Subsistence Consumption and Rising Saving Rate

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1 Subience Conumpion and Riing Saving Rae Kenneh S. Lin a, Hiu-Yun Lee b * a Deparmen of Economic, Naional Taiwan Univeriy, Taipei, 00, Taiwan. b Deparmen of Economic, Naional Chung Cheng Univeriy, Chia-Yi, 6, Taiwan. Abrac Thi paper inveigae he implicaion of he permanen income hypohei wih ubience conumpion being he driving force of a riing aving rae during economic developmen. To olve he difficuly ha ubience conumpion i unavailable, we ue coinegraing regreion o generae he unobervable, ubience-level adjued aving rae erie, and hen e he orhogonal condiion impoed by he model uing he generaed erie. The implicaion of he model canno be rejeced for Taiwan aiically, bu receive weak uppor for Japan. JEL claificaion: E Keyword: Saving rae; Subience conumpion; Permanen income hypohei * Correponding auhor: Hiu-Yun Lee, Deparmen of Economic, Naional Chung Cheng Univeriy, Ming-Hiung, Chia-Yi 6, Taiwan. TEL: ex Fax:

2 . Inroducion The aving rae roe in he po-war period for many counrie wih a noiceable excepion being he U.S., and here exi ubanial cro-counry dipariy in he lope of riing aving rae. Thi paper udie he long-run behavior of he aving rae in he framework of he permanen income model, and he ubience level of conumpion i he key driving force. When conumpion i near he ubience level, an agen major concern i meeing he ubience requiremen, and he elaiciy of ineremporal ubiuion in conumpion i cloe o zero. If he economy grow a a uained rae, agen become more willing o ubiue curren conumpion for fuure conumpion. Tha i, he ubience requiremen can generae a riing aving rae. Once he imporance of he ubience requiremen in conumpion deciion decline, he aving rae behave more like a aionary variable. The idea ha ubience conumpion induce a ime-varying aving rae i no Thee ylized fac were documened in Maddion (99). An alernaive approach in modeling he poiive relaionhip beween growh and aving would be he life cycle model of conumpion. However, recen cro-counry regreion did no find populaion-relaed variable uch a he populaion growh rae, meaure of he age rucure, and moraliy rae o be ignifican facor in accouning for he counry-difference in he aving rae (Rebelo, 99).

3 new. Zellner (960) howed ha ubience conumpion can make he raio of opimal conumpion o permanen income depend on he level of permanen income. Chriiano (989) inroduced he ubience level of conumpion in he repreenaive agen uiliy funcion. Given cerain parameerizaion, he model wa able o accoun for he hump-haped paern of Japan' aving rae in he po-war period. Rebelo (99) alo ued he uiliy funcion wih he ubience level of conumpion o explain he cro-counry difference in he growh rae of conumpion wih a perfec inernaional capial marke. Chaerjee (994) argued ha if he economy grow oward he eady ae and here exi a minimum conumpion level requiremen, hen he average aving propeniy i poiively relaed o wealh. Recenly, Ogaki, Ory and Reinhar (996) eimaed a model ha emphaize he role of ubience conumpion and found rong empirical uppor for he hypohei ha he aving rae and i eniiviy o he inere rae are a riing funcion of income. According o he permanen income hypohei, when agen ave only for conumpion moohing, change in aving reflec anicipaed change in fuure income. In addiion, here i a iling moive relaed o any dicrepancy beween he ubjecive dicoun facor and he marke dicoun facor. Wih a perfec inernaional capial marke, mo growh model wih andard preference imply ha conumpion

4 and oupu growh would equalize acro counrie. The model predic ha he aving rae conain no upward rend a he U.S. obervaion over he pa one hundred year. However, during he proce of economic developmen he aving rae rie in many counrie. A riing aving rae indicae ha he growh of income oupace he growh of conumpion. Therefore, imperfec inernaional capial mobiliy i neceary o have cro-counry dipariy, or he real inere rae mu be implauibly high in order o generae a riing aving rae in low-income counrie. In hi paper, we ry o provide an alernaive explanaion for a riing aving rae while mainaining he aumpion of perfec capial mobiliy. The ubience level of conumpion impoe eable rericion on he rend and cyclical properie of aving rae and labor income growh. We how ha once he ubience requiremen i properly conidered in meauring he aving rae, he adjued aving rae become a aionary erie. However, economerician canno oberve he ubience conumpion and hi caue difficuly in regular eimaing. Ogaki, Ory and Reinhar (996) aeed a range of value of ubience conumpion around he value of US$3 (985 price) found for India by Akeon and Ogaki (993). Raher han aigning he value, hi paper employ a wo-ep economeric procedure o olve he difficuly ha ubience conumpion i 3

