Resurrecting the Role of Real Money Balance Effects

Transcription

1 Resurreng he Role of Real Money Balane Effes José Dorh Ths Verson: Noveber 2007 Frs Verson: January 2006 Absra Ths paper presens a sruural eonoer analyss ha suggess ha oney sll plays an ndependen role n he oneary ranssson ehans n he ned Saes. In parular, ndaes ha real oney balane effes are quanavely poran bu saller han hey used o be n he early poswar perod. Therefore, he spefaon of oney deand s neessary n order o deerne he evoluon of nflaon and oupu, even f he enral bank onrols he neres rae. The epral evdene presened has hree addonal plaons. Frs, by nludng real oney balane effes no he sandard sky pre odel, wo sylzed fas an be explaned: he odesly proylal real wage response o a oneary poly shok and he supply sde effes of oneary poly. Seond, uh hgher volaly of oupu and uh lower volaly of neres raes should arse under he opal oneary poly when here exs real oney balane effes of he agnude esaed n hs paper. Thrd, he reduon n he sze of real oney balane effes an aoun for a sgnfan delne n aroeono volaly. Ths would suppor fnanal nnovaon as a poenal soure of he Grea Moderaon. JEL Classfaon: E3, E32, E52 Keywords: real oney balane effes, oneary poly, nflaon and oupu I hank Jord Gal for hs valuable gudane, as well as Paula Busos, Fabo Canova, Alber Mare, Raón Maron, Anono Moreno, Albero Marn, Laura Mayoral and Thjs Van Rens for helpful dsussons. I also hank parpans a he Royal Eono Soey Annual Conferene 2007 and he Sprng Meeng of Young Eonoss 2006; and senar parpans a nversa Popeu Fabra, Bank of England and Cenral Bank of Peru. Any reanng errors are ne. nversa Popeu Fabra. Cona auhor: joseanono.dorh@upf.edu

2 . Inroduon The sandard New Keynesan odel, oonly used n dsussons abou oneary poly analyss, assgns no role o oney n he oneary ranssson ehans. In fa, he sandard odel s a ashless one. The wdespread 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 enral bank onrols neres raes (whou respondng o oney) and real oney balane effes are no quanavely poran. Woodford evaluaes he sze of hese effes o be very low afer albrang he oney n uly funon (MI) odel for he.s eonoy 2. In addon, Ireland provdes eonoer esaes of a bgger sruural odel, by usng Maxu Lkelhood (ML), ha suppor Woodford s poson abou he neglgble sze of real oney balane effes. The prevous onlusons onras wh soe epral redued for evdene. Melzer (200) shows ha oney s a sgnfan deernan of onsupon growh n he S, onrollng for he shor er real neres rae, s lags and lagged values of onsupon growh. Nelson (2002) and Hafer e al. (2007) fnd he sae resuls as Melzer for S bu usng oupu gap nsead of onsupon. Gven ha he sruural analyss and he redued for evdene pon n wo dfferen dreons, n hs paper, I revs he porane of real oney balane effes by usng a sruural esaon ehodology dfferen fro he ones proposed by Woodford and Ireland. I provde epral evdene showng ha hese effes are sll quanavely poran n ned Saes bu lower han hey were n he early poswar perod. Therefore, real oney balanes ener drely n he aggregae deand; whh ples ha he spefaon of oney deand s sll relevan n order o deerne nflaon and oupu. Moreover, I show and analyze hree addonal poran plaons of y epral evdene on real oney balane effes. Frs, he odesly proylal real wage response o a oneary poly shok and he supply sde effes of oneary Real oney balane effes exs when 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. In he oney n uly funon fraework, real oney balane effes ake plae when uly s non-separable n onsupon and real oney. 2 MCallu (2000) perfors a dfferen albraon exerse ha leads o he sae onluson. 2

3 poly an be explaned by he exsene of quanavely poran real oney balane effes n a odel wh sky pres and flexble wages 3. Seond, he desgn of he opal oneary poly should ply uh hgher volaly of oupu and uh lower volaly of he neres rae when here are real oney balane effes. Thrd, he dnshen n he sze of real oney balane effes, whh ourred n he begnnng of he 980 s, an explan a sgnfan reduon n he volaly of oupu and nflaon. Ths would suppor he hypohess ha fnanal nnovaon explans par of he Grea Moderaon n.s. The paper s organzed as follows. Seon 2 presens he MI odel and desrbes he equlbru ondons ha deerne he Euler equaon and he oney deand ha are used n he epral par. The odel allows, bu does no requre, ha real oney balane effes arse fro non-separable uly n onsupon and real oney. I s shown ha he sze of hese effes s gven by he elasy of argnal uly of onsupon wh respe o real oney dvded by he oeffen of rsk averson. Seon 3 presens he ehodology and he eonoer spefaon used n order o esae he paraeers ha easure he agnude of real oney balane effes. The esaes, robusness exerses and a oparson beween y esaon proedure and hose of Woodford and Ireland are also presened n hs seon. Seon 4 onans he analyss of he hree addonal plaons of y epral evdene. Seon 5 onludes. 2. Money n ly Funon Model In hs seon, I presen brefly a slghly odfed verson of hs odel developed by Woodford (2003). The an goal of hs par s o show he log-lnearzed represenaon of he Euler equaon (IS urve or aggregae deand) and oney deand (LM urve) ha are gong o be used n he epral par. 3 There exs oher explanaons for hese sylzed fas. The os oon explanaon for he odesly proylal real wage response afer a oneary poly shok s he exsene of sky pres and sky wages. The supply sde effes of oneary poly are oonly explaned wh he os hannel of oneary ranssson. 3

4 The represenave household seeks o axze he followng expeed dsouned uly: E [ ( C, M / P ; ξ ) V ( H ] 0 ) 0 β () where 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, P s he pre of he sngle good n ers of oney n perod, ξ s a dsurbane n he lqudy serves provded by oney and H s he quany of labor suppled (easured n hours). The perod ndre uly s oposed by he su of wo funons: and V. The funon s onave and srly nreasng n eah of he arguens (onsupon and real oney balanes). All hese assupons are onssen wh he rofounded ransaon os odel and shoppng e odel. Moreover, uly s allowed o be non separable n onsupon and real oney balanes. However, he sgn of s no assued beause he prevous rofounded odels do no provde. If 0, hen uly s separable n onsupon and oney; and, onsequenly, here are no real oney balane effes. I s also assued ha dsurbanes n lqudy serves affe boh he argnal uly of onsupon and oney ( 0, 0 ). Fnally, he funon V s an nreasng and onvex funon ha represens he dsuly of labor. ξ ξ Noe ha s assued ha he ndre uly funon s separable wh respe o labor 4. Ths eans ha argnal uly of onsupon and real oney balanes do no depend on. Therefore, as s shown laer, labor affes neher he Euler equaon nor he oney deand equaon drely. The axzaon of he expeed uly s subje o an nereporal budge onsran of he for: 0 0 0, [ PC + M ] A0 + E0Q0, [ W H T ] E Q (2) 0 4 Ths assupon s onssen wh a rofounded ransaons oss odel bu s no wh a shoppng e odel. 4

5 5 where +, 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, 0 A s he nal level of wealh, W s he nonal wage per hour worked and T represens ne (nonal) ax olleons by he governen. Moreover, Q, 0 s a sohas dsoun faor ha sasfes,0 0 Q and + 0 0, 0 s s Q E. I s also worh nong ha he pre of a rskless one perod bond s gven by: [ ], + + Q E (3) The household s opzaon proble s hen o hoose proesses C, M, H 0 for all daes 0, sasfyng (2) gven s nal wealh A 0 and he good pre, he nonal wage and he sohas dsoun faors ha expes o fae, so as o axze (). The frs order ondons assoaed wh he household s proble are:, ) ; /, ( ) ; /, ( P P Q P M C P M C β ξ ξ (4) P M C P M C ) ; /, ( ) ; /, ( ξ ξ (5) H P W P M C H V ) ; /, ( ) ( ξ (6) Equaon (4) s a sandard nereporal opaly ondon (Euler equaon) whereas equaons (5) and (6) are he opaly ondons for oney deand and labor supply respevely. sng (3) and (4), I an rewre he Euler equaon as:

6 + ( C, M / P β E (7) ( C, M / P ) P + ) P In order o ondu he epral par of he paper, I jus need o approxae ondons (7) and (5) 5. A log lnear approxaon o ondon (7) s hen gven by: E ξ ˆ ˆ C+ C ) E ( ˆ ˆ ) (ˆ ˆ ) ( ) + + Eπ + + E ξ ξ + (8) σ σ σ ( where C Cˆ + log, ˆ log, ˆ P log, ˆ π log( ), σ, C + πp C and, C,, π 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. Equaon (8) represens he bass for buldng he aggregae deand blok n os of he aroeono odels ha are used for oneary poly analyss. In fa, equaon (8) obned wh a arke learng ondon ha wll be seen laer opleely defnes he aggregae deand n a losed eonoy whou apal. The paraeer σ s he oeffen of relave rsk averson. Aordng o he assupons I ade on he uly funon, s srly posve. The paraeer s he elasy of argnal uly of onsupon wh respe o real oney. The porane of real oney balane effes s gven by he rao, whh easures he effe of a one peren devaon of oney σ fro s seady sae on he perenage devaons of onsupon fro s seady sae 6. If hs rao s sgnfanly dfferen fro zero, hen real oney affes drely aggregae deand; and, onsequenly, nfluenes he equlbru evoluon of all he 5 Condon (6) an also be log lnearzed and be aken no aoun when esang real oney balane effes. However, gven ha usng (6) ples posng he assupon of flexble wages, s hosen n hs paper no o do. The reason s ha s preferable o have an esae of real oney balane effes ha s no sensve o he assupon abou wage seng. 6 I an also be shown ha he oponens of hs rao are poran deernans of he wegh of oupu n he welfare loss funon when real oney balanes effes are allowed n a odel. I dsuss he pa of hese oponens laer. 6

7 aroeono varables. Noe ha n hs odel, real oney balane effes arse fro non-separable uly n onsupon and real oney balane effes ( dfferen fro zero). A orrespondng log lnear approxaon o ondon (5) s gven by: ξ ξ η Cˆ η ( ˆ ˆ ) + ξ (9) ) ˆ ( σ + whereη v + σ, η σ + +, σ + + ˆ log, σ, + C v and v,, 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. The las er represens a oney deand shok (gven by a lnear funon of he dsurbane on he lqudy serves provded by real oney balanes). Fnally, s assued ha hs dsurbane has ean equal o zero and follows he auoregressve proess: ξ ρξ ξ + η (0) where η s an nnovaon wh ean zero and serally unorrelaed. These assupons on hs dsurbane and s nnovaon are onssen wh he sruure of he oney deand shok ha s assued n he leraure 7. In equlbru all oupu us be onsued, hus plyng a goods arke learng ondon gven bycˆ Yˆ 8. Ths ondon ould be used n order o wre (8) and (9) as a funon of he perenage devaon of oupu (nsead of onsupon) fro s seady sae. I onsder hs alernave n he epral par of he paper. Moreover, 7 See Ireland (2004) and Bouakez e al. (2005). 8 Noe ha hs ondon also holds n seady sae, whh eans hac Y. 7

8 8 when goods arke learng s obned wh (8), he aggregae deand arses n s usual for n aroeono odels. 3. New Esaes of Real Money Balane Effes Ths seon onans four pars. In he frs one, I desrbe he eonoer spefaon used o esae jonly he Euler equaon and he oney 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 answer how poran real oney balane effes are fro a quanave pon of vew. Two robusness exerses on he esaon proess are presened n he hrd subseon. Fnally, I ake a oparson of y esaon proedure wh hose of Woodford (2003) and Ireland (2004) n order o undersand why y esaes are dfferen fro hers. 3. Eonoer Spefaon In order o perfor he GMM ehnque, wo orhogonaly ondons an be nferred fro he odel developed n he prevous seon. One an be nferred by obnng equaons (8), (9) and (0) n he followng way: frs, by usng (0), we an opue he las expeaon er ha s presen n equaon (8). Then, we have: E E ξ ρ ξ η ξ ρ ξ ξ ξ ξ ) ( ) ( ) ( () sng () and (9), we an rewre (8) n he followng way: ) ( ) ( ) ˆ (ˆ ) ˆ ˆ ( ) ˆ ˆ ( v E E C C E σ µ σ ρ π σ σ ξ (2) where ξ ξ ξ µ and ( ) C v ˆ ˆ ˆ ˆ + η η

