Public debt competition and policy coordination

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1 03/04/5 Pulc de compeon and polcy coodnaon Aa Yaa Nagoya Cy Unvey Aac Th pape analye he conequence o de polce n a wo-peod/wo-couny model. Whehe o no pulc de compeon eul n le ecen eouce allocaon eween pvae and pulc conumpon han unde polcy coopeaon amguou a po. The geae de wll eul n malle pulc good povon and malle pvae capal, alhough dec-nanced lump-um ane ene agen hough geae cuen conumpon. Aumng log-lnea uly and Co-Dougla poducon uncon, we can how ha pulc de compeon wll lead o geae pulc de and geae magnal ae o uuon eween pulc and pvae conumpon n each couny han unde polcy coopeaon. Keywod: cal compeon; pulc de; nenaonal capal moly JEL clacaon: E6; F34; H63 Coepondence: Aa Yaa, Gaduae School o Economc, Nagoya Cy Unvey, Yamanohaa, Muho-cho, Muho-u, Nagoya , Japan Emal: yaa@econ.nagoya-cu.ac.p

2 . Inoducon Snce he wold nancal c n 007 o 008, mo o he developed coune have nceaed he pulc de/gdp ao mulaneouly. Even hoe o mo EU coune have a exceeded he pecondon o a mo 60% o he de/gdp ao o onng he Euopean Moneay Unon accodng o he Maach Teay ee Fgue. Th n cona o he elavely aonay pulc de/gdp ao o he coune eoe he c. Snce he de/gdp ao have en n many, u no all, developed coune mulaneouly, hee ha eemed o e no ageemen on pulc de polcy eween coune n epone o he c. Thee ac ae an ngung queon: I he coune a o nceae he pulc de ndependenly, wee he level o pulc de geae han, equal o o malle han he one whch would e oaned unde polcy coodnaon? Govenmen may y o nceae he ocal welae y ung pulc ond and nceang cuen ncome o he domec agen pulc de no neual n he Bao 974 ene. Roun and Sach 989 poned ou ha Bao hypohe canno e appled o Euopean and ohe coune, and hey emphaed he mpoance o a polcal aco, ha, he degee o coheon n he govenmen. 3 I ha een nowaday well peceved ha naonal cal dec ceae negave exenale o ohe naon, o example, hough hghe nenaonal nee ae, heey ang he co o de nance o many ohe govenmen e.g., Hunga and Nelen, 998; Blanchad and Summe, 984. Thee govenmen ehavo may lead o he o-called pulc de compeon. Chang 990 howed ha he nenaonal exenale aocaed wh pulc de compeon eween coune eul n necenly lage cal dec, alhough aumng away phycal capal oc. Moe ecenly, Peon and Taelln 995 howed n a wo-couny model ha polcy coopeaon leave oh coune ee o, callng o a lage uplu han non-coopeave polcymang, and alo ndcaed ha unde cean condon, oh In 005, he Saly and Gowh Pac wa eved o a o e lexly applcale and, heeoe, he EU coune have een admed o have he udge dec/gdp ao hghe han 3% ae he evon. In ac, he pmay alance o coune uch a Fance, Gemany, U.S. and Canada howed a uplu n 000, maye a a eul o educng pulc de n he 990. Noway and Sweden ae excepon among hee coune. 3 Howeve, Edn and Ohlon 99 howed ha he eul o he geae udge dec unde mulpay coalon govenmen ound y Roun and Sach 989 manly due o mnoy govenmen, wheea De Haan and Sum 997 dd no nd even h ac lae. Woo 003 oaned he eul mla o hoe n De Haan and Sum 997 n a compehenve e ung a panel o 57 coune ove he peod om 970 o 990.