5 unavailable. We fir ue Park (99) canonical coinegraing regreion (CCR) o generae he unobervable, ubience-level adjued aving rae erie. We hen apply he Generalized Mehod of Momen (GMM) o e he orhogonal condiion impoed by he model uing he adjued aving rae and labor income growh rae erie. In an empirical inveigaion, we ak wheher he aving rae erie in Japan and Taiwan i conien wih he long-run predicion of our model. Thee wo counrie were near ubience a he end of World War II, and managed o have uained and impreive growh in he pa fory year. They did no begin wih a high aving rae, bu experienced a dramaic increae during economic developmen. Hence, our focu i no on why hee counrie ave a lo, bu raher on why hey have riing aving rae. The remainder of he paper i a follow. The nex ecion preen a permanen income model wih he ubience requiremen. Secion 3 ue he oluion for he Euler equaion and he ineremporal budge conrain o derive he long-run implicaion for he aving rae. Secion 4 propoe a wo-ep economeric procedure for parameer eimaing and hypohei eing. Secion 5 decribe he ime erie daa for Japan and Taiwan and preen he empirical reul. The la ecion conain ome concluion. 4

6 . A model wih a ubience level of conumpion The repreenaive agen face he problem of chooing a coningency plan of conumpion {, 0}, o a o maximize c E ) 0 0 U( c ; ubjec o b ( r)( b y c ), wih b given. Here y i he privae agen 0, labor income a ime, b i he non-human wealh valued in uni of conumpion good held a he beginning of period, and r i he conan real rae of reurn on non-human wealh. Funcion U(c ; ) i he ime eparable uiliy funcion of conumpion a ime wih U ( ; ) 0 and U ( ; ) 0. Term i he c c poiive rae of ime preference, and E denoe he mahemaical expecaion condiioned on he informaion e available a he beginning of ime,. Term capure he exience of ubience conumpion, becaue marginal uiliy of conumpion hoo off o infiniy a conumpion decreae oward : lim U ( c ; ). c To model he ubience level of conumpion, we ue he following log verion of he HARA (hyperbolic abolue rik averion) uiliy funcion: 3 3 The widely ued quadraic uiliy funcion ha wo undeired feaure for he purpoe of our udy. 5

7 U c ; ) ln( c ). ( Here i aumed o evolve according o E ) ( m for all in which m i a conan. Two pecificaion of were ued in previou udie. Fir, he ubience level of conumpion i conan over ime ( 0 ) in Rebelo (99) and Akeon and Ogaki (993). Second, he ubience level of conumpion ha a linear ime rend: ( m) wih m 0 in Chriiano (989). The Euler equaion for he repreenaive agen problem i 0 ( r)( c ) ( )( c ), () in which i he lea quare projecion error ha aifie E[ ] 0 and reflec new abou fuure income. 4 I i clear from () ha marginal uiliy i convex in c under he logarihm-form uiliy funcion. An increae in uncerainy raie he expeced marginal uiliy of conumpion. To mainain he equaliy in he Euler equaion, he expeced fuure conumpion mu increae relaive o curren conumpion. Furhermore, we aume ha E [ ] for all. Auming ha he ubience level of conumpion doe no grow, equaion () yield he following log-normal approximaion: Fir, i implie he finie marginal uiliy for any admiible level of conumpion. Second, he ineremporal elaiciy of ubiuion fall a he level of conumpion increae. 4 A i common in empirical reearch, we ake condiional expecaion o be linear lea-quare projecion on he informaion e. 6

8 E c c r, () in which 0 / c i he ineremporal elaiciy of ubiuion. Term i no longer conan and i converge o one when conumpion grow a a uained rae. The larger he value of i, he eaier i i for privae agen, in erm of uiliy, o forego curren conumpion for fuure conumpion, and hu he higher he expeced conumpion growh rae i. The poiive relaionhip beween and c implie ha agen in he high-income economy are more willing o ubiue curren conumpion for fuure conumpion han hoe in he low-income economy. Hence, he flucuaion of conumpion in he high-income economy could be higher han hoe in he low-income counerpar. The expeced conumpion growh rae i deermined by wo equally conribuing facor. Fir, ( r ) characerize he opimal repone of conumpion deciion o he real rae of reurn on he non-human wealh. When he real rae of reurn exceed he rae of ime preference, here i an incenive for privae agen o increae conumpion in he fuure. The higher real rae of reurn caue he ineremporal conumpion pah o il oward fuure period. Second, / repreen he effec of uncerainy in fuure even on he conumpion profile, ince aving provide a reerve again any bad oucome from fuure even. Privae agen prefer o defer curren conumpion for higher fuure conumpion in he face of uncerainy. We call 7

9 aving induced by he above wo facor he eae aving and precauionary aving, repecively. Wihou he ubience conumpion ( ), equaion () predic ha any cro-counry difference in conumpion growh mu be aribued o he cro-counry difference in or or preference in a world wih a perfec inernaional capial marke. The riing ineremporal elaiciy of ubiuion apparenly offer an explanaion for he cro-counry difference in conumpion growh. Anoher approach aume ha he rae of ime preference fall a an economy become richer. 5 Uing he Indian village panel daa, Akeon and Ogaki (993) found ha he rae of ime preference i conan acro poor and rich houehold, while he ineremporal elaiciy of ubiuion i higher for rich houehold han i i for poor houehold. 3. Saving rae and he ubience conumpion The Euler equaion i only one of he neceary condiion for opimizaion o ha he implied aving rae could be inconien wih he budge conrain. In hi ecion we ue he Euler equaion and he budge conrain o yield a igher 5 Geroviz (983) emphaized he imporance of nuriion and healh in he deerminaion of aving behavior. In hi model, he probabiliy of urvival depend on an agen' conumpion in he previou period and he rae of ime preference decreae a he previou period' conumpion increae. 8