9 The frs orhogonaly ondon oes fro equaon (2) and arses fro he fa ha, under raonal expeaons, he foreas error n onsupon one perod ahead should be unorrelaed wh he nforaon se daed a perod and earler. Then, hs orhogonaly ondon s gven by: ( ) ( ) ˆ ˆ ρ ξ µ σ + v E ( C C ) ( ˆ ˆ ) (ˆ ˆ ) + + π + σ σ σ + z 0 (3) where z denoes a veor of varables daed a perod and earler. The seond orhogonaly ondon oes fro equaon (8) and (9) and arses fro he properes of he nnovaonη. nder raonal expeaons, hs nnovaon should be unorrelaed wh earler nforaon. Then, he followng orhogonaly ondon an be esablshed: E {[ ˆ ( ) ( ˆ C + η ˆ ˆ ρ ˆ η C + η ( ˆ ˆ )] z } 0 η ξ (4) ˆ where z - denoes a veor of varables daed a perod - and earler. The orhogonaly ondons gven by equaons (3) and (4) onsue he bass for esang he sruural paraeers of he odel va GMM. Noe ha here are egh sruural paraeers n he syse: σ,,,, v, σ, ρ ξ and µ. 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 down ore drely fro frs oens of he daa 9. I se he usng her averages durng he saple perod. The res of paraeers are esaed. 9 Gven a defnon of oney, here s agreeen abou wha,, 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)). 9

10 Before perforng he esaon, one eonoer ssue should be faed. In sall saples, he way he orhogonaly ondons are wren (or noralzed) affes he GMM esaes 0. More spefally, here s no agreeen abou how o spefy he orhogonaly ondon (3) 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 (3) s gven by he followng expresson : E {[ ˆ ˆ ˆ ˆ σ ( C C ) + ( ˆ ˆ ) ( ρ ) µ ( σ + ) v ] z } 0 π ξ (5) Hansen and Sngleon (983) and Hall (988) use noralzaon (3) and (5) respevely, whou allowng for he exsene of real oney balane effes ( 0) and he presene of oney deand shoks ( µ 0) n he Euler Equaon. Hansen and Sngleon esae he oeffen of relave rsk averson, whereas Hall esaes s reproal (he nereporal elasy of subsuon). They fnd very dfferen resuls, as surveyed n Neely e al. (200) and onfred by updaed esaes perfored by Capbell (2003) 2. 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 wo alernave spefaons of he orhogonaly ondons are aken no aoun n order o see how sensve he resuls are o he noralzaon ssue. Spefaon onsders equaons (5) and (4) whereas spefaon (2) onsders equaons (3) and (4). 3.2 Daa and Baselne Esaes The daa ha I use s ned 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 0 See Capbell (2003), Halon e al. (2005), Neely e al. (200) and Yogo (2004). Noe ha noralzaon (5) arses fro ulplyng he orhogonaly ondon (3) by σ. 2 Capbell (2003) repors pon esae of 0.7 and 5 for he oeffen of relave rsk averson when he uses noralzaon 2 and 0 respevely. Hs pon esaes oes fro an esaon of he Euler Equaon only, whou allowng he exsene of real oney balane effes. 0

11 neres rae pad on oney s easured by M2 oney own rae, expressed n quarerly ers. Consupon and real oney balanes are expressed n per apa 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 3. 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 way o show 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 2- >0 ples ha (M2-M) furnshes lqudy serves aordng o he odel and ha + >0. So, afer opung he average own rae of reurn of (M2-M) and opare wh 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 4. Table presens he GMM esaon of he sruural paraeersσ,, σ, ρ ξ and µ. I also shows he rao, whh easures he porane of he real oney σ balane 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 wo spefaons of he orhogonaly ondons dsussed earler and 3 There exss alernave ways o derend e seres. In hs ase, I follow he proedure presened n Ireland (2004). 4 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 whereas real oney arke funds do no. So, her proposal of a oneary aggregae ha provdes lqudy serves s M2 nus real oney arke funds. However, 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.

12 wo ses of nsruens 5. Sandard errors (wh a Newey Wes orreon) for all he paraeer esaes are repored n brakes. INSERT TABLE Soe neresng resuls arse fro hese esaons, whh 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 are hgher han Ths resul onrass onsderably wh hose provded by Woodford (2003) and Ireland (2004), who oban pon esaes of 0.05 and 0.00 respevely for hs rao. Woodford uses a albraon proedure, whereas Ireland perfors Maxu Lkelhood esaon. A dealed analyss of he oparson of hese resuls wh ne s presened n a speal subseon laer. Seond, he esaes of he oeffen of rsk averson are srly posve and sgnfanly dfferen fro zero n all he ases. Ths resul s onssen wh he resron I posed heoreally on hs paraeer. Thrd, all he pon esaes of he degree of rsk averson 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 beween and 2.4 when nsruenal varables and noralzaon (5) are used. Fourh, he elasy of argnal uly of onsupon wh 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 6. 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 oney plays an ndependen role n he oneary ranssson ehans. Ffh, boh paraeers of he oney deand are also sgnfanly dfferen fro zero. Sxh, he oney deand shok s 5 Se nludes neres rae, nflaon, real oney balanes and onsupon fro -3 o -6. Se 2 nludes he sae varables bu jus unl There are soe rofounded odels where an be negave. One of he s he shoppng e odel where onsupon and lesure are srong subsues, a suaon ha Wang and Yp (992) desrbe as orrespondng o an asse subsuon odel. 2

13 que perssen. Ths resul s onssen wh hose found by Ireland (2004, 200) and Bouakez e al (2005). Fnally, he valdy of all he regressons s onfred by he p- value for he Hansen s J sas of overdenfyng resrons wh a sgnfane level of 5 peren. Fro Table, s lear ha real oney balane effes are quanavely poran bu he agnude s no apparen. nder noralzaon, he rao s around 0.6; σ whereas under noralzaon 2, s around 0.3. The an reason behnd hs resul s ha he esae of he degree of rsk averson s very sensve o he noralzaon n he GMM esaon. sng noralzaon, he degree of rsk averson s lose o ; whle n he seond noralzaon s around 2. Fnally, here exs nor dfferenes n he esaes of he elasy of argnal uly of onsupon and n hose of he neres rae seelasy. The pon esaes of are beween 0.5 and 0.7; whereas hose of η go fro 6.0 o All he neres rae seelasy esaes are n lne wh he oney deand esaon perfored by Reynard (2004) 8 for he poswar perod. 3.3 Robusness Exerses In hs subseon, I perfor wo robusness exerses. Frs, I use he goods arke learng ondon so ha Cˆ Yˆ andc Y. Seond, I hek sub saple sably sng GDP Daa Clearly, onsupon s dfferen fro oupu n he daa. However, I wll assue ha onsupon equals oupu beause a lo of aroeono sudes (e.g. Ireland (2004)) pose hs ondon n he esaon of aroeono odels. Then, I spefy he orhogonaly ondons n he sae way as I dd when onsupon was used. 7 These pon esaes for he neres seelasy ply ha he neres rae elasy s beween and He uses oupu and M2 nus nsead of onsupon and M2 respevely n order o perfor hs oney deand sudy. 3

14 Spefaon onsders equaons (5) and (4) whereas spefaon (2) onsders equaons (3) and (4). Boh spefaons pose ha onsupon equals oupu. The laer eans ha Cˆ Yˆ n (3), (4) and (5). Moreover, soe paraeers hange her defnon n he equaons as follows: y σ σ y, Y yy y, y η η y v + σ y, σ + Y v The frequeny of he daa and he saple perod are he sae as n prevous subseon. Now, 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 per apa 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 shows he rao, whh 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 boh spefaons of he orhogonaly ondons dsussed earler and wo ses of nsruens 9. Sandard errors (wh a Newey Wes orreon) for all he paraeer esaes are repored n brakes. INSERT TABLE 2 9 Se nludes neres rae, nflaon easured by he GDP deflaor, real oney balanes and oupu fro -3 o -6. Se 2 nludes he sae varables bu jus unl -5. 4

15 nder boh spefaons, he esaes of he real oney balane effes are sasally sgnfan and uh hgher han hose obaned when onsupon s used. When noralzaon s used, he pon esaes are beween.2 and.3; whle hey are around 0.5 when he seond noralzaon s used. Therefore, all hs evdene ples ha he resul obaned n he baselne ase s no drven by usng onsupon nsead of oupu. The paraeerσ easures he nverse of he neres sensvy of real expendure y ha s exlusvely due o he neres rae hannel 20. The pon esaes are srly posve (as heory preds) and sasally sgnfan. When noralzaon s used, hey are around 0.3. Ths value s sall and very lose o wha has been found n oher aroeono papers ha esae hs paraeer. Roeberg and Woodford (997) fnd ha s equal o 0.6 whereas Aao and Laubah (2003) esae equal o nder noralzaon 2, he pon esaes are uh hgher (around ) and suppor he sandard prae n aroeonos of albrang hs value equal o one. Moreover, 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 y onsupon ( σ ), whh akes sense. The nuon s as follows: 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 When oupu s used nsead of onsupon, represens he elasy of argnal uly of real noe wh respe o real oney. All he pon esaes for hs paraeer are sasally sgnfan and very slar o hose found when onsupon was used. Therefore, he an onlusons relaed o hs paraeer do no hange: uly s non-separable and s srly posve. Moreover, an be onluded ha he nrease n he esaes of he real oney balane effes when he goods arke learng ondon s posed are assoaed wh he drop nσ. y 20 When here are real oney balane effes, a hange n he neres rae affes aggregae deand hrough wo hannels: he neres rae hannel and he real oney balane effe hannel. The neres rae hannel s he one by whh neres raes pa on he desred ng of prvae expendures. The oher hannel s he one by whh a oveen n he neres raes affes argnal uly of onsupon hrough her pa on real oney balanes. 2 Boh papers onsder ashless sky pre odels. 5

16 Boh paraeers of he oney deand are also sgnfanly dfferen fro zero. Aordng o hree ou of he four esaes, anno be rejeed ha noe elasy ( η y ) s equal o, whh s onssen wh several epral sudes abou oney deand. Moreover, he pon esaes of he neres rae seelasy go fro 3.4 o 5.4. All hese values are plausble under he oney deand esaon for he poswar perod perfored by Reynard (2004). He fnds a pon esae of 0.4 for hs paraeer, wh a sandard error of Fnally, he las olun of he able repors he p-value for he Hansen s J sas of overdenfyng resrons, whh onfrs he valdy of all he regressons wh a sgnfane level of 5 peren 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 wo sub-saples: 959:-979:4 and 980:-2004:4. The begnnng of he seond sub-saple s hosen suh ha ondes wh he begnnng of he saple used by Ireland (200, 2004). Ths sraegy allows a far oparson of y esaes wh hs. Resuls are presened n Table 3 for boh spefaons of he orhogonaly ondons and he nsruen se 23. INSERT TABLE 3 The quanave porane of real oney balane effes s also onfred by hs exerse. nder boh spefaons, he rao σ s posve and sgnfanly dfferen fro zero aross sub-saples. However, he pon esaes are no onsan aross e. Pror o 980, hey are 0.85 and 0.74; whle sne 980 hey are 0.54 and 0.2. Thus, hs resul suggess ha real oney balane effes would have dnshed s 22 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. 23 Resuls are very slar when Se 2 s used. 6

17 quanave porane n he reen perod. Neverheless, he agnude of he reduon n he sze of real oney balane effes s no apparen. Noe ha he derease wh noralzaon 2 s uh hgher han he one wh noralzaon. Oher neresng resuls arse fro hese esaons, whh are robus o he spefaons. Frs, he esaes of he oeffen of relave rsk averson and he elasy of argnal uly of onsupon are lower sne 980. Seond, he reduon n he elasy of argnal uly of onsupon s he an deernan of he derease n he sze of real oney balane effes. Thrd, he neres seelasy has nreased onsderably sne 980. Fourh, he degree of perssene of he oney deand shoks s hgher. 3.4 Prevous Sudes on Real Money Balane Effes: a oparson The esaes of he paraeer ha easures he quanave porane of real oney balane effes dffer draaally fro hose obaned before n he leraure. Therefore, s neresng, a hs pon, o undersand why hs an be so. For hs reason, n hs subseon, I desrbe he esaon proedures perfored by Woodford (2003) and Ireland (2004); and hen, opare he wh y proedure. Woodford, by usng a albraon proedure and onsderng he goods arke learng ondon, suggess a value of 0.05 for he sze of real oney balane effes. Ths resul s obaned by seng σ 0. 6 and The frs paraeer s albraed usng y an esae fro a sudy perfored by Roeberg and Woodford (997). To oban a value for, he uses he followng relaon pled by he MI odel: η η y v + σ y + (6) Noe ha an be found, 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. 7

18 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 Clearly, here exs wo poran dfferenes beween Woodford s proedure and ne. Frs, he defnon of oney s dfferen: oneary base versus M2. Seond, he ehodology of esaon s also dfferen: albraon versus GMM. In order o llusrae how hese wo dfferenes explan he dsrepany beween y esaes and he one presened by Woodford, I perfor wo dfferen albraon exerses ha are shown n Table 4. Calbraon follows Woodford (2003) bu hanges only he defnon of he oney for M2; and onsequenly, hanges appropraely he oney veloy and he neres rae seelasy. Ths exerse shows how Woodford onluson on real oney balane effes hanges wh he defnon of oney. I an be seen ha here exss a huge hange. The sze of real oney balane effe goes fro 0.05 o Therefore, he defnon of oney aers onsderably. Calbraon 2 jus hanges he degree of rsk averson used n Calbraon by assung an esae onssen wh y epral evdene n order o see how GMM esaes ake a dfferene. The sze of real oney balane effes agan hanges draaally gong fro 3.05 o 0.49 (a value ha s very lose o he average of all y baselne esaes). Therefore, he esaon ehnque also aers. INSERT TABLE 4 Ireland esaes a sall aroeono odel by ML, onanng seven relaons: an Euler equaon, a M2 oney deand equaon, a Phllps urve, an neres 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 weny paraeers ha he esaes by usng quarerly daa ha run fro 980: hrough 200:3 and posng he arke learng ondon. One of hese paraeers s. Ireland esaes equal o zero, σ y wh a sandard error of The pon esaes of he deernans of hs rao were obaned n wo dfferen ways: σ y was albraed and se equal o, whereas was esaed. Ireland argues ha σ y was albraed beause prelnary aeps o 8

19 esae, desrbed n Ireland (200), led o unreasonably hgh levels of hs paraeer. There exs hree poran dfferenes wh respe o Ireland s proedure. Frs, n he presen sudy, boh paraeers ha deerne he sze of real oney balane effes are esaed. In fa, I always fnd reasonable degrees of rsk averson, so I do no need o pose reasonable values on hs paraeer. Seond, he odel he esaes s uh bgger han he one I esae (7 equaons versus 3 equaons I esae). Thrd, he eonoer proedure s dfferen: ML versus GMM. I s lear ha he frs dfferene goes n favor of y approah. The seond dfferene eans ha he poses ore sruure; and herefore, ore ross equaon resrons n hs esaon. For nsane, aong oher resrons, he poses n hs esaon ha f oney eners he IS urve, should also ener n he Phllps urve. Clearly, he rsk of sspefaon s uh hgher n Ireland s approah. Thus, aordng o he rera of nzng sspefaon, he seond dfferene also goes n favor of y approah. However, s no lear whh eonoer proedure s beer. For hs reason, s useful o dsuss on he onvenene of eah eonoer ehod. Cohrane (200) ephaszes ha he ssue of whh eonoer proedure s he bes n suh rusanes s absoluely open. He pons ou ha here are no heores or Mone Carlo sulaons ha sugges whh one s preferable. I s known ha f he odel s orre, ML s ore effen han GMM. However, s very dfful o argue ha an eono odel s opleely well spefed. In parular, n he ase of Ireland, here are hree reasons why hs odel ould be sspefed. Frs, he arke learng ondon n he way he poses does no hold: onsupon s dfferen fro oupu. Seond, hs spefaon of he Phllps urve ould be 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 urve. Thrd, no all he shoks neessarly sasfy he noraly assupon. Then, gven ha he onsseny of he esaes obaned by ML s very sensve o he sspefaon of he odel, Ireland esaes ould be nonssen. 9

20 GMM allows he researher o esae par of he odel, lng he proble of sspefaon. In parular, he odel I esae s slen abou he arke learng ondon, he Phllps Curve, he oneary poly rule and he evoluon of wo of he shoks onsdered by Ireland (produvy and preferene shoks). In hs sense, fewer assupons on he sruure of he odel are needed n order o ge onssen esaes. However, GMM has also soe dsadvanages, he an one beng he use of rrelevan nsruens (or weak denfaon). Sok e al. (2002) ephasze ha esaes ay be very sensve o he hoe of nsruens when here s weak denfaon. The esaes I presen by usng boh spefaons see no o have hs proble. 4. Iplaons of y fndngs In prevous seon, I presen eonoer esaes ha sugges ha real oney balane effes are quanavely poran bu lower han hey used o be n he begnnng of he 980 s. Gven he odel used o evaluae he exsene of real oney balane effes, he resuls ples ha uly s non-separable, and ha oney plays a dre role n deernng he dyna behavor of nflaon and oupu. Moreover, here are hree addonal poran plaons of y evdene on real oney balane effes ha I analyze n hs seon. Frs, he exsene of quanavely poran real oney balane effes n a odel wh sky pres and flexble wages s a possble explanaon for wo sylzed fas: he odesly proylal real wage response o a oneary poly shok and he supply sde effes of oneary poly. Seond, ondonal on produvy and oney deand shoks, uh hgher volaly of he oupu and uh lower volaly of he neres rae should arse under he opal oneary poly when here exs real oney balane effes of he agnude esaed n hs paper. Thrd, he reduon n he sze of real oney balane effes an explan an poran par of he dnshen n he volaly of nflaon and oupu. Ths would suppor he hypohess ha fnanal nnovaon s an poran soure of he Grea Moderaon. Before analyzng hese plaons, I need o exend he odel I derved n seon 2 by allowng for onopols opeon, sky pres a la Calvo and a labor arke 20

21 wh flexble wages. Ths exenson allows e o have a Phllps urve and an equaon for he evoluon of real wages. As was enoned n seon 2, he Euler equaon and he oney deand equaon sll hold. The dervaon of hs exenson an be found n Woodford (2003). Gven ha I a also neresed n analyzng pulse responses of oupu and real wages 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. MI Model wh 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 a zero nflaon seady sae. Moreover, he albraon of he odel s presened. 4.. Equaons IS Curve: ˆ ˆ E ( Y + Y ) E ( ˆ ˆ ) (ˆ ˆ ) + + Eπ + σ σ (7) whereπ s nflaon and he res of he varables and paraeers are defned as n seon 2. Money Deand: ( ˆ ) ξ ˆ η Yˆ η ˆ + (8) wh ˆ 0 for sply. Ths assupon does no aler he resuls I presen here. Moreover, ξ s a oney deand shok ha follows an auoregressve proess of he for: 2

22 ξ ρ ξ + η (9) 2 where η s an..d. ean zero nnovaon wh varane σ η. e AS urve: ( α)( αβ )( ω + ω + σ η ) π (20) w p η ( ˆ x + ) + βeπ + α ( + ( ωw + ω p ) θ ) ωw + ω p + σ η where x s he oupu gap, defned as he dfferene beween aual oupu ( Yˆ ), and he naural level of oupu ( Yˆ ) 24. Moreover, α s he fraon of good pres ha rean n unhanged, β s he dsoun faor, θ s he elasy of deand, ω w he elasy of argnal dsuly of work wh respe o oupu and ω p s he negave of he elasy of argnal produ of labor wh respe o he level of oupu. I should also be noed ha n hs odel he elasy of real argnal os wh respe o aggregae oupu s equal oω + ω + σ w p η. Naural Oupu: ( + ω + ω ) Yˆ ˆ ξ (2) η n w p A + ωw + ω p + σ η ωw + ω p + σ where  represens he log devaon of he ehnology faor wh respe o s seady sae level. Ths faor follows an auoregressve proess of he for: Aˆ ρ ˆ + ς (22) a A 2 whereς s an..d. ean zero ehnology shok wh varaneσ ς. 24 The naural oupu s defned as he equlbru level of oupu a eah pon n e ha would be under flexble pres, gven a oneary poly ha anans. 22

23 Ineres Rae Poly Rule: ˆ + φ π π + φ x (23) x whereφ π > 0, φ x > 0 and s an exogenous oneary poly shok ha has he followng proess: ρ + ε (24) whereε s an..d. ean zero shok. Equaon for Real Wages 25 wˆ r ( ω + σ w ) Yˆ ˆ ω Aˆ w (25) where r wˆ s he real wage Calbraon The albraed paraeers of he odel are: σ.0, 0.48, η.0, η 7.0, β 0.99, θ, ω w 0.09, ω p 0.38, α 0.75, φ π 3.0, φ 0.5, ρ 0.96, ρ 0.95, ρ 0.6, σ η 0.004, σ x e a ς Aordng o he baselne esaes, he sze of he rao an ake four values: 0.33, σ 0.38, 0.59 and 0.6. For llusrave purposes, I explore a albraon ha ses he sze of he real oney balane effes equal o he ean of all hese possble values. The oeffen of rsk averson s se equal o ; and onsequenly, The values assgned o he paraeers of he oney deand are onssen wh y epral 25 Ths s pl by he soluon of he odel. I s no assued ad ho. 23

24 evdene and wh oher sudes as I dsussed n seon 3. The value for θ ples a arkup of 0 peren and s aken fro Gal e.al. (200). The paraeer ω p s obaned by eans of he followng proedure. I assue a Cobb Douglas aggregae produon funon of he for F(h)h λ. Gven hs produon funon, ω p. Then, usng λ he fa ha λ s equal o he arkup es he labor share (fro frs order ondons of he fr), ω p /(.x0.66) The value forα s onssen wh he aro sudy perfored by Gal and Gerler (999) and ples ha pres are fxed four quarers. Ths perod lengh s lose o he average pre duraon found n survey evdene. The oeffens of he neres rae rule are he sandard ones of a Taylor rule, exep forφ π, whh s hgher han he radonal value of The paraeer ω w s pked by assung an elasy of real argnal os of an ndvdual fr wh respe o s oupu equal o 0.47, whh s aken fro Roeberg and Woodford (997). The albraon of he perssene of he ehnology faor and he sandard devaon of s nnovaon s he sandard one n he leraure of Real Busness Cyle. Fnally, he degree of perssene of he oney deand shok and he sandard devaon of s nnovaon are albraed aordng o y epral evdene. 4.2 Analyzng he Modesly Proylal Real Wage Response o a Moneary Poly Shok I s a sylzed fa ha here s a very odes response of real wages relave o he one of oupu afer a oneary poly shok. Sudes developed by Alg e al. (2004) and Chrsano e al. (200) suppor hs sylzed fa by usng an pulse response funon derved fro a sruural VAR. The os oon explanaon for hs s he exsene of sky pres and sky wages 27. In hs seon, I show ha hs sylzed fa an also be explaned whou sky wages and wh real oney balane effes. Fgure dsplays he response of real wage and oupu o a onraonary oneary poly shok n he ase when The sold lne represens he response of oupu whereas he dashed lne represens he response of real wage. We an see ha he real 26 I s se equal o 3.0 n order o have a deernae equlbru. 27 See Woodford (2003). 24

25 wage response s uh lower han he one of oupu, as he epral sudes show. Moreover, he dfferene beween hese wo responses s nreased sgnfanly by he addon of real oney balane effes. Fgure 2 dsplays he responses when here are no suh effes and s lear ha he dfferene beween he responses s uh lower n hs ase. In parular, when here are no real oney balane effes, he response of real wages s a b hgher han he one of oupu. The dfferene beween Fgures and 2 s explaned by wo fas: real wage responds ore and oupu responds less when here are no real oney balane effes. Then, I an onlude ha he exsene of quanavely poran real oney balane effes an be a way o explan he very odes response of real wages relave o oupu afer a oneary poly shok. INSERT FIGRE INSERT FIGRE 2 The nuon behnd y resul s as follows. Afer a onraonary oneary poly shok, n a odel wh real oney balane effes, boh labor deand and labor supply ove n he sae dreon. On he one hand, he oneary onraon redues he deand for an ndusry s oupu, whh eans ha frs respond by lowerng her oupu and onsequenly labor deand. On he oher hand, nreases he opporuny os of holdng oney, and hene, dnshes real oney holdngs. Ths dnshen dereases he argnal uly of onsupon (gven ha argnal uly of onsupon depends posvely on real oney balanes), and herefore, nreases he real wage asked by labor supplers 28. The laer eans ha here s also a reduon n labor supply. Then, he pa of oneary poly s basally on average hours worked (and onsequenly on oupu), and no on real wages, gven he albraon I propose. 4.3 Analyzng he Supply Sde Effes of Moneary Poly Barh and Raey (200) show eprally ha a oneary poly shok an affe nflaon and oupu also hrough he supply sde. These effes are oonly explaned 28 Noe ha labor supply s gven n hs odel by w p v ( h ) h ( Y, ) 25

26 wh he os hannel of oneary ranssson, whh s presen when frs argnal os depends drely on he nonal neres rae 29. In a general equlbru odel, hs hannel s usually norporaed by assung ha frs us borrow oney o pay her wage bll. The need o borrow nrodues an addonal oponen o he os of labor. In hs seng, he argnal os of hrng labor s he real wage ulpled by he gross nonal neres rae. So, when he neres rae nreases, he argnal os of hrng nreases beause of hese effes, and hene, nflaon. Noe also ha he supply sde effes of oneary poly are assoaed wh a shf n he labor deand afer a oneary poly shok. In hs seon, I la ha hese effes an be due o he exsene of real oney balane effes. Moreover, I show ha he supply sde effes n hs ase are assoaed o shfs n labor supply. The aggregae supply urve, when real oney balane effes exs, s gven by equaon (2) of subseon 4.. Ths expresson allows for he exsene of supply sde effes ( α)( αβ ) hrough he er η î. Beause of he exsene of hs er, an α( + ( ω + ω ) θ ) w p nrease n he neres rae nreases nflaon, ananng fxed he oupu gap 30. The nuon s as follows: 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 wage asked by labor supplers. Then, hs ples ha real argnal os nreases, and hene, nflaon and he pre ndex also nrease. 4.4 Analyzng he Ipa of Real Money Balane Effes on he Desgn of Opal Moneary Poly In hs subseon, I analyze how real oney balane effes affe opal oneary poly analyss. In parular, I wll show how opal volaly of he eono varables hange when real oney balane effes are onsdered n he analyss. 29 See Barh and Raey (200). 30 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. 26

27 In order o haraerze he opal poly soluon, I assue full oen of he oneary auhory and a non dsored seady sae. nder hese assupons, Woodford (2003) shows ha he opal poly proble an be wren as: Mn 0 β L +.. p where L π + λ x + λ s he quadra perod loss funon wh he weghs ( λ x x ˆ and λ respevely) expressed by he followng forulas 3 : ( α )( αβ )( ωw + ω p + σ λx αθ ( + ( ω + ω ) θ ) w p η), ( α)( αβ ) η λ αθ ( + ( ω + ω ) θ) v w p Before solvng hs proble, s onvenen o ake soe oens on hese weghs. Frs, when he eonoy s ashless, v goes o nfny; and, herefore, he wegh on he neres rae goes o zero. Ths s he ase n he sandard opal oneary poly analyss. Then, an be shown n hs ase ha he opal volaly of nflaon and oupu gap s zero. Seond, when oney s nrodued n he analyss hrough separable uly n onsupon and real oney, hen λ s dfferen fro zero. Therefore, here exss a rade-off beween sablzng nflaon and he neres rae. Thrd, by onsderng non-separable uly ( dfferen fro zero), he wegh on he oupu gap dnshes wh respe o he ase of separable uly. The opal oneary poly proble should be solved subje o he onsrans posed by he equaons of he odel developed n prevous subseons. Noe ha hese equaons do no nlude he neres rae rule beause he dea of hs seon s o derve he opal poly. Afer perforng a nueral proedure, I fnd he soluon o hs proble. Then, by usng 00 sulaons of 00 years perod lengh, I opue he opal volaly of he an eono varables under wo dfferen senaros ( and 0 ). Table 4 presens he sandard devaon of he eono varables. The followng resuls eerge. Frs, when uly s non-separable, he opal 3 The abbrevaon..p n he objeve funon sands for ers ndependen of poly. 27

28 volaly of oupu and real oney balanes s uh hgher. The nuon of hs resul s as follows. The nroduon of non-separably n he uly funon dereases he porane of oupu gap sablzaon n favor of nflaon and neres rae sablzaon. Ths s also ranslaed n hgher volaly of oupu. Moreover, sne oupu affes oney hrough he oney deand equaon, he volaly of real oney nreases as well. Seond, he opal volaly of neres rae and real wages s lower. Thrd, he exsene of real oney balane effes does no affe sgnfanly he opal volaly of nflaon. Fourh, noe ha n he ase of separable uly, he opal volaly of nflaon s no zero beause oney s n he uly funon. In hs ase, as enoned before, here exss a rade-off beween sablzng nflaon and he neres rae. Clearly, hs rade-off s solved n favor of nflaon sablzaon. INSERT TABLE The Dnshen n he Sze of Real Money Balane Effes, Greaer Maroeono Sably and Fnanal Innovaon Sne 984, he.s. eonoy and oher ndusralzed eonoes have experened a subsanal delne of aroeono volaly. Ths phenoenon s known n he leraure as he Grea Moderaon. There exs a lo of poenal explanaons for hs phenoenon. Gal and Gabe (2007) lassfy all of he n wo groups. The frs one suggess ha he greaer aroeono sably s due anly o saller shoks hng he eonoy (good luk hypohess). The seond group arbues he reduon n aroeono volaly o hanges n he sruure of he eonoy and/or n he way poly has been perfored. Three explanaons an be dsngushed n hs group: beer oneary poly (Clarda e al. (2000)), proved nvenory anageen (Khan e al. (2002)) and fnanal nnovaon (Dynan e al. (2006)). In hs subseon, I show ha he dnshen n he sze of real oney balane effes an explan a sgnfan fraon of he reduon n nflaon and oupu volaly. Moreover, I argue ha hs resul suppors fnanal nnovaon as soure of he Grea Moderaon. In order o llusrae he frs pon, I analyze he behavor of he odel desrbed n seon 4. bu assung wo dfferen sruures of he eonoy 28

29 ha only dffer n he values for and η. The frs one (whh I refer o Pre 984 albraon) assues ha and η 4. 2 ; whle he seond one (whh I refer o Pos 984 albraon) ses and η These wo dfferen sruures are hosen suh ha he reduon of real oney balane effes s presen n he odel. Noe ha he sub-saple sably analyss presened n seon 3 suggess ha he sze of real oney balane effes has dereased anly due o a reduon n he elasy of argnal uly of onsupon wh respe o real oney balanes. Ths s why he rsk averson s kep onsan a and he elasy of argnal uly of onsupon wh respe o oney s hanged aross he wo albraons (or perods). Moreover, n order o f he ross equaon resron posed by he MI odel (equaon 6), a hange n he elasy of argnal uly of onsupon wh respe o oney requres an adjusen of he neres rae seelasy, gven ha he res of paraeers rean onsan. Ths explans why η goes fro 4.2 o 8.8. Table 6 presens he sandard devaon of nflaon and oupu generaed by he odel, onsderng he wo dfferen sruures of he eonoy (one before 984 and he oher one afer 984). The Pre 984 volales are noralzed o n order o falae oparson. I an be seen ha he reduon n he sze of real oney balane effes an aoun for 88 peren of he delne n oupu volaly and 5 peren of he delne n nflaon volaly. Ths resul suggess ha he dnshen of real oney balane effes an explan que well he reduon n oupu volaly bu oher explanaons, lke beer oneary poly, are neessary o fully explan he reduon of nflaon volaly. INSERT TABLE 6 Fro prevous analyss, and by a dre nerpreaon of he MI odel, ould see ha he derease n he elasy of argnal uly of onsupon wh respe o oney s an alernave soure of he Grea Moderaon. I la ha hs s no he os approprae way o undersand he resuls drven by he prevous sulaon. As Walsh (2003) pons ou, he MI approah has o be hough of as a shoru for a fully spefed odel of he ransaons ehnology faed by households ha gve rses o a posve deand for oney. Insead, he dnshen n he sze of real oney balane 29

30 effes should be nerpreed as resul of he fnanal nnovaon ha ook plae n.s. n he early 980 s. In order o suppor he laer arguen, I use he funonal equvalene beween he ransaon os odel developed by Sh-Grohé and rbe (2004) and he MI odel. By usng hs equvalene, an be expressed as: v(2s'( v) + vs''( v)) + s( v) + vs'( v) where s(v) represens a ransaon os ha s proporonal o onsupon purhases, s' ( v) denoes he frs dervave of he ransaon os funon wh respe o oney veloy and s' '( v) represens he seond dervave of he sae funon. Gven he prevous expresson, a plausble sory ha an explan he derease n s a fnanal nnovaon ha affes he ransaon os funon suh ha a reduon n hs paraeer akes plae. Therefore, hs analyss provdes foral suppor o he one developed by Dynan e al (2006), where hey onlude ha fnanal nnovaon s an poran soure of he greaer sably n he eonoy. 5. Conludng Rearks GMM jon esaon of he Euler equaon and oney deand, derved fro a sall sruural MI odel, suggess ha real oney balane effes, arsng fro nonseparable uly n onsupon and real oney, are sll quanavely poran. Ths fndng s onssen wh prevous redued for evdene provded by Melzer (200), Nelson (2002) and Hafer e al (2007). However, onrass onsderably wh he resuls found n prevous sudes by Woodford (2003) and Ireland (2004). Two poran dfferenes wh respe o Woodford s approah explan he dsrepany n resuls: he defnon of oney used (oney base versus M2) and he esaon proedure (albraon versus GMM). Wh respe o Ireland s approah, here are also wo poran aspes of he proedures ha drve he dfferen resuls: he sruure of he odel (7 equaons versus a subse ha nlude only hree of hose equaons) and he esaon proedure (ML versus GMM). 30

31 A sub-saple sably analyss suggess ha he sze of real oney balane effes s sll sgnfan bu lower han used o be before he begnnng of he 980 s. The an deernan of hs reduon sees o be he dnshen of he elasy of argnal uly of onsupon wh respe o oney. By usng a funonal equvalene beween he MI odel and he ransaon os odel developed by Sh-Grohé and rbe (2004), has been shown ha he derease n he elasy of argnal uly of onsupon wh respe o oney an be nerpreed as a hange n he ransaon os ehnology ha dnshes he porane of real oney balanes n he deernaon of onsupon or aggregae deand. There are four poran plaons of he epral evdene presened n he paper. Frs, oney s no redundan n order o deerne nflaon and oupu. Seond, he exsene of quanavely poran real oney balane effes n a odel wh sky pres and flexble wages an explan wo sylzed fas: he odesly proylal real wage response o a oneary poly shok and he supply sde effes of oneary poly. Thrd, he opal oneary poly hanges when here exs real oney balane effes of he agnude esaed n hs paper. In parular, uh hgher volaly of oupu and uh lower volaly of neres rae should be aaned. Fourh, he reduon n he sze of real oney balane effes an aoun for a sgnfan reduon n he volaly of nflaon and oupu. Ths suggess ha fnanal nnovaon, hrough a ehnologal progress n he ransaon ehnology, an be a soure of he Grea Moderaon. Fnally, hs paper uses he MI approah n he esaon proess for he followng reason. Gven ha he onluson ha real oney balane effes play a nal role n he oneary busness yle was derved by usng hs odel and wo dfferen sruural esaon ehnques, he use of he sae odel allows a lear and dre oparson of y analyss wh hose of prevous sudes. Noneheless, he MI odel has o be hough of as shoru of a fully spefed odel of ransaon ehnology. In hs sense, he evdene provded n hs paper suppors ha would be worh explorng he developen of odels ha provde plausble and lear sores ha generae he MI odel wh non-separable uly n onsupon and real oney balanes. So far, here exs rofounded odels ha provde a fraework o show ha he evoluon of he sze of real oney balane effes, arsng fro non-separable uly, s relaed wh 3