Asian Development Bank Institute. ADBI Working Paper Series

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1 ADBI Wokn Pe Sees De Poly nd Eonom Gowh n Smll Oen Eonomy Model wh Poduve Govenmen Sendn Koh Fum Tkeo Ho nd Ryoj Ohdo No. 22 Al 2 Asn Develomen Bnk Insue

2 Koh Fum s ofesso Osk Unvesy n Osk Jn. Tkeo Ho s leue Hosush Unvesy n Tokyo. Ryoj Ohdo s n ssoe ofesso Osk Cy Unvesy n Osk Jn. The vews exessed n hs e e he vews of he uhos nd do no neessly efle he vews o oles of ADBI he Asn Develomen Bnk ADB s Bod of Deo o he ovenmens hey eesen. ADBI does no unee he uy of he d nluded n hs e nd es no esonsly fo ny onsequenes of he use. Temnoloy used my no neessly e onssen wh ADB offl ems. The Wokn Pe sees s onnuon of he fomely nmed Dsusson Pe sees he numen of he es onnued whou neuon o hne. ADBI s wokn es efle nl des on o nd e osed onlne fo dsusson. ADBI enoues edes o os he ommens on he mn e fo eh wokn e ven n he on elow. Some wokn es my develo no ohe foms of ulon. Suesed on: Fum K. T. Ho nd R. Ohdo. 2. De Poly nd Eonom Gowh n Smll Oen Eonomy Model wh Poduve Govenmen Sendn. ADBI Wokn Pe 22. Tokyo: Asn Develomen Bnk Insue. Avlle: h:// Plese on he uhos fo nfomon ou hs e. Koh Fum: fum@eon.osk-u..j Asn Develomen Bnk Insue Ksumsek Buldn 8F Ksumsek Chyod-ku Tokyo -68 Jn Tel: Fx: URL: E-ml: nfo@d.o 2 Asn Develomen Bnk Insue

3 ADBI Wokn Pe 22 Fum Ho nd Ohdo As In hs e we exmne he effes of nodun onsns on ovenmen oown usn onnuous-me oveln eneons model of smll oen eonomy. We onsde ovenmen ln onsns on he moun of ovenmen onds ousndn y eslshn n ue lm o e level fo he o of ovenmen onds o oss domes odu. We fs show h hee exs mulle sedy ses n he model smll oen eonomy. One s sedy se wh hh owh he ohe sedy se wh low owh. We nex exmne how hnes n he e level fo onds ffe eonom owh es he sedy ses. If he eonomy hs osve moun of sse holdn we on he follown esuls. When he ovenmen uns ude suluse n nese n he e level fo ovenmen onds edues he owh e of he low-owh eonomy u ses he owh e of he hh-owh eonomy. Howeve when he ovenmen uns ude def n nese n he e level fo ovenmen onds ses he owh e of he low-owh eonomy u edues he owh e of he hh-owh eonomy. If he eonomy hs neve moun of sse holdn he esuls e muous. JEL Clssfon:

4 ADBI Wokn Pe 22 Fum Ho nd Ohdo Conens. Inoduon The Model Households The Fm The Govenmen Model Equlum Che of he Model s Sedy Ses Conludn Remks... 9 Aendx... Refeenes... 2