10 characerizaion for he aving rae. When conumpion grow a a uained rae and c, for all, equaion () can be approximaed a ] )[ ( ] [ c r c E. (3) Recurively ubiuing (3) ino he budge conrain under he aumpion ha m r and give he oluion of : / c p y c, (4) in which, i he permanen income a ime : r ) / / ( p y i i i p b y r E r r y 0, and i he permanen ubience conumpion a ime : r m m r /. The marginal propeniy o conume ou of permanen income ( ) ay conan over ime, bu he conumpion-permanen income raio will change wih he level of permanen income. The hree facor r, and deermine he value of. If r exceed, agen have incenive o increae fuure conumpion. Hence, he ineremporal paern of conumpion il oward fuure period and i a decreaing funcion of r. On he oher hand, when fuure even become more uncerain, agen 9

11 end o ave more of heir permanen income a he reerve again bad fuure oucome and i a decreaing funcion of. Unlike he quadraic uiliy funcion, when r he value of i ill le han one due o precauionary aving. Agen are more willing o ubiue curren conumpion for fuure conumpion only when curren and fuure ubience conumpion become le of a concern in conumpion deciion. I i unlikely ha p c / y ay conan during he period of economic developmen. The permanen ubience conumpion appear o be a ource of rend for he aving rae. However, he role of ubience conumpion in he ime profile of conumpion depend on he ign of m k, where k r / i he expeced growh rae of conumpion when here i no ubience requiremen. Conider ha he expeced growh rae of (m) i le han he lope of he ineremporal conumpion pah (k) and 0 for all. Since meeing fuure ubience conumpion i no a major concern for agen, agen end o ave le han wha hey would ave wihou he ubience conumpion. The expeced conumpion growh rae i le han k. For m k, he addiional fuure income generaed by eae aving and precauionary aving exacly offe he expendiure required for he fuure increae in he permanen ubience conumpion. The negaive effec of an increae in c on he marginal uiliy i exacly offe by he poiive effec of an increae in on he marginal uiliy. The expeced marginal rae of ubiuion beween curren conumpion and fuure conumpion ay conan over ime. Tha i, he ubience level of conumpion ha no effec on conumpion 0

12 deciion. For m k, we expec he ubience conumpion o grow faer han conumpion. Once agen worry abou he fa-increaing permanen ubience conumpion in heir deciion, hey mu ave more o mee fuure ubience conumpion. The conumpion pah mu il oward he fuure period o ha conumpion ay above i ubience level in every fuure period. Agen ave o urvive. Since he aumpion of r m and / required in he derivaion of (4) are no ufficien o pin down he ign of hereafer. m k, we aume ha k m 0 To preciely characerize he relaionhip beween conumpion growh and income growh, conider he following ranformaion of equaion (4): c y i i r ( j i r b E ) r j y y, (5) in which i he growh rae of labor income a ime : y ( ) y. The derivaion of (4) and (5) do no require any explici relaionhip among b, y and, excep ha heir expeced growh rae are all le han r, i.e., r and r m. Suppoe ha he growh rae of labor income i expeced o be greaer han ha of (m). When agen were near ubience, hey had o pend a ignifican porion of heir income in conumpion imply for urvival. Equaion (5) predic ha boh / and c / y are high in he early age of economic developmen. When heir y conumpion move away from he ubience level, agen are more willing o

13 ubiue curren conumpion for fuure conumpion o ha he ineremporal conumpion pah il oward fuure period. The raio / y here i he driving force for he declining conumpion-labor income raio during economic developmen. However, he effec on c / y i weaker a he level of labor income increae. On he oher hand, if he growh rae of labor income i expeced o be le han m, hen / y become an increaingly dominan driving force for he riing conumpion-labor income raio. The permanen ubience conumpion exer ronger influence on agen conumpion deciion a he economy grow. Since hi i an undeirable feaure of he model, uch a poibiliy i ruled ou on he ground ha he conumpion-labor income canno rie wihou an upper bound. To derive aving, le ŷ denoe he oal income, which i he um of labor income ( y ) and capial income ( rb /( r) ): r yˆ b y, r and he convenional aving i defined o be yˆ c. Generally, equaion (5) canno be ranformed in erm of hi aving. Define a new variable: ˆ yˆ c uch ha ŝ i he convenional aving when. For impliciy, will be referred o a ŝ

