņņgróó€(for€Leff)€and€Yņņgróó€(for€Mason).€€Finally,€the€Hausman„Š (#x' ŠńYńŠ (#x' ŠńYńWu€test€indicates€endogeneity€in€both€models.€€(The€results€ofŠ š#@( Šthese€tests,€first„stage€regressions,€and€OLS€estimates€of€theĻsaving€models€are€presented€in€Appendix€A.)ĢĢą  ąThe€second€modeling€issue€pertains€to€the€time„series€natureĻof€the€data.€€We€present€results€below€for€three€cross€sectionsĻ(1960s,€1970s,€1980s)€as€well€as€for€the€30„year€panel.€€TheĻpanel€approach€is€increasingly€used€in€cross„country€studies€but,Ļwe€will€argue€below,€must€be€assessed€with€care.€€Equation€(2)Ļpresents€a€generalized€rendering€of€the€model€within€a€panelĻframework.ĢĢÓÓ(2)€{1/(1„S/Y})ņņitóó€=ą0  ąššņņióó€+€ššņņtóó€+€šš€ņņlnóó(Y/N)ņņitóó€+€šš€(Y/N)ņņgróóņņitóó€+€š šņņ1óó€ņņlnóóD1ņņitóó€+€Š H ˜  Šš šņņ2óó€ņņlnóóD2ņņitóó€+€š šņņitóó.Šę6 (#(# ŠÓÓProvision€is€made€for€separate€terms€for€each€country€(ššņņióó)€andŠ vĘ  Šeach€time€period€(ššņņtóó).€€Assumptions€made€about€these€termsŠ >Ž  Šdictate€the€method€of€estimation.€€For€example,€if€one€were€toĻassume€them€to€be€constant€across€all€countries€and€periods,€thenĻa€single€intercept€would€suffice€and€a€"pooled"€regression€wouldĻbe€appropriate.ĢĢą  ąIn€contrast,€"fixed„effects"€modeling€(FEM,€or€covarianceĻmodeling)€provides€for,€in€our€case,€89€separate€countryĻintercepts€and€three€individual€period€intercepts.€€The€countryĻbinaries€control€for€influences€that€vary€across€countries€butĻare€reasonably€constant€over€time€within€countries.€€SuchĻinfluences€might€include€natural€resources€or€cultural€attitudesĻtoward€work€and€saving.€€The€time€binaries€control€for€global,Ļperiod„specific€influences€like€the€oil€shocks€of€the€1970s€andĻthe€worldwide€recession€of€the€1980s.ĢĢą  ąFinally,€"random„effects"€modeling€(REM,€or€error€componentsĻmodeling)€treats€ššņņióó€and€ššņņtóó€as€separable€components€of€the€errorŠ Ż! Šterm€and€are€assumed€to€adhere€to€the€classical€assumptions.€€REMĻis€more€efficient€than€FEM€since€it€models€many€intercepts€as€twoĻstochastic€terms€following€normal€distributions€with€zero€means.€ĻHowever,€REM€can€introduce€bias€and€inconsistency€into€theĻestimates€if€the€characteristics€being€modeled€by€ššņņióó€and€ššņņtóó€areŠ |"Ģ& Šcorrelated€with€any€of€the€independent€variables.ĢĢą  ąWhich€modeling€approach€is€preferred?€€The€literature€hasĻnot€coalesced€on€an€answer€to€this€question.€€On€the€one€hand,€€€ĻFEM€is€relatively€attractive€where€the€sample€represents€aĻsizeable€proportion€of€the€population,€a€feature€of€our€case.€€OnĻthe€other€hand,€FEM€may€be€less€attractive€where€one€or€more€ofĻthe€RHS€variables€are€temporally€"persistent"€(highĻautocorrelation)€since€their€approximate€constancy€correlatesĻwith€the€country„specific€constant,€also€a€feature€in€our€case.€€€Ļā āŠ +k&1 Šą  ąFor€several€reasons,€we€will€focus€on€FEM€as€our€preferredĻā ārendering€of€panel€estimation.€€First,€we€find€simultaneousĻmodeling€to€be€appropriate€to€the€problem€at€hand,€and€standardĻeconometrics€packages€(SAS€and€LIMDEP€were€used€here)€do€not€yetĻprovide€procedures€for€estimating€REM€in€an€instrumental„¼ńYń¼ńYńvariables€framework.€€Second,€based€on€statistical€tests,€FEMĻtypically€dominates€Pooled.ńYń׃`×ńYńńYń׃L×ńYńŻ ƒ>EˆŻņņŚ  Ś6Ś  ŚóóŻ  Ż×  ׀€€Finally,€estimates€obtained€byŠ ` ° Šusing€ten„year€aggregations,€which€should€attenuate€difficultiesĻarising€from€persistence,€are€little€changed€from€those€obtainedĻfrom€five„year€aggregations.€Ģ€Ģą  ąA€related€modeling€issue€pertains€to€potential€difficultiesĻof€pooling€country€experience€across€the€three€decades.€€While€weĻwould€like€to€extend€the€saving€models€to€take€advantage€of€timeĻseries€information€in€the€data,€Chow€tests€on€the€IV€estimatesĻfound€pooling€of€the€cross€sections€(thereby€constraining€theĻparameters€temporally€in€varying€degrees)€to€be€inappropriate€inĻone€of€the€four€cases,€and€marginal€in€another.€€Moreover,€panelĻresults€can€be€sensitive€to€which€parameters€are€allowed€to€varyĻacross€time€and,€unfortunately,€theory€is€not€strong€enough€toĻprovide€a€basis€for€selecting€among€alternative€restrictions.€€WeĻwill€therefore€concentrate€on€IV€cross„sectional€estimates€and€weĻprovide€panel€results€(Pooled€and€FEM)€for€comparison.ĢĢą  ąņņResultsóóĢĢą  ąThe€Leff€model€provides€mixed€results.€€On€the€one€hand,€itĻperforms€well€overall:€€the€adjusted€Rņņņņ2óóóó's€are€acceptable,€andŠ Č Šboth€the€life„cycle€proxy€(Y/Nņņgróó)€and€the€ņņlnóó(Y/N)€term€areŠ ą Šstatistically€significant.€€On€the€other€hand,€the€impact€ofĻdemography€is€weak,€although€possibly€changing€over€time.€€In€theĻ1960s€and€1970s€(and€in€the€pooled€sample),€dependencyĻcoefficients€are€small€and€not€statistically€significant.€€InĻcontrast,€in€the€full€sample€for€the€1980s,€both€youth€(D1)€andĻaged€(D2)€dependency€exert€negative€impacts,€€although€tests€ofĻchange€over€time€fail€even€at€the€10%€level.€€Finally,€the€FEMĻresults€show€differing€impacts€by€cohort,€an€admissible€resultĻtheoretically€but€one€that€is€infrequently€found€empirically.€Ļ(This€latter€result€is€not€robust€to€alternative€formulations.)€€ĢĢą  ąIn€short,€our€findings€in€Table€1€are€generally€consistentĻwith€a€broad€literature€evaluating€the€Leff€formulation€whereĻfairly€weak€demographic€effects€are€often€found€€Nevertheless,€weĻdo€find€some€mild€evidence€of€negative€youth€and€elderlyĻdependency€impacts€in€the€1980s.Ģā āŠ Ų'(#- Šą  ąThese€results€are€robust.