International factor mobility and long-run economic growth UNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics. By Mark Roberts.

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1 UNIVSITY OF NOTTINGHAM Dicion Paper in conomic Dicion Paper No. 09/07 Inernaional facor mobiliy and long-rn economic groh By Mark ober Jne DP 09/07

2 Inernaional facor mobiliy and long-rn economic groh Mark A. ober Univeriy of Noingham Jne 009 Key ord: precaionary aving, aggregaion effec, inernaional capial mobiliy, inernaional labor mobiliy, labor pply, economic groh Preliminary Abrac Long-rn economic groh i analyed in a global model ih many mall conrie prone o naional level oal facor prodciviy hock. The poibiliy of precaionary aving or diaving i a fncion of he higher-order momen and he cro-momen of he facor income diribion, hich in rn depend on he global regime governing facor mobiliy. Inernaional capial mobiliy generae precaionary aving by eliminaing inere ncerainy and by increaing earning ncerainy, hile inernaional labor mobiliy redce aving by achieving he oppoie. If firm operae nder a learning-by-doing invemen eernaliy, hee effec hen ranlae ino long-rn groh ocome. Hoever, beide hee ncerainy effec on aving, here are alo effec from aggregaion, facor price deerminaion and labor pply, hich ogeher ho ha inernaional capial mobiliy nambigoly promoe economic groh above he aarky level b ha he groh coneqence of inernaional labor mobiliy are le clear c hogh conflicing effec. I old like o hank Mike Bleaney for helpfl commen and feedback. Addre for correpondence: School of conomic, Univeriy of Noingham, Univeriy Park, Noingham, NG7 D. UK. Fa: mail: mark.rober@noingham.ac.k

3 . Inrodcion There i a large and ell eablihed body of lierare bil on he iniial inigh of omer 986, 990 and of Lca 988 ha he feare of non-decreaing ocial rern o capial cae hoehold aving o be a key deerminan of long-rn economic groh. A greaer par of hi ork ha ilied he common ampion ha hoehold ave only in order o mooh conmpion over he life-cycle in an environmen of cerainy. Hoever, parallel reearch ino he analyi of individal behavior ha conclded ha a coniderable par of hoehold aving - poibly a mch a 60% - i made for precaionary prpoe a a ay of dealing ih ncerainy. See, for eample, he paper by Skinner 988, Cabellero 990, Dardanoni 99, Hbbard, Skinner and Zelde 994, Carroll and Samick 998. In repone o hi, a nmber of paper have been developed o inveigae he macroeconomic implicaion of ncerainy and ih pariclar reference o he ie of long-rn groh. odrige 999 incorporaed idioyncraic ncerainy ino a macroeconomic model and replicaed he finding of prononced effec, hile oher, Devere and Gregor Smih 994, Obfeld 994,. Todd Smih 996, Ghoh and Ory 997, ankin 998 and Hek 999, have conidered macroeconomic orce of ncerainy. Thi preen paper i cloe in inenion o he paper by Devere and Smih and by Obfeld in aemping o deermine economic groh ihin an open economy by conidering he effec of inernaional facor mobiliy on macroeconomic ncerainy. In applicaion, hoever, i differ in five main area. Fir, i make an eplici conideraion of he early inigh of Sandmo 970 ha ncerainy ha an ambigo effec on aving, depending on heher i perain o earning income or o inere income. 45 I i eablihed ha a poiive hird While hee have ncovered ome inereing comparaive aic implicaion, qanifying he poible effec of pre macroeconomic rik on hoehold aving ha prodced diappoining rel. 4 The paper e he cene by qoing o conradicory aemen from Bolding 966 and Marhall 90 relaing, repecively, o earning and inere ncerainy. 5 The conervailing effec of hee o kind of ncerainy may help o eplain hy reearcher have been nable o find a conien ign for he correlaion beeen volailiy and groh.

4 derivaive for he iliy fncion i neceary and fficien for earning ncerainy o generae precaionary aving. There i alo a general aarene ha he effec of inere ncerainy can cae aving o repond in eiher direcion. A poiive hird derivaive i hen neceary b no fficien. Thee o poin are reieraed in Appendi A, hich ha been inclded in order o make o addiional b poibly leer knon poin. Thee are, fir, ha he mean vale of earning income i alo imporan for deermining he ign of he effec of inere income ncerainy on aving and, econdly, ha he ign and he magnide of covariance beeen earning and inere i alo relevan o he overall effec on aving. Secondly, he main moivaion of hi paper i he idea ha he inernaional facor mobiliy regime i crcial o he balance beeen hee o differen kind of ncerainy, ih implicaion for economic groh. Inernaional capial mobiliy i modelled a a regime ha eliminae inere ncerainy a he epene of increaing he ncerainy of earning hrogh he obvere effec of nleahing inernaional capial flo. On he oher hand, inernaional labor mobiliy, hich i given an analogo reamen, aler he paern of facor price volailiy and coneqenly revere he rel for precaionary aving. Th, he paper eend he grond covered by Devere and Smih 994 and of Obfeld 994 by conidering he implicaion for economic groh of he inernaional inegraion of labor marke a ell a capial marke. A hird deparre from hee o paper i he conideraion of an overlapping-generaion frameork ih finie live, hich allo he model o incorporae he inergeneraional rediribion effec preclded by repreenaiveagen, infinie-horion model. Forhly, or ampion ha he learning-by-doing echnology i global raher han naional - or, in oher ord, ha knoledge i perfecly inernaionally mobile i a orce of inernaional linkage even here he facor of prodcion are compleely immobile inernaionally. Thi ha o imporan implicaion. One i ha i open he door o he propery of convergence: in epecaion conrie ill converge o he ame long-rn groh rae ha i driven by he groh of freely dieminaed knoledge. The econd i ha ih conan rern o capial overall naional age and aving are concave in boh on and global capial, hich mean ha