14 aving hroughou he remainder of he paper. 6 A andard manipulaion of equaion (5) produce: ˆ y i i r E r r i r j ( j ). (6) y The permanen ubience conumpion ( / y ) i clearly a driving force for he riing aving rae. Imagine ha wo counrie have he ame ime profile of and. Equaion (6) implie ha he counry in he early age of developmen hould have a lower aving rae han he counry in he laer age of developmen. Thi i becaue agen in he early age of developmen have o pend mo of heir income imply for urvival. Afer an economy achieve a ufficienly high level of income, he imporance of he permanen ubience conumpion ( / y ) decline for driving he aving rae. Equaion (6) can be ued o examine he effec of change in he labor income growh on he aving rae, oo. To do hi we ake he fir-order Taylor expanion of i i ( r) ( around o obain i j j ) 6 Campbell (987) meaure aving a he dicrepancy beween dipoable income and conumpion divided by he marginal propeniy o conume ou of permanen income. Thu, he aving defined in our paper i proporional o he one in Campbell wih he proporionaliy facor. 3

15 i i ( ) ( i ), j i r j r r i0 i in which i he mean value of he labor income growh rae, and i ( r ) /( ) wih r. The abolue ummabiliy of {( ) } implie ha he fir and econd momen of i ( ) i0 i are well defined. Equaion (6) can hen be ranformed o y r r E r)( r ) ( i0 ( i, (7) i ) in which ˆ i he level of aving adjued for he permanen ubience conumpion. If i a aionary variable, hen he preen value of a fuure deviaion from i mean i aionary a well. Therefore, equaion (7) implie ha / y i aionary. Suppoe labor income growh i expeced o emporarily low down in he nex everal period. To keep conumpion on he planned pah, privae agen mu increae heir aving o ha higher fuure capial income can offe he decline in fuure labor income caued by he emporary lowdown. Hence, cyclical flucuaion of only induce flucuaion in aving. A menioned above, he declining paern of / y in economic developmen induce an upward rend in ˆ / y. Only he proper conideraion of he permanen ubience conumpion in meauring he aving rae 4

16 can eliminae he rend componen of he aving rae. 4. A wo-ep economeric procedure A hown in equaion (6), he permanen ubience conumpion ( ) i he driving force for he riing aving rae. One poenial problem in eimaing equaion (6) i ha economerician canno oberve. In hi ecion we propoe a wo-ep economeric procedure, which ue he informaion conained in he rend and cyclical properie of he aving rae, o olve hi problem. in which From equaion (6), i follow ha y ( r), y i i r( E E ) ( i r j j ) i he unpredicable reviion from o in he expeced value of human wealh. When / y, / y and are aionary variable, a linear combinaion of he hree aionary variable eliminae all erial correlaion and i compleely unpredicable wih repec o he pa informaion e. The above equaion implie a e of orhogonaliy rericion (or he momen condiion): 5

17 E r r z y y for any random vecor. z 0, (8) The GMM procedure appear o be uiable for eimaing parameer and eing he model by fiing equaion (8). Since he unoberved erie of he ubience level of conumpion ( ) can be compleely characerized by 0 and m under our pecificaion, 0 and m are reaed a parameer o be eimaed. However, one imporan aumpion under which large ample properie of GMM eimaor are derived i he aionariy of variable. When 0 and m are parameer o be eimaed, no all of he variable in equaion (8) can be ranformed ino aionary one. Thi rule ou he direc applicaion of he GMM procedure o equaion (8). For hi reaon, we propoe a wo-ep economeric procedure. In he fir ep we impoe he aionariy of / y a a rericion in eimaion, and hen generae a equence of / y uing he eimae of coinegraion eimaion. By he definiion of, he aionariy of / y implie ha here exi a lea a 3 vecor, e, for ŷ / y, c / y, and / y uch ha he hree variable are coinegraed. The coinegraion vecor implied by he model i e r k r k,,,, r r m r. r m 6

18 To obain he generaed erie of / y, conider he following aic regreion: c y e 0 e yˆ y e v y e 0 e yˆ y e ( m) y v, under he aumpion ha y ˆ /, c / y, and y / y are coinegraed. The heory predic, e e 0 [ ( r k) /( r m)] 0 e k / r, and / y e v. 0 Uing he eimaed value of e and eimaed reidual ( vˆ ) obained in he above 0 regreion can generae he unobervable / y erie. One raighforward approach i o apply OLS o he aic regreion. However, a argued in Campbell and Perron (99), when eiher he error erm v i erially correlaed or he innovaion in c / Granger caue eiher innovaion in y ˆ / y or y innovaion in / y, he OLS eimae of e i no aympoically opimal and may no have good finie ample properie. The aim here i no only eing he coinegraion bu alo finding he eimae of e, we hu apply Park (99) CCR procedure o he aic regreion and ue he Park (99) H(p,q) aiic for eing he coinegraion rericion. / Once he / y and y erie are conruced, he econd ep i o apply he GMM procedure o eimae relevan parameer and o conduc he hypohei eing for he orhogonaliy rericion uing he generaed erie of / y and 7