5 ADBI Wokn Pe 22 Fum Ho nd Ohdo. INTRODUCTION Poduve ovenmen sendn n ly n mon ole n he develomen of eonome s shown y Bo 99. A well onzed ole sysem eslshed ou helh fles suh s snon nd ohe ully ovded seves e ndsensle fo eonom develomen. Howeve s somemes dfful fo develon eonomes o fnne hese seves euse of dffules ollen enouh x evenue o fnne hem. Theefoe develon eonomes usully mus ely on he ssue of ovenmen onds o fnne hese oss. Develon eonome howeve e usully sho of household svns. Theefoe hey my need o nodue foen l no he eonomes houh he sle of ovenmen onds o foen nvesos. If hee e no deque ules o dslne ovenn suh oown hese ounes mh oow eyond he ly o ey. In f mny develon eonomes hve fed he sk of deful. In he 98 some ounes n Ln Ame eneoed he olons o foen lendes. In he le 99 Es Asn ounes nd Russ wee onfoned wh ueny ss euse of he flh of foen l. In hs e we exmne he effes of nodun ules onsnn ovenmen oown y usn onnuous-me oveln eneons model of smll oen eonomy. We ssume h he ovenmen ses onsns on he moun of ovenmen onds h my e ssued y eslshn n ue lm o e level fo he o of ovenmen onds o oss domes odu GDP. In losed eonomy deese n hs o mles he ovenmen ude nd hus deese n ovenmen sendn o n nese n x evenue. In he smll oen eonomy model n hs e howeve he ovenmen n oow fom od. Theefoe he mehnsm y whh he ovenmen fnnes s exendue n smll oen eonomes n e snfnly dffeen fom h n losed eonomes. We fnd onsns on ovenmen oown n he Msh Tey fomely he Tey of he Euoen Unon EU] nd n he Code fo Fsl Sly of he Uned Kndom. The Msh eon ses h meme ounes of he EU nd ounes h hoe o jon he EU mus mnn ovenmen onds o GDP o of less hn 6%. The ode n he Uned Kndom ses h he o mus e ke unde 3%. Thee exss onsdele eseh sed on endoenous owh models wh oduve ovenmen sendn nd ovenmen onds. Bue nd Tunovsky 999 exmned how x u o x u wh exendue u ffes he ovenmen s lon-un fsl lne. Gene nd Semmle nvesed how he fnnn mehods of ovenmen ffe he eonomy. Ghosh nd Moumous 24 onsdeed h enevolen ovenmen ems o mxmze he welfe of households nd endoenously omed vous fsl ules unde sndd ovenmen ude onsns nd he olden ule of ul fnne. The olden ule onsns ovenmen o use evenue sed y ssun onds fo ul nvesmen only. They omed oml fsl oly unde hee dffeen emes nd showed h he olden ule n e n effeve onsn. In ons wh hese sude Fum Iwsko nd Ohdo 28 nodued n ue lm o e level fo ovenmen de elve o he sze of he eonomy no n endoenous owh model wh oduve ovenmen sendn. They showed h hee wee wo equlums: one ssoed wh hh owh he ohe ssoed wh low owh. They lso showed h ovenmen use of nome xes o onds mde he esuls snfnly dffeen. In ul hey showed h n nese n onds ousndn edued he eonom owh e he hh-owh sedy se nd sed he owh e he low-owh sedy se.

6 ADBI Wokn Pe 22 Fum Ho nd Ohdo All he nlyses ed n he eedn h wee lmed o losed eonomy howeve. In hs e we exend he nlyss o smll oen eonomy h hs osve moun of sse holdns. When he ovenmen s unnn ude sulus wh suh n eonomy he low-owh sedy se n nese n he ue lm o e level fo ovenmen onds edues he eonom owh e. On he ohe hnd n nese n he ond ue lm ses he owh e of n eonomy hh-owh sedy se wh ude sulus. Ths esul shly onss wh he esuls of Fum Iwsko nd Ohdo 28]. Howeve when he ovenmen s unnn ude def wh he eonomy he low-owh sedy se nd neses he e level fo ovenmen ond he eonom owh e s sed. On he ohe hnd he owh e s edued when he ond e level s nesed n n eonomy hh-owh sedy se wh ude defs. If he smll oen eonomy hs neve moun of sse holdn he esul eomes muous. Aodn o onvenonl wsdom n nese n ovenmen onds sos ve svns h would fnne umulon of ve l hus edun he level of l sok o he owh e of he eonomy Modln 965. Howeve when ovenmen exendue omoes he oduvy of ve l n nese n oduve ovenmen exendue houh ssun onds n omoe l umulon o se he eonom owh e. The emnde of hs e s esened n fou seons. Seon 2 deses he onsuon of he model of smll oen eonomy. Seon 3 onsdes he equlum of h model. The he of model equlum s exmned n Seon 4. Seon 5 onns onludn emks. 2. THE MODEL We onsde smll oen eonomy wh oveln eneons. I s ssumed h he snle fnl ood nd l e feely ded. Howeve ndvduls nno me oss he ouny ode. A onnuous-me oveln eneons model whou neeneonl lusm s used sed on Blnhd 985. Eh ndvdul fes n nsnneous oly of deh whh s denoed y. We ssume hs oly s onsn houh n ndvdul lfe. A evey nsn of me new oho s on. In ode o smlfy he nlys s ssumed h he oulon of hs eonomy s onsn ove me. Theefoe he h e eomes he sme s he deh e h. We ssume h he oulon sze s uny. 2. Households We fs onsde eesenve household. Le v e onsumon me v of eneon whee eneon s mles households on me s. The exeed uly of eneon s me s ven y: EU E z ln v] e v dv whee s he e of me efeene. ln v] e v We ssume h hee exss n ully f nsune omny s ssumed y Blnhd 985. The omny olles funds nd nvess hem n fms o n he nenonl fnnl mke. The ovenmen moses x on he euns. We ssume h he x kes he esdene se fom. Aodn o esdene-sed xon he nome of esdens s xed unfom e edless of s soue ouny whle nonesdens nome s no xed. Reuns fe x e d o he nsued households sll lvn. The on offeed y he nsune omny edsues nome fom eole who dv 2