5 inernaional facor marke inegraion, heher relaing o capial or o labor, cae favorable aggregaion effec. Fifhly, in he la par of he analyi, e conider endogeno labor pply in erm of he variaion in hor pplied or he lengh of he period orked by he older generaion of he orking poplaion. Variable labor pply may inerac ih overall aving hrogh a variey of channel, affecing life-cycle aving by alering he mean vale of he facor price diribion and affecing precaionary aving by alering he higher-order momen and cro-momen of hee diribion. The ie are heher e po labor pply adjmen ameliorae he problem of ncerainy and he implicaion for he facor mobiliy regime. Throgho he analyi ncerainy derive from he npredicabiliy of oal facor prodciviy TFP. The fir main rel i ha nder aarky - in conjncion ih he ampion ha hoehold iliie are logarihmic fncion of conmpion - volailiy ha no effec on aving, ince i he poiive effec of earning ncerainy, ii he negaive effec of inere ncerainy and ii he negaive impac of he poiive covariance beeen hee o eacly cancel o. Alhogh aving remain a he cerainy-eqivalen level, here i a negaive aggregaion effec, ince he age and, hence, aving are concave fncion of he conry-level hock. Th, TFP volailiy redce he long-rn of global economic groh nder aarky iho affecing aving. Trning from aarky o perfec capial mobiliy, defined here he hole orld can borro and ave a a ingle inere rae, e find ha volailiy nambigoly raie groh above he aarky level. Thi i becae of an increae in precaionary aving a ell a he eliminaion of he advere aggregaion effec. The la of large nmber implie ha conry-pecific hock aggregae o ero, o removing inere ncerainy. The obvere of he nleahing of inernaional capial movemen in repone o ochaic conry difference in TFP raie earning ncerainy, caing a greaer rie in precaionary aving. In addiion, ince inernaional capial mobiliy bring abo a linear dependence of naional capial on global capial, he advere aggregaion effec nder aarky i lo. 4

6 A nmerical evalaion of hee nambigo qaliaive gain ha led o o conclion. Fir, a fairly heroic ampion abo he ie of he hock variance - alhogh alongide a poibly lo vale of niy for he ineremporal elaiciy of biion in conmpion - generae a mode gain in groh. Secondly, and more pecific o hi pariclar model, e find ha he aving effec are of a comparable magnide o he aggregaion effec. Baed on he ampion of a binomial hock diribion, here he o realiaion old imply a difference in he annal groh rae of %, e find ha he effec of moving from aarky o PCM old be raie he global average groh rae from.80% o.6%. Of hi 0.6% gain, 0.6% can be aribed o a rie in precaionary aving increae and he remaining 0.0% o an aggregaion effec. Folloing hi analyi, perfec labor mobiliy PLM i modelled in an analogo ay here an implici migraion arbirage aay any poenial difference in conrylevel age, here capial, inead, i deemed o be immobile. The coneqence of PLM i an increaed volailiy in inere rae, a hee no bear he fll brn of he hock. A may be dedced, iching from aarky o PLM enail a fall in precaionary aving, becae of he removal of earning ncerainy and becae of he amplificaion of inere ncerainy. Hoever, hi negaive effec on groh i offe by a poiive aggregaion, fond o be of a comparable magnide, effec vi-avi aarky, ince a common orld age alo implie ha aving and invemen level are he ame in all conrie. A priori, he ign of he combined effec canno be deermined, b he choen parameer vale gge ha PLM i conien ih an annal groh rae of.66% compared ih he aarkic eqivalen of.80%. In he final par of he analyi, ome alloance i made for an endogeno labor pply inofar a he old chooe he nmber of hor hey pply or he iming of heir reiremen. The qaliaive rel are inereing, alhogh he nmerical rel, baed on an argably lo elaiciy of labor pply, are ndramaic: here i an increae in he annal groh rae by abo 0.04% for each of he o facor mobiliy regime. The model i pecified ch ha labor pply repond poiively o change in he age, b negaively o a rie in inere income. Coneqenly, an endogeno labor pply i conien ih an increaed variance of earned income and inrodce a negaive covariance beeen earned and nearned income. 5

7 The re of he paper i organied a follo Secion preen a general frameork ha i fndamenal o he hole analyi. Profi-maimiing firm are inrodced along ih epeced-iliy-maimiing hoehold ha generally face boh earning and inere ncerainy. Secion, 4 and 5 eparaely conider each of he regime of aarky, PCM and PLM. Secion 6 hen re-evalae each of hee hree in he ligh of an endogeno labor pply. Secion 7 finally provide a brief mmary of he hole analyi and ome frher dicion.. The baic model The model i an open-economy verion of he Diamond 965 overlapping generaion model. I coni of many mall conrie, here each, indeed, alo conain many mall, idenical firm. ach firm prodce he ingle orld good nder condiion of perfec compeiion, according o he folloing echnology, y A B k, B A k A 0 for, 0 <, < and pr pr, o 0 Op in a repreenaive firm in cony i labor and capial inp. The erm depend on a prodciviy hock, and, a vale common o all conrie. y, here and k are i B repreen oal facor prodciviy, hich A, hich ha a mean and andard deviaion, A There are conan rern o cale ih repec o he firm on facor, o ha he prodcion fncion may be preened per capia in erm of i on yong orker. ven o, e ame here are o generaion a ork, he yong and he old, ho are eqally prodcive and alo eqally nmero in he amed abence of poplaion groh and preence of fll employmen. Wih repec o prodcion, hey differ o he een ha he yong pply an inelaic ni of labor, hile he old pply a 6

8 fracion,, 0 < <. Thi fracion i iniially regarded a a parameer b i laer deermined endogenoly. iher ay, i may be regarded a indicaive of par- ime b conined orking by he old, or ele he relaed erm may be inerpreed a he proporion of he adl life pen in reiremen. The oal labor pply for he repreenaive firm in conry, and alo for each conry, nder he ampion of a ni meare of firm, i. In addiion o hi labor inp, prodcion reqire capial, k, and here i alo a oal facor prodciviy TFP parameer, B, hich ranform he ervice of he o facor inp ino an op, y. TFP i deermined boh by a conry-pecific prodciviy hock, A, and a knoledge of he prodcion echnology, hich i acqired hrogh a proce of learning-by-doing, folloing Arro 96, hich i hen freely dieminaed o he re of he economy. The knoledge pill-over i amed o be global raher han naional in een, o ha an inernaional meare of he capial ock, he global average, k k, i pecified a he relevan variable for embodying echnology. Thi amon o he ampion ha knoledge i alay perfecly, inernaionally mobile, heher or no he facor of prodcion are. I alo enre ha, in epecaion, conrie converge o he ame long-rn groh rae irrepecive of facor mobiliy. Anoher implicaion of global knoledge - in conjncion ih he groh-generaing ampion of conan-rern-o-cale in overall capial - i ha conry-pecific, echnology hock are a orce of aggregaion effec a ill give rie o global aggregaion effec a ell a ncerainy. The orce of ncerainy are conry-pecific, ochaic hock o TFP,. Thee are independenly and idenically diribed. The ampion of a ymmeric and binomial hock diribion i made o obain analyic a be, linear and, a or, qadraic olion for he aving fncion in he preence of ncerainy. The feare of very, many mall conrie allo o appeal hrogho he analyi o he la of large nmber; and e may begin here by aing ha here i an abence of 7

