Fiscal and Monetary Policies and Economic Growth

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1 Fsal and oneay oles and Eonom Gowh osa Ala Aademy of Eonom Sudes Buhaes hs daf : Januay 23 epaed fo he Euopean oneay Unon Semna Euopean Unvesy Insue, Floene Eleon opy avalable a: hp://ssn.om/absa258

2 Absa he pape analyses he way n whh moneay and fsal poly nfluenes he pefomanes of eonom gowh. he analyss s made on he bass of a dynam model wh dsee vaables of he Sdaus- Bo ype, wh nfne-lved households and money n he uly funon. he model s wh a epesenave pvae agen and a govenmen seo onssng of a onsoldaed fsal auhoy and enal ban. Households eeve an exogenous peshable endowmen eah peod, dede abou onsumpon and pay ne eal lump-sum ax. he sae vaable of he model s govenmen deb, and he deson vaables ae: onsumpon and he amoun of money deaned by he agen. he opmaly ondons ae obaned by usng he axmum nple fo dsee dynam sysems. A qualave analyss of he opmal aeoes s pefomed, on he bass of he nfomaon povded by he axmum nple, onenng he dynams of he dual vaable and he popees of he Lagange mulples. Fnally, we analyze he nfluene of seveal moneay and fsal desons on he opmal aeoes and on he pefomane-funon of he model. JEL Clasfaon : C 6, D 99,E 3, E 4, E 62, E 63, H 62, H 63, O 4. Keywods: Eonom Gowh, oneay oly, Fsal oly, Fsal Solveny, axmum nple osa Ala, Dooal Shool of Fnane and Banng, Aademy of Eonom Sudes, 6 aa Romana, se., Buhaes, Romana e-mal: mala@ase.o mala@sane.o hp:// Eleon opy avalable a: hp://ssn.om/absa258

3 Conens.Inoduon he odel Household and Govenmen Behavo he Opmzaon oblem Qualave Analyss of Opmal aeoes ansvesaly Condons he Case of Benoull ype Uly Funons 3 3. Compably beween oneay and Fsal oly. Fsal Solveny.6 4. Conlusons..9 Refeenes 2 2

4 . Inoduon In een yeas elave effeveness of moneay and fsal poly aon on eonom gowh has been debaed by boh eonomss and poly maes. he adonal opmal ueny aeas leaue poned ou long ago ha, n a moneay unon, fsal poly has o play a moe mpoan ole n ylal sablzaon gven he loss of naonal moneay ndependene. hs s paulaly he ase f shos ae no pefely oelaed aoss fones. Fsal flexbly, ogehe wh budgeay dsplne and o-odnaon, has ome o be seen as a enal plla of fsal poly n a ueny aea (Commsson, 99). he Sably and Gowh a (SG) has been he opeaonal esponse of EU ounes o he ques fo budgeay dsplne n EU. Reen heoeal and empal developmens have shed new lgh on he old ssue of he neaon beween moneay and fsal auhoes. hee ae numeous sudes, boh heoeal and empal, analyzng he elaon beween nflaon and long-un gowh. In he pas deade he developmen of he endogenous gowh leaue poneeed by Rome (986), Luas (988), and Rebelo (99) has enhaned ou undesandng abou how an eonomy s gowh pefomane an be affeed by publ poles. Fo nsane, Bao (99) and Kng and Rebelo (99) sudy he effes of fsal poles, suh as govenmen spendng and axaon, on eonom gowh. he geneal onluson s ha axaon advesely affes long-un gowh pefomane and ha he quanave mpas ae muh lage han hose found n exogenous gowh models. Cha, Jones, and anuell (995) and van de loeg and Alogosoufs (994) examne he effes of moneay poles, suh as hanges n he gowh aes of nomnal money supply, on long-un eal avy. hese auhos fnd suppo fo he onvenonal wsdom ha nflaon and long-un gowh ae nvesely elaed. hese sudes also epesen an advane n ou undesandng of he mpa of alenave poles on nflaon and gowh. Reenly eonomss have been payng neasng aenon o a dynam geneal equlbum appoah o he heoy of pe level ha s ofen alled he fsal heoy of he pe level, o FL. hs way of hnng emphaszes he ole of fsal and moneay poly n deemnng he s and eun popees of govenmen 3

5 lables. I s paulaly useful n analyzng poposals fo lage-sale nsuonal hanges ha mply shfs n moneay and fsal poles. When dollazaon s onsdeed fom hs pespeve, some dsadvanages ae bough o lgh ha may no be so appaen fom ohe pons of vew. he so-alled fsal heoy of he pe level (FL) has hghlghed ha, f govenmen solveny s no guaaneed, moneay poly wll no be able o onol he pe level. In ode o ensue sably, fsal poly has o ea suffenly songly o a se n he nees ae n he even of nflaonay pessues by neasng he pmay suplus. In ohe wods, moneay poly amng a eepng nflaon n he as he ECD s mandaed o behave has o go hand-n-hand wh a fsal poly obeyng a solveny onsan. One he FL s appled o he EU nsuonal se-up, howeve, seemngly dffeen onlusons ae dawn. Whle Sms (999) onsdes he aash um SG ules nsuffen o ule ou FL s doom senao, Canzone and Dba (2) onlude ha he SG appeas fa oo s fom he pon of vew of guaaneeng fsal solveny. he lae auhos, n paula, all fo shfng aenon fom aual o ylally-adused budge balanes n assessng he omplane of EU membes wh budgeay pudene so as no o hampe fsal sablzaon. 2. he model 2. Household and govenmen behavo In hs seon we sudy a dynam model, ognally due o Obsfeld and Rogoff (983), ha shows how sandad moneay models have a onnuum of equlbum me pahs fo he nflaon ae. he model s a Sdaus Bo ype model wh nfne-lved households and money n he uly funon. Suh models ae ones n whh s ommon fo Radan equvalene esuls o be obaned, whh maes he fsals heoy s lam moe emaable han f developed n a model of he ovelappng geneaons ype. hs ype of models was used by seveal 4

6 auhos, suh as Woodfod (994, 995, 2), Sms (994, 996), Callum (998), Bue (999, 2), Kohelaoa and helan (999), Chanda and Nolan (22). he model s wh a epesenave pvae agen and a govenmen seo, onssng of a onsoldaed fsal auhoy and enal ban. hee s no uneany and maes ae omplee. me ndexed by s measued n dsee nevals of equal lengh, nomalzed o uny. Households eeve an exogenous peshable endowmen, y >, eah peod, onsume and pay ne eal lump-sum ax h. he money pe of oupu n peod s. he quanes of money and nomnal bonds ousandng a he begnnng of peod (and he end of peod -) ae denoed, espevely B. he s one-peod s-fee nomnal nees ae n peod, and he one-peod s-fee eal nees ae n peod. he Fshe equaon s: whee π π. he sngle-peod household budge onsan s: B B y h, (2) () We denoe: W B (3) In ode o ansfom nequaly (2) no an equaon, we nodue he sla vaable x : W W x ( y h ), x, In equlbum, when planned expendue equals supply, follows ha he eonomy-wde esoue onsan s gven by: g y, (5) (4) 5

7 6 whee we denoed by g eal govenmen expendue n peod. Equaon (4) beomes: ( ), x, x h g W W (6) o, ( ) x g h W W ( 6 ) whee g h s pmay suplus. he dffeene equaon an be solved fowad o yeld: W B W ( ) x g h (7) If he ansvesaly ondon: W lm (8) s sasfed, hen, fom (7), follows: ( ) x g h B (9) Relaonshp (9) epesens a solveny ondon fo he govenmen, o a non- onz game ondon (As and aellno 998). Fom (9), subsung y g, we oban he solveny ondon fo households: B ( ) ] x h y ()