7 ADBI Wokn Pe 22 Fum Ho nd Ohdo hve ded o hose who e sll lvn. An ndvdul s emum s equl o hs o he oly of deh. The nsued who e sll lvn n eeve he nsune emum s well s he nees fe x when he o she s lende. When he nsued s oowe he o she n only eeve he nsune emum nd ys he nees. Thu he flow ude onsn of eh onsume s w ] w < whee s fnnl sses me of eneon nd snds fo he wold nees e h s onsn ove me due he ssumon of smll ouny. The ovenmen moses x on he we nome of he household nd he x e kes he sme e s h of he nees x h. As menoned ove when kes neve vlue he nees ymen s no xed. We ssume h he nsune emum s no xed. We fuhe ssume h n ndvdul sules one un of lo nelslly h he we e w does no deend on he e of households nd h he newly on households e no endowed wh ny fnnl sses: s The oml ondons e ven y: 2 < ] T lm T e T 3 ] T lm T e < The fs equon 2 s he Eule equon nd he seond equon 3 s he nsvesly ondon. Aumulon of fnnl sses s deemned y 2 nd 3 fo ven nd w. { } Inen ude onsn nd mkn use of 2 nd 3 esul n he follown onsumon funon of eneon s me : h ] whee h s he humn welh me : h v w v ex ] dz dv ex v w v ] dz dv T < Len ee vle X defned y X x e x e ds fo eh vle x we fnd he ee onsumon funon: Tme dffeenon of 4 leds o he follown onsumon dynms: C A H ] 4 ] C s ] C 5 ] C < s ] 3

8 ADBI Wokn Pe 22 Fum Ho nd Ohdo 2.2 The Fm Follown Bo 99 he ovenmen sules oduve ul seves. The oduon funon kes he follown fom: Y F K G L 6 whee Y K G nd L e ouu ve l oduve ul seve nd lo nu esevely. Ths oduon funon ssfes he sndd neolssl he eselly he onsn euns o sle n oh nus. Aodnly we n nsfom hs no he follown nensve fom: G L K 7 Y f K f x K whee x G L /K. The fs ode ondons fo of mxmzon eome s follows: w f x G ωg 8 f x f x x 9 whee he wold nees e s onsn euse of he ssumon of smll ouny. Thu x eomes onsn ove me. We denoe hs onsn vlue s x. Fo le use we lule he follown: 2.3 The Govenmen G Y G f x K x f x The ovenmen fnnes s exendue y wo mehods. One s y levyn n nome x nd he ohe s y ssun onds. Thu he ovenmen's ude onsn s whee B snds fo ovenmen onds. B G A w A B B G w A < We ssume h he ovenmen hs n ue lm o e level fo ovenmen onds ousndn. The ovenmen es o mnn he o of onds o GDP onsn level. We ssume h he ovenmen djuss B /Y dully so h equls he ond e level n he lon un s follows: φ φ > 2 whee nd φ eesen he e level of ovenmen onds nd he djusmen oeffen of he ule esevely. Theefoe ven hs djusmen ule he ovenmen n oow fom he od o lne s ude. 3. MODEL EQUILIBRIUM We deve he equlum hs of he eonomy. In ode o deve he dynm sysem we defne he follown vles: C /Y A /Y nd Y / Y. Fom 5 we on he follown: 4

9 ADBI Wokn Pe 22 Fum Ho nd Ohdo 5 < ] ] 3 By he defnon of ee sses nd 8 we on he follown: < ] A C G x f A A C G x f A A Ths n e ewen s follows: < ] ] ω ω 4 Fom we on < ] ] ω ω 5 Noe h he seond em of he h sde of hs equon mens he my lne e GDP. Susun 2 no 5 we n on < ˆ ] ] ω φ φ ω φ φ 6 Beuse n he lon un he follown elonsh holds: < ] ] ω ω 7 When he households e edo h susun 6 no 3 nd 4 leds o he follown dynm sysem: ] 8 ω ]. 9 On he ohe hnd when he households e deo h < we on ] ˆ 2 ω ] ˆ.2 When he households e edo h 8 9 nd 2 onsue he dynm sysem of he eonomy. On he ohe hnd when he households e deo h < 2 2 nd 2 onsue he dynm sysem of he eonomy. Beuse 8 nd 9 do no ffe 2 s enouh o onsde only 8 nd 9. The sme les o 2 nd 2. We nex exmne he sedy se of he eonomy whee nd eome onsn ove me. We use he hse dm o do hs. lne s defned y he follown:

10 ADBI Wokn Pe 22 Fum Ho nd Ohdo By dffeenn 22 wh ese o we on d d ω. 22 ω ω ] We n show h lne s uwd slon downwd slon when he numeo of 23 kes osve neve vlue h ω > <. Fue shows n uwd slon lne nd Fue shows downwd slon lne esevely. When he x e kes suffenly le vlue nd he e level of ovenmen ond s suffenly smll lne eomes uwd slon. If he ovenmen uns ude suluse he esul s shown n Fue ends o e. If on he ohe hnd he ovenmen uns ude def lne eomes downwd slon nd he esul s shown n Fue ends o e. Fue : Model Dynms wh Govenmen Bude Suluses Low GowhE 2 Hh GowhE 2 6

11 ADBI Wokn Pe 22 Fum Ho nd Ohdo Fue : Model Dynms wh Govenmen Bude Defs Low GowhE 4 Hh GowhE 3 2 When he households e deo h < lne eomes ˆ ω ] < <. 24 When lne eomes uwd slon hs mles h ω >. Theefoe when he nequly ˆ > hold lne lso eomes uwd slon. We n heefoe < de lne s shown n Fue. < lne s defned y he follown ω ω ] 25 Ths s onvex ol. When < lne s defned y he follown: < ω ω ] < 26 7

12 ADBI Wokn Pe 22 Fum Ho nd Ohdo Ths s sh lne. We fous on he ses whee sedy ses exs. Beuse nd e jum vle ll sedy ses hve o e exmned. Thee n exs wo sedy ses. Fom 7 we n show h he eonomy h hs smlle moun of sses e GDP exhs hhe owh e. Thu n Fue E E 3 s he sedy se wh hh owh whle E 2 E 4 s he sedy se wh low owh. 4. CHARACTER OF THE MODEL S STEADY STATES Comve ss nlyses of he sedy ses e ondued o exmne he he. When he eonomy hs osve moun of sse holdns e GDP y usn 8 nd 9 we on he follown: 2 2 ω ] ω ] ] ω d d ] ω ω d d 24. When he my lne e GDP ω he sedy se kes osve neve vlue he oodnes of he veo h s mulled y d ke osve neve vlues. We on he effes of hne n he e level of ovenmen onds on he sse holdns when keen he x e onsn d s follows: d 27 ω ] d J 2 Hee J snds fo he deemnn of he oeffen mx of 27. Beuse he sedy se E exhs he sddle on sly he deemnn of he Jo mx J kes neve vlue. On he ohe hnd euse he sedy se E 2 nd E 4 e soue h unsle he deemnns of he Jo mx J 2 4 ke osve vlues see Aendx fo hese sns. F suose h he my lne kes osve vlue oh sedy se h ω >. Consumon mus ke osve vlues he sedy se nd he nequly > holds oh sedy ses. Then he esul of he omve ss fo he sse holdns he sedy se E s oose h he sedy se E 2. An nese n he e level of ovenmen onds edues he level of sse holdns he sedy se E. On he ohe hnd n nese n he e level of ovenmen onds neses he level of sse holdns he sedy ses E 2 nd E 4. We nex onsde how n nese n he e level of ovenmen onds ffes he owh e of he eonomy. Fom 25 n nese n he e level of ovenmen onds deeses he level of sse holdns he sedy se wh hh owh. By kn oun of 7 we n show h hs deese ses he owh e of he eonomy he sedy se E. Theefoe n nese n he e level of ovenmen onds ses he owh e of he hh-owh eonomy. On he ohe hnd s sed efoe we on he oose esul he sedy ses E 2 nd E 4. An nese n he e level of ovenmen onds edues he owh e of he low-owh eonomy. 8