9 global ncerainy, becae conry-level hock m o ero ih he eience of very, many mall conrie. A noed, each firm in each conry prodce he ingle, orld good nder he condiion of perfec compeiion, o ha profi are ero. Marginal co-prodc eqaliaion hen lead o he folloing invere facor demand for he firm, Ak k, Ak k The marginal co of invemen comprie boh he inere rae and he depreciaion rae. Since he laer i 00%, according o he al ampion for a half-life period, he marginal co i in effec he inere facor,. The inere facor and he age are each poenially ochaic hrogh heir common dependence on he TFP hock,, alhogh heir acal properie ill be hon o depend on he facor mobiliy regime in place. Hoehold live, ork and conme for o period b ave only in he fir. Saving i nderaken no only o mooh conmpion, b alo a a poible repone o facor income ncerainy. Saving i decided afer he fir-period age ha been deermined, o ha i repond o he fir-period TFP hock realiaion in addiion o being formlaed in anicipaion of he econd-period TFP hock diribion. 6 Second-period ncerainy implie he folloing epecaional form for he hoehold iliy fncion, U β ln ln Thi logarihmic pecificaion, alhogh andard, in he preen cone enable o obain boh racable olion o he model and an inereing benchmark cae. The ampion of a o-period iliy fncion and of binomial and ymmeric hock prodce he folloing implified fir-order condiion for he hoehold maimiaion in he preence of ncerainy, 6 An alernaive o hi ampion i conidered in Appendi A. 8

10 β here he o ocome for he hock are indeed and. 0, 4 I i orh noing ha he logarihmic iliy fncion render epecaion of he raio of fre facor price,, o be of relevance raher han eparae epecaion of each of hee o variable. Thi mean ha nder aarky, here each conry facor price are joinly and mliplicaively dependen on he ame level of TFP, he facor price raio i naffeced by he hock, and, hence, aving i deermined a he cerainy-eqivalen level. Thi pariclar cae, here boh facor of prodcion, capial and labor, are compleely immobile a he global level, i he fir o be conidered. Folloing hi, aarky ill be compared ih perfec capial mobiliy here labor i deemed o be immobile and hen ih ha perfec labor mobiliy alo in he abence of capial mobiliy. Finally, he analyi ill make an alloance for an endogeno econdperiod labor pply nder each of he hree facor mobiliy regime.. Aarky Under aarky, eqaion and ffice a he olion for each conry inere facor and age. The o main characeriic of aarky, are, peraining fir o he capial marke, ha each conry,, capial ock i deermined by i on aving, k, 5 and ha, ih reference o boh facor marke, a menioned, hock o TFP, - or merely he level of TFP, B k. - have no impac on relaive facor price, 9

11 The fre capial ock i deermined by crren aving according o eqaion 5, and a hi i knon 7, o oo i he fre relaive facor price. Th, ih a logarihmic iliy fncion, aving i naffeced by he anicipaion of ncerainy, and i olved a β AUT 6 β el One: Saving nder aarky i a he cerainy-eqivalen level, if he orce of ncerainy i hock o oal facor prodciviy and if he iliy fncion are logarihmic. The rel ha ncerainy ha no effec on aving nder aarky may be eplained in erm of i implicaion for he age and inere facor diribion, he deail of hich are given in Appendi A. Fir, he independen variance of fre age income i a orce of precaionary aving, ince he logarihmic iliy fncion ha a poiive hird derivaive, he neceary and fficien condiion. Secondly, a niary elaiciy of ineremporal biion in conjncion ih a poiive mean vale for fre earning implie ha he anicipaed variance of inere income redce aving. Thirdly, he poiive covariance beeen age income and inere income nder aarky, caed by TFP hock nder aarky, redce aving frher. Thee la o negaive effec happen o eacly cancel he fir poiive effec, o ha aving i naffeced by ncerainy, h remaining a he life-cycle level. Combining eqaion,, 5 and 6 give capial accmlaion in conry a k AUT Ω k k β A Ω, μ 7 β μ The compoie parameer Ω i he groh facor ha old emerge in he abence of TFP volailiy, 0 k k,.,, ince hi, ih he ymmery ampion, alo implie 7 We are orking ihin he al raional epecaion paradigm of parameer cerainy hereby individal kno he aggregae ocome of heir deciion. 0

12 Noe ha he ime-erie, j k, j,,..., here j, j,,... old generally coni of poiive and negaive vale, prodce a negaive correlaion beeen volailiy and conry-level groh. Thi rel provide a poible a raionale for he empirical finding of a negaive correlaion beeen groh and volailiy in he paper by amey and amey 995 and by Kneller and Yong 00, even hogh hi relae o he cro-ecional daa. 8 Wha migh eem o preen a prima facie cae for abiliaion policy merely reflec he fac ha an irredcible ochaic erm,, i being raied o he poer of 0 < <, in he eqaion for k. 9, here qaion 7 may alo be aggregaed paially o obain a olion for global economic groh. Thi admi an addiional concaviy, ince he implici eqaion for k conain k raied o he poer of, here 0 < <. In obaining a olion, e ee ha nder aarky k i predeermined by he previo level of on-conry aving,, o ha i i necearily ncorrelaed ih he crren hock groh may hen be approimaed by G AUT k k Ω var. Global ln β A Ω, μ 8 β μ [The deail are given in Appendi B.] I i eviden ha TFP volailiy, > 0, redce global economic groh belo he volailiy-free facor Ω, enirely becae of aggregaion effec. Hoever, for a banial magnide of hee hock, he effec on aggregae groh in eqaion 8 i qie mall. 8 Thi hold even hogh here he hock variance i amed o be common o all conrie. 9 An alernaive poibiliy i inveigaed by Blackbrn and Pelloni 005.

13 If, for eample, 0. 5 and 0., according o eqaion, he difference beeen a poiive hock 0. 5 and a negaive hock 0. 5 i % groh per annm over a deignaed eny-five year period. Thi level of volailiy old redce he global average annalied groh rae by abo one-fifh of a percenage poin. 0 We no conider he regime of perfec capial mobiliy. 4. Perfec capial mobiliy PCM I i raighforard o model inernaional capial mobiliy in i abole or perfec PCM form a he cae here all hoehold ave and here all firm borro a a ingle, orld inere rae,,. The propery of conan ocial rern o capial and he ampion ha echnology i inernaional raher han naional, repecively, imply ha he relevan inere rae i pinned don a a parameer and ha hi parameer i a compoie of inernaional parameer. Invering eqaion give an epreion for each conry invemen demand a a fncion of hi ingle inere facor,, Ak k Aggregaion acro all conrie hen give, cov, Ak k k Combining hee o eqaion give k k cov, ach conry capial ock relaive o he global average relae poiively o i marginal prodciviy vi a vi he re of he orld. Moreover, no only are capialrich conrie hoe bjec o favorable TFP hock, b each conry capial ock i a linear fncion of hi hock, hich ha implicaion for aggregaion. 5 0 The fir calclaion i % hich prodce 0.04%, derive from he fac ha var ln 0. 0 cov. a 0. and he econd,

14 Ne eliminaing he common facor, k, in he aggregaed form above and hen reinvering he eqaion give he olion for he orld inere facor nder PCM, cov A PCM 9 While he global demand for capial i indeerminae, i qaniy i pplydeermined by aggregaed orld aving. From he compeiive-marke, ero profi condiion, he age for each conry i hen deermined a PCM cov A k, 0 The obvere of a ingle orld inere rae nder PCM i ha inernaional capial movemen amplify he effec on age of TFP hock. More preciely, he elaiciy of he age ih repec o he hock, ln ln eqaion for aarky b niy in eqaion 0 for PCM., i in Iniially, e fi labor pply and a a level common o all conrie, o ha eqaion 9 and 0 are rerien a,, PCM A PCM A k We may dra he folloing conclion. el To: The effec of PCM i o a redce he variance of he inere facor o ero, b raie he variance of he age, c raie he global average of he age and d lead o no change in he global average of he diconed fre age ih an ambigo effec on he global average of he inere facor. See Appendi C for he deail and proof. While par a merely conie or definiion of PCM and par b reflec a general implicaion of i, he remaining par c and d are pecific o hi pariclar model Par c and d a fir glance appear conradicory, b are no, becae he mean of he raio of he age o he inere facor differ from he raio of he mean age o he mean inere facor.

15 and follo from he ampion of a global echnology along ih conan ocial rern o capial. PCM Ne conidering aving, he PCM rericion i applied o he fir-order condiion 4, hich generae a qadraic form for he aving fncion, β PCM β β, PCM > 0 β β here k Noe ha he eliminaion of he variance erm,, cae he olion o rever o he linear form in eqaion 6. Corollary o el To: Saving i higher nder PCM han nder aarky. Par a and b of el To imply ha here i an addiional, precaionary elemen o aving nder PCM for nchanged mean vale of facor price, becae of boh an increae in he volailiy of fre earning income and he eliminaion of inere ncerainy, hich i capred by he preence of in eqaion here > 0. Par c and d alo gge ha here ill alo be an incremenal rie in life-cycle aving, becae he mean vale of facor price do change and in ay ha i favorable - ih a rie in he mean vale of crren earning and a fall in ha of diconed fre earning. In comparion ih aarky in eqaion 5, he capial ock of any conry i no deermined by global raher han naional aving pl i on TFP hock, PCM, k Global capial accmlaion i k, 4 4

16 A olion for groh i obained by adding p eqaion acro all conrie. Thi enail anoher poiive aggregaion effec, a f,.. f,.. >. Thi conve effec i favorable o capial accmlaion nder PCM, and h ppor he hr of he rel o far, b i dicarded in ndly complicaing he olion for hi cae. Coneqenly, a impler form for he olion i obained, β A G G PCM PCM, > 0 μ β μ μ here μ, 5 hich bear cloer comparion ih eqaion 8, providing he fir major rel. Propoiion One: i Global economic groh i higher nder perfec capial mobiliy han aarky, ii and here i a poiive relaionhip beeen volailiy and global economic groh. Thi follo from el One, To and he Corollary and i alo eviden from a comparion of eqaion 8 and 5, ince > 0 implie ha G > Ω >. PCM G AUT There are o reaon hy PCM ill raie he inernaional economic groh rae. One i ha i give rie o precaionary aving; he econd i ha aggregaion effec from capial marke inegraion lead o an increae in global life-cycle aving. I i alo orhy of noe ha hile he correlaion beeen volailiy and groh i negaive nder aarky, i i poiive nder PCM, hich gge ha, in general, he ign of he correlaion may depend on he degree of capial marke inegraion. Obfeld 994 obain he ame baic rel hrogh a porfolio effec ihin a infinie-lived, repreenaive-agen here only inere rik an ie. For each conry here are o invemen raegie, involving a high rik b high rern prodcion echnology and a lo rik and afer alernaive. The benefi of inernaional financial inegraion i in faciliaing greaer rik-diverificaion, hich encorage hoehold o inve more in he rikier b more prodcive echnologie. Devere and Smih 994 provide a imilar model in hich he main par of heir analyi cenre inead on earning ncerainy from endomen hock. 5

17 Inernaional inegraion hen provide inrance again eogeno conry-pecific hock, hich acally cae aving and groh o fall nder PCM hrogh removing he moive for precaionary aving. Their econdary applicaion coincide ih or on in conidering TFP hock ha joinly earning and inere ncerainy. Hoever, heir applicaion of an infinie-lived, repreenaive-agen model mean heir rel depend on he ign of he inere rae repone and, hence, on he pecificaion of he iliy fncion. Wihin he general CA cla, he logarihmic fncion provide a borderline, neral cae here inernaional capial marke inegraion ha no effec; and ncerainy ill raie/loer groh in heir model, if he elaiciy of ineremporal biion i greaer/le han niy. In conra ih or on conideraion of a finie-horion model, PCM raie economic groh above he aarky level for any vale of he CA, hile he logarihmic cae remain an inereing benchmark cae, b for an enirely differen reaon ha here TFP volailiy ha no effec on aving nder aarky. Again o evalae he rel, e elec he vale, β 0. 8, 0. 8, in addiional o he previo one, 0. and Fir, e find ha nder PCM he annalied average groh rae i 0.6% higher above he volailiy-free cae, hich i de o precaionary aving, ince aggregaion effec are aben by conrcion. Hoever, he economically meaningfl comparion i o be made beeen aarky and PCM for he given level of volailiy, here aggregaion effec appear. Accordingly, a e have already fond ha aarky redce he annalied groh rae by 0.0%, i i a maer of dedcion ha PCM ill raie he annal groh rae by 0.6% above he aarky level, of hich j nder a half may be aribed o precaionary aving and he re o aggregaion. In erm of he accmlaed effec over ime, or fairly genero ampion abo he degree of TFP volailiy implie ha he orld old on average be 9.5% richer afer eny-five year of fll capial marke inegraion. 5. Perfec labor mobiliy PLM They alo dra aenion o he poin ha inegraion may redce elfare, depie he fac i allo for inrance, becae invemen i already a an inefficienly lo level in he preence of an eernaliy and i redced even frher. 6

18 Or aenion no rn o inernaional labor marke inegraion. Alhogh ome meare of global labor mobiliy i clearly obervable, he limiing cae of perfec labor mobiliy PLM i mch le plaible becae of relaive co. Neverhele, i i conidered in order o reveal he flavor of he rel for a more limied form of labor mobiliy and a comparaive cae of inere. I i modelled analogoly, here implici poplaion movemen old arbirage aay any poenial conry earning difference nil a ingle orld age i obained. Thi old reqire ha ome par of he labor force, e ame he yong generaion, i able o migrae iho incrring any co. 4 In order o iolae hi pariclar cae, e abrac from he poibiliy ha here i any parallel mobiliy in capial. 5 The baic rel i hen ha hock o TFP ill lead o increaed volailiy in he inere rae a hich hoehold and firm ave and borro, b ha age remain a a cerain and global level. The oal labor pply in each conry i no he variable,, Y, L Y L, here he nmber of yong orker, Y L,, i deermined crrenly and here he nmber of old orker, ho ere previoly he yong, Y L,, a deermined previoly. The demand for labor in each conry a a fncion of a common orld age, L Ak Y, Y, L, i K 6 The ampion ha only he yong migrae convenienly mean ha ha and Y L, are ncorrelaed - and o oo are and Y L,, hen endogeno labor in erm of hor i conidered frher belo. Frhermore, ince and K are alo ncorrelaed, folloing from he amed abence of any capial mobiliy, eqaion 6 may be aggregaed paially a 4 More properly, here yong orker do no beqenly rern o heir conrie of birh, e hold ame ha he migraion deciion hold ideally be baed on an evalaion of relaive life-ime iliie raher han of crren age. Hoever, he migraion problem become convoled, here here i no capial mobiliy and hence a conino diribion of inere rae caing a conino diribion of life-ime iliie boh for he conrie of birh and for he poenial ho conrie. 5 If boh capial and labor are boh amed o be perfecly mobile, he frher ampion of conan rern o cale hen implie ha negaive conry-level TFP hock old eliminae hole economie. 7

19 L Ak K L. 7 Thi i inerpreed a he global labor marke eqilibrim condiion, here L, Y, Y, L L, L, i he inernaional average pply of orker from each generaion. I may hen be invered, ing k K L A k, o give he age olion, Thi i hen rerned o eqaion 6 o deermine he labor pply per head of i on yong poplaion for each conry, Y, Y, k L L, k hich bear comparion ih labor i immobile. 8 for he iniial formlaion in eqaion here ach conry inere facor i hen olved from he ero profi condiion a A, PLM 9 Naional hock o TFP no affec only inere rae, hich mean a greaer elaiciy of repone, ln ln : a in eqaion 9 for PLM compared ih in eqaion for aarky, a hree-fold increae if. Iniially, a e are impoing an eogeno labor pply in erm of hor for all conrie,,, o ha eqaion 8 and 9 are lighly modified o PLM A k A 0 8

20 We can conclde he folloing. el Three: The effec of PLM i o a redce he variance of he age o ero, b raie he variance of he inere facor, c raie he global average age, d raie he global average of he fre diconed age ih an ambigo effec on he global average inere facor. See Appendi D for he deail and proof. Again Par a i by definiion of PLM and he oher par are by implicaion; b i a more general implicaion, hile c and d are pecific o hi model. Corollary o el Three: Saving i loer nder PLM han nder aarky provided ha he effec of a higher age in par c doe no dominae he oher. A for par a and b of el Three, he redcion in earning ncerainy and he rie in earning ncerainy m each cae diaving relaive o he aarky cae. The facor price effec in par c and d hold impinge on life-cycle aving, b he combined effec are no clear. The aving fncion for each conry become PLM β β λ β β λ ε β β λ >, ε > 0, Since age and he epeced fre diribion of inere rae are he ame for each conry, i follo ha, ; o ha eqaion and he previo o give, afer ome maniplaion, he folloing epreion for global economic groh nder PLM. 9

21 G PLM β φ φ β φ β here φ Thi give rie o he econd major rel. A Propoiion To: i Global economic groh i loer higher nder inernaional labor mobiliy han aarky if i large mall in hich cae ii here ill be a negaive relaionhip beeen volailiy and groh nder inernaional labor mobiliy. Proof: See Appendi. Qaliaively, e canno be re of he effec of PLM compared ih aarky. Hoever, if e apply he ame parameer vale a before, e find ha moving from aarky o PLM redce he annal groh rae from.80% o.66%. Thi i parly conied by a fall in precaionary aving, ince earning ncerainy i eliminaed and inere ncerainy i amplified, b i offe by a poiive aggregaion effec caed by age eqaliaion. Since he volailiy-free cae of.00% preclde boh ncerainy and aggregaion effec, e may dedce ha hee o oppoing effec are repecively reponible for -0.4% and 0.0% of he -0.4% change. Thee relaive magnide depend, of core, on he nmerical vale, epecially ha of, hich ha been e a. We can mmarie all he rel obained o far, here he labor pplie have been fied a a common parameer, in he folloing able. Table One: conomic Groh here labor pply i eogeno Inernaional regime Annal groh rae No volailiy benchmark.00% aigned Aarky.80% Perfec capial mobiliy.6% 0

22 Perfec labor mobiliy.66% 6. ndogeno labor pply 6. Hoehold opimiaion revied Given he logarihmic form of he iliy fncion, he preence of inere rae effec on aving i de o he epeced preence of fre earning, ince hoehold pply labor in he econd-period of heir live. Thi pply p o no ha been reaed a eogeno in order o limi he cope of he analyi, b no e eend i o foc on he ineracion beeen TFP volailiy o ee ho hi may modify he rel for he relaionhip beeen he facor mobiliy regime and economic groh. An increae in he mean vale of econd-period hor, for eample, old redce fir-period earning hrogh an indirec effec of oal labor pply on he age and raie econd period earning hrogh he dominance of he direc effec. Boh of effec of old raie life-cycle aving hrogh conmpion-moohing, hile a fall in average labor pply old, of core, have he oppoie effec. Anoher qeion i ho ill he poibly ochaic nare of labor pply inerac ih precaionary aving? In order o aner hi, e agmen he hoehold iliy fncion ih a erm ha repreen he diiliy of econd-period labor pply. Mainaining a general logarihmic form, he era erm, be enjoyed in he econd period,, i inclded o capre he era leire o β ln ln U ln The ne parameer i he emi- elaiciy of iliy ih repec o leire. 6 6 We hold add ha Flodén 006 ha already provided an analyi of he relaionhip beeen labor pply and aving in he mid of ncerainy, hich i more general ince here i no pecificaion of fncional form b alo more pecialied o he een ha earning ncerainy i conidered o he eclion of inere ncerainy.