ńYń׃e×ńYńńYń׃l×ńYńŻ ƒ>EˆŻņņŚ  Ś7Ś  ŚóóŻ  Ż×  ׀€Concentrating€on€the€fullŠ ° Šā āsample,€they€are€found€in€models€that:€€(1)€exclude€periodĻbinaries;€(2)€use€10„€versus€5„year€aggregation€periods€to€exposeĻpossible€impacts€of€persistence€(dependency€impacts€are€weaker);Ļ(3)€employ€GDS€versus€GNS€(the€D1€impact€in€the€1980s€disappears,Ļalthough€the€D2€negative€impacts€are€somewhat€stronger€in€panel€ĢĢ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€Table€1ĢĢ€€€€€Dependency€and€the€Aggregate€Saving€Rate:€€The€Leff€ModelĢŌ€@X1שXXģŪŌŌ€@¤1ש{©@X1×ŌÓ  ÓÓ  Óą€(#Q(#ąˆĢŌ€P¤1ש{©@¤1×Ōņņą€(#Q(#ąóóˆĢ€€€€€€€€€|€ņņ€€€€€€€€€€€€€€€€€€Full€Sample€€€€€€€€€€€€€€€€€€óó€|€ņņ€€€€€€€€€€€€€€€€€€€LDCs€Only€€€€€€€€€€€€€€€€€€€óóĢ€€€€€€€€€|€ņņ€€€€€€€Cross„Sections€€€€€€ó󀀀ņņ€€€Panel€Data€€€€óó€|€ņņ€€€€€€€Cross„Sections€€€€€€ó󀀀ņņ€€€Panel€Data€€€€óóĢ€€€€€€€€€|€ņņ1960„70ó󀀀ņņ1970„80ó󀀀ņņ1980„90ó󀀀ņņ€Pooledó󀀀ņņ€€FEM€€óó€|€ņņ1960„70ó󀀀ņņ1970„80ó󀀀ņņ1980„90ó󀀀ņņ€Pooledó󀀀ņņ€€FEM€€óóĢ€€€€€€€€€|€€€(1)€€€€€€€(2)€€€€€€€(3)€€€€€€€(4)€€€€€€€(5)€€€|€€€(6)€€€€€€€(7)€€€€€€€(8)€€€€€€€(9)€€€€€€(10)€Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ĢY/Ngr€€€€|€€0.03**€€€€0.01*€€€€€0.01**€€€€0.02**€€€€0.02**€|€€0.01*€€€€€0.01*€€€€€0.02**€€€€0.02**€€€€0.02**Ģ€€€€€€€€€|€(3.38)€€€€(2.23)€€€€(2.96)€€€€(5.64)€€€€(4.99)€€|€(1.74)€€€€(2.04)€€€€(3.60)€€€€(5.21)€€€€(4.16)Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģln(D1)€€€|€€0.02€€€€€-0.05€€€€€-0.11*€€€€-0.02€€€€€€0.14**€|€€0.14€€€€€€0.03€€€€€-0.02€€€€€€0.05€€€€€€0.12*€Ģ€€€€€€€€€|€(0.44)€€€€(0.90)€€€€(2.12)€€€€(0.63)€€€€(3.03)€€|€(1.62)€€€€(0.39)€€€€(0.25)€€€€(1.24)€€€€(2.14)Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģln(D2)€€€|€€0.00€€€€€-0.01€€€€€-0.08**€€€-0.02€€€€€-0.06€€€|€€0.00€€€€€-0.01€€€€€-0.06€€€€€-0.02€€€€€-0.02Ģ€€€€€€€€€|€(0.08)€€€€(0.33)€€€€(2.87)€€€€(1.01)€€€€(1.84)€€|€(0.04)€€€€(0.19)€€€€(1.50)€€€€(0.73)€€€€(0.57)Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģln(Y/N)€€|€€0.09**€€€€0.07**€€€€0.07**€€€€0.08**€€€€0.20**€|€€0.09**€€€€0.08**€€€€0.08**€€€€0.08**€€€€0.20**Ģ€€€€€€€€€|€(5.34)€€€€(5.40)€€€€(6.39)€€€(10.29)€€€€(6.80)€€|€(4.81)€€€€(4.87)€€€€(6.04)€€€€(8.91)€€€€(6.14)Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢConstant€|€-4.68**€€€-4.31**€€€-3.93**€€€-4.43**€€€-5.13**€|€-5.18**€€€-4.63**€€€-4.36**€€€-4.72**€€€-5.09**Ģ€€€€€€€€€|(15.11)€€€(15.48)€€€(15.01)€€€(27.44)€€€(22.33)€€|(12.06)€€€(13.14)€€€(12.74)€€€(23.51)€€€(18.69)Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢR€Squared|€€0.40€€€€€€0.42€€€€€€0.64€€€€€€0.47€€€€€€0.81€€€|€€0.24€€€€€€0.24€€€€€€0.49€€€€€€0.29€€€€€€0.76ĢAdj€R-Sq.|€€0.39€€€€€€0.41€€€€€€0.63€€€€€€0.46€€€€€€0.77€€€|€€0.22€€€€€€0.21€€€€€€0.47€€€€€€0.28€€€€€€0.71Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢStd€Error|€€0.12€€€€€€0.10€€€€€€0.08€€€€€€0.10€€€€€€0.06€€€|€€0.13€€€€€€0.11€€€€€€0.08€€€€€€0.11€€€€€€0.07Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģ#€of€Obs€|€€€176€€€€€€€176€€€€€€€176€€€€€€€528€€€€€€€528€€€|€€€130€€€€€€€130€€€€€€€130€€€€€€€390€€€€€€€390Ģ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģp-values€from€Tests€of€Joint€Significance€€„„€€H0:€ln(D1)€=€ln(D2)€=€0ĢD1€&€D2€€|€0.868€€€€€0.596€€€€€0.018*€€€€0.596€€€€€0.002**€|€0.233€€€€€0.857€€€€€0.254€€€€€0.174€€€€€0.086Ģ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģp-values€from€Test€of€Coefficient€Difference€€„„€€H0:€ln(D1)€=€ln(D2)ĢD1€&€D2€€ńYńŌ% €M ŌńYń|€0.607€€€€€0.338€€€€€0.499€€€€€0.887€€€€€0.000**€|€0.103€€€€€0.579€€€€€0.413€€€€€0.062€€€€€0.036*ĢĢp-values€from€Hausman„Wu€Test€for€Exogeneity€€„„€€H0:€€Y/Ngr€is€ExogenousĢŌ‡Y¤1ש{©P¤1×Ō€€€€€€€€€|€0.010**€€€0.695€€€€€0.035*€€€€0.000**€€€0.000**€|€0.270€€€€€0.563€€€€€0.003*€€€€0.001**€€€0.005**ĢŌ#†P¤1ש{©Y¤1×°c#Ō€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģp„values€from€Tests€for€Changes€over€Time€€„„€€H0:€1960€=€1970€=€1980ĢModi.€Chow€„„„„„„„„„„€.203€€„„„„„„„„„„€|€€€€€€€€€€€€€€€€€€|€„„„„„„„„„„„€€.645€€„„„„„„„„€|Ģln(D1)€€€€€„„„„„„„„„„€.257€€„„„„„„„„„„€|€€€€€€€€€€€€€€€€€€|€„„„„„„„„„„„€€.338€€„„„„„„„„€|Ģln(D2)€€€€€„„„„„„„„„„€.228€€„„„„„„„„„„€|€€€€€€€€€€€€€€€€€€€|€„„„„„„„„„„„„€.655€€„„„„„„„„€|Ģņņ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€Ļą€(#}(#ąóóˆĢNotes:€Models€run€with€2SLS€(see€Appendix€A).€€*€and€**€=€significant€coefficients€at€5%€and€1%€levels;€t„¼ńYń¼ńYńvalues€are€in€parentheses.€€The€modified€Chow€test€checks€for€constancy€of€all€coefficients€with€theĻexception€of€the€intercept€(which€are€allowed€to€vary€in€Pooled€and€FEM;€coefficients€for€the€time€andĻcross„section€binaries€are€not€shown.).€€The€dependent€variable€and€the€model€are€described€the€text.€ĢŌ€¤Iœ¤{©P¤1×ŌŌ€XģŪX]¤¤IœŌŠ 6)†$; Šestimation);ńYń׃Z×ńYńńYń׃ ×ńYńŻ ƒ>EˆŻņņŚ  Ś8Ś  ŚóóŻ  Ż×  ׀(4)€exclude€countries€of€unusual€influence€(D1€is€Š ° Šsomewhat€stronger€in€the€1970s€and€in€panel€estimation);€and€(5)Ļare€fitted€by€OLS„„with€and€without€White„corrected€standard€Ģerrors€(D1€is€somewhat€stronger€in€the€1980s€and€changesĻsignificantly€between€the€decades).ĢŌ€oXģŪXXXģŪŌĢą  ąLeff's€pioneering€model€is€eclectic€in€its€theoreticalĻundergirding€and,€because€of€this,€is€somewhat€difficult€toĻinterpret.€€Could€it€be€that€a€more€tightly€specified€andĻinterpretable€life„cycle€formulation€would€modify€our€assessmentsĻof€the€impacts€of€demography?€€We€next€turn€to€such€a€model.ĢĢĢŌ  Ō3.0€€€ņņThe€Mason€Model:€Theory€and€Empirical€SpecificationóóĢĢą  ąFormal€life„cycle€modeling€of€consumption€and€saving€can€beĻbased€on€individuals€or€households.€€We€focus€on€households,Ļwhose€"age"€begins€at€household€formation€(e.g.,€marriage).€€TheĻfundamental€hypothesis€is€that€households,€faced€with€an€incomeĻthat€varies€predictably€and€systematically€over€a€lifetime€(anĻinverse€U€curve),€will€attempt€to€smooth€their€consumption.€€ThisĻresults€in€an€age„specific€pattern€of€saving„„dissavingĻ(borrowing)€to€finance€expenditures€during€early€years€andĻretirement,€and€saving€during€most€working€years€(Modigliani€andĻBrumberg€(1954),€and€Modigliani€and€Ando€(1957)).€€Accounting€forĻthe€impact€of€this€pattern€on€economy„wide€saving€can€be€complexĻand€requires€the€weighting€of€age„specific€household€saving€byĻthe€relative€share€of€households€by€age.€€ĢĢą  ąņņThe€Basic€Life„Cycle€ModelóóĢĢą  ąMason€(1981,€1987)€presents€a€life„cycle€micro„theoreticĻmodel€of€household€consumption€and€develops€its€macro„¼ńYń¼ńYńimplications€under€steady„state€growth€in€both€per€capita€incomeĻand€population.€€(Technical€details€are€provided€in€Appendix€B.)€ĻFrom€our€perspective,€there€are€two€key€assumptions.€€First,€in€aĻnarrow€version€of€the€model,€households€balance€lifetime€incomeĻagainst€lifetime€consumption€so€that€wealth€at€householdĻdissolution€is€zero€or,€if€not€zero,€households€leave€bequestsĻthat€are€assumed€to€be€independent€of€the€number€of€children.€ĻThus,€the€number€of€children€has€no€impact€on€lifetime€wealthŠ š#@( Šaccumulation.€€In€this€case,€the€number€of€children€influencesĻthe€composition€and,€importantly,€the€ņņtimingóó€of€consumption€(andĻsaving),€but€ņņnotóó€the€total€ņņlevelóó€of€consumption€(and€saving)€overĻthe€life€cycle.€€Second,€households€consume€two€goods„„child„¼ńYń¼ńYńrearing€activities€and€all€other€activities.€€ĢĢą  ąIn€such€a€setup,€aggregate€saving€across€a€household's€lifeĻcycle€would€be€zero.€€The€economy„wide€savings€rate€is€thereforeĻa€function€of€the€age€distribution€of€households,€the€ageĻdistribution€of€income,€and€the€distribution€and€timing€ofĻconsumption€between€child„rearing€and€all€other€activities.€ĻThese€are€three€separable€influences€on€economy„wide€savings€thatĻcan€be€analyzed€individually.ĢĢą  ąThe€impact€on€saving€of€a€change€in€the€age€distribution€ofĻhouseholds€or€the€age€distribution€of€per€capita€income€dependsĻon€the€timing€of€consumption€relative€to€earning.€€If€earningĻgenerally€precedes€consuming,€i.e.,€if€households€are€netĻcreditors€during€their€lifetime,€younger€age€distributions€favorĻhigher€saving€rates.€€If€households€are,€on€average,€netĻcreditors,€a€country€with€a€high€rate€of€population€growth€willĻhave€a€higher€proportion€of€households€in€the€younger,€highĻsaving€age€group€and€a€lower€proportion€in€the€older,€low€savingĻage€group.€€The€growth€rate€of€population€(Nņņgróó)€is€thusŠ Øų Šņņpositivelyóó€associated€with€saving.ńYń׃h×ńYńńYń׃j×ńYńŻ ƒ>EˆŻņņŚ  Ś9Ś  ŚóóŻ  Ż×  ׊ pĄ ŠĢą  ąLikewise,€in€a€country€with€a€high€rate€of€per€capita€incomeĻgrowth,€the€lifetime€income€of€younger€households€will€beĻsubstantially€higher€than€the€lifetime€income€of€older€(retired)Ļhouseholds.€€To€the€extent€that€younger€households€are€savers,€asĻcompared€with€older€households,€aggregate€saving€will€be€higher.€ĻHence,€the€growth€rate€of€per€capita€income€(Y/Nņņgróó)€is€positivelyŠ č8 Šassociated€with€economy„wide€saving.ĢĢą  ąThese€two€influences€are€both€components€of€economic€growth,Ļi.e.€Yņņgróó€š š€Nņņgróó€+€Y/Nņņgróó.€€Within€this€model,€the€impact€on€savingŠ  X# Šā āof€these€two€growth„rate€effects€are€hypothesized€to€be€the€Š Š $ Šsame.ńYń׃p×ńYńńYń׃m×ńYńŻ ƒ>EˆŻņņŚ  Ś10Ś  ŚóóŻ  Ż×  ׀€Each€simply€gives€more€weight€to€the€higher€(lower)Š ° Šā āsavers€in€households€where€population€and/or€income€growth€ratesĻincrease€(decrease).€€Because€of€this,€these€have€been€termedĻ"ņņrate„of„growthóó"€effects.€€ĢĢą  ąThe€magnitude€and€direction€of€the€rate„of„growth€effectsĻdepend€on€the€age€profile€or€timing€of€consumption€and€earning.€ĻIn€a€growing€economy,€any€change€in€household€behavior€thatĻincreases€the€average€number€of€years€by€which€consumption€lagsĻearning€has€a€positive€impact€on€saving.€€The€traditional€youthĻdependency€hypothesis€is€that€consumption€during€the€child„Ļrearing€years€increases€with€the€number€of€children€being€rearedĻor€the€youth€dependency€ratio.€€If€this€is€indeed€the€case,€aĻhigher€youth€dependency€ratio€leads€to€a€decline€in€theĻconsumption€lag€and,€if€growth€is€positive,€a€reduced€savingĻrate.ĢĢą  ąA€well„known€feature€of€the€life„cycle€model€is€that€changesĻin€the€age€profile€of€consumption€and€earning€have€no€impact€onĻthe€aggregate€saving€rate€if€the€rate€of€economic€growth€is€zero.€ĻAt€any€point€in€time,€higher€(lower)€saving€among€youngĻhouseholds€would€be€offset€by€lower€(higher)€saving€by€oldĻhouseholds.€€Whereas€in€the€presence€of€growth,€young€householdsĻare€more€numerous€or€have€higher€lifetime€wealth,€their€behaviorĻdominates€the€compensating€behavior€of€older€households.ĢĢą  ąWhile€the€model€just€described€has€only€two€goods€andĻfocuses€solely€on€youth€dependency€(D1),€a€wider€model€could€beĻevaluated€incorporating€aged€dependency€(D2).€€Tests€on€theĻefficacy€of€this€model€are€provided€below.€€For€the€present,€weĻwill€focus€solely€on€D1,€the€formulation€most€examined€in€theĻliterature.ĢĢą  ąņņEmpirical€FormulationsóóĢĢą  ąIn€empirical€analyses,€the€life„cycle€model€can€beĻformulated€in€varying€degrees€of€complexity.€€The€first€and€mostĻ"basic"€formulation€assumes€that€youth€dependency€affects€theĻtiming,€but€not€the€level,€of€lifetime€consumption€(e.g.,€S/Y€=Ļf(Yņņgróó,€D1ššYņņgróó)).€€The€second€"extended"€model€allows€both€forŠ (#x' Štiming€and€level€impacts€(S/Y€=€f(Yņņgróó,€D1*Yņņgróó,€D1)).€€Finally,Š š#@( Šeither€of€these€models€may€be€embellished€with€factors€consideredĻrelevant€to€determining€saving€(indices€of€capital€marketĻdevelopment,€size€of€the€urban€sector,€etc.)Ģā āŠ '`", Šą  ąIn€these€models,€for€the€reasons€noted€above,€the€growth„¼ā āńYń¼ńYńrate€term€(Yņņgróó)€has€an€expected€positive€sign€and€the€consumptionŠ xČ Štiming€term,€which€interacts€dependency€with€income€growthĻ(D1*Yņņgróó),€is€predicted€to€have€a€negative€sign.€€The€impact€ofŠ X Šchildren€on€bequests€(D1)€is€uncertain:€€positive€if€householdsĻraise€total€bequests€in€response€to€additional€children;€zero€ifĻtotal€bequests€are€independent€of€the€number€of€children;€orĻnegative€if,€for€example,€children€are€thought€to€provide€oneĻform€of€old„age€security.€€ĢĢą  ąņņResultsĢóóĢą  ąGenerally€speaking,€the€results€in€Table€2€reveal€that€theĻlife„cycle€model€commands€strong€support€both€in€the€full€and€inĻthe€LDC€samples.ńYń׃r×ńYńńYń׃q×ńYńŻ ƒ>EˆŻņņŚ  Ś11Ś  ŚóóŻ  Ż×  ׀€In€8€out€of€10€regressions,€the€Yņņgróó€terms€areŠ  š  Šindividually€significant,€and€in€all€10€regressions,€the€two€YņņgróóŠ hø  Šterms€(including€the€D1€interaction)€are€jointly€significant.€ĢĢą  ąMore€important€for€our€present€purposes,€demographic€impactsĻare€consistently€found,€although€with€some€variation€in€form.€ĻThe€rate„of„growth€D1€effect€is€negative€and€significant€in€allĻcross„sections€for€the€full€sample,€all€panel€estimates€for€bothĻsamples,€and€in€the€1980s€among€the€LDCs.€€In€contrast,€directĻdemographic€effects€(D1)€are€not€as€strong.€€Still,€negative€andĻsignificant€effects€emerge€in€the€full€sample€for€the€1980s€asĻwell€as€the€FEM€estimates.ĢĢą  ąThese€findings€are€generally€robust.ńYń׃@×ńYńńYń׃sc×ńYńŻ ƒ>EˆŻņņŚ  Ś12Ś  ŚóóŻ  Ż×  ׀€They€are€found€inŠ Č Šmodels€that:€€(1)€exclude€period€binaries;€(2)€use€10„€versus€5„Ģyear€panels€(the€rate„of„growth€D1€effect€is€now€insignificant€inĻthe€FEM€estimates);€(3)€employ€GDS€versus€GNS;€(4)€exclude€fourĢcountries€(Uganda,€Nicaragua,€Chile,€Uruguay)€with€exceptionallyĻlarge€variance€in€net€factor€income;€(5)€exclude€countries€ofĻunusual€influence€(although€the€D1€impact€appears€somewhatĻstronger);€(6)€substitute€D3€(the€sum€of€youth€and€agedĻdependency€impacts)€for€D1;€and€(7)€incorporate€both€youth€andĻaged€dependency€separately€(the€aged€terms€are€insignificant€inĻnine€of€ten€regressions).€€The€most€dramatic€changes€result€whenĻthe€model€is€fitted€with€OLS€(either€with€or€without€standardĻerrors€which€are€White„corrected€for€possibleŠ (#x' Šheteroscedasticity).€€Under€OLS,€the€life„cycle€effects€(directĻand€interacted€with€D1)€are€much€weaker€while€the€directĻdependency€impacts€are€stronger.€€Clearly,€appropriate€correctionĻfor€simultaneity€bias€is€important€in€this€model.€€Consistently,Ļresults€similar€to€OLS€are€obtained€when€employing€an€instrumentĻset€which€is€correlated€with€the€saving€residuals.€€(See€alsoĻAppendix€A.)ĢĢ€€€€€€€€€€€€€€€€€€€€€€€€Table€2ĢĢ€€€€Dependency€and€the€Aggregate€Saving€Rate:€€The€Mason€ModelŌ€aX1שXoXģŪŌŌ€a¤1ש{©aX1×ŌŌ‡d¤1ש{©a¤1×ŌŠ € Š  ŠŌ#†a¤1ש{©d¤1×ė#ŌŅ„°ŅĢŌ€U¤1ש{©a¤1×Ōņņą€T$T$ąóóˆĢ€€€€€€€€€€€|€ņņ€€€€€€€€€€€€€€€€€€Full€Sample€€€€€€€€€€€€€€€€€€óó€|€ņņ€€€€€€€€€€€€€€€€€€€LDCs€Only€€€€€€€€€€€€€€€€€€€óóĢ€€€€€€€€€€€|€ņņ€€€€€€€Cross„Sections€€€€€€ó󀀀ņņ€€€Panel€Data€€€€óó€|€ņņ€€€€€€€Cross„Sections€€€€€€ó󀀀ņņ€€€Panel€Data€€€€óóĢ€€€€€€€€€€€|€ņņ1960„70ó󀀀ņņ1970„80ó󀀀ņņ1980„90ó󀀀ņņ€Pooledó󀀀ņņ€€FEM€€óó€|€ņņ1960„70ó󀀀ņņ1970„80ó󀀀ņņ1980„90ó󀀀ņņ€Pooledó󀀀ņņ€€FEM€€óóĢ€€€€€€€€€€€|€€€(1)€€€€€€€(2)€€€€€€€(3)€€€€€€€(4)€€€€€€€(5)€€€|€€€(6)€€€€€€€(7)€€€€€€€(8)€€€€€€€(9)€€€€€€(10)€Ģ€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ĢYgr€€€€€€€€|€€0.36**€€€€0.30**€€€€0.28**€€€€0.40**€€€€0.14**€|€-0.13€€€€€€0.18€€€€€€0.33**€€€€0.74**€€€€0.24**Ģ€€€€€€€€€€€|€(6.04)€€€€(4.28)€€€€(4.36)€€€€(9.34)€€€€(3.38)ńYńŌ% €v ŌńYń€€|€(0.37)€€€€(1.38)€€€€(4.16)€€€€(5.11)€€€€(3.42)Ģ€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģln(D1)*Ygr€|€-0.08**€€€-0.07**€€€-0.06**€€€-0.09**€€€-0.03**€|€€0.04€€€€€-0.04€€€€€-0.07**€€€-0.17**€€€-0.05**Ģ€€€€€€€€€€€|€(5.74)€€€€(4.06)€€€€(4.00)€€€€(8.73)€€€€(3.42)€€|€(0.45)€€€€(1.19)€€€€(3.89)€€€€(4.88)€€€€(3.45)Ģ€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģln(D1)€€€€€|€€0.06€€€€€-0.06€€€€€-0.07*€€€€€0.00€€€€€„0.09**€|€€0.09€€€€€-0.05€€€€€-0.08€€€€€€0.01€€€€€„0.03Ģ€€€€€€€€€€€|€(1.06)€€€€(1.32)€€€€(2.08)€€€€(0.01)€€€€(2.76)€€|€(1.00)€€€€(0.74)€€€€(1.42)€€€€(0.24)€€€€(0.66)Ģ€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢConstant€€€|€-4.77**€€€-4.27**€€€-4.26**€€€-4.55**€€€-4.13**€|€-5.06**€€€-4.34**€€€-4.24**€€€-4.58**€€€-4.38**Ģ€€€€€€€€€€€|(19.87)€€€(21.78)€€€(28.54)€€€(38.64)€€€(32.27)€€|(12.46)€€€(13.75)€€€(18.21)€€€(18.14)€€€(19.28)Ģ€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģ€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢR€Squared€€|€€0.29€€€€€€0.32€€€€€€0.50€€€€€€0.35€€€€€€0.82€€€|€€0.08€€€€€€0.13€€€€€€0.36€€€€€€0.13€€€€€€0.74ĢAdj€R-Sq.€€|€€0.28€€€€€€0.31€€€€€€0.50€€€€€€0.34€€€€€€0.76€€€|€€0.05€€€€€€0.11€€€€€€0.35€€€€€€0.11€€€€€€0.68Ģ€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢStd€Error€€|€€0.15€€€€€€0.13€€€€€€0.10€€€€€€0.14€€€€€€0.06€€€|€€0.15€€€€€€0.13€€€€€€0.11€€€€€€0.20€€€€€€0.07Ģ€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģ#€of€Obs€€€|€€€176€€€€€€€176€€€€€€€176€€€€€€€528€€€€€€€528€€€|€€€130€€€€€€€130€€€€€€€130€€€€€€€390€€€€€€€390ĢĢp-values€from€Tests€of€Joint€SignificanceĢYgr€Terms€€|€0.000**€€€0.000**€€€0.000**€€€0.000**€€€0.003**€|€0.018*€€€€0.001**€€€0.000**€€€0.000**€€€0.003**ĢD1€Terms€€€|€0.000**€€€0.000**€€€0.000**€€€0.000**€€€0.000**€|€0.474€€€€€0.187€€€€€0.000**€€€0.000**€€€0.000**ĢĢp-values€from€Hausman„Wu€Test€for€Exogeneity€€„„€€H0:€€Ygr€is€ExogenousĢ€€€€€€€€€€€|€0.000**€€€0.000**€€€0.000**€€€0.000**€€€0.001**€|€0.090€€€€€0.019*€€€€0.000**€€€0.000**€€€0.000**ĢĢp„values€from€Tests€for€Changes€over€Time€€„„€€H0:€1960€=€1970€=€1980ĢModi.€Chow€„„„„„„„„„„€.369€€€„„„„„„„„„€|€€€€€€€€€€€€€€€€€€|€„„„„„„„„„„„€.090€€€„„„„„„„„€|ĢYgr€€€€€€€€„„„„„„„„„„€.587€€€„„„„„„„„„€|€€€€€€€€€€€€€€€€€€€|€„„„„„„„„„„„€.284€€€„„„„„„„„€|Ģln(D1)*Ygr€„„„„„„„„„„€.544€€€„„„„„„„„„€|€€€€€€€€€€€€€€€€€€|€„„„„„„„„„„„€.257€€€„„„„„„„„€|Ģln(D1)€€€€€„„„„„„„„„„€.087€€€„„„„„„„„„€|€€€€€€€€€€€€€€€€€€€|€„„„„„„„„„„„€.240€€€„„„„„„„„€|Ģņņ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€Ļ€ą€T$T$ąóóˆŠ ø$ 3 ŠŅ°„ŅSee€note€to€Table€1.€Ō€UX1ש{©U¤1×ŌŌ€bXģŪX{©UX1×ŌŠ N%ž 4 ŠĢą  ąOur€results€complement€those€in€recent€studies€which€tend€toĻevaluate€a€"hybrid"€rendering€of€saving€that€combines€Leff€(a€Y/NĻeffect)€and€Mason€(a€Yņņgróó*D1€effect).€€In€contrast€to€many€ofŠ <(Œ#8 Šthese€studies,€our€framework€follows€the€Mason€life„cycle€model€Ļmore€closely€and,€in€estimation,€considers€Yņņgróó€to€be€endogenous.€Š Ģ)%: ŠWith€these€important€differences€we€find€that€the€demographicĻņņtimingóó€effects€(Yņņgróó*D1)€have€a€relatively€greater€influence€onŠ \+¬&< Šsaving€than€do€the€demographic€ņņlevelóó€effects€(ņņlnóó(D1)).€€On€theŠ $,t'= Šother€hand,€the€cross„section€estimates€for€the€full€sample€findĻD1€effects€for€the€1980s.€€In€the€literature€the€results€areĻmixed€on€these€matters.€€In€a€time„series€study€of€seven€AsianĻcountries€by€Fry€and€Mason€(1982),€both€the€timing€and€the€levelĻeffects€were€found€to€be€statistically€significant.€€Mason'sĻ(1981)€earlier€paper€focusing€on€a€cross„section€of€69€countriesĻfor€the€1960s€gives€similar€(although€less€precise)€estimates.€ĻHiggins'€(1994)€exploratory€results€(table€I)€come€closest€toĻours,€but€in€his€preferred€modeling€the€impact€of€demography€onĻthe€timing€of€life„cycle€saving€is€never€statisticallyĻsignificant.€€Collins€(1991)€obtains€both€timing€and€(ņņpositiveóó)Ļlevel€effects,€but€only€when€two€low„income€countries€are€omittedĻfrom€her€10„country€Asian€sample.€€Taylor€and€Williamson€(1994)Ļfind€only€(ņņnegativeóó)€level€effects€for€their€long„term€historicalĻstudy€of€Argentina,€Australia,€Canada,€and€the€United€States;Ļlife„cycle€timing€plays€no€role.€€In€all€studies,€then,Ļdependency€counts,€but€the€way€in€which€it€exerts€its€impactĻvaries€considerably.€ĢĢą  ąOur€empirical€results€can€be€brought€into€sharper€focusĻthrough€an€examination€of€the€elasticities€of€S/Y€with€respect€toĻYņņgróó€and€D1,€as€well€as€the€estimates€of€S/Y€at€mean€values€of€YņņgróóŠ h Šand€D1€for€each€decade.€€These€are€presented€in€table€3,€whereĻfor€brevity€we€employ€the€parameter€estimates€for€the€mid€periodĻ(the€1970s)€and€full€sample€(col.€2€in€table€2).ĢĢą  ąDo€these€new€saving€results€show€demographic€factors€to€beĻquantitatively€important?€€Clearly€yes.€€First,€considerĻelasticities€calculated€at€the€1970s€mean€Yņņgróó€and€D1.€€S/Y€isŠ ą Šmuch€more€sensitive€to€D1€(an€elasticity€of€„2.08)€than€to€YņņgróóŠ XØ Š(an€elasticity€of€.47).€€Next,€consider€the€second€column€whereĻYņņgróó€is€held€constant€while€D1€follows€its€path€through€the€threeŠ č8 Šdecades.€€While€the€importance€of€demography€to€changes€in€savingĻbetween€the€1960s€and€1970s€was€relatively€modest€(a€smallĻdecline€in€D1€resulted€in€an€estimated€increase€in€S/Y€of€.7%),Ļthe€much€larger€decline€in€D1€in€the€1980s€resulted€in€aĻpredicted€sizeable€increase€in€S/Y€of€2.1%.€€Finally,€considerĻthe€second€row€which€tracks€Yņņgróó€while€holding€D1€constant.€€Life„Š ˜!č% ŠńYńŠ xČ! ŠńYńcycle€impacts€reduced€predicted€saving€for€the€1980s€by€aĻwhopping€2.8%€from€the€1970s€(due€to€a€decline€in€Yņņgróó).€€InŠ (#x' Šshort,€the€net€reduction€of€ņņactualóó€saving€over€the€decade€of€1.8%Ļis€notably€impacted€by€two€demographic€forces:€€a€negative€life„¼ńYń¼ńYńcycle€impact€from€the€economic€slowdown€offset€by€half€due€to€Ļdeclining€dependency€over€the€decade.ĢĢą  ąWhile€this€assessment€utilizes€the€parameters€of€the€1970s,Ļuse€of€each€decadeššs€own€parameters€(cols.€1„3€in€table€2)€andŠ  (š#. Šā āmean€values€indicates€that€the€elasticities€change€slightly,€butŠ o)æ$/ Šsystematically€over€time.ńYń׃V×ńYńńYń׃w×ńYńŻ ƒ>EˆŻņņŚ  Ś13Ś  ŚóóŻ  Ż×  ׀€The€elasticities€for€S/Y€withŠ ° Šā ārespect€to€D1€for€the€1960s,€1970s,€and€1980s€are,€respectively,ĢĢ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€Table€3ĢĢ€€€€€€€€Elasticities€and€Estimates€of€S/Y€for€Alternative€€€€€€€€€Ļ€€€€€€€€€€€€€€€€€€€€€€Values€of€Yņņgróó€and€D1Š ` ° Šņņą€(#}(#ąˆĢņņ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€óóĢ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€Year€(Ygr)€€€€€€€€€€€€€€€€€€€Ģ€€ņņYear€(D1)ó󀀀€€€€ņņ1960s€(5.04)€€€€€€€€€1970s€(4.17)€€€€€€1980s€(2.40)óóĢĢ1960s€(72.95)€€„2.35€[.49]€{14.5}€€„2.22€[.45]€{13.3}€€„1.85€[.33]€{10.7}Ģ1970s€(71.03)€€„2.19€[.50]€{15.4}€€ņ ņ„2.08€[.47]€{14.1}ó 󀀄1.75€[.35]€{11.3}Š b  Š1980s€(66.15)€€„1.84€[.54]€{17.8}€€„1.77€[.50]€{16.1}€€„1.53€[.38]€{12.7}ĢĢMean€S/Y€€€€€€€€€€€€€€€€€€€{13.2}€€€€€€€€€€€€€€{14.0}€€€€€€€€€€€€€€{11.5}Ģņņ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€óóĢŌ‡b©Iœ ©XbXģŪŌŌ‡J©1שS©b©IœŌNotes:€The€elasticity€of€S/Y€w.r.t.€D1€is€listed€first€followed€by€the€elasticity€w.r.t.€Ygr€in€square€brackets€and€estimated€S/Y€in€{}€brackets.€Š V¦  ŠDecadal€mean€values€of€D1€and€Ygr€(parenthetically€noted€as€row€and€column€headings)€were€used€in€conjunction€with€parameter€estimates€fromĻthe€1970s€full€sample€(col.€2,€table€2)€for€these€calculations.€€The€emboldened€values€are€the€estimates€relevant€to€the€1970s.óóŠ zŹ  ŠŌ#†b©Iœ ©{©J©1×X²#ŌŌ#†bXģŪXS©b©Iœ9²#ŌĢ„2.36,€€„2.08,€and€„2.04.€€The€corresponding€elasticities€for€YņņgróóŠ Ō$ Šare€.33,€.47,€and€.52.€€Thus,€over€time€S/Y€is€becoming€slightlyĻmore€sensitive€to€changes€in€Yņņgróó€(life€cycle€impacts)€butŠ d“ Šslightly€less€sensitive€to€demography€(D1).€€We€conclude,€then,Ļthat€demography's€notable€impact€on€saving€over€time€is€dueĻprimarily€to€the€increase€in€the€pace€of€D1€decline€andĻsecondarily€to€its€increasing€sensitivity€to€lifecycle€effects.ĢĢą  ąAt€any€rate,€our€conclusions€are€several.€€(1)€At€theĻmargin,€S/Y€is€quite€sensitive€to€dependency€and€relativelyĻinsensitive€to€economic€growth.€€(2)€Although€more€sensitive€toĻdependency,€the€saving€declines€of€the€1980s€are€attributable€inĻsubstantial€part€to€severe€declines€in€economic€growth.€€FallingĻdependency€rates€played€an€ameliorating€role€in€this€decline.€Ļ(3)€The€manner€in€which€dependency€exerts€its€influence€may€beĻchanging€as€well,€although€these€findings€are€mixed€and€not€asĻstrong.€€ĢĢ4.0€€ņņSummary€and€ConclusionsóóĢĢą  ąIt€appears€that€the€widely€observed€finding€in€theĻliterature€showing€little€or€no€relationship€between€populationĻgrowth€(and€dependency)€and€saving€requires€modification.€€First,Ļwhile€it€is€consistent€with€an€update€of€the€hybrid€(Keynesian,€Ļlife„cycle)€Leff„type€model,€in€a€more€clearly€interpretableĻlife„cycle€framework€(a€la€Mason)€the€role€of€demography€isŠ \'¬"/ Šstrong€over€the€30€years,€although€the€form€which€it€takes€(life„¼ńYń¼ńYńcycle€versus€lifetime€level)€may€vary€over€time€and€place.€ĻOverall,€demographic€factors€accounted€for€a€major€portion€ofĻchanges€in€saving€across€countries€and€over€time.€€These€findingsĻappear€to€be€quite€robust€and€relatively€insensitive€to€variousĻsamples,€estimation€procedures,€variable€definitions,€functionalĻforms,€and€the€like.ĢĢą  ąWe€appear€also€to€have€ruled€out€the€role€of€demography€viaĻsavings€impacts€as€an€explanation€of€the€"new"€negativeĻcorrelations€between€population€and€per€capita€output€growth€inĻthe€1980s.€€While€life„cycle€impacts€were€quantitativelyĻimportant€in€accounting€for€saving€since€1960,€their€impactsĻtended€to€ameliorate€the€S/Y€decline€induced€primarily€by€world„¼ńYń¼ńYńwide€recession€in€1980.€€Perhaps€more€to€the€point,€our€estimatesĻreveal€that€the€elasticity€of€saving€with€respect€to€youthĻdependency€remained€virtually€constant€between€the€1970s€andĻ1980s.€€Of€course,€while€such€a€result€does€not€solve€the€new„¼ńYń¼ńYńcorrelation€puzzle,€the€Leff€and€Mason€frameworks€have€beenĻuseful€in€framing€the€issues.€€Nevertheless,€they€are€ratherĻsimple€renderings€of€a€complex€topic.€€The€next€challenge€is€toĻdevelop€modeling€extensions€or€alternative€paradigms.€€OurĻfindings€demonstrate€the€relevance€and€potential€productivity€ofĻsuch€a€research€focus€in€contributing€to€the€never„ending€debateĻon€the€consequences€of€population€growth.€ĢŠ  8ˆ Š€€€€€€€€€ņņAppendix€A:€Variables€and€Intermediate€ResultsóóĢĢą  ąņņInstrumental€Variablesóó.€€Per€capita€GDP€growth€(Y/Nņņgróó€as€inŠ @ ŠLeff)€and€GDP€growth€(Yņņgr,óó€as€in€Mason)€are€plausibly€endogenousŠ X Šin€a€savings€model.€€(The€Hausman„Wu€test€indicates€this€to€beĻthe€case€for€several€of€the€Leff€and€Mason€models.)€€Since€theĻchoice€of€instruments€used€to€cope€with€endogeneity€can€be€asĻimportant€to€obtaining€unbiased€and€consistent€estimates€as€theĻuse€of€2SLS,€we€have€approached€this€choice€with€considerableĻcare.€€We€begin€with€a€superset€of€15€variables€that€correlateĻwith€Y/Nņņgróó€and€Yņņgr€óóas€revealed€in€(1)€a€large€and€growingŠ € Š  Šempirical€literature€on€the€"new€growth€economics"€(e.g.,€BarroĻand€Lee€1993,€Fagerberg€1994);€(2)€an€early€life-cycle€savingĻstudy€by€Mason€(1981);€and€(3)€some€of€our€recent€work€(KelleyĻand€Schmidt€1994).€€For€brevity€we€rely€on€the€extensive€defenseĻof€each€of€these€variables€as€provided€in€that€literature.€ĢĢą  ąA€good€set€of€instruments€should€be€well€correlated€withĻY/Nņņgróó€(for€Leff)€or€Yņņgróó€(for€Mason)€and€uncorrelated€with€theŠ Ą Šsaving€residuals.€€The€following€procedure€helps€to€ensure€theseĻtraits€for€both€the€Leff€and€Mason€models.€€(1)€All€variables€areĻinitially€included€in€2SLS€estimation€of€saving€using€pooled€dataĻover€the€period€1960-1990.€€The€saving€residuals€are€regressed€onĻthe€first„stage€variable€set€and€the€insignificant€instrumentsĻprovide€an€initial€"core€set"€of€around€five€instruments.€€Ģ(2)€That€core€set€is€assessed€for€the€first€trait€by€a€joint€testĻin€the€first„stage€regression€on€those€instruments€not€includedĻin€the€saving€equation.€€An€overidentification€test€suggested€byĻDavidson€and€MacKinnon€(1993,€pp.€235„236)€examines€the€secondĻtrait.€€The€initial€core€set€passed€both€tests.€€(3)€This€coreĻset€is€augmented€separately€by€each€of€the€remaining€instrumentsĻand€submitted€to€the€same€two€tests.€€In€general,€the€instrumentĻset€with€the€highest€ņņp„valueóó€from€the€overidentification€testŠ °  Šcomprises€the€new€core€set.€€In€a€few€cases€where€ņņp„valuesóó€wereŠ xČ! Šclose€between€two€contenders,€the€instrument€with€the€mostĻexplanatory€power€in€the€first„stage€regression€was€chosen.€€Ģ(4)€The€third€step€is€repeated€until€all€alternative€instrumentĻsets€fail€the€overidentification€test€(i.e.,€ņņp„valueóó€less€thanŠ ˜!č% Š0.05).€€ĢĢą  ąTable€A.1€describes€all€variables€used€in€this€analysis€andĻflags€with€an€asterisk€those€instruments€ultimately€selected€forĻfirst„stage€regressions.€€Table€A.2€presents€an€analysis€of€theseĻinstruments€as€well€as€OLS€estimates€for€the€Mason€model.Š  H&˜!+ ŠŃX°ŃŃX°ŃńYńŌ% €D ŌńYńą@Š\ģąTable€A.1ˆĢĢą@EģąVariables:€Definitions,€Sources,€Descriptive€StatisticsˆĢĢŅ„°ŅŅŠ°ŅŌ€bIœ XbXģŪŌŌ*nƒg<idnŌŌ,Źdd ŌŌ,Ødd ŌŌ,hdd ŌŌ,dd ŌŌ,@dd ŌŌ,(dd ŌŌ+  ŌŠ # x  „„……#ŠVariable€as€Used€forŠ 3€R"Ü„" „„……3ŠĢDefinitionŠ N€R=.a "ĻĻR „„……NŠĢPdŠ N€R=.a "ĻĻR „„……NŠĢSrceŠ N€R=.a "ĻĻR „„……NŠMeanĢ(Std€Dev)Š J€R9.a "ĻĻR „„JŠLeffŠ 9€R(õ"R „„9ŠMasonŠ -#õ"R ……-ŠŠ  ‘9 ……ŠŠ  ‘9 ……ŠŠ  ‘9 ……ŠŠ  ‘9 ……Šņ ņņņVariables€in€Saving€Modeló óóóŠ  ¶  Šln(GNC/Y)Š  B ź  Šln(GNC/Y)Š  B ź  ŠSaving€measure,€discussed€more€fully€in€textŠ  B ź  ŠAvgŠ  B ź  ŠPWTŠ  B ź  Š„4.46€€(0.14)Š  B ź  ŠY/NgrŠ  [   ŠYgrŠ  [   ŠGDP€growth€rate,€per€capita€or€aggregate,ĻrespectivelyŠ  ą ˆ ŠGrŠ  [   ŠPWTŠ  [   Š€1.76€€(2.86)Ģ€3.87€€(2.83)Š  ą ˆ Šln(D1)Š  ł ”  Šln(D1)Š  ł ”  Šln(Youth€dependency€%):€(Pop€0„14)€/€(Pop€15„64)Š  ł ”  ŠAvgŠ  ł ”  ŠWBŠ  ł ”  Š€4.19€€(0.38)Š  ł ”  Šln(D2)Š   ŗ  Šln(D2)Š   ŗ  Šln(Aged€dependency€%):€(Pop€65+)€/€(Pop€15„64)Š   ŗ  ŠAvgŠ   ŗ  ŠWBŠ   ŗ  Š€2.10€€(0.50)Š   ŗ  ŠŠ  +Ó  Šln(D1)YgrŠ  +Ó  Šln(D1)€š"š€YgrŠ  +Ó  ŠŠ  +Ó  ŠŠ  +Ó  Š16.29€(12.35)Š  +Ó  Šln(Y/N)Š  Dģ  ŠŠ  Dģ  Šln(Per€capita€GDP)€in€1985€US€$1,000Š  Dģ  ŠBOPŠ  Dģ  ŠPWTŠ  Dģ  Š€0.77€€(1.01)Š  Dģ  ……Šņ ņņņPotential€Additional€Instruments€for€Y/Ngr€or€Ygr€(Those€used€are€denoted€by€an€*)ó óóóŠ  ] Š*ln(Y/N)Š  ‘9 Š*ln(Y/N)Š  ‘9 Šln(Per€capita€GDP)Š  ‘9 ŠBOPŠ  ‘9 ŠPWTŠ  ‘9 Š€0.77€€(1.01)Š  ‘9 Š*AgL/NgrŠ  ŖR Š€AgLgrŠ  ŖR ŠAgricultural€labor€force€growth€rate,€per€capitaĻor€aggregate,€respectivelyŠ  /× ŠGrŠ  ŖR ŠWBŠ  ŖR Š„0.08€€(2.20)Ģ„2.19€€(1.59)Š  /× Š*NAgLgrŠ  Hš Š*NAgL/NgrŠ  Hš ŠNon„agricultural€labor€force€growth€rate,€perĻcapita€or€aggregate,€respectivelyŠ  Ķu  ŠGrŠ  Hš ŠWBŠ  Hš Š„0.08€€(2.20)Ģ€1.54€€(1.39)Š  Ķu  Š€I/Y%Š  ęŽ" Š*I/Y%Š  ęŽ" ŠGross€domestic€investment€share€in€GDPŠ  ęŽ" ŠBOPŠ  ęŽ" ŠPWTŠ  ęŽ" Š16.35€€(9.06)Š  ęŽ" Š*NetG/Y€%Š  ’§$ Š*NetG/Y€%Š  ’§$ ŠGovernment€spending,€netted€of€education€andĻdefense,€share€in€GDPŠ  „,% ŠAvgŠ  ’§$ ŠPWT,ĻBLŠ  „,% Š€7.63€€(4.37)Š  ’§$ Š€Dfns/Y€%Š  E' Š€Dfns/Y€%Š  E' ŠGovernment€defense€spending€share€in€GDPŠ  E' ŠAvgŠ  E' ŠBLŠ  E' Š€3.26€€(3.45)Š  E' Š*TT€chgŠ  ¶^) Š*TT€chgŠ  ¶^) ŠPeriod€change€in€terms€of€trade,€weighted€by€BOPĻ(X+M)/GDPŠ  ;ć* ŠChgŠ  ¶^) ŠWB,ĻPWTŠ  ;ć* Š„4.17€(14.80)Š  ¶^) Š*ln(BMP)Š  Tü, Š€ln(BMP)Š  Tü, Šln(Black€market€premium€on€foreign€exchange)Ģ€€Note:€1€=€no€BMP.