13 ADBI Wokn Pe 22 Fum Ho nd Ohdo In he nlyss of losed eonomy Fum Iwsko nd Ohdo 28 showed h n nese n he e level of ovenmen onds edues he eonom owh e he sedy se wh hh owh. The oose esul ons n he sedy se wh low owh. The esen nlyss of smll oen eonomy shly onss wh he esul. In losed eonomy le moun of ovenmen onds lowes ve l n n oen eonomy howeve ovenmen n oow fom od. Theefoe he mehnsm y whh he ovenmen fnnes s exendue n oen eonomes woks n dffeen wy fom h n losed eonomes. Seond suose he ovenmen uns ude defs he oh low-owh nd hhowh sedy se h ω <. As n e seen fom 25 he esuls oned e omleely oose nd e sml o hose oned y Fum Iwsko nd Ohdo n hs se. In he model howeve he ovenmen mus mke s my lne osve n he lon un. When he eonomy hs neve moun of sse holdns e GDP y usn 2 nd 2 we on he follown: Consequenly we n on ˆ 2 ω ] 2 ω ] d d ˆ d ω d d ω ω ω ] ˆ d 3. 3 J 2 Beuse he elemen of he fs olumn nd he fs ow of he deemnn kes neve vlue he esul eomes muous n hs se. 5. CONCLUDING REMARKS A model of smll oen eonomy wh oveln eneons s onsued. The ovenmen sules oduve sendn n he eonomy. A oly ule fo ovenmen oown s nodued when he ovenmen eslshes onsns on he moun of ovenmen onds ousndn n he fom of n uwd lm o e level fo he o of ovenmen onds o GDP. We fs show h hee exs mulle sedy ses n he model smll oen eonomy. One s sedy se wh hh owh he ohe sedy se wh low owh. We nex exmne how hnes n he e level fo he o of ovenmen onds o GDP ffe he eonom owh es of he sedy ses. If he eonomy hs osve moun of sse holdn we on he follown esuls. When he ovenmen s unnn ude suluse n nese n he e level fo ovenmen onds edues he owh e of he lowowh eonomy u ses he owh e of he hh-owh eonomy. Howeve when he ovenmen s unnn ude def n nese n he e level fo ovenmen onds ses he owh e of he low-owh eonomy u edues he owh e of he hh-owh eonomy. The esuls oned n hs e hve mlons fo some Asn eonomes. Eonomes wh hh owh nlude he Peole s Reul of Chn nd Ind. On he ohe hnd eonomes wh low owh nlude Jn. Chnes n he ue lm o e level fo ovenmen onds ousndn would hve dffeen mlons fo hese wo yes of 3 9

14 ADBI Wokn Pe 22 Fum Ho nd Ohdo eonomes. Le us onsde he Jnese eonomy. The Jnese ovenmen s now unnn le defs o oe wh eonom dffules. An nese n he e level fo ovenmen onds ould hus omoe owh of he Jnese eonomy. Howeve he ovenmen nno oee wh ude defs onnuously. In he lon un mus un ude sulus. Hene onluson of hs e s h onnued neses n he e level fo he o of ovenmen onds o GDP n edue he owh of he Jnese eonomy. If he smll oen eonomy hs neve moun of sse holdn he model odues muous esuls. Whle he eonomes of develoed oune suh s Uned Se n hve neve moun of sse holdn develon eonomes fe vous dffules when hey hve neve moun of sse holdns. Theefoe he nlyl esuls n hs se do no hve ny mlons fo develon eonomes.

15 ADBI Wokn Pe 22 Fum Ho nd Ohdo APPENDIX Lelzn 8 nd 9 ound he sedy se E 24 we on 24. Due o he she of he uves deed n Fues nd he sn of he deemnn of he Jo mx kes neve vlue he sedy se E nd kes osve vlues he sedy ses E 2 nd E 4.

16 ADBI Wokn Pe 22 Fum Ho nd Ohdo REFERENCES Bo R. J. 99. Govenmen Sendn n Smle Model of Endoenous Gowh. Jounl of Poll Eonomy : s3-s25. Blnhd O De Def nd Fne Hozons. Jounl of Poll Eonomy 932: Bue N. nd Tunovsky S Bude Blne Welfe nd he Gowh Re: "Dynm Son" of he Lon-un Govenmen Bude. Jounl of Money Ced nd Bnkn. 3 2: Fum K. T. Iwsko nd R. Ohdo. 28. De Poly Rule Poduve Govenmen Sendn nd Mulle Gowh Phs. Moeonom Dynms 2 4: Ghosh S. nd I. A. Moumous. 24. Endoenous Gowh Welfe nd Budey Remes. Jounl of Moeonoms 26 4: Gene A. nd W. Semmle An Endoenous Gowh Model wh Pul Cl nd Govenmen Boown. Annls of Oeons Reseh 88: Endoenous Gowh Govenmen De nd Budey Remes. Jounl of Moeonoms 22 3: Modln F. 96. Lon-Run Imlons of Alenve Fsl Poles nd he Buden of he Nonl De. Eonom Jounl 7 284: