Resurrecting the Role of Real Money Balance Effects

Transcription

1 Resurreng he Role of Real Money Balane Effes José Dorh June 2006 (frs draf: January 2006) Absra Ths paper provdes epral evdene ha oney plays an ndependen role n he oneary ranssson ehans. In parular, suppors ha real oney balane effes are quanavely poran. Ths ples ha e anno absra fro oney deand paraeers n order o deerne nflaon and oupu, even n an eonoy here he Cenral Bank onrols he neres rae. Moreover, I sho and analyze hree addonal plaons of hs evdene. Frs, he exsene of quanavely poran real oney balane effes n a odel h sky pres and flexble ages s an alernave heoreal explanaon for o sylzed fas: he odesly proylal real age response o a oneary poly shok and he supply sde effes of oneary poly. Seond, here are poran quanave dfferenes n he responses of nflaon, oupu and real ages o oneary poly shoks aong he ase here real oney balane effes plays no role and he ase here suh effes are quanavely poran. In he laer ase, he pa on nflaon and real ages s onsderably loer, hereas he pa on oupu s sgnfanly hgher. Thrd, a uh hgher volaly of he oupu gap should arse under he opal oneary poly hen here are real oney balane effes of he sze esaed here. JEL Classfaon: E3, E32, E52 Keyords: real oney balane effes, oneary poly, nflaon and oupu I hank Jord Gal for hs valuable gudane, as ell as Fabo Canova, Alber Mare, Raón Maron, Laura Mayoral and Thjs Van Rens for helpful dsussons. I also hank senar parpans a Unversa Popeu Fabra, he Cenral Bank of Peru and he Sprng Meeng of Young Eonoss Any reanng errors are ne. Unversa Popeu Fabra.

2 . Inroduon The sandard Ne Keynesan odel, oonly used n dsussons abou oneary poly analyss, s a ashless one. The despread use of hs ype of odels s jusfed by Woodford (2003) and Ireland (2004). Woodford argues ha oney does no play an poran role n deernng he equlbru of he eono varables beause he Cenral Bank onrols neres raes and real oney balane effes are no quanavely poran 2. In addon, Ireland provdes eonoer esaes, by usng Maxu Lkelhood (ML), ha suppor Woodford poson abou he neglgble sze of he real oney balane effes. Four poran rss have been argued o he use of ashless eonoes n oneary eonos. The frs one s proposed by Carlsro and Fuers (2004), ho sugges ha oney alays aers for opal oneary poly analyss, even f does no have a role n shapng he dyna behavor of he eono varables. Ther reasonng s as follos. Real oney balanes are useful beause hey provde lqudy serves. Ths usefulness s proxed by assung ha real oney yelds uly. Thus, even f oney ers do no appear n he odel, here are norave plaons as real balanes sll affe elfare hrough her presene n uly funon. They sho ha hen oney eners n he uly funon, he elfare loss funon no only nludes nflaon and oupu gap varably (as n he ashless ase) bu also he neres rae varably. Moreover, hey onlude ha opal oneary poly responds less o nflaon and oupu gap han n he ashless ase, sne people dslke neres rae varably beause of he exsene of oney deand 3. Real oney balane effes exs hen onsupon (or aggregae deand) s drely nfluened by he level of real oney balanes held by prvae seor, for reasons ha are ndependen of oveens n he neres raes ha ordnarly aopany a hange n real oney supply. Then, her exsene ples ha real oney eners drely n he IS urve besdes he real neres rae and, onsequenly, affes he equlbru evoluon of all he eono varables. In he oney n uly funon fraeork, he exsene of real oney balane effes ples ha uly s nonseparable n onsupon and real oney. 2 Woodford uses a albraon proedure o suppor hs poson. 3 The oeffen assoaed h he neres rae varably er n he loss funon s affeed by oney deand paraeers. 2

3 The seond one s ha real oney balanes an affe he spread or rsk preu beeen he shor er seures and any oher fnanal asses beause hey are perfe subsues 4. Ths rs has been suggesed by Kng (999, 2002), Bernanke and Renhar (2004), aong ohers; and analyzed n deal by Andres, Lopez- Saldo and Nelson (2004). They use a general equlbru odel h opzng agens and perfe asse subsuon o suppor heoreally ho hese effes gh ork. Spefally, her odel deand sde onsss on an IS urve ha onans he real shor er and long er neres raes, an arbrage ondon ha relaes he shor er asse, he long er asse and he rsk preu (hh depends on real oney) and a oney deand. Clearly, n hs ase, e anno absra fro oney n order o deerne he equlbru of he eono varables, hh eans ha oney plays an ndependen role n he oneary ranssson ehans. Noe ha f he spread ere no be affeed by he real oney balanes, hen aggregae deand ould be ren only as a funon of he shor er real neres rae and unneresng onsan or exogenous rsk preu (slar o he oon IS urve used n odern aroeono odels of he Ne Keynesan ype) 5. Moreover, he exsene of hs hannel ples ha oneary poly s no poen o affe aggregae deand hen he shor er s zero (here s no lqudy rap) 6. Hoever, afer albrang her odel, Andres e al onlude ha oneary poly gh affe aggregae deand hrough hs hannel bu odesly fro a quanave pon of ve. The hrd one s laed by Melzer (200) and opleened by Nelson (2002). Melzer argues ha all he oneary ranssson ehans anno be suarzed by a sngle neres rae (usually he shor er neres rae), as s pled by he ashless eonoy odel. He suppors hs ve by presenng epral redued for evdene ha shos ha oney s a sgnfan deernan of onsupon groh n he US, onrollng for he shor er real neres raes. 7 Aordng o h, hs epral fndngs refle ha real oney s a good proxy for he any real neres raes (pl and expl) ha aer for aggregae deand. Melzer provdes he follong nuon for hy real oney s a good proxy: oney deand gh, lke aggregae deand, be a 4 Soe auhors all hese effes on rsk preu as porfolo balane effes or porfolo subsuon effes. 5 For ore deals on hs explanaon, see Nelson (2003b, pp 2,22). 6 See Kng (999,2002) and Bernanke and Renhar (2004). 7 Nelson (2002) fnds he sae resuls as Melzer for US and UK bu usng oal oupu nsead of onsupon. 3

4 funon of any neres raes. Hoever, he does no provde an opzng odel n order o explan hy hs gh be so. Nelson (2002) solves hs shorong and proves ha sandard opzng IS-LM odel (onssen h Melzer s redued for evdene) an aoun for Melzer s dea on oney deand one he odel allos he exsene of porfolo adjusen oss. The fourh one s proposed by Nelson (2003a), ho pons ou ha he use of ashless eonoes gnores he value of real oney as ndaor for oneary poly. In parular, he shos ha he opal response of neres raes o oney groh s 33 peren hgher han n he ase ha oney does no have a role of ndaor. Ths resul oes fro an analyss here oney has a role of ndaor beause urren shoks on oupu are no observable o oneary auhory. Fro prevous dsusson, s lear ha oney aers for elfare analyss and ha has a role of ndaor (or proxy varable) bu s no obvous ho uh aouns for he oneary ranssson ehans. Theoreally, oney has an ndependen role n he ranssson ehans beause of he exsene of real oney balane effes and/or porfolo subsuon effes. Hoever, so far, quanave analyss suggess ha hey are odes. In hs paper, I revs he porane of real oney balane effes by usng an alernave ehodology o he ones proposed by Woodford and Ireland. I provde epral evdene shong ha hese effes are quanavely poran. Ths ples ha real oney balanes ener drely n he aggregae deand; and, onsequenly, ha e anno absra fro oney deand paraeers n order o deerne nflaon and oupu, even n an eonoy here he Cenral Bank onrols he neres rae. Moreover, I sho and analyze hree addonal poran plaons of hs evdene. Frs, he exsene of quanavely poran real oney balane effes n a odel h sky pres and flexble ages s an alernave heoreal explanaon for o sylzed fas: he odesly proylal real age response o a oneary poly shok and he supply sde effes of oneary poly. Seond, here are poran quanave dfferenes n he responses of nflaon, oupu and real ages o oneary poly shoks aong he ase here real oney balane effes plays no role and he ase here suh effes are quanavely poran. In he las ase, he pa on nflaon and real ages s 4

5 sgnfanly loer, hereas he pa on oupu s sgnfanly hgher. Thrd, he desgn of he opal oneary poly should ply a uh hgher volaly of he oupu gap n he ase hen here are real oney balane effes. The os oon explanaon for he odesly proylal real age response afer a oneary poly shok s he exsene of sky pres and sky ages 8. In hs paper, I sho ha hou sky ages and h real oney balane effes, hs sylzed fa an also be explaned. The nuon of hs resul s as follos: afer a oneary poly shok, n a odel h real oney balane effes, boh labor deand and labor supply ove n he sae dreon. Then, he pa of oneary poly s basally on average hours orked (and onsequenly on oupu), and no on real ages. The supply sde effes of oneary poly are oonly explaned h he os hannel of oneary ranssson 9. Ths hannel s presen hen frs argnal os depends drely on he nonal neres rae. In a general equlbru odel, hs hannel s usually norporaed by assung ha frs us borro oney o pay her age bll. Then, oonly, he supply sde effes of oneary poly are assoaed h a shf n he labor deand afer a oneary poly shok. In hs paper, I propose ha hese effes an be assoaed o shfs n labor supply. The nuon s as follos: an nrease n he neres rae nreases he opporuny os of holdng oney, and onsequenly, dnshes he real oney holdngs. Ths dnshen dereases he argnal uly of onsupon (gven ha argnal uly of onsupon depends posvely on real oney balanes), and onsequenly, nreases he real age asked by labor supplers. Then, hs ples ha real argnal os nreases, and onsequenly, nflaon and he pre ndex also nrease beause of hese effes 0. The paper s dvded no 5 seons. Seon 2 presens he Money n Uly Funon (MIUF) odel and desrbes he equlbru ondons ha deerne he Euler Equaon and he Money Deand ha are gong o be used n he epral par. In Seon 3, I expose he ehodology and he eonoer spefaon used n order o 8 See Woodford (2003). 9 See Barh and Raey (200). 0 I should be noed ha he oal effe on nflaon afer an nrease n neres rae s negave n he odel I presen. Ths eans ha he radonal deand sde effes are ore poran han he supply sde effes. 5

6 esae he paraeer ha easures he real oney balane effes. The esaes, robusness exerses and relaed oens are also presened n hs seon. Seon 4 onans he analyss of he hree addonal plaons of y epral evdene. Conlusons are gven n Seon Money n Uly Funon Model In hs seon, I presen brefly a verson of hs odel developed by Woodford (2003). The an goal of hs par s o sho he log-lnearzed represenaon of he Euler Equaon (IS urve) and Money Deand (LM urve) ha are gong o be used n he epral par. Throughou he paper, I assue ha he ndre uly funon s separable h respe o labor. Gven hs assupon, n hs seon, I an ake o addonal ones n order o splfy he dervaon of he equaons I a neresed n. These are: flexble pres and no labor arke. When ndre uly s separable h respe o labor, hese o addonal assupons do no affe he dervaon and splfy he exposon 2. The represenave household seeks o axze he follong expeed dsouned uly 3 : E0 β U ( C, M / P ) () =0 here 0< β < s a dsoun faor, C s he level of onsupon of he eonoy s sngle good, M s he household s end-of-perod oney balanes and P s he pre of he sngle good n ers of oney n perod. The perod ndre uly funon U sasfes sandard neolassal assupons: s onave and srly nreasng n eah Ths assupon avods ha labor ers ener drely eher n he Euler Equaon or n he Money Deand. 2 I an be shon ha he sruure of he Euler Equaon and Money Deand s nvaran o any assupon abou pre or age seng hen ndre uly s separable h respe o labor. 3 Gven ha labor does appear neher n he Euler Equaon nor n he Money Deand, I absra fro n he ndre uly funon n hs seon. 6

7 of he arguens (onsupon and real oney balanes). All hese assupons are onssen h a rofounded shoppng e odel. Moreover, s alloed ha argnal uly of onsupon depends on real oney balanes, hh eans ha uly an be non separable n onsupon and real oney balanes. Hoever, he sgn of U s no assued beause he rofounded shoppng e odel does no provde. Wang and Yp (992) shoed, by usng hs odel, ha U 0 holds only f onsupon and lesure are opleens and greaer onsupon rases he argnal produvy of oney n redung shoppng e. If U =0, hen uly s separable n onsupon and oney; and, onsequenly, here are no real oney balane effes. The axzaon of he expeed uly s subje o an nereporal budge onsran of he for: = 0 0 0, [ PC + M ] W0 + E0Q0, [ PY T ] E Q (2) = 0 here = +, s he nonal neres rae pad on a rskless one perod bond, s he nonal neres rae pad on oney balanes held a he end of perod, Y s an exogenous endoen of he sngle good and olleons by he governen. Moreover, T represens ne (nonal) ax Q 0, s a sohas dsoun faor ha sasfes Q0,0 = and E 0Q0, =. I s also orh nong ha he pre of a = + s 0 rskless one perod bond s gven by: s + = E [ Q ], + (3) The household s opzaon proble s hen o hoose proesses C, M 0 for all daes 0, sasfyng (2) gven s nal ealh W 0 and he goods pres and he sohas dsoun faors ha expes o fae, so as o axze (). The frs order ondons assoaed h he household s proble are: 7

8 8, ) /, ( ) /, ( = P P Q P M C U P M C U β (4) P M C U P M C U = ) /, ( ) /, ( (5) Equaon (4) s a sandard nereporal opaly ondon (Euler equaon) hereas equaon (5) s he opaly ondon for oney deand. Usng (3) and (4), I an rere he Euler equaon as: ) /, ( ) /, ( = + P P P M C U P M C U E β (6) In order o ondu he epral par of he paper, I need o approxae ondons (6) and (5). A log lnear approxaon o ondon (6) s hen gven by: ) ˆ (ˆ ) ˆ ˆ ( ) ˆ ˆ ( = E E C C E π σ σ (7) here = C C C log ˆ, = log ˆ, + + = log ˆ, ) log( ˆ = P P π π, CU U = σ, U U = and π,,, C are he seady sae values of he nonal neres rae, onsupon, real oney balanes and gross nflaon respevely. Has over varables ndae log devaons fro rend or seady sae. The paraeer σ s he oeffen of relave rsk averson. Aordng o he assupons I ake on he uly funon, s srly hgher han zero. The paraeer s he elasy of argnal uly of onsupon h respe o real oney. The porane of real oney balane effes s gven by he rao σ, hh

9 easures he effe of a one perenage devaon of oney fro s seady sae on he perenage devaons of onsupon fro s seady sae 4. If =0, hen uly s addvely separable and here are no suh effes. The laer ples ha e an absra fro any effes of varaons n real oney on he equlbru ondons ha deerne nflaon under an neres rae rule. I an also be proved, by exendng hs odel allong he exsene of a Phllps urve (oupu s endogenous n hs ase), ha =0 ples ha real oney does play any role neher on he equlbru ondons ha deerne oupu hen Cenral Bank onrols he neres rae 5. Noe ha hen 0, here exs real oney balane effes and her porane for he oneary ranssson ehans ould depend on he sze of relave o he one ofσ. A orrespondng log lnear approxaon o ondon (5) s gven by: ˆ ( ˆ ˆ ) = η Cˆ η (8) here η v + σ, σ + = C v = and v, η +, σ + = + ˆ = log, + = U σ, U, are he seady sae values of oney veloy, he nonal neres rae pad on oney and he opporuny os of holdng oney respevely. The paraeers η and η are he onsupon elasy and he neres seelasy of oney deand orrespondngly. Aordng o he assupons on he uly funon, boh of he are srly posve. Marke learng ondons ould be used n order o re (7) and (8) as a funon of he perenage devaon of oupu (nsead of onsupon) fro s seady sae, akng no aoun ha Cˆ = Yˆ andc = Y. I ll onsder hs alernave n he epral par of he paper. 4 I an also be shon ha he oponens of hs rao are poran deernans of he egh of oupu n he elfare loss funon hen real oney balanes effes are alloed n a odel. I dsuss he pa of hs rao laer. 5 See Woodford (2003, haper 4). 9

10 3. Ne Esaes of Real Money Balane Effes Ths par onans four subseons. In he frs one, I desrbe he eonoer spefaon used o esae jonly he Euler Equaon and he Money Deand by applyng he Generalzed Mehod of Moens (GMM). In he seond one, I presen he daa and baselne esaes of he odel n order o anser ho poran real oney balane effes are fro a quanave pon of ve. Soe robusness exerses o he esaon proess are presened n he hrd subseon. Fnally, I ake a dealed oparson of y resuls h hose of Woodford (2003) and Ireland (2004). 3. Eonoer Spefaon In order o perfor he GMM ehnque, o orhogonaly ondons an be nferred fro he odel developed n he prevous seon. The frs one oes fro equaon (7) and arses fro he fa ha, under raonal expeaons, he foreas error n onsupon one perod ahead should be unorrelaed h he nforaon se daed a perod and earler. Then, hs orhogonaly ondon s gven by: E ˆ C ˆ C ) ( ˆ ˆ ) (ˆ ˆ ) = 0 + π + z σ σ ( + (9) here z denoes a veor of varables daed a perod and earler. The seond orhogonaly ondon oes fro equaon (8) and arses fro allong a easureen error er n he oney deand equaon 6. Then, hs eans ha equaon (8) does no hold exaly beause of hs error. Therefore, f I assue ha he easureen error a perod s no orrelaed h earler nforaon, he follong orhogonaly ondon an be esablshed: 6 Canova (2006) onsders hs possbly beause onsupon an be easured h error. 0

11 E v + σ Cˆ σ σ + ( ˆ ˆ ) z = 0 ˆ (0) here z - denoes a veor of varables daed a perod - and earler. The orhogonaly ondons gven by equaons (9) and (0) onsue he bass for esang he sruural paraeers of he odel va GMM. Noe ha here are sx sruural paraeers n he syse: σ,,,, v andσ. All of he are no sulaneously denfable fro he syse. For hs reason, hree of he (,, v ) are albraed o perfor he esaon, beause hey are pnned don ore drely fro frs oens of he daa 7. I se he usng her averages durng he saple perod. The res of paraeers are esaed. Before perforng he esaon, one eonoer ssue should be faed. In sall saples, he ay he orhogonaly ondons are ren (or noralzed) affes he GMM esaes 8. More spefally, here s no agreeen abou ho o spefy he orhogonaly ondon (9) n order o esae σ and, he se of paraeers ha easure he porane of real oney balane effes. An alernave noralzaon for he oen resron (9) s gven by he follong expresson 9 : E {[ ˆ σ ( Cˆ Cˆ ) + ( ˆ ˆ )] z } 0 ˆ = π () Hansen and Sngleon (983) and Hall (988) use noralzaon () and (9) respevely, hou allong he exsene of real oney balane effes ( =0). Hansen and Sngleon esae he oeffen of relave rsk averson, hereas Hall esaes s reproal (he nereporal elasy of subsuon). They fnd very 7 Gven a defnon of oney, here s agreeen abou ha,, v are n he odel. In fa, all oneary odels used for aroeono analyss se he equal o her averages durng he saple perod. Ths s no he ase for he res of paraeers. For nsane, he range of values used n albraon for σ goes fro 0.6 (Woodford (2003)) o 0 (he axu level onsdered plausble by Mehra and Preso (985)). 8 See Capbell (2003), Halon e al (2005), Neely e al (200) and Yogo (2004). 9 Noe ha noralzaon () arses fro ulplyng he orhogonaly ondon (9) by σ.

12 dfferen resuls, as s surveyed n Neely e al (200) and onfred by updaed esaes perfored by Capbell (2003) 20. In parular, he pled oeffen of relave rsk averson esaed by Hall s uh hgher han he one drely esaed by Hansen and Sngleon. Then, hese o alernave spefaons of he orhogonaly ondons are aken no aoun n order o see ho sensve he resuls are o he noralzaon ssue. Spefaon onsders equaons () and (0) hereas spefaon (2) onsders equaons (9) and (0). 3.2 Daa and Baselne Esaes The daa ha I use s Uned Saes quarerly daa and runs fro he frs quarer of 959 hrough he fourh quarer of Consupon s easured by real personal onsupon expendures, real oney balanes are easured by dvdng M2 oney sok by he CPI, nflaon s easured by hanges n he CPI, he neres rae s easured by he hree-onh Treasury bll rae, expressed n quarerly ers and he neres rae pad on oney s easured by M2 oney on rae, expressed n quarerly ers. Consupon and real oney balanes are expressed n perapa ers, by dvdng by he vlan nonnsuonal populaon, age6 and over. Pror o esaon, he logarh of per-apa onsupon and per-apa real oney balanes have been derended by usng a deerns lnear rend n order o ge saonary seres, gven ha he applaon of GMM requres hs knd of seres. Gven hs daa se, v = (M2 onsupon veloy), = and = The eleon of M2 as he oneary aggregae o be used n hs sudy s relaed o he fa ha s he one ha nludes all he asses ha provde lqudy serves. Gven ha s lear ha M furnshes hese serves, a ay o sho ha M2 s he orre easure of oney s by argung ha (M2-M) also provdes lqudy serves. To es he laer, I hek f he opporuny os of (M2-M) s sgnfanly dfferen fro zero. The nuon for hs oes fro he fa ha U 2- >0 ples ha (M2-M) furnshes lqudy serves aordng o he odel and ha = + >0. So, afer 20 Capbell (2003) repors pon esae of 0.7 and 5 for he oeffen of relave rsk averson hen he uses noralzaon and 9 respevely. Hs pon esaes oes fro an esaon of he Euler Equaon only, hou allong he exsene of real oney balane effes. 2

13 opung he average on rae of reurn of (M2-M) and opare h he average rae of reurn of he shor er Treasury bond, I ge ha he average opporuny os of holdng M2-M s peren annually. Then, (M2-M) provdes lqudy serves 2. Table presens he GMM esaon of he sruural paraeersσ, and σ. I also shos he rao, hh easures he porane of he real oney balane σ effes; and he onsupon elasy ( η ) and neres seelasy ( η ) of oney deand pled by he esaed and albraed paraeers. The resuls are presened for he o spefaons of he orhogonaly ondons dsussed earler and four ses of nsruens 22. In all he ases, I use a Neey Wes HAC ovarane arx and he prehenng opon. Soe neresng resuls arse fro hese esaons, hh are robus o he spefaons and o he se of nsruens. Frs, real oney balane effes are quanavely poran. In all he ases, he rao s sgnfanly dfferen fro σ zero and s pon esaes hgher han 0.3. Ths resul onrass a lo h hose provded by Woodford (2003) and Ireland (2004), ho oban pon esaes of 0.06 and respevely for hs rao. Woodford uses a albraon proedure, hereas Ireland perfors Maxu Lkelhood esaon. A dealed analyss of he oparson of hese resuls h ne s presened n a speal subseon laer. Seond, anno be rejeed ha he oeffen of rsk averson s equal o or 2. Ths resul suppors he albraon used for hs paraeer n varous aroeonos sudes. Thrd, he onsupon elasy of oney deand s around, hh s onssen h any epral sudes abou oney deand. Fnally, he valdy of all he regressons s onfred by he p-value for he Hansen s J sas of overdenfyng resrons h a sgnfane level of 5 peren. 2 Alernavely, Alvarez e al (2003) deopose (M2-M) no savng deposs, e deposs and real oney arke funds. They onlude, by dong he sae ype of analyss I do, ha savng deposs and e deposs provde lqudy serves hereas real oney arke funds do no. So, her proposal of a oneary aggregae ha provdes lqudy serves s M2 nus real oney arke funds. Hoever, s dfful o argue ha real oney arke funds furnsh no lqudy serves. In fa, hey are exreely lqud (os even hekable), have essenally no defaul rsk and no neres rae rsk. 22 Se nludes 4 lags of neres rae, nflaon, real oney balanes and onsupon. Ses 2 and 3 nlude he sae varables bu jus 3 and 2 lags of he respevely. Se 4 onsss of he sae varables ha are n se bu exludng he frs lag of eah varable. 3

14 Table Esaes of he sruural paraeers of he odel: Spefaon : σ σ σ η η J-Tes Se (0.372) (0.88) (.622) (0.03) (0.257) (.236) Se (0.399) (0.90) (.42) (0.6) (0.295) (.442) Se (0.542) (0.280) (4.092) (0.46) (0.46) (.858) Se (0.524) (0.280) (7.029) (0.2) (0.309) (.484) Spefaon 2: σ σ σ η η J-Tes Se (3.646) (.423) (83.726) (0.058) (0.267) (.243) Se (5.92) (2.327) (45.633) (0.06) (0.356) (.363) Se (8.434) (3.9) (266.76) (0.04) (0.446) (.29) Se (37.529) (6.096) (89.656) (0.07) (0.33) (0.967) Noe: Sandard errors are shon n brakes 4

15 Fro Table, s lear ha real oney balane effes are quanavely poran bu s no apparen he agnude of hs effes. In fa, under spefaon all he pon esaes of σ are beeen 0.63 and 0.66; hereas under spefaon 2, hey are beeen 0.32 and 0.4. So, n order o be ore prese, s neresng o ry o ake a lear ase abou he desrably of one of he spefaons. I argue ha spefaon s preferable o spefaon 2 for hree reasons. Frs, sees ha he forer s no affeed by eak denfaon hle he laer one s. Sok e al (2002) sugges ha GMM esaes n nonlnear odels 23 an be very sensve o hanges n he se of nsruens hen here s a eak denfaon proble 24. Fro Table, s lear ha pon esaes fro spefaon do no hange so uh, hereas hose fro spefaon 2 hange draaally. For nsane, he pon esaes of he oeffen of relave rsk averson under spefaon 2 are beeen 6.9 and 20.2, hereas hose under spefaon are beeen.3 and Then, sees ha spefaon 2 suffers of a eak denfaon. Seond, esaes fro spefaon are ore effen. Thrd, n alos all he ases, pon esaes fro spefaon anno be rejeed by spefaon 2; hle pon esaes fro spefaon 2 are srongly rejeed by spefaon. Gven ha I argue ha spefaon s preferable, I ll onenrae on dsussng only he resuls fro ha do no belong o he general resuls I presened earler. The oeffen of relave rsk averson s posve and sgnfanly dfferen fro zero n all he ases. Ths resul s onssen h he resron I posed heoreally on hs paraeer. The pon esaes are around.5 and are onssen h hose obaned by Hansen and Sngleon (983), ho perfor a Maxu Lkelhood esaon of he Euler Equaon hou onsderng real oney balane effes. Moreover, all he pon esaes for hs oeffen belong o he 95 peren onfdene nerval of provded by Capbell (2003). Whou akng no aoun real oney balane effes, he suggess values for hs oeffen beeen and 2.4 hen nsruenal varables and noralzaon are used. 23 Noe ha boh spefaons of he odel are nonlnear n he sruural paraeers. 24 In a sngle lnear odel, he proble of eak denfaon s equvalen o he proble of eak nsruens. 25 Ths resul s onssen h he dsrepany beeen Hansen and Sngleon (983) and Hall (988) esaes. In fa, he oeffen of relave rsk averson s uh hgher under spefaon 2 (he one h he noralzaon used by Hall) han under spefaon. 5

16 The elasy of argnal uly of onsupon h respe o real oney balanes (he paraeer ) s sgnfanly dfferen fro zero and srly posve. Ths resul ples ha uly s no separable n onsupon and oney and dsards he possbly ha hs paraeer ould be negave 26. Moreover, fro he laer resul and he fa ha he rao ha easures he porane of real oney balane s sgnfanly dfferen fro zero, an be onluded ha e an no absra fro oney deand paraeers n order o deerne nflaon and oupu, even n an eonoy here he Cenral Bank onrols he neres rae. Boh paraeers of he oney deand are also sgnfanly dfferen fro zero. The onsupon elasy ( η ) s lose o n all he ases. The neres rae seelasy pon esaes go fro 4.4 o All hese values are n lne h he oney deand esaon perfored by Reynard (2004) 28 for he posar perod. To of he (hose loer han 5) also belong o he 95 peren onfdene nerval of [.5, 4.9] provded by Alg e al (2004). 3.3 Robusness Exerses In hs subseon, I perfor hree robusness exerses. Frs, I use arke learng ondon so ha Cˆ = Yˆ andc = Y. Seond, I verfy f y resuls are robus o he nluson of labor arkes and sky ages. Thrd, I hek sub saple sably. In all hese ases, spefaon s he only one used for he reasons dsussed n he prevous subseon Usng Marke Clearng Condon 26 There are soe rofounded odels here an be negave. One of he s he shoppng e odel here onsupon and lesure are srong subsues, a suaon ha Wang and Yp (992) desrbe as orrespondng o an asse subsuon odel. 27 These pon esaes for he neres seelasy ply ha he neres rae elasy s beeen and He uses oupu and M2 nus nsead of onsupon and M2 respevely n order o perfor hs oney deand sudy. 6

17 Clearly, onsupon s dfferen fro oupu n he daa. Hoever, I ll use he arke learng ondon beause a lo of aroeono sudes (e.g. Ireland (2004)) pose n he esaon of aroeono odels. Then, I spefy he orhogonaly ondons n he follong ay: E {[ ˆ σ ( Yˆ Yˆ ) + ( ˆ ˆ )] z } 0 ˆ + y + + = π (2) E v + σ y ˆ + Y + σ + σ + ˆ ( ˆ ˆ ) z = 0 (3) here z denoes he se of nsruens, paraeers are he sae as before. Y v = n hs ase and all he res of he The frequeny of he daa and he saple perod are he sae as n prevous subseon. No, oupu s easured by real GDP, real oney balanes are easured by dvdng M2 oney sok by he GDP deflaor, nflaon s easured by hanges n he GDP deflaor and he neres raes are he sae as before. Real GDP and real oney balanes are expressed n perapa ers, by dvdng by he vlan nonnsuonal populaon, age6 and over. Pror o esaon, he logarh of per-apa real GDP and per-apa real oney balanes have been derended by usng a deerns lnear rend n order o ge saonary seres, as requred by GMM esaon. Agan, (,, v ) are albraed and he res of paraeers are esaed. Gven ha I use daa on oupu, v = Table 2 presens GMM esaes of he sruural paraeersσ y, and σ. I also shos he rao, hh easures he porane of real oney balane effes; and σ y he noe elasy ( η y ) and neres seelasy ( η ) of oney deand pled by he esaed and albraed paraeers. The resuls are presened for he spefaon 7

18 of he orhogonaly ondons dsussed earler and four ses of nsruens 29. In all he ases, I use a Neey Wes HAC ovarane arx and he prehenng opon. Table 2 Esaes of he sruural paraeers of he odel: USING THE MARKET CLEARING CONDITION σ σ y σ y η y η J-Tes Se (0.228) (0.079) (6.87) (3.08) (0.63) (.87) Se (0.279) (0.085) (7.483) (.559) (0.82) (.990) Se (0.338) (0.5) (.429) (.203) (0.208) (2.478) Se (0.292) (0.) (9.485) (0.988) (0.207) (.987) Noe: Sandard errors are shon n brakes In hs ase, he pon esae for real oney balane effes are uh hgher han hen onsupon s used. In all he ases, he rao s hgher han. Hoever, hs σ y rao s no presely esaed beause σ y has a hgh sandard error relave o s pon esae. In spe of he lo preson n alulang he real oney balane effes, an be onluded ha hey are sgnfanly dfferen fro zero beause an be rejeed ha s equal o zero and he sze of relave o σ y s hgh. 29 Se nludes 4 lags of neres rae, nflaon easured by he GDP deflaor, real oney balanes and oupu. Ses 2 and 3 nlude he sae varables bu jus 3 and 2 lags of he respevely. Se 4 onsss of he sae varables as n se, exludng he frs lag of eah varable. 8

19 When he arke learng ondon s used, represens he elasy of argnal uly of real noe h respe o real oney. The pon esaes for hs paraeer are beeen 0.32 and 0.36, hh dffer fro hose found by usng onsupon. Hoever, he an onlusons relaed o hs paraeer do no hange: uly s no separable and s srly posve. The paraeerσ easures he nverse of he neres sensvy of real expendure y ha s exlusvely due o he neres rae hannel 30. The pon esaes go fro 0.5 o The agnude of all of he s onssen h oher aroeono papers ha esae hs paraeer. Roeberg and Woodford (997) fnd ha s equal o 0.6 hereas Aao and Laubah (2003) esae equal o Hoever, as dsussed n one of he prevous paragraph, he esaon of hs oeffen s no very prese. In fa, n all he ases, I anno reje ha s equal o zero. I should be noed ha he values obaned for he neres sensvy of oal oupu σ ) are hgher han hose found for he neres sensvy of real onsupon ( σ ), ( y hh akes sense. The nuon s as follos: sne he purhases of nvesen goods (nluded n oupu and no n onsupon) are lkely o be ore neres rae-sensve, s reasonable ha σ s hgher hanσ. y Boh paraeers of he oney deand are also sgnfanly dfferen fro zero. The noe elasy ( η y ) s very lose o, hh s onssen h a lo of epral sudes abou oney deand. Moreover, he pon esaes of he neres rae seelasy go fro 7.2 o 9.7. All hese values are plausble under he oney deand esaon for he posar perod perfored by Reynard (2004). He fnds a pon esae of 0.4 for hs paraeer, h a sandard error of When here are real oney balane effes, a hange n he neres rae affes aggregae deand hrough o hannels: he neres rae hannel and he real oney balane effe hannel. The neres rae hannel s he one by hh neres raes pa on he desred ng of prvae expendures. The oher hannel s he one by hh a oveen n he neres raes affes argnal uly of onsupon hrough her pa on real oney balanes. 3 Boh papers onsder ashless sky pre odels. 32 He uses M2 nus and repors neres elasy. The pl neres seelases have been alulaed by ulplyng he neres elasy by he nverse of he opporuny os of he oneary base. 9

20 Fnally, he las olun of he able repors he p-value for he Hansen s J sas of overdenfyng resrons, hh onfrs he valdy of all he regressons h a sgnfane level of 5 peren Inludng Labor Markes and Sky Wages So far, I jus onsder he Euler Equaon and he Money Deand o derve orhogonaly ondons and esae he porane of real oney balane effes. Ths analyss an be easly exended by addng o he syse a age nflaon dynas equaon ha also onans he paraeers ha easure he porane of hose effes 33. To do so, I need o assue a labor arke h saggered nonal age onras n he odel developed n seon 2. Ereg a al (2000) sho ha under hs addonal assupon, age nflaon an be desrbed by he follong relaon: ( α )( α β ) ˆ π = βe ˆ π + + ( rs ˆ ˆ ) (4) α ( + ϕθ ) hereπˆ s he absolue devaon of age nflaon fro s seady sae, ˆ s he log devaon of real age fro s seady sae, ϕ s he nverse of Frsh labor supply elasy, (-α ) s he probably of adjusng ages, β s he dsoun faor, he elasy of subsuon and θ s ˆ rs s he log devaon of argnal rae of subsuon beeen onsupon and lesure fro s seady sae. Gven ha he ndre uly funon allos non separably beeen onsupon and real oney and ha s separable h respe o labor, hen he follong expresson holds for he argnal rae of subsuon: vh ( h ) rs = (5) U ( C, ) 33 I do no onsder he possbly of addng an nflaon dynas equaon beause he ers ha deerne real oney balane effes do no appear n he spefaon of hs equaon h he argnal os. Gal and Gerler (999) ephasze ha hs s he orre one o esae he Phllps urve. 20

21 here v h ( h ) represens he argnal dsuly of labor and h s he nuber of hours orked. Noe ha he denonaor n (5) s he argnal uly of onsupon and s no only affeed by onsupon bu also by real oney balanes. A log lnear approxaon o (5) s hen gven by: rs ˆ = ϕhˆ + σ Cˆ ˆ (6) Then, usng (6) no (4), he follong expresson for he age dynas nflaon s obaned: ( α )( α β ) ˆ ˆ ( ˆ π ˆ = βeπ + + ϕh + σ C ˆ ˆ ) (7) α ( + ϕθ ) Usng equaon (7) and he raonal expeaons assupon, e an nfer he follong orhogonaly ondon 34 : ( )( ) α α β ˆ ˆ ( ˆ E ˆ π βπ + ϕh + σ C ˆ ˆ ) z = 0 (8) α ( + ϕθ ) In hs subseon, he real oney balane effes are esaed usng he orhogonaly ondons (0), () and (8) 35. Before proeedng o he esaon, noe ha by addng equaon (8), I nrease he nuber of sruural paraeers. No, here are en: he prevous sx ones plusϕ, α β andθ. As before, he hole se of paraeers anno be denfed sulaneously. Then, I perfor he follong exerse: o denfy all he paraeers ha I esaed n prevous subseons, gven v = 0. 29, = , = 0.036, β =0.99, θ =, ϕ = and dfferen values forα. Ths exerse allos e o explore ho age skness affes he porane of real oney balane effes. 34 Equaon (8) refles ha under raonal expeaons, he foreas error n age nflaon one perod ahead should be unorrelaed h he nforaon se daed a perod and earler. 35 Gven ha he ndre uly funon s separable h respe o labor, he Euler Equaon and Money Deand derved n seon 2 sll hold. Therefore, he orhogonaly ondons (0) and () an sll be used. 2

22 The esaon proedure s GMM. The saple perod goes fro he frs quarer of 959 o he hrd quarer of The daa for onsupon, real oney, neres raes and nflaon s he sae as n subseon 3.2. Hours orked are easured by non-far busness hours and onvered o per-apa ers by usng he vlan non-nsuonal populaon, age6 and over. Nonal ages are easured by he nonal hourly nonfar busness opensaon, hereas age nflaon s easured he hange n he logarh of hs opensaon. Nonal ages are onvered o real ers by dvdng by he CPI ndex. Pror o esaon, he logarh of per-apa onsupon, perapa real oney balanes and real age have been derended by usng a deerns lnear rend n order o ge saonary seres. The se of nsruens used nludes o lags of real oney balanes, onsupon, nflaon, hours and real age. The resuls are shon n Table 3 for sx dfferen degrees of age skness. The an resuls sll hold. Real oney balane effes are quanavely poran and her agnude s roughly he sae as n he baselne esae (beeen 0.6 and 0.7). The paraeer ha easures he degree of non separably beeen onsupon and real oney s sll posve and sgnfanly dfferen fro zero 36. Hoever, s agnude depends on he degree of age skness. Fro he able, s lear ha he hgher s hs degree, he hgher s. The sae ours for he oeffen of relave rsk averson, hh s nreasng n he degree of age skness. Noe ha he perenage hanges n σ and fro one degree of age skness o anoher one s basally he sae, suh ha he rao σ degree of skness. s roughly he sae aross he dfferen I s also orh nong ha he esaes obaned hou onsderng age dynas (hose n Table ) are very lose o he ones assung nonal age skness h α beeen 0.4 and 0.8. Ths eans ha absrang fro age dynas, hen he degree of skness s relavely hgh, does no affe he pons esaes onsderably. I s also neresng ha, hen he age skness s hgher or equal o 0.4, he pon esaes for he oeffen of relave rsk averson, he elasy of argnal uly of 36 When e onsder a flexble nonal age ( α =0), s sgnfanly dfferen fro zero, a 6 peren sgnfane level. 22

23 onsupon and he neres seelasy are very dfferen fro hose obaned hen he degree of age skness s loer or equal o 0.2. For nsane, σ s beeen.3 and.5 n he frs ase; hle s beeen 0.3 and 0.7 n he seond ase. Table 3 Esaes of he sruural paraeers of he odel: (Consderng age dynas addonaly) Values for α σ σ σ η η J-Tes (0.409) (0.233) (.22) (0.087) (0.304) (.253) (0.323) (0.76) (8.460) (0.073) (0.252) (0.96) (0.292) (0.56) (6.665) (0.08) (0.250) (0.895) (0.225) (0.097) (5.50) (0.49) (0.244) (.575) (0.236) (0.09) (4.370) (0.23) (0.256) (2.005) (0.229) (0.097) (2.940) (0.288) (0.466) (4.049) Noe: Sandard errors are shon n brakes The valdy of all he regressons s onfred by he p-value for he Hansen s J sas of overdenfyng resrons h a sgnfane level of 5 peren. Thus, hs es does no allo dsngushng he onvenene of he assupon of sky ages, neher he degree of he. Therefore, n hs seon, he an onluson s ha he resul of he porane of real oney balane effes holds afer addng a spefaon of a age dynas. I an also be onluded ha s exsene s onssen h boh sky and flexble ages. 23

24 3.3.3 Sub-Saple Sably In hs seon, I explore f he baselne esaes (hose fro Table ) are sensve o he eleon of he saple. In order o do, I dvde he full saple n o equally sze sub-saples: 959:-98:4 and 982:-2004:4. Resuls are presened n Table 4. Table 4 Esaes of he sruural paraeers of he odel: Sub saple sably 959: - 98:4 σ σ σ η η J-Tes Se (0.29) (0.2) (4.762) (0.045) (0.09) (.029) Se (0.278) (0.4) (5.673) (0.073) (0.236) (.788) Se (0.338) (0.58) (5.688) (0.04) (0.332) (2.245) Se (0.299) (0.99) (9.972) (0.063) (0.98) (.829) 982: :4 σ σ σ η η J-Tes Se (0.44) (0.062) (3.602) (0.24) (0.27) (2.640) Se (0.26) (0.088) (4.778) (0.65) (0.79) (3.66) Se (0.283) (0.00) (5.26) (0.44) (0.20) (3.976) Se (0.74) (0.059) (3.540) (0.097) (0.60) (3.785) Noe: Sandard errors are shon n brakes 24

25 The quanave porane of real oney balane effes s also onfred by hs exerse. The rao σ s posve and sgnfanly dfferen fro zero aross subsaples 37. Hoever, he pon esaes are no onsan aross e. Pror o 982, hey are beeen 0.53 and 0.64; hle sne 982 hey are n he range of 0.9 and Thus, hs resul suggess ha real oney balane effes ould have dnshed s quanave porane n he reen perod. The reduon of hese effes s basally explaned by he hange n he paraeer. Before 982, s pon esaes are beeen 0.70 and 0.96; hereas sne 982 hey are beeen 0.4 and 0.9. I s also neresng ha he resuls sugges a derease n he oeffen of relave rsk averson. The an pa of hs reduon over prevous resuls s ha a value of 2 for hs oeffen s srongly rejeed n he reen perod. By oher hand, anno be rejeed a value of for hs oeffen n alos all he ases presened a Table Ths resul srenghs he use of logarh uly n onsupon. The pled onsupon elasy and neres seelasy also hange aross subsaples. The pon esaes of he frs one dnsh fro values roughly around.90 o values around I s also neresng o noe ha anno be rejeed ha he onsupon elasy s equal o n he reen perod, exep n he ase hen se 4 s used. Fnally, he neres seelasy has nreased onsderably. 3.4 Prevous Esaes on Real Money Balane Effes: a oparson In hs sudy, all he pon esaes of he paraeer ha easures he quanave porane of real oney balane effes are beeen 0.2 and 0.7; exep n he ase hen he arke learng ondon s posed n he full saple esaon. In he laer ase, hey are beeen.2 and 2.2. In any ase, all hese esaes dffer very uh fro hose of Woodford (2003) and Ireland (2004). I s neresng, a hs pon, o analyze arefully hy hs s so. In order o falae he oparson, I onsder he 37 In all he ases, he paraeer s sgnfanly dfferen fro zero a 5 peren sgnfane level, exep hen se 3 s used n he perod 982:-2004:4. In hs ase, s sgnfanly dfferen fro zero a 0 peren sgnfane level. 38 I an be rejeed a 5 peren only hen se s used n he reen perod. 25

26 pon esaes.2 hen he arke learng ondon s used and 0.6 hen he arke learng ondon s lef asde. In boh ases, hese values are roughly speakng he ode of all he esaes perfored usng he hole saple. Woodford, by usng a albraon proedure and onsderng he arke learng ondon, suggess a value of Ths resul s obaned by seng σ = 0. 6 and = 0.0. The frs paraeer s albraed usng an esae fro a sudy perfored by Roeberg and Woodford (997). To oban a value for, he uses he follong relaon pled by he MIUF odel: y η η y = v + σ y + (9) Noe ha gven he noe elasy, he neres seelasy, he oney veloy, he neres rae, he neres rae pad on oney and he nverse of he neres sensvy of real expendure ha s exlusvely due o he neres rae hannel, an be found. He onsders η y = and η =28 fro a long run oney deand sudy perfored by Luas (2000). He also ses v = 4 (oneary base veloy), = 0 and = When I use he hosen value fro he full saple esaon h he arke learng ondon, here are o poran dfferenes beeen Woodford s esae and ne. The frs one s he ehodology of esaon and he seond one s he defnon of oney. Gven ha n hs par I a neresed n shong dfferenes ong fro ehodology, I sho ho uh ould be f I used Woodford ehodology bu σ y onsderng M2 as oney. In hs ase, v = (M2 veloy), = and = Keepng he res of paraeers ha Woodford assues, = 0.08 andσ = 0. 6, suh ha he rao s equal o 0.5. Thus, an be seen ha he y dfferene beeen hs esae and ne oes anly fro he ehodology (0.5 versus.2). Lkese, he dfferen proedure ples dfferen esaes basally for 26

27 he paraeer (0.08 versus 0.36). Ths dsrepany s anly explaned by a dfferen esae of he neres seelasy (28 versus 7) 39. An alernave oparson o Woodford s esae an be done f I esablsh he relaon beeen hs esae and ne hou usng he arke learng ondon. I onsder hs oparson ore useful, gven ha onsupon s no equal o oupu n he daa. Then, n hs ase, besdes he ehodology and he oney aggregae onsdered, he use of onsupon ll ake also a dfferene. Agan, o fnd he dfferene aong y esae and Woodford s beause of he ehodology, I adjus he one he uses by akng no aoun M2 oney and onsupon. In hs ase = 0. and = 40, suh ha he rao s 0.. Thus, he dsrepany beeen hs esae and ne oes anly fro he esaon proedure (0. versus 0.6). Lkese, he dfferen ehodology ples dfferen esaes basally for he paraeer (0. versus.00). Ths dsrepany s anly aouned by he dfferene n he esae of he neres seelasy (28 versus 4). σ Ireland esaes a sall aroeono odel by ML, onanng seven relaons: an Euler Equaon, a Money Deand equaon, a Phllps Curve, an Ineres Rae Rule, a proess for a preferene shok, a proess for a oney deand shok and a proess for a ehnology shok. All hese relaons onan eny paraeers ha he esaes by usng quarerly daa ha run fro 980: hrough 999:2 and posng he arke learng ondon. One of hese paraeers s. Ireland esaes equal o -0.02, σ y h a sandard error onfdene of Hs pon esaes of he deernans of hs rao are as follos: = andσ = Behnd hs esaes, here s a y oplee dfferen pure fro he one I presen: real oney balane effes are neglgble, an be negave and he neres rae hannel s very eak (noe haσ y = ). Hs resuls on and σ y are srange and onrad nuve grounds. 39 Noe fro equaon (9) ha s dereasng n he neres rae seelasy. 40 I do no only adjus oney veloy by usng onsupon ( v = n hs ase) bu also he oeffen of relave rsk averson. As has been dsussed earler, ould be expeed ha >. Then, I pk he value of beause s sandard n aroeono albraon exerses σ σ y and anno be rejeed by any of he esaes I presen. The res of paraeers are he sae as n he prevous oparson. 27

28 There are soe rofoundaons ha an suppor a negave value for he elasy of argnal uly of real noe h respe o real oney. Hoever, hs negave value ples ha an nrease n real oney s assoaed h a derease n oupu. Moreover, hs pled esae of he degree of he neres sensvy of real expendure ha s exlusvely due o he neres rae hannel s very lo and onrads poran epral evdene. In parular, hs esae s very far fro hose obaned by Roeberg and Woodford, and Aao and Laubah, ho fnd equal o 0.6 and 0.26 respevely. Agan, I an esablsh o ypes of oparsons h Ireland resuls. The frs one an be ade by usng y esaes h he arke learng ondon posed; he seond one an be ade by ong. When I esae he odel onsderng he arke learng ondons, here are o densons n hh Ireland s approah and ne are dfferen: he eonoer ehodology and he saple used. In hs ase, I la ha he dsrepany n he esaes s basally beause of he dfferene n he eonoer proedure. In he frs par of Table 5, I presen esaes hen arke learng ondon s posed and hen he sae perod ha Ireland uses s aken no aoun. The pon esae for s., hh s very lose o he esae usng he hole σ y saple (.2). Thus, he dfferene reles on he dfferen eonoer ehodology. For hs reason, s onvenen o dsuss on he onvenene of eah approah (ML versus GMM). Cohrane (200) ephaszes ha he ssue on hh eonoer proedure s he bes s absoluely open. He pons ou ha here are no heores or Mone Carlo sulaons ha sugges hh one s preferable. I s knon ha f he odel s orre, ML s ore effen han GMM. Hoever, s very dfful o argue ha an eono odel s opleely ell spefed. In parular, n he ase of Ireland, here are hree reasons hy hs odel an be sspefed. Frs, he arke learng ondon n he ay he poses does no hold: onsupon s dfferen fro oupu. Seond, hs spefaon of he Phllps Curve sees nadequae. He defnes n ers of he derended oupu and real oney balanes; nsead of usng, as he heory suggess, he real argnal os. Galí and Gerler (999) pon ou ha he laer ouperfors derended oupu n he esaon of he Phllps Curve. Thrd, all he shoks do no have o sasfy he 28

29 noraly assupon. Then, gven ha he onsseny of he esaes obaned by ML s very sensble o he sspefaon of he odel, Ireland esaes ould be nonssen. Table 5 Esaes of he sruural paraeers of he odel: 980:-999:2 USING THE MARKET CLEARING CONDITION σ σ y σ y η y η J-Tes (0.50) (0.068) (7.838) (.289) (0.5) (2.203) WITHOUT THE MARKET CLEARING CONDITION σ σ σ η η J-Tes (0.303) (0.23) (7.667) (0.29) (0.30) (.567) Noes: Sandard errors are shon n brakes For llusrave purposes, Se 2 has been used n he esaon GMM allos he researher o esae par of he odel, dnshng he proble of sspefaon. In parular, he odels I esae are slen abou he Phllps Curve, he oneary poly rule and he evoluon of all he shoks onsdered by Ireland. In hs sense, feer assupons on he sruure of he odel are needed n order o ge onssen esaes. Hoever, GMM has also soe dsadvanages, beng he an one he use of rrelevan nsruens (or eak denfaon). Sok e al (2002) ephasze ha esaes ay be very sensve o he hoe of nsruens hen here s eak denfaon. The esaes I presen by usng spefaon do no have hs proble. Then, I ould sugges ha I fnd onssen esaes h he GMM proedure, hh are preferable o he ones of Ireland. Besdes, I fnd esaes ha are ore reasonable han hose obaned by Ireland h ML. More presely, y esae of he degree of he neres sensvy of real expendure ha s exlusvely due o he neres rae hannel s ore n lne h prevous esaes found by usng alernave ehods. Moreover, onrary o Ireland, I fnd ha he elasy of argnal uly of 29

30 onsupon s srly posve, hh ples ha an nrease n real oney s assoaed h an nrease n oupu. If I leave asde he arke learng ondon, hen y proedure ples one ore dfferene han before. Besdes he dfferen eonoer ehodology and he saple eployed, n hs ase onsupon s used nsead of oupu. Fro he seond par of Table 5, s lear ha he dfferene n saple does no explan he dfferen resuls. Moreover, f I opare he esaes by usng oupu and onsupon alernavely, I an fnd ha poran par of he dfferene oes fro leavng asde he arke learng ondon (.2 versus 0.6). Then, an be esablshed ha roughly half of he absolue dfferene oes fro usng onsupon and half fro he dfferen proedure n hs ase. 4. Iplaons of y fndngs In prevous seon, I provde epral evdene ha shos ha real oney balane effes are quanavely poran. Ths ples ha uly s no separable n onsupon and oney, and ha e an no absra fro oney deand n order o deerne nflaon and oupu, even n an eonoy here he Cenral Bank ses he neres rae. Moreover, here are hree addonal poran plaons of hs evdene ha I analyze n hs seon. Frs, he exsene of quanavely poran real oney balane effes n a odel h sky pres and flexble ages s a possble explanaon o o sylzed fas: he odesly proylal real age response o a oneary poly shok and he supply sde effes of oneary poly. Seond, here are poran quanave dfferenes n he responses of nflaon, oupu and real ages o oneary poly shoks aong he ase here real oney balane effes plays no role and he ase here suh effes are quanavely poran. Thrd, he desgn of he opal oneary poly ples a uh hgher volaly of he oupu gap han n he ase hen here are no real oney balane effes. Before sarng analyzng hese plaons, I need o exend he odel I derved n seon 2 by allong onopols opeon, sky pres a la Calvo and a labor 30

31 arke h flexble ages. Ths exenson allos e o have a Phllps urve and an equaon for he evoluon of real ages. As as enoned n seon 2, he Euler Equaon and he Money Deand equaon sll hold. Hoever, I need o rere he Euler Equaon and he Money Deand by usng he onep of he oupu gap. I all hs reren Euler Equaon he IS urve. The dervaon of hs exenson an be found n Woodford (2003). Gven ha I a also neresed n analyzng pulses responses of nflaon, oupu and real ages o a oneary poly shok, I also defne a oneary poly rule as a par of he odel. Ths rule s a sandard Taylor Rule ha responds o urren nflaon and o urren oupu gap. 4. MIUF Model h Monopols Copeon, Sky Pres and Flexble Wages. In hs par, I presen all he equaons ha I need n order o explan all he plaons of y epral evdene. All of he are log-lnearzed around he seady sae. IS Curve: x n n σ ˆ E π ) σ ( ˆ ˆ ) + E ( Yˆ Yˆ ) (9) = E x+ ( + + σ + here x s he oupu gap, π s nflaon, of he varables and paraeers are defned as n seon 2. n Yˆ s he naural level of oupu 4 and he res Money Deand: ˆ = η x η ˆ + η Yˆ (20) n 4 I s defned as he equlbru level of oupu a eah pon n e ha ould be under flexble pres, gven a oneary poly ha anans funon of ehnology shoks only. =. In hs odel, he naural oupu s exogenous and s a 3