Moneary Poliy and Durable Goods Rober B. Barsky ederal Reserve Bank of Chiago Chrisopher L. House Universiy of Mihigan and NBER Chrisoph E. Boehm Universiy of Mihigan Miles S. Kimball Universiy of Mihigan and NBER Marh 26, 2015 Absra We analyze moneary poliy in a New Keynesian model wih durable and non-durable goods, eah wih a separae degree of prie rigidiy. Durabiliy has profound impliaions for he business yle properies of he model and is response o ineres rae inervenions. Sine uiliy depends on he servie flow from he sok of durables, he flow demand for new durables is inherenly sensiive o emporary hanges in he relevan real ineres rae. or a suffiienly long-lived ideal durable, we obain an inriguing varian of he well-known divine oinidene in his ase, he oupu gap depends only on inflaion in he durable goods seor. We use numerial mehods o verify he robusness of his analyial resul for a broader lass of model parameerizaions. We hen analyze he opimal Taylor rule for his eonomy. If he moneary auhoriy plaes a high weigh on sabilizing aggregae inflaion hen i is opimal o respond o seoral inflaion in dire proporion o he seoral shares of eonomi aiviy. However, if he moneary auhoriy wans o sabilize he aggregae oupu gap, i pus disproporianae weigh on inflaion in durable goods pries. JEL Codes: E31, E32, E52 Keywords: Taylor rule, inflaion argeing, eonomi sabilizaion. Barsky: barsky@frbhi.org; Boehm: hrisboe@umih.edu; House: house@umih.edu; Kimball: mkimball@umih.edu. 1
1 Inroduion Moneary poliy is ofen as in erms of oupu and inflaion argeing. If he ederal Reserve arges headline inflaionheniimpliilyweighsdifferen seoral (or regional) inflaion measures aording o heir overall share of Gross Domesi Produ. While weighs proporional o seor size appear naural, i is no lear ha he enral bank should rea inflaion in differen seors symmerially. We argue in his paper ha opimal moneary poliies should ofen plae greaer weigh on inflaion in durable goods seors. In earlier work (Barsky, House and Kimball 2007, hereafer BHK), hree of us demonsraed ha he reaion of New Keynesian models wih durable and non-durable goods depended imporanly on wheher durable goods had fleible pries or siky pries. In he speial ase in whih durable goods pries were fully fleible, aggregae employmen and oupu would no rea o hanges in he money supply. Pu differenly, money was neural wih respe o aggregae oupu. In he presen paper, we eend he earlier analysis in wo imporan dimensions. irs, we fous on he model in whih boh durables and non-durable goods have siky pries whereas heearlierpaperfousedprimarilyonhe aseinwhihdurablegoodshavefleible pries. Seond, as in Carlsrom and uers [2006] and Monaelli [2009], we onsider ineres rae rules raher han money supply rules. These eensions lead o several key resuls. irs, we obain wo Phillips Curves one for he durable goods seor and one for he non-durable goods seor. Using an approimaion ehnique, we hen show ha he oupu gap (i.e., GDP gap) depends only on inflaion in he durables seor. Hene, he enral bank an ensure ha aual oupu equals poenial oupu by sabilizing durable goods pries. Seond, epeed inflaion in he durable goods seor losely raks he nominal ineres rae. As a resul, seing he nominal ineres rae is essenially equivalen o seing inflaion epeaions for he durable goods seor. Third, we derive a uiliy-based seond-order approimae welfare funion for he model. The objeive inludes he oupu gaps and inflaion measures of boh seors separaely. We hen onsider opimal moneary poliy in he model wih durable and non-durable goods. We onsider boh ad ho objeives as well as he uiliy-based rierion. or eah rierion, we analyze he opimal Taylor rule as in Boehm and House [2014] (he opimal Taylor rule is haraerized by he oeffiiens ha maimize he objeive funion subje o he onsrain ha he moneary auhoriy follows an ineres rae rule of he Taylor form). or he ad ho objeives, he moneary auhoriy minimizes a weighed sum of he oupu gap 2