3 coune may have an ncenve o even unlaeally devae o he Nah aege. 4 Aumng a wo-peod/wo-couny model, he peen pape analye he conequence o pulc de compeon on he de level and compae hem wh hoe o polcy coodnaon eween coune. Alhough he magnal co o pulc conumpon hown o e alway hghe n Nah compeon han unde polcy coopeaon a any pulc de level, he magnal ae o uuon eween pulc and pvae conumpon,.e., he magnal ene o pulc conumpon, may no e geae unde coopeave opmum, a well nown n he leaue. By pecyng he uly and poducon uncon, hown ha pulc de Nah compeon end o lead coune o moe exceve pulc de han unde he polcy coodnaon. The geae de wll eul n a malle pulc good povon n he uue, alhough geae cuen conumpon ene agen hough dec-nanced lump-um ane. The nex econ noduce he model, whch mla o hoe n Wldan 988 and Yaa 04 cal compeon model. The conequence o Nah compeon and polcy coodnaon wll e examned and compaed n Secon 3. The nal econ povde ema.. Model Thee ae wo coune n he wold. Each couny aumed o e nhaed y a ngle mmole houehold ha ha ome unpeced egon-xed aco, whle capal move eely aco he ode. We alo aume ha he me hoon o he wold dvded no wo peod, he eng he peen and he econd he uue. The nal eouce endowmen n each couny a he egnnng o he peod denoed a R,. The nal eouce ae held y he houehold n each couny. The houehold allocae he nal dpoale eouce eween peen conumpon and avng o he uue. The poducon o pvae good undeaen only n he econd peod, ung homogeneou capal and he couny-xed aco. The govenmen n each couny ue pulc ond o nance lump-um ane o he domec houehold n he peod, and povde pulc good and epay de, nancng hem y un axe on capal, n he econd peod. Snce he nee on pulc de pad a he mae nee ae, he aggegae avng n he wold ae equaled o he um o he aggegae capal and pulc de n he wold a a whole n 4 Fcal coodnaon n a moneay unon ha alo een dcued ee, o example, Levne and Bocne, 994; Beema and Jenen, 005; Oano, 04. 3

4 equlum. Capal pad magnal poduc and he emande pad o he local edence a eun on he xed aco. Focung on he de polcy o each govenmen, we aume ha he ax ae n he econd peod ae declaed wh he govenmen commmen n he peod.. Houehold Opmaon o he houehold n couny can e wen a Max c, c u c [ u c g ] uec o R c and c, whee u c [ u c g ] he neempoal uly uncon o he houehold n couny, c conumpon o couny n h -h peod h,, h g pulc good povded n he econd peod, denoe avng n couny, denoe lump-um ane om he govenmen n couny n he econd peod, he woldwde eun ae on avng.e., one plu he nee ae n he econd peod, and and o he eun on he xed aco a po om he poducon n couny. denoe he me peeence aco, 0. The -ode condon o he uly maxmaon gve he ollowng condon: u ' c u ' c 0. 3 The opmal avng plan can e wen a 5,, whee 0, 0 and Poducon Po maxmaon o he pvae good poduce n couny can e wen a Max 5 whee he poducon uncon cly concave n capal oc. he ue co o capal and denoe he un ax on capal n couny n he econd peod 0. The -ode condon o po maxmaon : ' The ucp epeen he paal devave wh epec o he vaale, e.g., /. 4

