Pepecive on Econoic Eucion Reech Inee Re, Govenen Bon Sle, n he IS LM Moel T. Wino Fiel n Willi R. H 1 Abc: The convenionl wio i h inee e, pive inveen, n el oupu e ll ffece b he govenen bon le equie o finnce buge efici. Mine coeconoic exbook, howeve, ipl no uch effec. We eone h he eon fo hi eul i he bence of finncil welh effec on one en in he IS LM oel. When uch n effec i inclue, bon le un ou o hve conequence h e conien wih convenionl wio. In hi ppe, we o hough hee iue, poining ou hoe e whee he icuion of he econoic effec of govenen bon le i confuing, incoplee, n, in oe ce, incoec. Inoucion In ecen e hee h been heighene concen ong pofeionl econoi n in he finncil couni eging he coeconoic conequence of ubnil n peien govenen efici. 2 Thi concen h cenee on he inee e effec of govenen bon le n he conequen cowing ou of pive inveen h e econoic gowh n lowe fuue living n. 3 Given he ignificnce of hee iue, one woul expec coeconoic exbook o conin ceful nli of he effec of eb finnce ficl cion on he inee e n icuion of he coniion une which hee bon le will, o will no, cow ou pive pening. Supiingl, quie he oppoie i ue. When nlzing 1 Fiel: Pofeo, Depen of Econoic, Je Mion Univei, Hionbug, VA, USA. Phone: 540 568 3097 Fx: 540 568 3010 FIELDSTW@JMU.EDU H: Pofeo, Depen of Econoic, Mii Univei, Oxfo, OH, USA Phone: 513 529 4352 Fx: 513 529 8047 HARTWR@MUOHIO.EDU (Coeponing Auho). The uho hnk wo nonou efeee fo ve helpful coen on n elie veion of hi ppe. 2 In 2000, he feel govenen n buge uplu of $236.2 billion. Following he 2001 eceion n he Buh x cu, he govenen buge hife o $157.8 billion efici in 2002 followe b efici of $377.6 billion in 2003, $412.7 billion in 2004, $318.3 billion in 2005, $248.2 billion in 2006, $160.7 billion in 2007, n $454.8 billion in 2008. Wih TARP n n $857 billion iulu pckge, he 2009 efici oe o $1.4 illion. [Souce: Hioicl Buge D, CBO, Jnu 2010.] 3 In hp con o hee concen i Bo [1974, 1979, 1989, 2008] evivl of he Ricin Equivlence Theoe which, in i onge fo, e h efici o no e. 43
Volue 7, Nube 1, Sping 2011 he ho un effec of bon finnce ficl opeion, o ex ignoe hi iue logehe n focu ine on he inee e effec euling fo he chnge in el oupu following he ficl opeion. Ou pupoe in hi ppe i o o hough hee iue, poining ou hoe e whee he ine view of he econoic conequence of govenen bon le o finnce ie in govenen pening (o x cu) i confuing n/o incoplee. We eplo he IS LM fewok i povie he o convenien pegogicl n concepul vehicle fo unifie icuion of hee iue. The Bic IS LM Moel The ho un oel in o exbook, which we efe o he bic oel, i he fixe pice, en of peio IS LM fewok wih welh, howeve efine, ben fo boh he conupion n one en funcion. 4 Algebicll, hi oel i: (IS) = c ( ) + i( ) + g (LM) (, ) (1) =, (2) whee: i oupu, i x evenue, i he (el) inee e, c( ) i eie conupion 5, i () i eie inveen, g i govenen puche of goo n evice, (, ) i he el en fo one, = M/P i he el one uppl, n P i he (fixe) pice level. While genell no explici, ceinl iplici in hi oel i he govenen buge conin equiing govenen puche of goo n evice o be finnce b oe cobinion of xe, bon le, n one ceion: 6,7 g B M g + +. (3) P P 4 See, fo exple, Abel, Bennke, n Couhoe [2008], Blnch [2006], Donbuh, Fiche, & Sz [2008], Foen [2009], Goon [2006], n Mnkiw [2007]. 5 I i he incoe vible in he conupion funcion h iinguihe he Ricin view fo he ine view. In he Ricin view, conupion epen on penen, o lifeie, incoe h ke ino ccoun cuen n ll fuue x libiliie, incluing fuue xe equie o p off he govenen eb incue in he cuen peio o equie o p inee foeve on h eb if i i no o be pi off. 6 We ue h ech govenen bon i conol ping $1/e in inee o h he ke pice cn be wien copcl $1/. B g i he nube of govenen bon ouning. To iplif, we ignoe inee pen on he ouning ock of govenen bon (i.e., on he ccuule eb). 44
Pepecive on Econoic Eucion Reech In he bic oel, ie in g unccopnie b chnge in eihe M o neceil iplie eb finncing. Thi eul i illue in Figue 1. Sing fo equilibiu poin A, whee 1 i nul oupu, bon finnce ie in govenen expeniue fo g 1 o g 2 hif he IS cuve o he igh. equilibiu i given b poin C. The new ho un 3 2 1 D A C B LM 1 (M 1 /P 1 ) IS(g 2 ) IS(g 1 ) 1 2 3 Figue 1 A Bon Finnce Rie in g The n explnion of he juen nic i follow. The ie in g 1 1, 1 c incee ggege en n iniill cue oupu o ie b = [,] 3 g whee c i he ginl popeni o conue. In Figue 1, hi coepon o he oveen fo poin A o poin B. A poin B, he goo ke i bck in equilibiu, bu he one ke i ou of equilibiu. The ie in oupu o 3 incee he ncion en fo one (ince = > 0), inucing he pive eco o ell bon in vin ep o buil i one holing. The pice of bon fll, n 7 Thee e wo iionl buge conin in he oel, he econoic conequence of which e fequenl ovelooke when nlzing he coeconoic effec of bon finnce ficl opeion. The fi i he fi buge conin which equie h inveen expeniue be finnce b pive bon le: i() = ΔB p /P, whee B p i he nube of pive bon ouning. We ue pive bon n govenen bon e pefec ubiue n h, like govenen bon, ech pive bon i conol ping $1/e in inee. Selling pive bon i he onl opion vilble o fi o finnce inveen becue we ue h ll fi pofi e pi o houehol ivien. We lo ignoe inee pen on he ouning ock of pive bon. The econ conin, he houehol buge conin, equie cuen conupion plu ving o be finnce b cuen peio ipoble incoe: c( ) + ( ). 45
Volue 7, Nube 1, Sping 2011 ie, cuing inveen, hence oupu, o fll bck oewh fo 3 o 2. The finl equilibiu i poin C, whee he en fo one h eune o i oiginl level. 8 The ipon poin hee i h in he bic oel he ie in o 2 i full expline b he incee in h logicll pecee i. The incee ock of govenen bon ol o finnce he ie in g h no inepenen effec on he inee e. 9 Thi bief oveview of he effec of eb finnce ie in g ie evel ineeing queion. One, wh chceiic of he bic IS LM oel peven i fo cpuing n inepenen effec of govenen bon upplie on he inee e? Two, how cn he oel be lee o cpue hi inepenen effec, n wh i he econoic juificion fo he leion? An hee, wh e he coeconoic conequence fo oupu, he inee e, n he cowing ou of pive expeniue in oel in which incee upplie of govenen bon hve n inepenen effec on he inee e? I i o hee queion h we now un ou enion. Welh Effec in he Bic Moel In n peio, econoic gen hve ock of el finncil welh,, equl o he ock inheie fo he peviou peio plu he flow of ving (he chnge in el welh) ove he peio, o: 8 In he Ricin view, b con, bon finnce (penen) ie in g ignl highe fuue xe equl in peen vlue e o he ie in g. Penen incoe woul, heefoe, fll cuing conupion o fll, n ving o incee, b he ie in g. The IS cuve woul ein ion in Figue 1 leving oupu, he inee e, n inveen unchnge. 9 The conex of he one peio eul peene bove (A B C in Figue 1) i h of fixe pice oel in which he level of oupu i eniel eeine b ggege en (coeponing o he ineecion of he IS n LM cuve). In he long un, he exce en genee b he bon finnce ie in g ie he pice level, hifing he LM cuve lef unil new long un equilibiu i eche poin D in Figue 1. The iing pice level euce he el one uppl n, once gin, cue pive eco gen o ep o elloce hei finncil pofolio w fo bon n ow one. The pice level, n heefoe, u coninue o ie unil inee elic pive pening (inveen in he bic oel) h been euce b he e oun he ie in g. In ohe wo, cowing ou i coplee in he long un. Bu ill hee i no inepenen effec of govenen bon le on nowihning he fc h he ock uppl of hee bon i inceing peio b peio (uing h he incee in g i penen). The iionl ie in (fo 2 o 3 ) i full ccoune fo b he ie in P. 46
Pepecive on Econoic Eucion Reech = 1 + (4) in which 1 i el finncil welh he en of he peviou peio, n i eie ving in peio. Thi welh u be hel in oe fo in pive eco e pofolio. An ince in hi oel he onl finncil e e one n bon (govenen plu pive), hee i n iplie finncil welh conin (FWC) equiing he en fo one plu he en fo bon o equl ol el finncil welh. Moeove, ince ol el finncil welh coni of he el uppl of one plu he el uppl of bon, he FWC equie: M P B + () + b () (5) P in which () i he el en fo one in peio, n b ( ) i he el en fo bon in peio. 10 The FWC i one of evel conienc elionhip (he ohe being he viou buge conin) equie of ll well pecifie coeconoic oel. Ju buge conin ipoe e of ing up coniion on he pee of he flow vible of he oel, 11 he FWC ipoe e of ing up coniion on he pee of he one n bon en equion (i.e., on he ock vible). 12 Specificll, hee ing up coniion e: b 1 (6) + + b + b 0 0 (7) (8) 10 The (el) uppl of one in peio i equl o he uppl inheie fo he peviou peio, M 1 /P, plu n chnge in he one uppl, M /P, in peio. Siill, he ock uppl of govenen n pive bon in peio equl he ock on hn he en of he peviou peio,, plu he flow uppl of govenen n pive bon in peio. The flow uppl of govenen bon, B g /P, i eeine b he govenen buge conin, Equion 3, while he flow uppl of pive bon, B p /P i eeine b he fi buge conin (ee foonoe 6). 11 Fo exple, he equieen h he ginl popeni o conue plu he ginl popeni o ve equl 1.0 i eicion (o ing up coniion) ipoe b he houehol buge conin on he conupion ving eciion of houehol. 12 To ou knowlege Bin n Tobin [1968] wee he fi o explicil ecognize he ing up coniion iplie b he finncil welh conin. 47
Volue 7, Nube 1, Sping 2011 in which =, b b, = =, b b, = =, nb = b. The eicion iplie b equion 6, 7, n 8 enfoce conien behvio on he p of welh hole in he pive eco. Equion 6 equie he pive eco o bob ll incee in welh ino hei pofolio. Equion 7 n 8 goven he copoiion of he pive eco finncil welh pofolio. Specificll, holing welh conn, n chnge h,, ie he en fo one u euce he en fo bon b n equl oun. Fo exple, ceei pibu ecee in he inee e will incee he en fo one (ince < 0 ) n ecee he en fo bon b he e bolue oun (ince b = ). 13 A iil concluion hol fo ceei pibu chnge in incoe. An incee in incoe, holing welh conn, ie he en fo one (ince > 0 ) he expene of he en fo bon (ince b = ). 14 I now be ppen wh he bic IS LM oel fil o cpue n inepenen bon uppl effec. The one en funcion in he bic oel [i.e., ( ) =, ] oe no inclue ol finncil welh ( ) n guen. I follow iecl h = 0 which, vi equion 6, iplie b = 1. Theefoe, n incee in he uppl of govenen bon equie o finnce highe level of g (o, oe genell, efici) neceil genee n equl incee in he en fo bon. An ince he bon uppl n bon en cuve hif igh b he e oun hee cnno be n inepenen bon uppl effec on he inee e in he bic IS LM oel. 13 Hee we e ignoing, fo iplici, n inee inuce chnge in he ize of he finncil welh pofolio. 14 Thi ing up coniion be he o ifficul o gp. An incee in incoe ffec boh he eie copoiion n he eie ize of he pive eco finncil welh pofolio. The copoiion effec i he effec of he chnge in incoe on he eie en fo one n bon holing welh conn. Thi i he effec cpue b equion 8. The ize effec i he ipc of he chnge in incoe ove ie on finncil welh ue o he incoe inuce chnge in eie ving. Equion 6 enue h hi incee in welh will be bobe ino pive eco e pofolio. 48
Pepecive on Econoic Eucion Reech Thi oucoe i illue in Figue 2 in which he econo i iniill in equilibiu poin A in pnel (). A hi iniil equilibiu, ggege oupu ( 1 ) equl ggege en ( c + i + g), n pive ving () equl inveen [ i ) ] plu he govenen efici (g 1 1 ). In he one ke, pnel (b), equilibiu i poin A whee he el en fo one equl he el one uppl. In he bon ke, pnel (c), he el uppl of bon equl he el en fo bon poin A. The el uppl of bon i he ouning ock of pive n govenen bon he en of he peviou peio ( b 1 B = 1 ) plu he el flow uppl of bon uing P he peio ( b ) equie o finnce inveen [ i ) ] n he govenen efici ( g1 1). To iole he effec of n incee uppl of govenen bon in he bic IS LM oel, we hol govenen pening n xe conn g 1 n 1, epecivel. In iion, we ue h g 1 > 1 n h he exce govenen pening i finnce b bon le. We hen k wh hppen in he following peio (i.e., in +1)? Since g n e unchnge in peio +1, he IS cuve ein ion i iniil (i.e., peio ) poiion in pnel (). The LM cuve u ein ion well, fo eon h cn be een in pnel (b) n (c). In +1, he uppl of bon u incee o finnce h peio inveen plu he govenen efici. Since inveen n he govenen efici e he e in peio +1 in peio, he bon uppl cuve will hif o he igh b + = i ) + ( g ), now ping hough poin B in pnel (c). b 1 ( 1 1 1 A fo he en fo bon, he flow of ving inceen welh, n, ince = i( ) + ( g ), i follow h he peio +1 chnge in finncil welh ( + 1 ) neceil equl b + 1, he chnge in he ol uppl of bon. Thi incee in welh u be bobe ino pive eco pofolio, n he oun bobe b incee bon en i eeine b ( 1 b which, in he bic IS LM oel, equl 1. ( 1 Accoingl, bon en hif igh in pnel (c) b o poin B. Since + 1 = = b + 1 boh cuve hif igh b he e oun, hee i no effec on he inee e. An 49
Volue 7, Nube 1, Sping 2011 incee uppl of govenen bon o finnce efici (o, fo h e, pive bon ol o finnce inveen) i bobe ino pive eco pofolio wihou geneing n upw peue on he inee e. Finll, hee i no ipc in he one ke, hence no effec on he LM cuve. The one uppl i exogenou n unchnge in peio +1, o he one uppl cuve ein ion. The one en cuve lo ein ion in peio +1 becue one en i no ffece b welh ccuulion (i.e., becue = 0 ). LM(M 1 /P 1 ) A 1 IS(g 1, 1 ) () 1 M 1 /P 1 b = b (,, ); = 1 + b 1 + = b (,, +1 ); +1 = + A 1 1 (,) A B b b 1 b + 1 = b + 1 b +1 = b + i( 1 ) + (g 1 1 ) = + i( 1 ) + (g 1 1 ) (b) 1 M/P, (c) b 1 Figue 2 b b +1 b,b Finncing Defici wih Bon Sle in he Bic Moel Cpuing he Diec Ipc of n Incee Suppl of Bon The iple oificion of he bic oel h pei n inepenen bon uppl effec i n expnion of he one en funcion o inclue econ cle 50
Pepecive on Econoic Eucion Reech vible, nel ol el finncil welh ( ). Wih hi chnge, he one en funcion becoe: (,, ) = (9) in which he pil eivive of el one en wih epec o ol el finncil welh ( = ) i ue o lie beween zeo n one. Wih hi pecificion, n incee in ol el finncil welh ie boh he el en fo one n he el en fo bon, bu neihe incee b uch. Theefoe, n incee in he uppl of govenen bon o finnce ie in g (o, fo h e, o finnce n on going efici) genee n exce uppl in he bon ke which hen exe inepenen upw peue on he inee e. We efe o he incluion of ol finncil welh in he one en funcion he pofolio effec. A puel pegogicl level, he guen fo incluing welh in he one en funcion (n heefoe ipling n inepenen bon uppl effec) i wofol. Fi, fo he ve beginning of one u of econoic uen e ugh h n incee in he uppl of oehing lowe i pice. Ye, in he bic IS LM oel n incee in he uppl of bon fil o lowe he pice of bon (i.e., fil o ie he inee e). 15 Teche of coeconoic houl unen n be ble o explin wh he bence of welh n guen in he one en funcion le o hi eul, even if he chooe no o ech he expne oel. Secon, even he o bic heo of finnce eche u h econoic gen houl iveif hei pofolio holing in oe o pe inveen ik. 16 In he (wo e) IS LM oel he noinl eun on one i fixe while he eun on bon i uncein. Conequenl, holing poion of one welh in he fo of one i one w inee, he onl w in he IS LM oel in which ik vee gen cn iveif hei welh pofolio n euce ovell ik. 17 I houl be ephize h hi ppel o 15 Inee, he uho of hi ppe hve h (pecepive) uen ke noe of hi eciel o eul in cl. 16 See Tobin (1958). 17 Fien (1958) lo exploe he ole of he buge conin in en heo pplie o one holing. Hi ppoch ephize he iponce of penen incoe (i.e., welh) he ppopie 51
Volue 7, Nube 1, Sping 2011 ik veion in non ochic oel i eel heuiic h eche cn ell uen o help he unen wh n inepenen bon uppl effec igh exi in he IS LM oel. 18 The expne IS LM oel now coni of hee equion: (IS) = c( ) + i( ) + g (10) (LM) = (,, ) (11) (TFW) + = + ( ) c( ) = 1 1 (12) Equion 10 i he bic IS cuve, equion 11 i he expne LM cuve, while equion 12 efine ol el finncil welh (TFW) he u of welh cie ove fo peio 1 plu pive ving uneken in peio. 19 The fi ipon iffeence iplie b hi expne IS LM oel i he lope of he LM cuve ielf. In he bic IS LM oel, he lope of he LM cuve i: LM = > 0 B con, he lope of he expne LM cuve, equion 11, i: 20 LM ( + [1 c ]) = > 0 (13) (14) conin vible fo he en fo one ( well fo ohe e). In uizing hi lieue, Goon (2006, pg. 438) e h he pofolio ppoch pioneee b boh Tobin n Fien ke he en fo one funcion of boh incoe n welh, no ju incoe. 18 Fo exple, Kene peculive en fo one i fequenl invoke n explnion fo inee elic one en in non ochic IS LM oel. 19 An lene eho of efining ol finncil welh i he uppl of e ppoch. In hi ppoch = 1 + + fo he peviou peio, ( g) ( p) + b b + b ( g) ( p), whee 1 i he ol el uppl of one n bon i he cuen peio chnge in he el one uppl, n b i he cuen peio chnge in he ol el uppl of bon. While he chnge in he one uppl i exogenou, he chnge in he el uppl of govenen bon i eeine b he ( g) govenen buge conin, b g, while he chnge in he uppl of pive bon i ( ) eeine b he fi buge conin, b p i( ). Subiuing fo he buge conin (g) ( p) fo b n b ino he expeion fo given bove iel = 1 + (g ) + i(). Since = (g ) + i(), i follow h he wo ppoche e equivlen. 20 In Equion 14, c i he Mginl Popeni o Conue, o 52
Pepecive on Econoic Eucion Reech Coping hee eul, we ee h he expne LM i eepe hn he bic LM cuve. Thi i becue he bic LM cuve cpue onl he ipc of ie in oupu on he ncion en fo one while he expne LM cpue hi effec plu he pofolio effec iing fo he oupu inuce ie (vi ving) in ol finncil welh. cuve. Thi i illue in Figue 3. LM 1 i he bic LM cuve, n LM 2 i he expne Now uppoe h, ing fo poin A whee he one ke i in equilibiu on boh cuve, hee i $1 ie in oupu o 2 = 1 +1 while he inee e ein unchnge 1. Thi coepon o he oveen fo poin A o poin B. Wih LM 1, he ie in incoe incee he ncion en fo one b, ceing exce one en equl o poin B. Wih LM 2, howeve, he incee in incoe: (1) incee he ncion en fo one b n (2) incee ving n hence ol finncil welh b (1 c ) which incee one en b 1 c ). Fo LM 2, hen, he exce en fo one poin B i equl ( o + 1 c ), which clel i gee hn he exce one en ( coeponing o LM 1. A eul, i ke lge ie in o eoe equilibiu 2 on LM 2 ( 3 poin D) hn on LM 1 ( 2 poin C). Thu, he expne LM u be eepe. 3 D LM 2 1 2 A B C LM 1 Poin B [LM 1 ]: ( ) 1 = [LM 2 ]: ( ) 1 = + ( 1 c ) 1 2 = 1 + 1 Figue 3 The Expne LM Cuve v. he Bic LM Cuve 53
Volue 7, Nube 1, Sping 2011 Ficl Polic Reviie Hving epecifie he IS LM oel in uch w o cpue he ipc on finncil ke of incee bon upplie, we now evii he coeconoic conequence of bon finnce ie in g. Figue 4 pi he IS cuve wih boh LM cuve fo Figue 3. The iniil ho un equilibiu i poin A whee oupu i 1 n he inee e i 1. Now uppoe h hee i bon finnce ie in govenen expeniue fo g 1 o g 2 h hif he IS cuve o IS(g 2 ). Uing he bic LM cuve, he new ho un equilibiu will be poin B. Oupu incee o 3 he inee e ie o 2 vi he oupu effec icue elie. Uing he expne LM cuve, howeve, he en fo one lo ie becue of he incee in ol el finncil welh, ceing iionl exce en in he one ke ( well iionl exce uppl in he bon ke). The pofolio effec, hen, ie he inee e beon 2 o 3 (eucing he ie in oupu o 2 fo 3 ) he econo ove o ho un equilibiu poin C. LM 2 3 2 C B LM 1 1 A 1 2 3 IS(g 2 ) IS(g 1 ) Figue 4 A Bon Finnce Rie in g in he Bic n Expne Moel Inuiivel, he incee uppl of bon equie o finnce he highe level of g i no longe being offe b n equl incee in bon en. Conequenl, he bon en cuve hif igh b le he bon uppl cuve, puing iionl upw peue on he inee e. We popel cll hi bon uppl effec, n i i hi effec h how up in Figue 4 he e ie in he inee e fo 2 o 3. 54
Pepecive on Econoic Eucion Reech Mheicll, he uliplie fo bon finnce ie in govenen expeniue in he expne IS LM oel i: g = (1 c ) + ( i 1 ) + (1 c )( i ) + = + > 0. (15) The pofolio o bon uppl effec i he hi e in he enoino of equion 15, n i pen, bu oe no eliine, he incee in oupu in Figue 4. 21 I i ineeing o noe h he pofolio effec will cue oupu o ecline in fuue peio if he bon finnce ie in g i penen. To unen wh hi i o, conie wh hppen in peio +2. Govenen pening i unchnge g 2 which en he IS cuve ein ion. The expne LM cuve, howeve, i no ble. Peio +2 ving incee ol finncil welh n heefoe he en fo e (i.e., he en fo one plu he en fo bon). Inveen, i (), plu he govenen efici (g ) eeine he peio +2 incee in he uppl of bon. An ince ving u equl inveen plu he govenen efici, i follow h: + 2 = + b = = b = i( ) + ( g ). (16) Wih > 0, he incee in bon en will be le hn he incee in bon uppl. Thi pu fuhe upw peue on he inee e in +2, cow ou iionl inveen pening, n cue oupu o fll. Gphicll, hi effec i cpue b n upw hif in he LM cuve in peio +2. Thi hif coninue peio fe peio o long ving, hence he chnge in ol finncil welh, i poiive. Mheicll, he peio +2 chnge in oupu euling fo he upw hif in he LM cuve i: = (1 c )( + i ) + < 0. (17) 21 If = 0, equion 15 euce o he bic IS LM uliplie fo bon finnce ie in g. 55
Volue 7, Nube 1, Sping 2011 Equion 17 i unbiguoul negive. 22 So, following bon finnce ie in g h incee oupu in he cuen peio (equion 15), oupu fll in fuue peio ue o he coninue upw peue on he inee e (n coninue cowing ou of pive inveen) cue b he eil inceing uppl of govenen bon 23, 24 equie o finnce he efici on peio b peio bi. Concluion In hi ppe we hve icue he ine view, i ppe in lo ll coeconoic exbook, of he effec on he inee e of n incee in he uppl of bon equie o finnce n incee in govenen pening. Fo pegogicl pepecive, we hve foun uch h eche houl fin confuing. The bic IS LM oel h i coonl eploe iplicil ue hee i no ipc on he inee e fo he le of govenen bon vi he finncil ke. The incee uppl of govenen bon i bobe ino pive eco pofolio wihou equiing n incee in he inee e. A eul, efici iing fo n incee in govenen expeniue h no inepenen effec on he econo. In ohe wo, efici o no e. Howeve, when we expn he IS LM oel o incopoe finncil welh effec on one en, we fin h efici o e, n h he e in w h i full conien wih he concen expee b pofeionl econoi n he couni. 22 To eeine he peio +2 ipc on oupu, we ewoe equion 10, 11, n 12 in line fo n olve fo he euce fo equion fo oupu. Since > 0, ol finncil welh ene hi equion wih one peio lg n negive effec on oupu. An ince ving inceen welh, oupu u coninue o fll o long ving i poiive. Thi effec (fo one peio) i given b equion 17. 23 Ou nli i coningen upon he bence of welh effec in he conupion funcion. If govenen bon e coniee welh b he pive eco, n if welh h poiive effec on conupion, he IS cuve woul hif upw, chnging ou eul. We ignoe he welh effec on conupion fo wo eon. One, i h been icue wiel in he lieue, n wo, i ec fo ou pi objecive which i o exploe he finncil ke ipc of n incee uppl of bon h ccopnie eb finnce ficl opeion. A welh effec on conupion coul, of coue, offe he fuue peio ecline in oupu iing fo he pofolio effec. 24 Becue he LM cuve hif lef long ving i poiive, ving u equl zeo in he long un. An ince = i( ) + ( g ), i follow h i( ) = ( g ) in long un equilibiu. Thi lo iplie longun uliplie fo bon finnce incee in g of zeo ( eul h, ineeingl, oe no hinge on pice flexibili). 56
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