and oal inflaion. The more he moneary auhoriy ares abou oupu sabilizaion, he more emphasis he bank will plae on durable goods inflaion. In onras, if he moneary auhoriy ares primarily abou sabilizing aggregae inflaion hen i is opimal o weigh seoral inflaion in proporion o eah seor s share in GDP. The remainder of he paper is se ou as follows. Seion 2 reviews he lieraure. Seion 3 presens he basi model and performs several numerial illusraions of he basi mehanisms a work. Seion 4 presens he welfare objeives and analyzes he opimal Taylor rule. Seion 5 onludes. 2 Relaed Lieraure Our paper relaes o wo bodies of work. The firs is a growing lieraure on muliseoral New Keynesian models. The seond is he lieraure on inflaion argeing and opimal poliy. The anonial New Keynesian model inludes only a single nondurables seor and absras from differenes in prie rigidiy aross goods. 1 Reenly, many researhers have urned heir aenion o sudying muli-seor New Keynesian models. Early onribuions o his lieraure inlude Ohanian and Sokman [1994], Ohanian e al. (1995), Aoki [2001] and Barsky e al. [2003]. Aoki [2001] onsiders a wo seor model in whih one seor has siky pries while he oher has fleible pries. Aoki s analysis shows ha moneary poliy should arge inflaion in he seor wih siky pries. Aoki s resul is quie naural and aniipaes he analysis in Carvalho [2006] who shows ha in models wih many differen degrees of prie rigidiy, he seors wih he greaes prie rigidiy end o have a muh larger influene on he equilibrium behavior han he seors wih more fleible pries. This effe is pariularly pronouned if here are srong sraegi omplemenariies aross firms. Barsky e al. [2007] (BHK) show ha fleibly pried durable goods have a srong endeny o generae negaive omovemen in response o moneary poliy shoks. Carlsrom and uers [2006] demonsrae ha seoral omovemen in New Keynesian models an be subsanially srenghened by inluding wage rigidiies, redi onsrains and invesmen adjusmen oss. Carlsrom e al. [2006] analyze a wo-seor New Keynesian model o see wheher equilibrium deerminay depends on he inflaion rae he moneary auhoriy arges. As we do in our 1 See Woodford [2003] and Gali [2008] for omprehensive presenaions of he sandard New Keynesian model. 3
model, hey allow for he possibiliy ha prie rigidiy an differ aross he seors. They show ha he well-known Taylor priniple, whih requires ha he enral bank reas more han one-for-one o aggregae inflaion, an be weakened in a muli-seor model. Speifially, if he enral bank reas more ha one-for-one o any individual seoral inflaion rae hen he equilibrium will be deerminae. Bils, Klenow and Malin [2012] analyze a muli-seor DSGE model ha shares many feaures of our model and use i as a basis for esing wha hey refer o as Keynesian Labor Demand. Unlike our framework, hey limi he degree o whih faors an move beween seors. This implies ha marginal oss will differ by seor. As in our model, seors wih greaer durabiliy are muh more sensiive o relaive prie shoks in heir seing. The auhors show ha markups in durables seors appear subsanially more ylial han markups in non-durable seors. Muh of he lieraure on inflaion argeing fouses on he differene beween headline inflaion and ore inflaion. Beause headline inflaion inludes energy pries while ore inflaion does no, energy prie shoks will ause he wo series o differ. 