19 / y. The GMM eimaor are inrumenal variable eimaor exploiing he momen condiion: E[ ] 0. When here are over-idenifying rericion, he z aiic can be ued o e he validiy of he orhogonaliy condiion. Thi wo-ep procedure doe no aler he aympoic diribuion of he GMM eimaor and e aiic, becaue our coinegraing regreion eimaor i uper conien and converge faer han he GMM eimaor. 5. Daa and empirical reul In hi ecion, we explain he daa ued in eimaion and e reul o examine he empirical validiy of he ubience level of conumpion a a ource of generaing a riing aving rae. The po-war annual daa on real per capia conumpion, dipoable income, and compenaion of employee are obained from Japan and Taiwan. Since he compenaion of employee i no comparable wih he concep of labor income in he model, we follow Blinder and Deaon' (985) procedure o decompoe proprieor' income (or income from privae unincorporaed enerprie) ino he labor and capial componen according o heir overall hare. We hen conver nominal, aggregae magniude o a real, per capia bai by dividing by he available general price index 8

20 and oal populaion. Finally, wo pecificaion for he growh rae of he ubience level of conumpion are conidered: m 0 (he conan ubience level of conumpion) and m 0.3% (he ubience level of conumpion grow a he annual rae of 0.3%). Japanee daa are from Hiorical Saiic of Japan and Japan Saiical Yearbook. The ample period of he daa erie for Japan i For Taiwan, we ue wo differen meaure of labor income. Daa from Taiwan Naional Income Accoun begin earlier, bu ceae o repor he eparae proprieor' income erie ince 987. Thu, our fir Taiwan daa e (TWI) i over he period 95 o 987. Daa from Survey of Family Income and Expendiure in Taiwan begin laer and he erie in 965, 967, and 969 are inerpolaed due o lack of daa. The econd Taiwan daa e (TWII) i from 964 o 996. Becaue he proprieor' income equence in wo Taiwan daa e are no compaibly conruced, hey canno be combined o one. Figure plo he peronal aving rae for he wo counrie. 7 The high aving rae for Japan and Taiwan in he po-world War II period ha araced lo of aenion in empirical udie. The wo counrie did no begin wih a high aving rae, bu boh 7 Here he peronal aving i obained by ubracing privae conumpion from dipoable income. 9

21 experienced dramaic increae in he aving rae during economic developmen. 8 A for Japan' peronal aving rae, i diplay a pronounced hump-haped paern. Iniially i wa very low, reached i fir peak in 96 and a higher peak around , and hen eadily fell o i curren aionary rae. Like Japan, Taiwan' peronal aving rae alo exhibied an upward rend and hen reached a peak around 986 (TWI) or 993 (TWII). However, i i oo early o conclude ha Taiwan' aving rae will flucuae around he curren aionary rae. The wo counrie experienced riing aving rae in he proce of economic developmen. A heir economie maured, he aving rae in boh Japan and Taiwan began o decline oward he end of 970 and 980, repecively. For he hree daa e (one for Japan, wo for Taiwan), he raio uing he conruced labor income exhibi a mooher paern han ha uing wage compenaion, which indicae high mobiliy beween employee and owner of privae unincorporaed enerprie for privae agen in reponding o exernal hock. More imporanly, he proprieor' income, which i he major componen of houehold income in he early age of developmen, uually exhibi a differen rend from he 8 On he oher hand, baed on 5 OECD counrie for he period , Carroll and Summer (99) preened low frequency evidence ha here wa a nearly perfec equaliy beween conumpion growh and income growh. The aving rae i aionary. 0

22 wage compenaion. The dipoable income-labor income raio uing conruced labor income are ploed in Figure. Te for difference aionariy To e he difference aionariy (or uni roo non-aionariy) for each componen of c /, ˆ /, and / ), we apply Park and Choi' (988) J(,q) e and / y ( y y y y Augmened Dickey-Fuller (ADF) e. Given he known growh rae of and, y an arbirary choice of he iniial value of he / y erie will no change i nonaionariy. We imply aume ha he iniial ubience conumpion i niney percen of acual conumpion here. Thi arificial ubience conumpion raio equence, denoed a a / y, i ued o ubiue he unobervable y erie in / he uni-roo e. The null of difference aionary i rejeced when he J(p,q) aiic i maller han he criical value abulaed in Park and Choi (988). The parameer p in he J(p,q) e i he order of he ime polynomial in he null (uni-roo) hypohei, while he q denoe he order of he ime polynomial in he fied regreion. The J(p,q) e doe no require he eimaion of he long-run variance and ha an advanage over he Phillip and Perron' e and ADF e in ha neiher he bandwidh parameer nor he order of auoregreion need o be choen. The Mone Carlo experimen alo how ha he

23 J(p,q) e ha a able ize and i no dominaed by he ADF e in mall ample in erm of power. Table diplay J(,q) e reul for he null of he difference aionariy for he hree daa e. We expec he difference aionariy for each componen of / y. The J(,q) e wih q, 5 canno rejec he null a he 5% ignificance level for a c / y, y ˆ / y and / y ( m 0 and m 0.3% ) a expeced. Furhermore, afer differencing all of hee erie, he J(,q) e doe rejec he uni-roo null excep for he a difference of c / in TWII and for he difference of / y in Japan. y We nex repor he ADF e for he null of difference aionariy wih a ime rend in Table becaue i wa widely ued in he lieraure. Since coniderable evidence exi ha daa dependen mehod for elecing he value of he lag order in he ADF regreion are uperior han chooing a fixed order a priori, we follow he recurive -aiic procedure uggeed by Campbell and Perron (99). Reul of he ADF e for he hree daa e are generally conien wih he J(,q) e. There are wo excepion: c / erie in TWI and he difference of c / y erie in TWII; heir y ADF e rejec he uni-roo hypohei firmly. Even hough he above reul hould no be viewed a concluive evidence on he difference aionariy, i i accepable o aume ha here exi uni roo in he individual componen of / y. Empirical reul of coinegraion regreion