5 The opmal demand plan o capal gven a:,. 7 Thu, he maxmed po wen a:,, ',, 8 whee ' 0..3 Govenmen Each govenmen chooe de polcy o maxme he welae o own couny nhaan, declang he ax ae o e adoped n he econd peod. The um o he epaymen o he pulc ond ued n he peod and pulc good hould e nanced y he ax evenue. Theeoe, pulc de polcy wll aec he pulc good povon n he econd peod, dependng upon change n he woldwde nee ae. In ohe wod, each govenmen may chooe own de polcy n epone o change n he ohe couny de polcy. Focung on he de polcy, we aume ha govenmen do no povde pulc good n he peod and ha govenmen e he capal ax ae a cean level,. 6 The udge conan o he govenmen n couny n he peod 9 whee he amoun o pulc ond ue. The econd-peod udge conan can e wen a: g. 0 Fo a gven ax ae, nce he govenmen can ndependenly chooe only one o he wo polcy vaale, he amoun o dec-nanced ncome ane and pulc good povon g, he pulc good povon deemned o a o ay he udge conan when pulc de choen y he govenmen..4 Capal mae equlum The equlum condon n he wold capal mae can e wen a:. The oal avng mu e equal o he um o capal nvemen and pulc de o oh coune. Savng and nvemen ae no necealy equal n each couny and capal oc n a couny may geneally e paly owned y he oegn houehold. 6 Yaa 04 analyed ax compeon n a mla model, aumng an endogenou avng-capal omaon. Howeve, he dd no conde pulc de. 5

6 .5 Equlum o he wold When he govenmen chooe de polcy,, we have a mae equlum ayng he ollowng condon: ' 0.,,,,. 3 The endogenou vaale ae and o polcy vaale.,.e.,, and,. Pulc good povon ae alo deemned endogenouly a a uncon o and o a o ay he udge conan 0. 7 Fom and 3, we oan / D 4 / D 5 / D 6 whee D ' ',, ;. Fo he aly o he mae, we aume ha D 0, wh whch we have / 0 and / 0 ; ohewe, moe de nduce moe capal nlow. 3. Nah equlum and coopeave de polcy In h econ we analye he Nah equlum n de compeon and he opmal coopeave de polcy eween he coune and hen compae hem om he vewpon o whehe o no he wold ageemen on de polcy decon eween coune deale o he uue welae o he coune Nah equlum The govenmen n couny chooe de polcy o a o maxme he neempoal welae o he houehold n own couny, ang he de polcy n he 7 Fom 0, g,, g, o,. 8 The peen model aume ha he me hoon o houehold and govenmen ae he ame a ha o he economy,.e., a dynay-ype model. Theeoe, he ocal oecve uncon con o peen and uue welae. 6

7 ohe couny,, a gven. The maxmaon polem o he govenmen n couny can e wen a: Max u R,, [ u,, ] 7 o gven and. Fom he -ode condon and mang ue o he haan uly maxmaon condon, we oan he ollowng condon: ' '. 8 u ' whee he le-hand de he magnal ae o uuon eween pulc good and econd-peod conumpon,.e., he magnal ene om an addonal upply o pulc good n em o he econd-peod conumpon, and he gh-hand de he magnal co. Fom 4 and 6, we can how he denomnao on he gh-hand de geae han. Fo he ae o expoonal mplcy we aume ha he coune ae ymmec n all apec, eng R R,,, and,, ;. In a ymmec equlum n whch no capal move eween coune,.e.,., we can how ha / ' / 0. 9 Mang ue o 9, 8 can e ewen a: ' /[ ]. 0 u ' The condon 0 mple ha pulc good ae excevely uppled elave o pvae econd-peod conumpon, nce, a well nown, he -e condon eque '/ u ',.e., he Samuelon ule. Th can e nepeed a ollow. Each govenmen wan o ae ene y choong geae pulc de nce ae he nee uden n Nah compeon le han ha would e n he cloed economy. The hghe nee ae end o nceae he epaymen co o pulc de n he econd peod, educng pulc expendue. On he ohe hand, pulc de cowd ou pvae capal omaon and heey deceae po o he couny xed-aco, educng pvae econd-peod conumpon. Condon 0 how ha he dec-nanced ane n he peod deceae pvae econd-peod conumpon moe han pulc good povon n he peence o un axaon on capal. 7