8 2.2 he Opmzaon oblem he epesenave onsume maxmzes he funonal J gven by (): J γ U, () whee U (, ) denoes he uly, neasng n boh agumens, sly onave and we dffeenable,.e.: and he Hessan: U U z s negave defne. oeove, (, ) >, U (, ) U (2) z > U z U zz (3) lm U, lm U z, z (4) lm U, We denoed by: (5) (6) and γ s he dsoun fao whh equals: γ ; δ > δ whee δ> s he subeve ae of me pefeene. (7) he epesenave agen maxmzes () sube o he followng dynam equaon: W gven and: ( )[ W ( y h )] x W (8) W (9) x (2) lm W (2) 7

9 8 Condon (9) an be wen as: o B B (9`) In ode o oban he opmaly ondons, we shall apply he axmum nple fo dynam sysems wh dsee vaables (Ala, 976). he Hamlonan s: ( ) ( ) [ ] { } ψ γ x h y W, U H ( ) ( ) [ ] ( ) { } λ x h y W x µ (22) whee we denoed by ψ he dual vaable, λ and µ ae he Lagange mulples oespondng o onsans (9) and (2). he opmaly ondons ae: x H H H (23) o ( ) ( ) ( ) µ ψ λ ψ γ λ ψ γ ' z ', U, U (24) he dynam equaon of he dual vaable ψ s:

10 o ψ H W ( ) ψ ( ) λ (25) ψ (26) Conenng he Lagange mulples, he axmum nple povdes he followng nfomaon: λ µ [ W ] ; λ ; µ x (27) Fom he seond ondon (29) we an see ha x > mples µ. In hs ase, fom he hd elaon (24) would follow Ψ µ, whh would mae he poblem senseless. I follows ha x,, hene he onsume budge onsan (2) on he opmal aeoy s sasfed as an equaly. Fom he fs elaon (27) follows ha λ > mples W,.e. B. In ohe wods, f λ >, hen he agen wll no buy bonds n he gven peod. We pefom he subsuons: ψ λ q ; α (28) γ γ In hs ase, he opmaly ondons (24) beome: U U, ( ) ( q α ), q ( ) α (29) and he dynam equaon beomes: o q γ ( )( q α ) 9

11 q q α (3) γ ( ) 2.3 Qualave analyss of opmal aeoes In wha follows, o falae he analyss, we assume ha he uly funon s sepaable n boh agumens: U (, ) V ( ) ϕ( ) (3) In hs ase, he opmaly ondons (29) beome: V '( ) ( ) ( q α ) (32) ϕ '( ) q ( ) α (33) If, n ohe wods, f he agen buys bonds he n h mulple α B > vanshes and he elaons (3) (33) beome: q q γ ( ) (34) V '( ) ( ) q (35) ϕ '( ) q (36) Wng he opmaly ondon (35) fo wo onseuve peods, we have: V '( ) ( ) q V'( ) ( ) q and, ang no aoun elaon (34), follows: V '( ) V '( ) γ (37)

12 Denong π (38) whee π - sands fo nflaon ae, elaon (37) beomes: ) V'( ) V'( δ (39) whee δ s he subeve ae of pefeene and s he s-fee eal nees ae. Relaon (39) allows o denfy he followng suaons: a) f δ, hen b) f δ >, hen > ) f δ <, hen < heefoe, dependng on he evoluon of nflaon and of he s-fee nomnal nees ae, onsumpon an be onsan, neasng o deeasng. o denfy he evoluon of he demand fo money, we use opmaly ondon (36). We oban: ( ) ' ' γ ϕ ϕ (4) o ' ' δ ϕ ϕ (4) If we adm ha: a) nflaon s onsan: π b)

13 ) δ π hen, fom (4), we oban: ϕ' ϕ' o and (42) π. hus, unde assumpons (a), (b), (), he demand fo money gowhs wh he same ae as nflaon: ( π) (43) 2.4. ansvesaly ondons Fo he opmal aeoes, he axmum nple povdes he ansvesaly ondon: lm ψ W (44) ang no aoun he subsuon (28), elaon (44) beomes: lm γ q W (45) Sne (45) beomes: W B wh B and, he ansvesaly ondon lm γ q B (46) 2

14 3 q lm γ (47) Fom he dynam equaon (34) fo he dual vaable, we oban: γ q q (48) ang no aoun elaon (48), he ansvesaly ondons an be wen as: B lm (46 ) lm (47 ) Rema: Relaon (2), gven eale, follows fom (46 ) and (47 ). If he nomnal s-fee nees ae s onsan:, (49) hen he ansvesaly ondons beome: B lm (46 ) lm (47 ) hs means ha he sequenes { N } B and { N } { should nease slowe han he sequene N

15 2.5. he ase of Benoull ype uly funons In ode o have a onvenen paame example, we assume ha he uly funons V(.) and φ(.) ae of Benoull ype,.e. he elasy of magnal uly s onsan. Le us suppose ha : V σ σ () ϕ whee σ (,). In hs ase, ondon (39) dedued fom he opmaly ondons beomes: (5) σ (5) δ Relaon (5) epesens a dynam equaon fo he onol vaable. As a mae of fa, s nown ha he Benoull ype uly funons ae he only uly funons allowng he nfeene of a dynam equaon fo he onol vaable. Relaon (5) shows ha, n ode o now he dynams of opmal onsumpon, s suffen o now he evoluon of he s-fee eal nees ae, as well as he nal value of onsumpon. Fom (5) follows: o σ (5 ) δ σ δ (52) As onens he demand fo money, fom elaons (35) and (36) we oban: ϕ V ( ) Subsung he expessons of he devaves, we oban (53) 4

16 σ ang no aoun ha, elaon (54) an be wen as: (54) σ (55) I an be seen ha he demand fo money neases as and nease and deeases as neases, whh s onssen wh he popees ha a funon of money demand should have. We denoe: m (56) Fom (55), follows: σ π m (57) I an be seen ha m deeases as he nflaon ae π neases. If he nomnal nees ae and nflaon ae ae onsan and, moeove, δ (58) π C hen, fom (5), follows ha onsumpon s onsan,.e., (59) In hs ase, he eal demand fo money wll also be onsan: m π Fom (58) we oban he nomnal nees ae: ( δ)( π) and fomula (6) beomes σ (6) (6) 5

17 m π ( δ)( π) σ (62) heefoe, unde he above assumpon, f he Cenal Ban dedes abou he magnude of he nflaon ae π, he magnude of he nomnal nees ae wll be gven by (6), and he eal demand fo money wll be gven by (62). 3. Compably beween oneay and Fsal oly. Fsal Solveny. he neaon beween moneay and fsal poly emans a op of nense nees o maoeonomss. In hs seon, we adop seveal smple assumpons onenng moneay and fsal poly, n ode o see how he Fsal Solveny ondons ae sasfed (hese ae, n fa, ansvesaly ondons (46 ) and (47 ) ). As onens he moneay poly of he Cenal Ban, we assume ha he followng ondons ae sasfed: a). onsan nflaon ae; b). onsan nomnal nees ae. oeove, we assume ha he nomnal nees ae s ha gven by he fomula (6), whh mples onsan onsumpon. Fo he sae of smply, we assume ha he exogenous endowmen y s he same n eah peod: y y y (63) Sne he eal govenmen expendue n eah peod s g y follows ha hs s also onsan, hene g g g (64) 6

18 Dvdng by he budge equaon (2) of he household, we oban Denong b B B y h (65) B ; m (66) and ang no aoun ha y-g, elaon (66) an be wen as b b (g h ) [m ( π) m ] (67) ang no aoun he assumpons onenng nflaon ae and nomnal nees ae, follows ha he eal demand fo money s also onsan: m m m (68) s magnude beng gven by elaon (62). Fomula (67) an be wen as: o b b (g - h ) - πm (69) b b - S whee we denoed by S pmay suplus nlusve of segnoage; (69' ) S h πm - g (7) As onens fsal poly, we assume a onsan lump-sum ax: h h (7) In hs ase, he pmay suplus nlusve of segnoage s onsan : S S (72) and equaon (69 ) beomes: b b - S (73) o b ( )b - ( )S (73') he soluon of he dffeene equaon (73 ) s 7

19 whee fom: b ( ) b - [( ) -) (74) b b ( ) ( ) ang no aoun ha B S (75) b (76) we oban fom (75) and B ( ) ( π) B ( ) B lm b S S (77) (78) he ansvesaly ondons wll be sasfed only f S b (79).e f he magnude of he lump-sum ax s h g π m b (8) We ema ha f he value of he ax s gven by (8), hen fom he dynam equaon (73), we oban b b b... b, N (8) 2.e. he eal deb s onsan, and he nomnal deb neases a he nflaon ae: B ( π) B (82) Fom he budge onsan equaon fo, we have whee m s gven. m m (83) 8

20 ang no aoun he elaon (62) follows ha: ( δ)( π) ( δ)( π) σ ( π) σ m (84) Fo he onsdeed hypoheses he opmal soluon s as follows: whee s gven n (84) σ..., (85) m m... m m, (86) I follows ha he nomnal money demand s gven by: ( π), (87) ang no aoun (), (3) and (5) he obeve funon beomes: σ J γ (88) σ Usng he opmal soluon gven by (85) and (86) we have: δ δ J (89) δ δ π Consdeng (84) follows J δ δ ( π) ( π) σ ( δ)( π) σ δ σ m o m ( δ)( π) δ π (9) One an obseve ha he obeve funon depends on he nflaon ae π, se by he Cenal Ban, as well as on he nal eal money balanes. 4. Conlusons We suded n hs pape a dsee me eonom gowh model, havng elemens of moneay and fsal poly. Fo he ase when he uly funon of he household s of Benoull ype, we obaned he dynam equaon of onsumpon. he dynams depend on he nomnal nees ae and on he nflaon ae. If he eal nees ae ondes wh he subeve dsoun ae, hen opmal onsumpon s onsan on he whole hozon. he eal demand fo money s also onsan. 9

21 Assumng a moneay poly ule wh onsan nomnal nees ae and onsan nflaon ae, we nfeed he fsal poly ules ompable wh hs one. Fsal solveny s an mpoan onen n he desgn of maoeonom poly n EU. Whn he model, fsal solveny ondons paally ondes wh he ansvesaly ondons povded by he axmum nple. hee ae a numbe of deons n whh ou analyss an be developed. Obvous exensons nlude he nopoaon of dsoonay axaon and of useful govenmen expendue and he way n whh hese onbue o he welfae of he agen. Refeenes As,. J. and Bu,. (2) Close o Balane o In Suplus A oly ae s Gude o he Implemenaon of he Sably and Gowh a. Jounal of Common ae Sudes, vol. 38, No. 4, pp As,. J. and Bu,. (2) Seng edum em Fsal ages n EU. n Bunla e al. (eds), pp Bao, R. J. (974), Ae govenmen Bonds Ne Wealh?, Jounal of olal Eonomy, vol 82, no 6, pp 95-7 Bao, R. J. (979), On he Deemnaon of he ubl Deb, Jounal of olal Eonomy, vol 87, no 5, pp 94-7 Bao, R. J. (98), Oupu Effes of Govenmen uhases, Jounal of olal Eonomy, vol 89, no. 6, pp Bao, R.J., (99), Govenmen Spendng n a Smple odel of Endogenous Gowh, Jounal of olal Eonomy 98, S3-S25 Bao, R.J., (995), Infaon n Eonom Gowh, Ban of England Quaely Bullen ay, Beesma, R. (2) Does EU Need a Sably a?. In Bunla e al. (eds), pp Beesma, R. and Uhlg, H. (999) An Analyss of he Sably and Gowh a. Eonom Jounal, Vol. 9, No. 4, pp

22 Beesma, R., Debun, X. and Klaassen, F. (2) Is Fsal oly Co-odnaon n EU Desable?. ape pesened a he Eonom Counl of Sweden Confeene aoeonom oly Co-odnaon n he EU: How Fa Should I Go?, Soholm, 28 ay Blanhad, O. (2) Commenay: Fsal oly n an Ea of Supluses: Eonom and Fnanal Implaons. Fedeal Reseve Ban of New Yo Eonom oly Revew, Vol. 6, No., pp Blanhad, O. J. (985), Debs, Defs and Fne Hozons, Jounal of olal Eonomy, 93, pp Bohn, H. (995), he Susanably of Govenmen defs n a Sohas Eonomy, Jounal of oney Ced and banng, 27, no., pp Bohn, H. (998), he Behavo of U.S. ubl Deb and Defs, Quaely Jounal of Eonoms, vol 3, no 3, pp Bo, W. A. (995), A Smple efe Foesgh oneay odel, Jounal of oneay Eonoms, vol, pp 33-5 Bue, W. H. (988), Deah, Bh, oduvy Gowh and Deb Neualy, he Eonom Jounal, vol 98, no 39, pp Bue, W. H. (998), he Young eson s Gude o Neualy, e Level Indeemnay, Inees Rae egs and Fsal heoes of he e Level, NBER Wong ape, no 6396, Cambdge, assahuses Bullad, J. and J. Keang, (995), he Long-Run Relaonshp Beween Inflaon and Oupu n oswa Eonomes, Jounal of oneay Eonoms 36 (3), Bu,. and ano, B. (2) Open Issues n he Implemenaon of he Sably and Gowh a. Naonal Insue Eonom Revew, No. 74, pp Bu,., Roege, W. and n Veld, J. (2) oneay and Fsal oly Ineaons unde a Sably a. EUI Wong apes, ECO No. 8 Calvo, G.A., (983), Saggeed es n a Uly axmzng Famewo, Jounal of oneay Eonoms, 2,3, Calvo, G.A., (985), aoeonom Implaons of he Govenmen Budge Consan: Some Bas Consdeaons, Jounal of oneay Eonoms, 5,95-2 Canzone,. B. and Dba, B.. (2) he Sably anf Gowh a: A Delae Balane o an Albaoss?. In Bunla e al. (eds), pp

23 Canzone,.B., C. Nolan and A. Yaes, (997), ehansms fo Ahevng oneay Sably: Inflaon ageng vesus he ER, Jounal of oney, Ced and Banng, 29(),44-6 Canzone,.B., R.E. Cumby and B.. Dba, (2), Is he e Level Deemned by he Needs of he Fsal Solveny?, Amean Eonom Revew, fohomng Chadha, J. S., and C. Nolan (22a), Inflaon vesus e-level ageng n a New Keynesan ao-model, he anhese Shool Chadha, J. S., and C. Nolan (22b), Opmal Smple Rules fo Condu of oneay and Fsal oly. Wong pape avalable a hp:// Chadha, J. S., N. Janssen and C. Nolan (2), oduvy and efeenes n a Small Open Eonomy, he anhese Shool, vol 69, pp 57-8 Cha, V.V., L. Jones, and R. anuell, (995), he Gowh Effes and of oneay oly, Quaely Revew, Fedeal Reseve Ban of nneapols, Fall, 8-32 Chsano, L. J., and. J. Fzgeald (2), Undesandng he Fsal heoy of he e Level, Fedeal Reseve Ban of Cleveland Eonom Revew, vol 36, no 2, pp -37 Clada, R., Gal, J. and Gele,. (999) he Sene of oneay oly: A New Keynesan espeve. Jounal of Eonom Leaue, Vol. XXXVII, pp Dx, A. and Lamben, L. (2a) Symboss of oneay and Fsal oles n a oneay Unon. Wong ape, neon/ucla, ah Dx, A. and Lamben, L. (2b) Fsal Dseon Desoys oneay Commmen. Wong ape, neon/ucla, Augus Dx, A. and Lamben, L. (2) oneay-fsal oly Ineaons and Commmen Vesus Dseon n a oneay Unon. Wong ape, neon/ucla, Augus Ehengeen, B. and Wyplosz, C. (998) Sably a oe han a no Nusane?. Eonom oly, No. 26, pp Eeg, C., D. Hendeson and A. Levn, (2), Opmal oneay oly wh Saggeed Wage and e Conas, Jounal of oneay Eonoms 46, Hamlon, J.D., and.a. Flavn, (986), On he Lmaon of Govenmen Boowng: A Famewo fo Empal esng, Amean Eonom Revew 76,4,

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