24 In he ligh of he reul obained in e for difference aionariy, we adop he following pecificaion for he re of he paper: c / y, y ˆ / y, and / y are aumed o have a uni roo around a linear ime rend. If he growh rae of labor income are aionary wihou a ime rend, hen equaion (7) implie ha he hree componen of / y are deerminiically coinegraed. Thu, we apply he CCR procedure 9 o c y yˆ ( m) e ) q i c e e 0 i (ime. y y i An imporan propery of he CCR procedure i ha linear rericion can be eed by e, which are free from nuiance parameer. Le H(p,q) aiic denoe he Wald aiic o e he hypohei p p q 0. Park (990) howed ha he H(p,q) aiic converge in diribuion o a ( q p) random variable under he null of coinegraion. According o Ogaki and Park' (997) definiion, o ay a e of difference aionary proce i deerminiic coinegraed require ha heir coinegraing vecor eliminae boh he ochaic and deerminiic rend. Sochaic coinegraion require only ha he ochaic rend componen of he erie are 9 The CCR procedure require an eimae of nuiance parameer uch a he long-run covariance of he diurbance in he yem. We ue Park and Ogaki (99) VAR prewhiening mehod wih Andrew (99) QS kernel and hi auomaic band widh parameer eimaor o eimae he nuiance parameer. The VAR of order one wa ued for prewhiening. 3

25 coinegraed. Therefore, he H(0,) aiic e he hypohei of he deerminiic coinegraing rericion while he H(,q) aiic e ochaic coinegraion. Table 3 repor he H(0,) e reul for he null of he deerminiic coinegraion among he hree componen of / y wih and wihou dummy variable. 0 The H(0,) e are more favorable for he pecificaion wih he dummy variable. Among he e aiic repored wihou a dummy variable, only one cae i inignifican a he 5% level (TWII wih m = 0.3%). While including dummy variable in regreion, none of he Taiwanee cae i ignificanly rejeced, bu he reul for Japan improve only marginally. The reul for he rejecion of deerminiic coinegraion appear o ugge ha he full e of aionariy rericion impoed by he aionariy of he growh rae of labor income and hu / y i oo rong for Japan. The ADF e how ha wheher he uni roo null for he growh rae of Japanee labor income fail or no depend on he rend pecificaion. The aiic favor he ime rend hypohei again he uni roo null. To ake ino accoun he decreaing growh rae of labor income in he raniion of developmen and o idenify he poible caue of he 0 There are wo even ha may be crucial for he aving behavior of open economie like Japan or Taiwan o change, he oil hock in 974 and he G5 Plaza Accord in Sepember 985. We eimae a crah model wih wo rucural breaking poin, 974 and 986, repecively. 4

26 rejecion, we drop he corending rericion among he individual componen of / y, and include a linear rend in he aic regreion. The H(,q) e i appropriae for eing he null of ochaic coinegraion among hree componen of / y. For Japan, he reul of he H(,q) e wih q =, 3, 4 (no repored here) favor he null of he ochaic coinegraion among hee variable now. Thee reul, ogeher wih he reul for he deerminiic coinegraion in Table 3, confirm ha he meaure of aving rae adjued for he permanen ubience conumpion can eliminae he rend componen once he growh rae of labor income i aionary. Table 3 alo repor coefficien eimae of and e e in he aic regreion uing Park' CCR procedure. Differen daa e yield very differen coefficien eimae. For example, when applying Japan and TWII wihou a dummy variable, he CCR eimae of e are all greaer han one. Noe ha e and ( r k) / r when he heoreical model i rue. According o our model, he real rae of reurn on he non-human wealh mu be well below zero and/or he expeced growh rae of conumpion wihou a ubience requiremen i negaive in order for o be above one, which i inconien wih he empirical regulariie of fa-growing Baed on he ize and power properie, Han and Ogaki (99) recommend he H(,q) e wih mall value of q when he ample ize i mall. 5