Š  ف- ŠAvgŠ  Tü, ŠBLŠ  Tü, Š€0.22€€(0.37)Š  Tü, Š*TotDisasŠ  ņš/ Š*TotDisasŠ  ņš/ Š%€of€population€affected€by€civil€strife,Ļdroughts,€earthquakes,€hurricanes,€floods€andĻstorms,€and€other€natural€disastersŠ  ü¤1 ŠAvgŠ  ņš/ ŠAIDŠ  ņš/ Š€1.16€€(3.69)Š  ņš/ Š€GER€PrimŠ  ½3 Š*GER€PrimŠ  ½3 ŠGross€enrollment€ratio€at€primary€levelŠ  ½3 ŠBOPŠ  ½3 ŠUNŠ  ½3 Š82.95€(29.47)Š  ½3 Š*GER€SecŠ  . Ö5 Š€GER€SecŠ  . Ö5 ŠGross€enrollment€ratio€at€secondary€levelŠ  . Ö5 ŠBOPŠ  . Ö5 ŠUNŠ  . Ö5 Š35.21€(28.62)Š  . Ö5 Š*ln(e0)Š  G!ļ7 Š*ln(e0)Š  G!ļ7 Šln(Life€expectation€at€birth)Š  G!ļ7 ŠBOPŠ  G!ļ7 ŠWBŠ  G!ļ7 Š€4.04€€(0.21)Š  G!ļ7 Š€ln(%Urb)Š  `" 9 Š*ln(%Urb)Š  `" 9 Šln(Urbanization)Š  `" 9 ŠBOPŠ  `" 9 ŠWBŠ  `" 9 Š€3.52€€(0.79)Š  `" 9 Š*DnsŠ  y#!!; Š€DnsŠ  y#!!; ŠDensity:€population/1000€per€sq€kmŠ  y#!!; ŠBOPŠ  y#!!; ŠWBŠ  y#!!; Š€0.16€€(0.57)Š €R y#!!; Š*ln(N)Š )€R’$:"=R )Š*ln(N)Š )€R’$:"=R )Šln(Population€/€1000)Š )€R’$:"=R )ŠBOPŠ )€R’$:"=R )ŠWBŠ )€R’$:"=R )Š€9.27€€(1.26)Š &’$:"=R ……&ŠPdą0 @ ąą0˜@j$@j$ąą @ ąAvg€denotes€period€average€of€annual€observations;€€Gr€denotes€continuous,€percentage€growthŠ «%S#? Šrate;€€Chg€denotes€change€over€period;€€BOP€denotes€beginning„of„period€value.Š &0&Ų#@˜j$˜j$ ……&ŠSrceą0 @ ąą0˜@j$@j$ąą @ ąPWT:€Summers,€Robert€and€Alan€Heston.€1995.€"Data€Update€5.6a,"€computer€diskette€based€on€"TheŠ I'ń$B ŠPenn€World€Tables€(Mark€5):€An€Expanded€Set€of€International€Comparison,€1950„1988."Š ˜j$˜j$ Šą0 @ ąą0˜@j$@j$ąą @ ąWB:€€World€Bank.€1994.€"World€Data€1994:€World€Bank€Indicators€on€CD„ROM."€Š ˜j$˜j$ Šą0 @ ąą0˜@j$@j$ąą @ ąBL:€€Barro,€Robert€and€Jong„Wha€Lee.€1993.€"Losers€and€Winners€in€Economic€Growth."€NBER€WorkingĻPaper€4341.€Cambridge,€MA:€NBER.€€Data€downloaded€from€http://nber.harvard.edu.Š ˜j$˜j$ Šą0 @ ąą0˜@j$@j$ąą @ ąUN:€€UNESCO.€Various€years.€ņņStatistical€Yearbookóó.€Paris:€United€Nations€Educational,€ScientificĻand€Cultural€Organization.Š ˜j$˜j$ Š€€€€€€AID:€€USAID,€Office€of€Disaster€Assistance.€€July€1989.€€"Disaster€History."€€Report€by€Labat„€€€€€Ļ€€€€€€€€€€€€€€€Anderson,€Inc.€22201.ĢQuinquennial€values€are€actually€three„year€averages,€centered€on€the€quinquennial€year.€€Consequently,Ļannual€series€were€constructed,€when€possible,€for€each€variable.€€Missing€values€were€filled€using€theĻrate€of€change€found€in€an€alternative€source.€€For€example,€PWT€values€were€extrapolated€to€1991€usingĻrates€of€change€from€WB.€€In€order€of€priority,€filling€series€were€WB€(including€a€1993€data€set€usedĻinternally),€PWT,€and€UN.Š .²+O   ŠŌ€bXģŪXĐbIœŌŅd„ŅŅdŠŅŠ  æ.g,Q Šą@Š\ģąTable€A.2ˆĢĢą@pHģąMason€Model:€Analysis€of€Instruments;€OLS€ResultsˆĢĢŌ€_X1שXbXģŪŌŌ€_¤1ש{©_X1×Ō€€€€€€€€€|€ņņ€€€€€€€Analysis€of€Instruments€€€€€€€óó€|€ņņ€€€€€€€€€€€€€€€€€€OLS€Results€€€€€€€€€€€€€€€€€€óóŠ x  Š€€€€€€€€€|€ņņ€€€€€1st€Stg€€€€€ó󀀀ņņ2nd€Stgó󀀀ņņOver€IDóó€|€ņņ€€€€€€€Cross„Sections€€€€€€ó󀀀ņņ€€€Panel€Data€€€€óóĢ€€€€€€€€€|€ņņ€€Ygr€€ó󀀀ņņ€D1*Ygró󀀀ņņ€Savingó󀀀ņņ2SLSResóó€|€ņņ1960„70ó󀀀ņņ1970„80ó󀀀ņņ1980„90ó󀀀ņņ€Pooledó󀀀ņņ€€FEM€€óóĢ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ĢYgr€€€€€€|€€€€€€€€€€€€€€€€€€€€€€0.40**€€€€€€€€€€€|€-0.07€€€€€€0.01€€€€€€0.07**€€€€0.02€€€€€€0.03*Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€(9.34)€€€€€€€€€€€€|€(0.95)€€€€(0.24)€€€€(2.41)€€€€(0.86)€€€€(2.11)Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€Ģln(D1)Yg€|€€€€€€€€€€€€€€€€€€€€€-0.09**€€€€€€€€€€€|€€0.02€€€€€€0.00€€€€€-0.02*€€€€€0.00€€€€€-0.01*Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€(8.73)€€€€€€€€€€€€|€(1.17)€€€€(0.03)€€€€(2.19)€€€€(0.42)€€€€(1.79)Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€Ģln(D1)€€€|€€€€€€€€€€€€€€€€€€€€€€0.00€€€€€€€€€€€€€|€-0.31**€€€-0.21**€€€-0.16**€€€-0.20**€€€-0.07*Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€(0.01)€€€€€€€€€€€€|€(3.49)€€€€(4.81)€€€€(6.99)€€€€(8.50)€€€€(2.23)Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģln(Y/N)€€|€-1.81**€€€-8.39**€€€€€€€€€€€€€€0.02€€€|Ģ€€€€€€€€€|€(7.16)€€€€(7.62)€€€€€€€€€€€€€€(1.20)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢNAgLgr€€€|€€0.28**€€€€1.21**€€€€€€€€€€€€€€0.00€€€|Ģ€€€€€€€€€|€(3.53)€€€€(3.48)€€€€€€€€€€€€€€(0.80)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢI/Y%€BOP€|€€0.09**€€€€0.37**€€€€€€€€€€€€€€0.00€€€|Ģ€€€€€€€€€|€(5.16)€€€€(4.61)€€€€€€€€€€€€€€(0.82)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢNetG/Y€%€|€-0.10**€€€-0.41**€€€€€€€€€€€€€€0.00€€€|Ģ€€€€€€€€€|€(3.74)€€€€(3.74)€€€€€€€€€€€€€€(0.01)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢTT€chg€€€|€€0.01€€€€€€0.06€€€€€€€€€€€€€€€€0.00€€€|Ģ€€€€€€€€€|€(1.92)€€€€(1.89)€€€€€€€€€€€€€€(1.64)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢTotDisas€|€-0.11**€€€-0.49**€€€€€€€€€€€€€€0.00€€€|Ģ€€€€€€€€€|€(3.65)€€€€(3.77)€€€€€€€€€€€€€€(1.22)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢGER€Prim€|€-0.02*€€€€-0.06*€€€€€€€€€€€€€€€0.00€€€|Ģ€€€€€€€€€|€(2.26)€€€€(2.05)€€€€€€€€€€€€€€(0.21)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģln(e0)€€€|€€6.38**€€€25.11**€€€€€€€€€€€€€-0.10€€€|Ģ€€€€€€€€€|€(4.70)€€€€(4.24)€€€€€€€€€€€€€€(1.28)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģln(%Urb)€|€€0.59*€€€€€2.84*€€€€€€€€€€€€€€-0.01€€€|Ģ€€€€€€€€€|€(2.36)€€€€(2.58)€€€€€€€€€€€€€€(0.43)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|Ģln(N)€€€€|€€0.20*€€€€€0.76*€€€€€€€€€€€€€€€0.00€€€|Ģ€€€€€€€€€|€(2.31)€€€€(2.02)€€€€€€€€€€€€€€(0.01)€€|Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|ĢConstant€|-22.94**€€-89.23**€€€-4.55**€€€€0.40€€€|€-3.22**€€€-3.59**€€€-3.84**€€€-3.67**€€€-3.95**Ģ€€€€€€€€€|€(4.50)€€€€(4.01)€€€(38.64)€€€€(1.35)€€|€(8.52)€€€(19.07)€€€(39.55)€€€(36.98)€€€(28.17)Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ĢR€Squared|€€0.33€€€€€€0.33€€€€€€0.35€€€€€€0.02€€€|€€0.27€€€€€€0.33€€€€€€0.57€€€€€€0.37€€€€€€0.84ĢAdj€R-Sq.|€€0.31€€€€€€0.31€€€€€€0.34€€€€€-0.01€€€|€€0.25€€€€€€0.32€€€€€€0.56€€€€€€0.36€€€€€€0.81Ģ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ĢStd€Error|€€2.35€€€€€10.26€€€€€€0.14€€€€€€0.14€€€|€€0.13€€€€€€0.11€€€€€€0.08€€€€€€0.11€€€€€€0.06Ģ#€of€Obs€|€€€528€€€€€€€528€€€€€€€528€€€€€€€528€€€|€€€176€€€€€€€176€€€€€€€176€€€€€€€528€€€€€€€528ĢĢp-values€from€Tests€of€Joint€SignificanceĢInstrmnts|€0.000**€€€0.000**€€€€€€€€€€€€€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ĢYgr€Terms|€€€€€€€€€€€€€€€€€€€€€0.000**€€€€€€€€€€€|€0.000**€€€0.004**€€€0.003**€€€0.000**€€€0.000**ĢD1€Terms€|€€€€€€€€€€€€€€€€€€€€€0.000**€€€€€€€€€€€|€0.000**€€€0.000**€€€0.000**€€€0.000**€€€0.001**ĢĢChi„Squared€Statistic€from€Davidson„MacKinnon€Overidentification€TestĢ€€€€€€€€€|€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€9.26€€€|ĢĢņņ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€óóĢNotes:€€The€dependent€variables€for€the€1st€Stg€regressions€are€Ygr€and€ln(D1)*Ygr;€for€the€Over€IDĻtest,€2nd€Stg€residuals;€for€all€other€columns,€the€saving€measure€described€in€the€text.€€*€and€**Ļdenote€significant€coefficients€at€5%€and€1%€levels;€t„values€are€in€parentheses.ĢŠ  ų* (D ŠŃ°XŃѰXŃŌ€¤Iœ¤{©_¤1×ŌŌ€XģŪX]¤¤IœŌ€€€€€€€€€€ņņAppendix€B:€€The€Life„Cycle€FormulationóóŠ ° ŠĢą ¼ ąMason€(1987)€formulates€a€model€in€which€aggregateĻeconomic€growth€enhances€household€savings€by€shifting€the€ageĻdistribution€of€households€into€the€younger,€higher„income,Ļhigher„savings€cohorts€(population€growth)€and/or€byĻdisproportionately€shifting€lifetime€income€to€these€cohortsĻ(growth€in€per„capita€income).€€The€magnitude€of€the€growthĻeffect€is€influenced€by€the€extent€to€which€consumption€lagsĻearnings.€€That€is,€where€Aņņyóó€represents€the€average€age€ofŠ ø   Šearning€and€Aņņcóó€the€average€age€of€consuming,€the€more€negativeŠ € Š  Šis€(Aņņyó󀄀Aņņcóó)€the€larger€will€be€the€positive€impact€of€incomeŠ H ˜  Šgrowth€on€the€savings€rate.€€The€empirical€model€is€couched€inĻterms€of€the€consumption€rate,€c€(=€1€„€savings€rate).€€TheĻbasic€equation€is:ĢĢą ¼ ąln(c)€=€aņņ0óó€+€(Aņņyó󀄀Aņņcóó)€Yņņgróó;Š 0€  ŠĢwhere€Yņņgróó€is€the€growth€rate€of€aggregate€income.Š Ą ŠĢą ¼ ąAņņcóó,€in€turn,€is€a€budget„share„weighted€mean€of€theŠ P  Šaverage€activity€ages,€Aņņ1óó€(child„rearing)€and€Aņņ2óó€(all€otherŠ h Šactivities).€€Under€appropriate€assumptions€regarding€theĻutility€function,€the€budget€shares€are€uniquely€determined€byĻthe€quantity€of€child„rearing€relative€to€other€activities.€ĻMason€specifies€this€relative€quantity€as€the€youth€dependencyĻratio,€defined€as:€ĢĢą ¼ ąD1€=€population€ages€0„14/population€ages€15+.ĢĢThe€empirical€representation€for€child„rearing's€budget€share,Ļchņņ1óó,€is:Š č8 ŠĢą ¼ ąchņņ1óó€=€aņņ1óó€+€bņņ1óó€ln(D1).Š xČ! ŠĢą ¼ ąAfter€substitution,€the€estimation€equation€is:ĢĢą ¼ ąln(c)€€=€€aņņ0óó€€+€€[aņņ1óó€+€bņņ1óó€ln(D1)]€(Aņņ1ó󀄀Aņņ2óó)€Yņņgróó€€+€€bņņ2óó€Yņņgróó.Š ˜!č% ŠĢThe€coefficients€of€this€model€are€most€easily€interpreted€inĻthe€context€of€Mason's€own€parameter€estimates,€all€of€whichĻare€statistically€significant.ĢŅHdŅĢą ¼ ąln(c)€=€„.168€+€[.434€+€.215€ln(D1)]€(Aņņ1ó󀄀Aņņ2óó)€Yņņgró󀄀4.32€Yņņgróó.Š H&˜!+ ŠŅ°HŅĢaņņ0óó€contains€two€components,€one€of€which€is€approximationŠ Ų'(#- Šerror.€€If€approximation€error€is€negligible,€then€aņņ0óóŠ  (š#. Šrepresents€the€natural€log€of€the€average€household's€lifetimeĻconsumption€ratio.€€Here,€ln(.845)€=€„.168,€implying€a€lifetimeĻsavings€rate€of€15.5%.€€bņņ1óó€will€be€positive€when€the€demand€forŠ ų*H&1 Šchildren€is€price€elastic€or€when€an€adult„equivalencyĻframework€holds.€€Since€bņņ1óó€is€0.215,€one€of€these€two€casesŠ ˆ,Ų'3 Šprevails.€€aņņ1óó€is€an€estimate€of€the€maximum€budget€shareŠ ° Šdevoted€to€childrearing€(occurring€when€D1€is€unity).€€In€thisĻcase,€that€maximum€share€is€43.4%.€€Finally,€bņņ2óó€provides€anŠ @ Šestimate€of€(Aņņyó󀄀Aņņ2óó).€€Here,€the€lag€between€earning€income€andŠ X Šconsuming€non„child„rearing€activities€is€estimated€to€be€4.32Ļyears.ĢĢą ¼ ąEstimation€of€the€Mason€model€is€complicated€by€the€termĢ(Aņņ1ó󀄀Aņņ2óó).€€After€some€simplifying€assumptions,€Mason'sŠ š @ Šestimation€of€Aņņ1óó€uses€data€on€the€Total€Fertility€Rate€(TFR),Š ø   Šthe€mean€age€at€childbearing,€and€secondary€and€tertiaryĻenrollment€ratios.€€Aņņ2óó€uses€data€on€the€life€expectancy€at€ageŠ H ˜  Š20,€and€the€assumed€mean€age€of€household€formation.€€While€theĻTFR€is€available€over€many€years€for€a€broad€set€of€countries,Ļthe€latter€four€variables€are€not.€€If€one€were€to€impose€theĻconstraint€that€(Aņņ1ó󀄀Aņņ2óó)€were€constant€across€countries€andŠ hø  Štime,€then€Mason's€model€reduces€to:ĢĢą ¼ ąln(c)€€=€€aņņ0óó€+€bņņ1óóņņ*óó€ln(D1)Yņņgróó€+€(aņņ1óóņņ*óó€+€bņņ2óó)€Yņņgróó;Š Ą ŠĢwhere€aņņ1óóņņ*óó€and€bņņ1óóņņ*óó€represent€the€original€coefficients€multipliedŠ P  Šby€the€mean€(Aņņ1ó󀄀Aņņ2óó)€and€where€the€influence€of€variation€inŠ h Š(Aņņ1ó󀄀Aņņ2óó)€is€assumed€into€the€error€term.€€Š ą0 ŠŠ  Øų Šņņą@R\FąREFERENCESˆŠ ° 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