8 3. Polcy coodnaon Nex, we examne he de polcy unde an nenaonal ageemen on de polcy heeae, emed coopeave de polcy. When de polcy ae coodnaed o e he ame eween ymmec coune, home avng wll equal oegn avng; ha, all home avng wll e nveed n he home couny, and all he oegn avng wll e nveed n he oegn couny, epecvely. Thu, ollowng Kehoe 989, he ocal welae maxmaon polem o govenmen eemle ha o a govenmen n a cloed economy. Theeoe, n examnng he coopeave de polcy, we conde he opmal de polcy n a cloed economy, whee avng ae equal o capal omaon,.e.,,,, whle he govenmen udge conan n he wo peod ae and g, epecvely. The ocally opmal condon ll gven y 8. Howeve, n he cloed opmum, he eec o a change n de polcy on capal and he eun ae ae gven a: ~ D ~ D ~ whee D '. Fom a eaon mla o ha n he pevou cae o open ~ econome, we aume ha D 0. Then, we have / 0 and / 0. Snce we can alo how ha / ' / 0, he opmum condon can e wen a: ' /[ ]. 3 u ' Tha, even n he cloed economy cae, he govenmen wll no acheve he e opmum. Th ecaue pulc good ae nanced y he evenue om doonal un capal axaon, le he co o epaymen o pulc de. Tha, pulc de no neual. Theeoe, a change n pulc de ale he opmal neempoal eouce allocaon. 3.3 Compaon eween Nah equlum and coopeave opmum and he polcy mplcaon Now we compae he level o pulc de n he Nah equlum and coopeave opmum. A can e een om 4-6 and -, he macoeconomc vaale ae deen value n he wo uaon. Theeoe, we examne whehe he 8

9 coopeave opmum level o pulc de geae han, equal o o malle han he level a he Nah equlum y evaluang he Nah equlum condon n em o he value a he coopeave opmum. Aachng he ucp OpenNah o he Nah equlum and Coopeao n o Coopeave opmum, epecvely, and mang ue o 4-6 and -, we can how ha ' u ' Coopeaon Coopeaon 4 OpenNah whee oh de ae evaluaed y he coopeave opmum value ee Appendx A. Theeoe, he Nah equlum and he coopeave opmum do no concde. The magnal co o pulc good n em o pvae econd-peod conumpon n he Nah equlum alway lowe han unde he coopeaon o any. Snce he magnal co hould e equal o he magnal ene.e., he magnal ae o uuon eween pvae and pulc conumpon, he nequaly eem o mply ha '/ u ' Coopeaon '/ u ' OpenNah hold. Howeve, no necealy he cae nce he magnal ene and co o he Nah compeon wll no concde a he coopeave opmum. A well nown, we canno ay a po whehe he level o pulc de n he Nah equlum geae han, equal o, o malle han he opmum level unde coopeave de polcy e.g., Anon and Sen, 974. Pulc de cowd ou pvae capal omaon, ang he nee ae. The nceaed nee ae wll e malle n an open Nah equlum han unde he coopeaon ee 6 and. When no gea o negavely lage, he negave eec o he hghe nee ae on capal omaon hough change n avng wll e geae unde he coopeaon. Th n un end o ae he nee ae moe. Whle he hghe nee ae aec povely pvae econd-peod conumpon, he malle pvae capal educe he econd-peod conumpon hough change n po. On he ohe hand, he hgh nee ae ogehe wh he educed pvae capal deceae pulc good povon. Thu, whehe he magnal ae o uuon eween pulc and pvae conumpon n a Nah equlum geae han, equal o o malle han ha unde polcy coopeaon depend on he epecve eec o de ue on he pulc and pvae conumpon n he epecve uaon. Thu, we nex examne he level o pulc de n Nah equlum and unde 9

10 coopeaon y pecyng he uly uncon a a log-lnea uncon o lecycle conumpon and pulc good,.e., ln c [lnc ln g] whee denoe he me dcoun aco, and he poducon uncon a a Co-Dougla poducon uncon,.e., A whee 0. 9 Wh hee peccaon, we oan he Nah equlum condon: R /{ } 5a [ '] and he coopeave opmum condon: R /{ } 5 [ '] whee A an A. Fom hee condon, we can oan he ollowng eul: Popoon Aume a log-lnea uly uncon o pvae and pulc conumpon and a Co-Dougla poducon uncon. In a Nah equlum each govenmen wll have geae pulc de and povde le pulc good han unde a coopeave de polcy. Poo: See Appendx B. Snce pulc de cowd ou pvae capal omaon, heey educng he ax evenue, and he epaymen o he de educe he popoon o he ax evenue pen on pulc good povon, a geae pulc de lead o elavely le pulc good n a Nah equlum. Theeoe, a can e een y deenang he le-hand de o 5 wh epec o he pulc de level, we can how ha he magnal ae o uuon eween pulc and pvae conumpon geae n a Nah equlum han unde he coopeave equlum n hee peccaon o uncon, '/ u ' OepnNah '/ u ' Coopeaon. I hould e noed ha alhough he nequaly eem o mply ha he eouce allocaon eween pulc and pvae conumpon n he econd peod moe ecen n he Nah equlum, he coune have un capal axe whch caue doon n he neempoal eouce allocaon,.e., n he econd-e opmum eng. Thu, doe no necealy mply he welae o coune hghe n he Nah equlum. 9 Condeng he cae o ymmec coune, we om he upecp. 0

11 A h age we conde a many-couny cae ely. We can how ha when he nume o coune goe o nny, we wll have he Samuelon ule o pvae and pulc conumpon n he econd peod n each couny n Nah equlum ee Appendx B. Howeve, he ule n uch a Nah equlum wll no e he neempoal woldwde -e opmum nce coune wll have moe pulc de when he nume o coune nceae. In ac, even he nume o coune wee o each nny, he coopeave opmum would no ay he Samuelon ule. I hould e noed ha h hold even ll unde moe geneal uly and poducon uncon ee Appendx A. Th uaon emncen o a pone dlemma Concludng ema We have hown ha coune may have geae pulc de n Nah equlum han unde polcy coodnaon. Th eul can e nuvely nepeed a ollow. A e n he nee ae due o an nceae n pulc de condeed o e lowe n Nah equlum han unde coopeaon y each govenmen nce he hoc wll e aoed y he wold capal mae, ha, he cowdng-ou eec condeed o e pead ove coune. On he ohe hand, he cowdng ou eec n a couny wll aec he economy unde he coopeave polcy eween ymmec coune a each economy cloed. A a nal ema, we ely conde he welae eec o de polcy. Dec-nanced ncome ane n a couny do no lowe he neempoal ocal welae o he economy. Alhough he econd-peod conumpon and pulc good povon deceae, he -peod conumpon wll nceae. The neempoal welae eec depend on he elave magnude o hee wo eec. Howeve, a couny ha geae pulc de n he peen peod, he welae o he economy n he uue wll e lowe. In h ene, Nah pulc de compeon h he heave uden o dec-nanced expendue n he peen o he uue. Appendx A Fom 4 6, we have 0 Wldan 988 cauoned ha ymmec Nah equla may no e he only one pole.

12 0 ' ' OpenNah A and, om 0 ' Coopeaon. A Snce oh de o A and A ae evaluaed a coopeave opmum, we have OpenNah Coopeaon ] ' ' '][ [ 0 '] [ A3 whee we aume ha 0 D and 0 ~ D alway hold. In a ymmec couny cae, A3 ecome OpenNah Coopeaon 0 ] ' [. A3 I pove u ucenly mall o negave, he deence on he gh-hand de o A3 wll e gea. Appendx B F we dene a uncon:,, ] [ n A A n A, A4 whch he econd em o he denomnao on he gh-hand de o 5a when n and ha o 5 when n. Then he yem o he equaon ],, /[ n R A5,, A6 gve he oluon, o a gven n, n, whee

13 3 A n[ A A ] [ ] A7 A n[ A A 0 ] [ A ] 0. A9 n n [ A A ] The gn o A7 amguou. In ode o examne he gn o A7, we examne he eec o an nceae n he nal eouce on Nah equlum capal oc, d / dr. Fom A5 and A6 we oan A8 H H H d / dn d / dn 0 B A0 whee d d H { [ R '] [ R ] } d d A H { [ R ]} 0 A B 0 A3 H A 0. A4 Fom A0 and aumng H H H H 0, we oan d dr H B. A5 I plaule ha an nceae n he nal eouce nceae he equlum capal oh n Nah equlum and n coopeave opmum.e., o n,. Aumng h cae and ang A3 no condeaon, we can aume ha H 0. A6 Fom A5 and A6, we have H H H d / dn d / dn 0 H3 A7 whee H3 0. A8 n 3

14 Theeoe, we oan d dn d dn H H H3 H 0 A9 H3 0. A0 Fom A9 and A0, pulc de geae n a Nah equlum han unde polcy coopeaon whle pvae capal omaon malle n he Nah equlum. The vaale n n A4 can e een a he nume o coune n he cae o a many-couny Nah equlum a can e een om he analye n Wldan 988 and Yaa 04. Theeoe, he eul A9 mple ha a he nume o coune nceae n Nah equlum, he pulc de o each couny wll e geae. 4

15 Acnowledgemen The auho han he emna pacpan a he Nagoya Macoeconomc Wohop o he commen. Reeence Anon, A. B., Sen, N., 974. Pgou, axaon and pulc good. Revew o Economc Sude 4, 9-8. Bao, R. J., 974. Ae govenmen ond ne wealh? Jounal o Polcal Economy 86, Beema, R. M. W. J., Jenen, H., 005. Moneay and cal polcy neacon n a mco-ounded model o a moneay unon. Jounal o Inenaonal Economc 67, Blanchad, O., Summe, L. H., 984. Pepecve on hgh wold eal nee ae. Boong Pape on Economc Acvy 5, Chang, R., 990. Inenaonal coodnaon o cal dec. Jounal o Moneay Economc 5 3, de Haan, J., Sum, J., 997. Polcal and economc deemnan o OECD udge dec and govenmen expendue: a envegaon. Euopean Jounal o Polcal Economy 34, Eden, P., Ohlon, H., 99. Polcal deemnan o udge dec: coalon eec veu mnoy eec. Euopean Economc Revew 358, Hunga, H., Nelen, S. B., 998. I coodnaon o cal dec neceay? Cene o Economc Polcy Reeach Dcuon Pape No Levne, P., Bocne, A., 994. Fcal polcy coodnaon and EMU: A dynamc game appoach. Jounal o Economc Dynamc and Conol 8 3-4, Oano, E., 04. How mpoan cal polcy coopeaon n a cuency unon? Jounal o Economc Dynamc and Conol 38, Peon, T., Taelln, G., 995. Doule-edged ncenve: Inuon and polcy coodnaon. In: G. M. Goman, K. Rogo ed. Handoo o Inenaonal Economc. Noh-Holland, Amedam, Chap. 38, pp Roun, N., Sach, J. D., 989. Polcal and economc deemnan o udge dec n he ndual democace. Euopean Economc Revew 335, Wldan, D., 988. Nah equlum n model o cal compeon. Jounal o Pulc Economc 35, Woo, J., 003. Economc, polcal, and nuonal deemnan o pulc dec. Jounal o Pulc Economc 873-4,

16 Yaa, A., 04. Capal ax compeon and coopeaon wh endogenou capa; omaon. Revew o Inenaonal Economc 3,

17 Fgue. Pulc de/gdp ao 80 % yea Aua Belgum Canada Denma Fance Gemany Geece Iceland Ialy Luxemoug Neheland Noway Pougal Span Sweden Sweland Uned Kngdom Uned Sae Souce: OECD 0 OECD Economc Ouloo No. 9: Sac and Poecon 7