2 Bodensein e al. [2008] use a New Keynesian DSGE model o show ha poliy rules ha respond o headline inflaion are assoiaed wih signifianly differen ouomes han poliies ha respond o ore inflaion. In a relaed sudy, Huang and Liu [2005] use a DSGE model o analyze wheher he enral bank should arge he Consumer Prie Inde or he Produer Prie Inde. Their analysis suggess ha he enral bank should inlude boh measures o maimize welfare. Using a faor-augmened veor auoregression (AVAR), Boivin e al. [2009] find ha seoral pries are siky wih respe o aggregae shoks even hough hey are quie responsive o seor-speifi shoks. Theywrie ()hepiurehaemerges ishusoneinwhih many pries fluuae onsiderably in response o seor-speifi shoks, bu hey respond only sluggishly o aggregae maroeonomi shoks [...] (A) he disaggregaed level, individual pries are found o adjus relaively frequenly, while esimaes of he degree of prie rigidiy are muh higher when based on aggregae daa (See Boivin e al. 2009, p. 352). Balke and Wynne [2007] sudy he reaion of relaive pries underlying he Produer Prie Inde in response o a variey of measures of hanges in moneary poliy. They argue ha, empirially, moneary poliy sysemaially alers real relaive pries suggesing ha differenial prie rigidiy is an imporan feaure of he eonomies reaion o moneary poliy. Leih 2 Bodensein e al. [2008] noe ha many enral banks differ as o whih inflaion rae hey use for heir inflaion arge. 4
and Malley [2007] esimae New Keynesian Phillips urves for differen indusries wihin U.S. manufauring. They find evidene of subsanial variaion aross indusries in prie rigidiy. Some produers rese pries one every 8 monhs. A he oher end of he sperum, some produers rese pries one every 24 monhs. Similarly, Imbs e al. [2011] use seoral daa on produion and pries in rane o esimae sruural parameers of New Keynesian Phillips Curves. Like he Leih and Malley sudy, Imbs e al. find subsanial variaion in prie rigidiy aross seors. While here is work doumening differenes in prie adjusmen aross produs, here has been less work fousing on prie rigidiy for durable goods. Some prominen sudies have daa ha indiaes ha pries are fairly rigid for boh durable and non-durable goods. In he Bils and Klenow [2004] sudy, he auhors repored ha durables and non-durables have omparable frequenies of prie adjusmen (he monhly frequeny is roughly 30 peren per monh for boh durable and non-durable goods; quoed pries for servies hange less frequenly). In a follow-up sudy o he Bils and Klenow, Nakamura and Seinsson [2008] repor evidene for a limied number of durable goods suggesing ha durable good pries adjus relaively infrequenly and when hey do adjus, he prie hanges are ofen moivaed by sales evens or oiniding wih produ subsiuions. 3 Model The model eends he wo-seor environmen in BHK o inlude several imporan feaures. irs, unlike he model in BHK, moneary poliy is as in erms of a Taylor rule. The Taylor rule we onsider sipulaes a nominal ineres rae as a funion of oupu gaps (he differene beween aual oupu and he level of oupu ha would prevail if all pries were fleible) and inflaion. Beause he model has wo seors, our Taylor rule an respond differenially o inflaion raes in he durable and non-durable seors. Seond, in keeping wih he esablished New Keynesian lieraure, we inlude boh shoks o he naural level of oupu (modelled as shoks o seoral produiviy) and os-push shoks shoks o seoral Phillips Curves. inally, as in Boehm and House [2014] we assume ha he oupu gap is measured wih error. Measuremen error shoks are no only realisi (see e.g., he referenes in Boehm and House [2014]) bu hey also serve o naurally emper he reaion of he moneary auhoriy o fluuaions in eonomi aiviy. If he enral bank does no ompleely rus is urren measures of eonomi performane hen i will be opimal o under-rea o measured hanges 5
in inflaion and oupu. Below we presen he key sruural equaions governing he model. Addiional model deailsaswellasompuerfiles are available from he auhors by reques. 3.1 Households The represenaive household reeives flow uiliy from onsumpion of a non-durable good C, a sok of durable goods D and real money balanes M /P. The household reeives disuiliy from labor N. Households disoun fuure uiliy flows a he subjeive ime disoun faor β. We assume ha he uiliy funion akes he following semi-parameri form E X j=0 ½ β η+1 η U (C +j,d +j ) ψ n η +1 N η +j + Λ µ M+j P +j As in BHK, we will ake he flow uiliy funion U ( ) o be given by ¾. (1) U (C +j,d +j )= " µ σ ψ σ 1 C ρ 1 ρ +j +(1 ψ ) D ρ 1 ρ +j ρ # σ 1 σ ρ 1. Here σ is he ineremporal elasiiy of subsiuion, ρ is he elasiiy of subsuiion beween durable and non-durable onsumpion. The parameer η represens he rish labor supply elasiiy and he funion Λ ( ) desribes he uiliy benefi of real money holdings. We assume ha Λ 0 > 0 and Λ 00 < 0. Sine we fous on ineres rae rules in our analysis, he preise naure of he funion Λ ( ) is irrelevan. The household seeks o maimize (1) subje o he nominal budge onsrain P C + P X + S + M = W N + R K + S 1 (1 + i 1 )+M 1 + Π (2) and he law of moion for durable goods D = D 1 (1 δ)+x. (3) Eah period, he household earns labor inome W N and apial inome R K. As in Barsky e al. [2007] we assume ha he he sok of produive apial K is eogenously fied. 3 Here, X denoes dae purhases of new durables and δ denoes he depreiaion rae of he durable. 3 This assumpion is innouous. See Barsky e al. [2007] for furher disussion of his poin. 6
Noe ha durables and non-durables have differen nominal pries P and P.inally,S is nominal saving (whih will be zero in equilibrium) and Π denoes nominal profis and oher lump-sum ransfers reurned o he household. i is he nominal ineres rae. or simpliiy we le U C, and U D, denoe he flow marginal uiliy of non-durable onsumpion and he flow marginal uiliy assoiaed wih a given durable sok. Le q be he shadow value (in uiliy unis) of an addiional uni of he durable i.e., he Lagrange muliplier assoiaed wih he onsrain (3). The firs order ondiions for N, C, X and S require he following opimaliy ondiions, U C, q = P P, (4) and U C, 1 P ψ n N 1 η = W U C, = W q, (5) P P q = U D, + β (1 δ) E [q +1 ] (6) 1 = β (1 + i ) E U C,+1. (7) P+1 Condiion (4) is he inraemporal opimaliy ondiion haraerizing he opimal mi of durable and non-durable goods onsumpion by he household. The household s opimal labor supply is haraerized by ondiions (5). Equaion (6) relaes he shadow value of addiional durables o he disouned flow uiliy of he durable U D,. inally, (7) is a sandard Euler equaion for non-durable onsumpion goods. Noe ha, by ombining (7) wih (4), we have an Euler equaion for durable goods purhases, P q =(1+i ) βe q +1. (8) P+1 The isher equaions for he durable and non-durable goods give he e pos real rae of reurn for good j = C, X as 1+r j +1 =(1+i ) P j P j (9) +1 3.2 irms and Priing We model prie rigidiy using a sandard Calvo mehanism for wo seors. inal goods in boh he durable and non-durable seors are produed from inermediae goods aording o 7
he CES produion funions Z 1 X = 0 (s) ε ε 1 ε ε ds 1 (10) and Z 1 C = 0 ε ε 1 ε (s) ε ds 1 (11) where ε j > 1 for j = C, X. The elasiiy parameers ε j are ime-varying omponens of he model. Below we epliily onsider eogenous shoks o hese parameers as a way of generaing eogenous fluuaions in desired markups and hus inroduing os-push shoks o inflaion. inal goods produers are perfely ompeiive and ake he final goods pries P j and inermediae goods pries p j (s) as given. I is sraighforward o show ha demand for eah inermediae good has an isoelasi form µ p ε (s) =X (s) (12) P and µ p ε (s) =C (s). (13) P Compeiion among final goods produers ensures ha he final goods nominal pries are ombinaions of he nominal pries of he inermediae goods used in produion, P = Z 1 0 1 p 1 ε (s) 1 ε ds (14) P = Z 1 0 1 p 1 ε (s) 1 ε ds. (15) Inermediae goods are produed by monopolisially ompeiive firmswhoakehede- mand urves (12) and (13) as given when hey se heir pries. Eah inermediae goods firm in eah seor has a Cobb-Douglas produion funion (s) =Z [k (s)] α [n (s)] 1 α (16) (s) =Z [k (s)] α [n (s)] 1 α (17) 8