27 developing counrie. On he oher hand, when eimaing he deerminiic coinegraion regreion wih dummy variable, only he TWII eimae of e are greaer han one. Since a reaonable hould be poiive and le han one, our following dicuion will focu on he cae where he eimae of e i le han one. Tha i, we ue he daa e of Japan and TWI and heir eimae wih dummy variable included in he CCR regreion for he re of he paper. We now ue he CCR eimae of e and he eimaed reidual ( vˆ ) in he aic 0 regreion o generae he / y erie. According o he model, when financing he permanen ubience conumpion i he major concern in agen' ineremporal deciion of conumpion in he early coure of economic developmen, he relaively high value of / y make he value of / y ignificanly higher han he ŝ / y counerpar. A he economy grow, he imporance of / y in he deerminaion of aving behavior decline and y i expeced o exer decreaing effec on / / y over ime. Evenually, / y and ŝ / y will converge, and ŝ / y become a aionary proce. Tha i, he permanen ubience conumpion conideraion i capable of inducing he aionariy of /. y Figure 3 and 4 plo hoe generaed erie for Japan and Taiwan. Unlike he hump- haped peronal aving rae in Figure, Japan' ŝ / y erie now exhibi wo 6

28 deeper rough around 967 and 985 and hree mild peak during he whole ample period. The difference beween / and ŝ / y conrac unil he fir oil hock, y bu afer ha i ha no endency for convergence. The ubience conumpion requiremen appear o be helpful in explaining he riing aving rae in he 950 and 60 only. On he oher hand, plo in Figure 4 clearly indicae ha he ubience level of conumpion effecively induce he aionariy of Taiwanee / y. When conducing he formal uni roo e, he null of he difference aionariy wihou ime rend for Taiwanee / y can be rejeced firmly under he ADF e and he J(p,q) e. However, for Japanee / y he ame null can be rejeced under he J(p,q) e only. The weak evidence for Japan i conien wih he le aifacory reul of he previou H(p,q) e. Empirical reul and e for orhogonaliy rericion In he econd ep we eimae r and conduc he e for he orhogonaliy rericion baed upon he CCR eimae of and he generaed / y erie. Since ( ) / y / y, / y doe no conain exra informaion once / and y have been choen a inrumen. The inrumenal variable choen for he benchmark GMM procedure are z { k / yk, k, k q}. The lag 7

29 lengh of he inrumen variable (q) i from o 4. A q increae, more orhogonaliy condiion are employed in he eimaion. Table 4 repor he GMM eimae of r wih m 0 and m 0.3%, and he correponding e aiic. The model' orhogonaliy rericion canno be rejeced and he eimae of r are ignificanly poiive in all cae. Alhough he null hypohei i aified, he GMM eimae of r are oo high for Japan o uppor he heoreical model excep for one cae: when m 0.3% and when he lag lengh of he inrumen variable i four. In oher cae, he eimae of r for Japan fall in he 38.4%-53.0% range. Excluding hee cae from conideraion, he GMM eimae of r for Taiwan range from 8.9% o 3.4%. The eimaion reul are very plauible from he viewpoin of he permanen income hypohei. The value of eimaed r are alo cloe o hoe obained in Hayahi (98). 3 Keep in mind ha e and e 0[ /( m / r)] when he model i rue. To ake accoun for he problem of meauremen error and ime aggregaion, we inroduce a fir-order moving average proce in he error erm and elec inrumen ha lag wo period or more. See, e.g., Hall (988), Heaon (995), and Ory and Reinhar (99). 3 Uing po-war U.S. ime erie daa, Hayahi obained he eimae of r ranging from 3.% wihou any rericion on he ize of he liquidiy-conrained houehold in he populaion o 7.3% wihou he equaliy rericion beween r and. 8

30 We now have he eimae of e, e and r, and herefore can recover he unobervable ubience level of conumpion. I i confirmed ha he conumpion expendiure i above i ubience counerpar during he whole ample period for Japan and Taiwan. In addiion, a eniiviy analyi i conduced wih differen growh rae abou he ubience conumpion. Given he preumpion ha he growh rae of he ubience conumpion canno be higher han he eady-ae growh rae of oupu, we raie m o 0.5% and % per year and repea all of he eimaion and e above. In general, he empirical reul are robu o he choice of m. However, when m i a high a %, he CCR eimaion implie a low rae of convergence and a le aionary / y erie. 6. Concluding Remark A poined ou by Rebelo (99) and oher, a ubience conumpion requiremen induce a riing aving rae. However, unobervable ubience conumpion caue difficuly in empirical udy. Thi paper employ a wo-ep economeric procedure o olve hi problem. We e he implicaion of he permanen income hypohei wih ubience conumpion ha a permanen ubience conumpion i he driving force of a riing aving rae during economic 9

31 developmen. Even hough he model compleely abrac from he demographic conideraion of he life-cycle hypohei, we have found ubanial evidence for he permanen income hypohei wih ubience conumpion in Japan and Taiwan afer WWII. The coinegraion and orhogonaliy rericion impoed by he model canno be rejeced for Taiwan aiically, and all of he eimae of parameer are ignifican and wih he correc ign. On he oher hand, we find weak uppor for Japan. The ubience conumpion requiremen i helpful o explain he riing aving rae in he 950 and 60, bu i appear no an imporan facor for he changing of Japanee aving rae ince he oil hock. 30

32 Reference Andrew, D.W., 99, Heerokedaiciy and auocorrelaion conien covariance marix eimaion, Economerica 59, Akeon, A. and M. Ogaki, 993, Wealh-varying ineremporal elaiciy of ubiuion: Evidence from panel and aggregae daa, Mimeo, Wahingon: Inernaional Moneary Fund. Blinder, A.S. and A.S. Deaon, 985, The ime erie conumpion funcion reviied, Brooking Paper on Economic Aciviy, Campbell, J.Y., 987, Doe aving anicipae declining labor income? An alernaive e of he permanen income hypohei, Economerica 55, Campbell, J.Y. and P. Perron, 99, Pifall and opporuniie: Wha macroeconomi hould know abou uni roo, in: O. Blanchard and S. Ficher, ed., Macroeconomic Annual, (MIT, Cambridge, Ma.) 4-0. Carroll, C.D. and L.H. Summer, 99, Conumpion growh parallel income growh: Some new evidence, in: B.D. Bernheim and J.B. Shoven, ed., Naional Saving and Economic Performance, (Chicago Univeriy, Chicago) Chaerjee, S., 994, Traniional dynamic and he diribuion of wealh in a neoclaical growh model, Journal of Public Economic 54,

33 Chriiano, L.J., 989, Underanding Japan aving rae: he reconrucion hypohei, Quarerly Review, Federal Reerve Bank of Minneapoli, Spring: 0-5. Geroviz, M., 983, Saving and nuriion a low income, Journal of Poliical Economy 9, Hall, R.E., 988, Ineremporal ubiuion in conumpion, Journal of Poliical Economy 96, Han, H.L. and M. Ogaki, 99, Conumpion, income, and coinegraion: furher analyi, Rocheer Cener for Economic Reearch Working Paper No Hayahi, F., 98, The permanen income hypohei: eimaion and eing by inrumenal variable, Journal of Poliical Economy 90, Heaon, J., 995, An empirical inveigaion of ae pricing wih emporally dependen preference pecificaion, Economerica 63, Maddion, A., 99, A long-run perpecive on aving, Scandinavian Journal of Economic 94, Ogaki, M., J.D. Ory, and C..M. Reinhar, 996, Saving behavior in low- and middle-income developing counrie, IMF Saff Paper 43, Ory, J.D. and C..M. Reinhar, 99, Privae aving and erm of rade hock: evidence from developing counrie, IMF Saff Paper 39,

34 Park, J.Y., 990, Teing for uni roo and coinegraion by variable addiion, Advance in Economeric 8, Park, J.Y., 99, Canonical coinegraing regreion, Economerica 60, Park, J.Y. and B. Choi, 988, A new approach o eing for a uni roo, CAE Working Paper No. 88-3, Cornell Univeriy. Park, J.Y. and M. Ogaki, 99, Inference in coinegraed model uing VAR prewhiening o eimae horrun dynamic, Rocheer Cener for Economic Reearch Working Paper No. 8, Univeriy of Rocheer. Rebelo, S., 99, Growh in open economie, Carnegie-Rocheer Conference Serie on Public Policy 36, Zellner, A., 960, Te of ome baic propoiion in he heory of conumpion, American Economic Review, Paper 50,

35 Table. J(p, q) aiic J(, ) J(, 3) J(, 4) J(, 5) Japan TWI TWII Japan TWI TWII c / y y / y / y c a m m 03. % / y y / y / y c a m m 03. % / y y / y / y a m m 03. % ( c / y ) 0.00* 0.058* 0.060* 0.074* ( y / y ) * 0.055* 0.53* / y a m m 03. % ( c / y ) * 0.048* 0.050* ( y / y ) * 0.06* 0.085* / y a m * 0.63* m 03. % * 0.74* ( c / y ) ( y / y ) * 0.047* 0.048* / y a m * 0.03* 0.08* 0.4* m 03. % 0.000* 0.03* 0.09* 0.7* Noe: * mean rejecion of he null a a 5% level. 34

36 Table. ADF e Japan TWI TWII Japan TWI TWII c lag aiic / y y / y / y c a m m 03. % / y * y / y / y c a m m 03. % / y 5 0. y / y / y a m m 03. % ( c / y ) * ( y / y ) * / y a m m 03. % ( c / y ) 3-5.6* ( y / y ) * / y a m * m 03. % a ( c / y ) * ( y / y ) * / y a m * m 03. % -4.60* Noe: * mean rejecion of he null a a 5% level, a mean rejecion of he null a a 0% level. 35

37 Table 3. Canonical Coinegraing Regreion Reul ê ê H(0,) Japan.040* * m 0 TWI 0.39* 5.70* 4.05* wihou TWII.95* 0.04* 3.954* dummy Japan.04* * m 03. % TWI 0.7* 5.398* 3.565* TWII.57* 0.06*.60 Japan 0.740* 0.09*.65* m 0 TWI 0.36* 4.796*.68 wih TWII.43* dummy Japan 0.730* 0.09* 0.685* m 03. % TWI 0.336* 4.9*. TWII.373* Noe: * mean ignifican a a 5% level 36

38 Table 4. Generalized Mehod of Momen Reul m 0 Japan Taiwan (TWI) q r r 0.437* * * * * * m 03. % q r r 0.384* * * * * * Noe: * mean ignifican a a 5% level. 37

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