23 In he econd-period here ha been already been deermined, he hoehold chooe i labor pply,, o maimie, i, i, i ln ln :, i, i, i, < 0, > 0, < 0, i Labor pply repond poiively o age change, becae he pecificaion i ch ha he biion effec dominae he income effec, b negaively o change in inere rae ih only an income. Coneqenly, an endogeno labor pply eacerbae he effec of earning ncerainy - becae he demand for labor i elaic, b dampen he effec of inere ncerainy by inrodcing a negaive correlaion beeen nearned and earned orce of income. ach of hee o ocome mean ha labor pply variabiliy i conien ih a rie in precaionary aving. 4 In olving he predeermined level of fir-period aving, he probabiliic repone of econd-period labor pply m be acconed for by he hoehold and, o, i i endogenied by incorporaing eqaion 4 ino he e ane iliy fncion, β ln ln β ln U ln ln The fir-order condiion, hihero given in eqaion 4, i modified o β In erm of calclaing a olion - raher han ih repec o he iniion - β no appear inead of β in eqaion 4 and niy replace he eogeno fracion,. conomic groh nder each of he hree main regime of aarky, PCM and PLM may no be conidered here, noaionally, he repecive ocome ih labor pply endogeneiy are deignaed a AUT*, PCM* and PLM* Aarky ih endogeno labor pply The fir main finding i ha nder aarky, becae of he amed logarihmic iliy from conmpion, hock o TFP do no affec labor pply, becae he raio

24 of earning o inere income remain nalered. Individal labor pply, alhogh endogeno, i invarian and deermined from eqaion,, 5 and 4 a AUT *, i AUT * el For: ndogeno labor pply i conan nder aarky. In he eqaion above e have diingihed beeen he individal i labor i, pply, AUT, and he conry-level, AUT*, becae he laer indirecly * affec he former hrogh conry-level age deerminaion - alhogh no vice vera. Symmery acro individal, AUT * *, i, i here, implie 6 The deparre from he previo analyi of an eogeno labor pply nder aarky old eem o be rivial, becae herea i a previoly defined a being parameric a, i i no derived a a deerminiic fncion of o parameer, he nely pecified,, and he eiing,. Coneqenly, he main analyical inere m relae o ho labor pply endogeneiy migh modify he rel for he o facor mobiliy regime. In order o iolae hee effec, e e he opimal, albei conan, aarky level of labor pply, * ino eqaliy ih he parameric level,. Thi i eqivalen o placing he folloing rericion on, he elaiciy of AUT leire, 7 6. PCM ih endogeno labor pply po labor pply nder PCM according o eqaion 9, 0, 4 ino 6 i cov, 8

25 cov, I i apparen ha he covariance,, i poiive, ince PCM > 0, b he le obvio deail of he olion are aigned o Appendi F, hich ho ha a maniplaion of eqaion 8 lead o PCM * qaion 6 ino 9 give PCM *, here PCM * < 0 Th, nder PCM, volailiy redce he epeced vale of econd-period labor pply, becae of he concave repone of labor pply o hock o earning. Hoever, he fall i qie mall: if nder aarky, 0.8, nder or mainained parameer vale, 0. and 0. 5, hen * Frhermore, for he average conry for hich pply i, AUT PCM 9, e po econd period-labor The aigned vale imply an ocome of 0.8 in he even of a poiive TFP hock and of for a negaive one. The facor price are hen olved a * * A 0 PCM PCM * PCM* A k PCM The remaining implicaion of PCM ih endogeno labor are no mmaried in he folloing o rel. el Five: If labor pply i endogeno, PCM inrodce a a poiive covariance beeen he age and labor pply, and cae b a fall in he mean vale of labor pply, and c a rie in he crren age, d a rie in he inere 4

26 facor, d a fall in he preen vale of fre earning income, e a rie in he normalied variance of fre earning. See Appendi F. el Si: If labor pply i endogeno, i perfec capial mobiliy cae groh o be even higher above he aarky level and ii he poiive relaionhip beeen volailiy and groh i renghened frher. From el Five. qaion 5 ih age hock alone nder PCM* implie ha aving i PCM β * β β, β β Again here i a favorable b complicaing aggregaion effec, hich i eclded; and eqaion 4 and 9- are combined o give G PCM * μ β ˆ β μ PCM μ * μ A PCM * * PCM here PCM *, PCM * All of he marginal effec of an endogeno labor pply reinforce he rel of Secion 4 ha PCM raie long-rn economic groh above he aarky level. The effec of a procyclical labor pply increae earning volailiy and, o, precaionary aving and he change in average facor price i ch a o promoe a rie in life-cycle aving. Hoever, he ie of he change i qie mall. The mainained vale of 0., 0. 8, β 0. 8 imply PCM * ,. μ., μ PCM *. and 0. 75, and ih 0. 5 A. 9 before, he effec of an endogeno labor pply i for he annal orld economic groh rae o rie from.6%, o.0% nder PCM., a 5

27 6. PLM ih endogeno labor pply qaion ih 8, 9 and 5 give he labor pply of an individal j in conry a, j PLM * Symmery acro all individal in conry and conry,, j PLM* o ha globally,,, implie ha for, PLM * PLM * > 0 4 TFP volailiy raie he mean vale of labor pply nder PLM above he aarkic level, becae of he conveiy of he repone o he hock, alhogh hi effec rn o o rivial, merely 0.80 inead of 0.8. The remaining rel are mmaried a follo. el Seven: If labor pply i endogeno, PLM cae a a negaive covariance beeen he labor pply and he TFP hock, b a rie in he mean vale of labor pply, and c a fall in crren earning, d a rie in he inere facor, e a rie in he preen vale of fre earning. el igh: If labor pply i endogeno, i perfec labor mobiliy cae economic groh o be loer han here i i eogeno, provided ha any poible 6

28 rie in precaionary aving i of a lo magnide, in hich cae ii he correlaion beeen volailiy and groh become more negaive. Thi follo from el Si and from eqaion 8, 9 and 4. The olion i raighforard, a aving remain he ame for each conry, and e find eqaion 5 ih he hock o inere rae in iolaion lead o he folloing modificaion of eqaion, PLM β β λ * β β λ ε β β λ >, ε > 0, 5 The modified implied facor price eqaion, * * A, 6 PLM PLM * * A k, 7 PLM PLM and he ame reaoning in Secion Five imply he groh facor i G PLM here β PLM * μ * * μ PLM μ PLM * β μ PLM * β * PLM A, PLM * The negaive covariance beeen he TFP hock and labor pply mean here i no ome meare of earning ncerainy, hich raie aving. Hoever, a in he previo cae of PCM, he overall effec of an endogeno labor pply i mall, raiing he annalied groh rae o.70%. 8 7

29 The folloing able replicae he rel from Table One and inclde hoe for hi preen Secion. Table To: conomic Groh Inernaional regime Annal inernaional groh rae ogeno Labor ndogeno Labor No volailiy benchmark.00% aigned.00% aigned Aarky.80%.80% Perfec capial mobiliy.6%.0% Perfec labor mobiliy.66%.70% 7. Smmary and dicion The prpoe of hi analyi ha been o conider he implicaion of more general form of ncerainy ihin a model of overlapping generaion. I applicaion a o an inernaional macro-model ih he coneqence ha he form of inernaional facor mobiliy regime a fond o be imporan for hoehold aving and for global economic groh. PCM a hon o raie aving by redcing inere ncerainy a he epene of increaing earning ncerainy; an analogo conideraion of PLM had he oppoie effec. On op of hi, he pecificaion of a global echnology alongide an effecive AK groh mechanim implied ha each form of facor marke inegraion led o a poiive aggregaion effec. Thi caed PCM o be nambigoly groh-enhancing, hile he impac of PLM depended on conervailing effec. Oher ahor, noably Obfeld 994 and Devere and Smih 994, have alo conidered he effec of PCM on precaionary aving, albei ihin alernaive, repreenaive-agen, infinie-horion model. Obfeld fond alo ha PCM raied aving b hrogh he lighly differen and more comple mechanim of ae diverificaion, hich made hoehold more illing o ave a riky rae of rern raher han faciliaing a general redcion in rik. For he cae of TFP hock in Devere and Smih, hich mached or on concern, he differen repreenaive- 8

30 agen, infinie-horion pecificaion caed heir rel o hinge on an inere rae effec and, h, criically depended on he form of he iliy fncion. To or knoledge o dae, no ahor have given a imilar reamen o he effec of PLM nor have inegraed an analyi of labor pply repone o ncerainy. A al, here are a nmber of cavea. One i ha a qaniaive evalaion of he rel confirmed he rel in Smih 996 for a cloed-economy ha macroeconomic ncerainy ha a mall qaniaive effec on aving. In miigaion, hi cold be de o impoing for analyical eae a niary and o a poibly oo lo vale of niy for he elaiciy of ineremporal biion in conmpion. One poible reolion for migh be o conider model ih nemploymen in hich he ncerainy of employmen ha a more poerfl effec on hoehold aving han he mere, aociaed ncerainy of income. The rim remain, hoever, ha relaively mall improvemen in groh ill have a componding effec on op ha ill evenally come o darf he magnide of any cyclical movemen. There i ill more o be done in modelling he ineracion beeen labor pply, folloing Flodén 006. Apar from he al life-cycle conideraion, he cope o be able o vary hor e po in repone o any kind of hock may have imporan implicaion for aving. We have conidered hi in a rericed ay, alhogh in or vie iho ndermining he relaive implicaion of he vario facor mobiliy regime. One obvio eenion i o conider ho an endogeno labor pply in all period old affec he rel. Hoever, he general area of labor pply affec i, of core, a poenially ide a he range of heorie governing he labor marke. Anoher poin i ha he effec of inernaional capial and labor mobiliy have been inveigaed eparaely and no imlaneoly. Thi a hoage o he ampion of inernal conan rern o cale, ince join facor movemen ih he reqiremen of non-negaive profi, old enail he lo of firm - and - and ih he ymmery ampion of firm ihin conrie he diappearance of hole conrie. For hi reaon, frher reearch hold rn oard conidering decreaing rern o cale ampion, here he nmber of firm can be deermined 9

31 and here foreign direc invemen in he ene of he migraion of firm old become an ie. The analyi o dae gge ha he effec on groh hrogh precaionary aving of movemen in boh capial and labor can go eiher ay, becae of ncerain effec on he anicipaed price diribion. A final poin i ha he qanified groh gain from facor marke inegraion have probably been nderaed by or ampion ha he global ranfer of echnology i independen of any accompanying movemen in he facor of prodcion, epecially, labor. Thi i a odd ih he finding in Keller 004 ho hoed ha echnology diffion and economic inegraion are eenially complemen: idea a bleprin may be ranmied elecronically, b heir fll, pracical implemenaion may alo reqire ha people move ih hem, o ha he groh-enhancing effec of labor mobiliy, a lea, have probably been nderaed. eference Arro, K.J. The economic implicaion of learning-by-doing, evie of conomic Sdie, 9,, 55-7 Blackbrn, K. and A. Pelloni 005, Groh, cycle and abiliaion policy, Oford conomic Paper, 57, 6-8 Bolding, K conomic Analyi, Volme I: Microeconomic, 4 h ed. Harper and o, Ne York. Caballero,. J. 990, Conmpion ple and precaionary aving, Jornal of Moneary conomic, 5, -6 Carroll, C.D and A.A. Samick 988, Ho imporan i precaionary aving? The evie of conomic and Saiic, Dardanoni, V. 99, Precaionary aving nder income ncerainy: a croecional analyi, Applied conomic,, 5-60 Devere, M.B. and G.W. Smih 994, Inernaional rik haring and economic groh, Inernaional conomic evie, 5,, Diamond, P.A Naional deb in a neoclaical groh model, American conomic evie, 55, Flodén, M. 006 Labor Spply and Saving Under Uncerainy, The conomic Jornal, 6,