Here Z and Z are seor-speifi produiviy shoks. The inermediae goods firms ake he nominal inpu pries W and R as given. Cos minimizaion implies ha wihin eiher seor firms hoose he same apial-o-labor raio, k j (s) n j (s) = Kj N j = K = α W N 1 α R where K j = R k j (s) ds and N j = R n j (s) ds are apial and labor used in seor j = C, X. Beause he produion funions ehibi onsan reurns o sale, and beause faors an freely move from one seor o anoher, he relaive marginal oss of produion are given simply by he raio of he produiviy erms. Speifially, he nominal dae marginal os in seor j is MC j = W µ α 1 K Z j = W 1 α N Z j f (N ) (18) where f (N) = 1 (N 1 α /K) α (keep in mind our assumpion ha he sok of produive apial is eogenously fied). As a resul, he relaive marginal os of produion is MC /M C = Z /Z. Noie ha in equilibrium, he nominal marginal oss are funions of aggregae employmen N raher han seoral employmen N and N. Nominal marginal oss an alernaively be epressed in erms of he underlying nominal inpu pries W and R as MC j = W 1 α R α Z j µ 1 α µ α 1 1 for j = X, C. 1 α α As in he sandard New Keynesian model, pries for eah inermediae good produer are governed by a Calvo mehanism. Imporanly we allow for differen degrees of prie rigidiy in eah seor. Le θ j be he probabiliy a prie is suk for firms in seor j. Thus, eah period in seor j, hefraion1 θ j of firms rese heir pries. Le p j, denoe he opimal rese prie for an inermediae goods firm ha reeives he Calvo draw in period. The opimal rese pries in eah seor are P h p j=0 (θ β) j i E U C,+j P ε 1 +j MC +j C +j, = μ, P h j=0 (θ β) j i E U C,+j P ε (19) 1 +j C +j P h p j=0 (θ β) j i E q +j P ε 1 +j MC +j X +j, = μ, P h j=0 (θ β) j i E q +j P ε (20) 1 +j X +j 9
where μ j, ε j εj 1 is he dae desiredmarkup.inalgoodspriesevolveaordingo h P = θ P 1 1 ε +(1 θ ) i 1 p 1 ε 1 ε, (21) h P = θ P 1 1 ε +(1 θ ) i 1 p 1 ε 1 ε, (22) 3.3 GDP, Marke Clearing and Moneary Poliy Nominal GDP for his model is naurally he oal dollar value of all final goods and servies produed in a given period, P Y Y = P X + P C. Real GDP is ompued as he Bureau of Eonomi Analysis does for he aual daa namely by fiing a se of onsan base-year pries P and P. Weakehebaseyearpriesobe1 so ha real GDP is simply Y = P X + P C = X + C. inally, he implii aggregae prie deflaor is ompued as he raio of nominal GDP o real GDP, P Y = P X + P C. X + C The aggregae rae of inflaion is simply he peren hange in he GDP deflaor, 1+π = P Y. P 1 Y The labor marke and he marke for produive apial mus be in equilibrium in eah period. This requires K = K + K and N = N + N. To lose he model, we assume ha he moneary auhoriy ses he nominal ineres rae aording o a generalized Taylor rule. In pariular, we onsider Taylor rules in he family i =ī + φ Y Y m + φ π, π + φ π, π (23) Here he noaion Y m indiaes ha he enral bank is reaing o he measured oupu gap. We assume ha he measured oupu gap is equal o he aual oupu gap plus a mean zero 10
i.i.d. measuremen error m Y,hais, Y m = Y + m Y. Thereaderwillnoiehahisspeifiaion ness he sandard Taylor rule for appropriae hoies of he reaion parameers φ. I is well known ha ineres rae rules of he form (23) may imply indeerminae equilibria for erain parameer values. We do no disuss he issue of indeerminay in his paper. Insead we appeal o he analysis in Carlsrom e al. [2006] who show ha equilibria in muliseoral models is deerminae provided ha he enral bank reas suffiienly srongly o any one omponen of inflaion. Thus, in wha follows, we assume ha φ π, 0, φ π, 0 and φ π, + φ π, > 1. 3.4 oring Variables There are several eogenous foring variables in he model. We allow for separae produiviy shoks o boh he durable and non-durable seors. These shoks move he fle-prie equilibrium or he naural level of oupu however hey do no shif he Phillips Curves separaely from heir influene on he marginal os. We also onsider shoks o he desired markups μ, and μ, in eah seor (hese shoks arise from shoks o he elasiiy parameers ε j ). Beause hese shoks affe he desired markups for he prie seers bu no he naural level of oupu, hey are onvenionally referred o as os-push shoks. We denoe he os-push shoks in eah seor as u j. The seoral produiviy shoks and os push shoks follow simple auoregressive proesses Z j = 1 ρ z,j + ρz,j Z j 1 + e z,j, and u j = 1 ρ u,j + ρu,j u j + e u,j for j = X, C. 4 In addiion, he model also inludes he measuremen error shok m Y. This shoks indues movemens in he real variables by promping undesirable hanges in moneary poliy. m Y is assumed o be serially unorrelaed and mean zero. 4 The os-push shoks u are slighly differen from he desired markups hemselves. In pariular one an show ha u j = μ j, 1 θ j 1 ρ u,j βθ j θ j 1 11
4 Analysis In his seion we analyze he model s equilibrium and sudy he properies of opimal Taylor rules. We begin by drawing ou several key properies of he model ha hold for low depreiaion raes. We hen urn our aenion o a speial ase of he model in whih he equilibrium and he assoiaed opimal Taylor Rule an be solved analyially. This limiing ase reveals several properies of opimal moneary poliy whih arry over o more general versions of he model. inally, we use numerial mehods o analyze more realisi versions of he model. 4.1 Key Properies of he Model Here we poin ou several imporan properies of he model equilibrium behavior. We derive wo New Keynesian Phillips Curves one for eah seor. We hen find epressions for he real GDP gap and he real employmen gap. inally, we solve for a seond-order aurae approimaion o he uiliy of he household whih an be epressed in erms of seoral inflaion and he seoral oupu gaps. Seoral Phillips Curves. ollowing he onvenion in he New Keynesian lieraure, we define real marginal os in eah seor as he raio of nominal marginal os o he seoral final prie. Tha is, m = MC, and m P = MC. Using he definiions of real marginal os P ogeher wih he log-linear versions of (19), (20), (21) and (22) sraighforward algebra shows ha he model implies wo (seoral) New Keynesian Phillips urves, π = λ fm + βe π +1 + u (24) where π = λ fm + βe π +1 + u (25) λ = (1 θ )(1 θ β) θ, and λ = (1 θ )(1 θ β) θ are parameers desribing he frequeny of prie adjusmen in eah seor. These oeffiiens 5 are someimes referred o as he miroeonomi raes of prie adjusmen. We use he sandard noaion of ṽ o denoe he peren hange in he variable v, haisṽ = dv/ v where dv = v v and v is he non-sohasi seady sae value of v. 6 5 See Leih and Malley [2007] for a deailed empirial analysis of seoral Phillips Curves aross U.S. manufauring. 6 Wih some abuse of noaion we also wrie π π π and ĩ i ī. 12
Real GDP Gap and he Aggregae Employmen Gap. or any variable v we define he gap as he log differene beween he equilibrium value of he variable and he value ha would be obained if pries were perfely fleible. We denoe he gap by ˆv =ṽ ṽ le where v le is he fle-prie value of he variable. We show ne ha he real GDP gap is approimaely onlyafunionofhegapinaggregaeemploymen. Reall ha eah inermediae goods firm hooses he same apial o labor raio, k = K n N. Then aording o (12) and (16), oupu for any single inermediae produer of new durables is (he alulaions for he non-durables are he same), (s) =X µ p (s) P ε µ α K = Z n (s) N Inegraing over durable goods inermediae firms and using N = R 1 0 n (s) ds gives X ξ = Z µ K N α N p (s) where ξ R ε 1 0 P ds is a measure of (ineffiien) prie and oupu variaion aross firms in he durable goods seor. (Similarly, for he non-durable goods seor we have prie variaion given by a erm ξ.) As shown in Gali [2008], in a neighborhood of he zero inflaion seady sae, ξ is 1 o a firs-order approimaion (see e.g., Gali 2008, p. 62). This implies ha real GDP is approimaely or in log deviaions, µ K Y N α [Z N + Z N ]. Ỹ Z +(1 α) Ñ where he aggregae produiviy erm is a weighed average of seoral produiviy Z = Z N N + Z N.TheGDPgap Ŷ N = Ỹ Ỹ le is hen Ŷ (1 α) ˆN. (26) Approimae Welfare Objeive. or he welfare analysis of his paper we onsider wo alernaive approahes. In line wih he New Keynesian lieraure, we firs derive a seond order 13