32 Ghoh, A.. and J.D. Ory 997, Macroeconomic ncerainy, precaionary aving and he crren accon, Jornal of Moneary conomic, 40, -9. Hek, P.A. 999, On endogeno economic groh nder ncerainy, Inernaional conomic evie, 40,, Hbbard,.G., Skinner, J. and S.P. Zelde 994, The imporance of precaionary moive in eplaining individal and aggregae aving, Carnegie ocheer Serie on Pblic Policy 40, 59-5 Norh-Holland Keller, W. 004 Inernaional echnology diffion, Jornal of conomic Lierare, XLII, Kneller,. and G. Yong 00, Bine cycle volailiy, ncerainy and long-rn groh, The Mancheer School, 69, 5, Special Ie, Lca,.. 988, On he mechanic of economic developmen, Jornal of Moneary conomic,,, -4 Marhall, A. 90, Principle of conomic, 8 h. ed. Macmillan, London. Menegai, M. 009, Opimal aving in he preence of o rik, Jornal of conomic,, Obfeld, M. 994, ik-aking, global diverificaion, and groh, American conomic evie, 84, 5, 0-9. amey, G and V. amey 995, Cro-conry link beeen he volailiy and groh, American conomic evie, 8, 5, 8-5 ankin, N. 998, Nominal rigidiy and moneary ncerainy, ropean conomic evie, 4, odrige, A. 999, Precaionary aving and economic groh, Jornal of Macroeconomic, Spring,,, 9-9 omer, P.M. 986, Increaing rern and long-rn groh, Jornal of Poliical economy, 94, 5, omer, P.M. 990, ndogeno echnological change, Jornal of Poliical economy, 98, 5, S7-0 Sandmo, A. 970, The effec of ncerainy on aving deciion, evie of conomic Sdie, 7, 5-60 Skinner, J. 988, iky income, life cycle conmpion and precaionary aving, Jornal of Moneary conomic,, 7-55 Smih,.T. 996, Cyclical ncerainy, precaionary aving and economic groh, conomica, 6,

33 Appendice Appendi A: Saving nder ncerainy A. Uiliy Conider he folloing o-period epeced iliy fncion, U β 0 here. i he ingle period iliy fncion, β i a bjecive dicon facor and i he epecaion operaor. The erm 0 i predeermined earning, i he choice variable of aving, hile and are realiaion from he diribion for fre earning and for he inere facor over hich epecaion m be formed. The ler eqaion i U F 0 β 0 A A Taylor erie epanion of arond he mean of,, give 4.. 6, 0. For CA and CAA 0, 0 here > 0 < iliy 0, 4 0. > 4 < A ; for qadraic Frher Taylor erie epanion arond he mean of,, for each of he righhand erm in A give A.

34 A A A..4 Combining he above erm and aking epecaion give, here i i,,..,, i A.4

35 Overlooking he higher-order momen and cro-momen above he variance and he covariance give A.5 The effec of rik-inverion < 0 i hrogh inere ncerainy alone and any effec from he conveiy of he marginal iliy 0 ork hrogh he ncerainy o conmpion caed by boh inere and age ncerainy, ince c c Uing Kimball 990 definiion of prdence 7, defined a θ c a analogo o he Arro-Pra concep of abole rik-averion, φ c, e can re-preen φ c A.6 θ c A. The ler eqaion Conider he maimiaion of he folloing o-period epeced iliy fncion, U β 0 The fir-order condiion i F F β 0 0 A Taylor erie epanion of arond i aken; and hen for he each erm involving, frher Taylor erie epanion arond. clding all higher order erm beyond he variance and covariance give 7 Kimball alo decribe prdence a he propeniy o prepare and forearm oneelf in he face of ncerainy, in conra o rik averion, hich i ho mch one dilike ncerainy and old rn aay from ncerainy if poible. 4

36 5 0 F β β and ing Arro-Pra definiion of abole rik-averion, c φ, and Kimball 990 analogo concep of prdence 8, defined a c θ, e obain 0 W W W c c F θ φ β here W,, W W W W c c θ φ An inerior olion reqiing 0 < U, implie ha 0 < F according o he definiion of F, o ha an implicaion of he implici fncion heorem i ha F ign ign. We may conider vario cae of he ler eqaion in F. A. arning ncerainy alone 0 c c F θ φ β > 0 W, if 0 > c θ A knon, i i neceary and fficien ha ha 0 > or 0 > c β in order for earning ncerainy o generae precaionary aving. arning ncerainy redce he epeced vale of fre conmpion leading o an increae in aving a a compenaing facor in obaining a higher epeced vale. A.4 Inere ncerainy alone 8 Kimball alo decribe prdence a he propeniy o prepare and forearm oneelf in he face of ncerainy, in conra o rik averion, hich i ho mch one dilike ncerainy and old rn aay from ncerainy if poible.

37 F θ c c 0 β φ > 0, if θ c > Again i i neceary for precaionary aving > 0 or θ c > 0, b i i no longer fficien becae of inere rik. Alhogh, a before, a rie in aving increae he epeced vale of fre conmpion a a compenaing facor for income ncerainy, aving i alo he orce of income rik, o ha here i a rade-off beeen epeced vale and variance leading o a generally ambigo aving repone. Thi cae i ofen conidered ih reference o a conan rae of relaive rikaverion CA iliy fncion, U φ c φ. The relaionhip beeen CA and prdence i φ φ θ c, o ha he above condiion for hi cae become φc φ φ > φ In he abence of a econd-period income, 0, precaionary aving only reqire φ >. Here aving i naffeced by inere ncerainy in he logarihmic cae φ, b redced if φ < in Marhall. Hoever, if here i a econd period income, > 0, Marhall cae become more likely a, precaionary aving reqire > fficien ha >. φ, for hich i i neceary b no A.5 Qadraic iliy [ φ c [ ] F 0 β W I i generally believed ha qadraic iliy i ynonymo ih he cae of cerainy eqivalence. Hoever, hi i ricly correc only for he cae of pre earning ncerainy, here W drop o of he ler eqaion. In general, inere ncerainy alo affec aving, and hi remain o for he cae of a qadraic iliy fncion. The effec ill be even be poiive, coniing precaionary aving, if 6

38 here i a negaive covariance beeen earning and inere income of fficien magnide. 9 Generally, ign ign if 0, W W W < Frhermore, if i fficienly mall, > 0 for a negaive covariance of any magnide. W A.6 The general effec of covariance More generally, he covariance beeen earning and inere ncerainy i imporan for aving. There ill be precaionary aving diaving if W > <0 θ c > < if Again for a CA, φ, here θ c φ F ign φ ign W, o ha a more poiive covariance beeen inere income and earning income raie precaionary aving only if he inere componen of fre income i large relaive o he earning componen or, if he iliy fncion i logarihmic, imply larger. A.7 Fir period income ncerainy Finally, here i alo he hypoheical cae ha he aving deciion i made prior o he realiaion of he fir period income 0, in hich cae he ler condiion old become 0 F β 0 A, < > if > 0 < We ee ha for he andard cae here > 0, he ncerainy of fir-period income hoever i i compried ill redce aving. 9 Thi baic rel ha alo recenly been dicovered by Menegai 009 in he lighly differen cone of earning income rik ih backgrond rik. 0 There m be precommimen o he iniial level of aving ih no poibiliy of beqen borroing or addiional aving in repone o he realiaion of income. Thi gge boh a conracal rigidiy and an abence of pplemenary loan and aving marke.. 7