approimaion of he represenaive onsumer s uiliy funion. Among ohers, Roemberg and Woodford [1999], Woodford [2003], and Coibion, Gorodnihenko, and Wieland [2012] have used his approah o sudy opimal poliy. Seond, we use an ad ho welfare rierion whih plaes greaer imporane on sabilizing oupu han uiliy-based rieria sugges. The following proposiion gives he approimae welfare objeive for a soial planner who ries o maimize he uiliy of he represenaive household. All proofs are in he appendi. Proposiion 1. The unondiional epeaion of he household s (saled) per period uiliy funion is E 2 U (C,D ) ψ n U C C where η+1 η N η η+1 = i σ 1 C hĉ V σ 1 U D D h i D U C C V ˆD +2 U DCD Ĉ Cov ˆD, U C N N C α + η 1 1 α V hŷ i ελ V [ π C, ] N X N C ελ V [ π X, ]+.i.p. + h.o.. U C σ C = and σ D = U D C U CC D U DD and.i.p. sands for erms independen of poliy and h.o.. for higher order erms. Sine onsumers are risk averse, greaer varianes of nondurable and durable onsumpion derease welfare. Consisen wih inuiion, he ovariane beween durables and nondurables onsumpion impas welfare wih a oeffiien ha rises in he degree of omplemenariy beween he wo. Ne, welfare dereases in oupu volailiy and his disuiliy from oupu volailiy falls wih he labor supply elasiiy η. inally, inflaion volailiy in boh seors redues welfare. This loss depends on he relaive seor size, he elasiiy of subsiuion ε and he miroeonomi raes of prie adjusmens λ and λ. 4.2 Ideal Durables We ne urn o a limiing ase of ideal durable goods in whih disoun raes and depreiaion raes are near zero. In his low-depreiaion limi, he durable good survives for an arbirarily long ime period and he household does no disoun he fuure relaive o he presen. ollowing BHK, we argue ha he shadow value q for suh long-lived durable goods is essenially onsan. This near onsany of q is equivalen o saying ha he ineremporal elasiiy of subsiuion for purhases of durables is eremely high. In his ase, he oupu 14
of he durable goods seor responds sharply o hanges in ineremporal relaive pries. Our limiing approimaion implies ha, for suffiienly low depreiaion and disoun raes, he ineremporal elasiiy of subsiuion for purhases of durable goods is infinie. or goods wih realisi depreiaion raes, he approimaion will be somewha less aurae. We hek his auray numerially and repor he resuls below. The shadow value of he durable good is he presen value of marginal uiliies of he servie flow of he durable, disouned a he subjeive rae of ime preferene and he rae of eonomi depreiaion. Tha is, " # X q = E [β (1 δ)] j U D,+j. (27) j=0 Two feaures guaranee ha, for long-lived durables, q will be approimaely invarian o ransiory shoks. irs, durables wih low depreiaion raes have high sok-flow raios. In our model, he seady sae sok-flow raio is 1/δ. A high sok-flow raio implies ha even relaively large hanges in durable goods produion have only small effes on he oal sok in he shor run. Tha is, for ransiory shoks, we an appeal o he approimaion D D. Beause he sok hanges only slighly, equilibrium hanges in he produion of durable goods enail only minor hanges in marginal servie flows U D,+j. Seond, if δ is suffiienly low, epression (27) is dominaed by he marginal servie flows in he disan fuure. Beause he effes of he shok are emporary, and beause D D, he fuure erms in (27) remain lose o heir seady sae values. Thus, even if here were signifian hanges in he firs few erms of he epansion, hese effes would have a small perenage effe on he presen value as a whole. This implies ha he model an feaure servie flows ha hange subsanially over ime due o omplemenariies wih oher variables ha fluuae in he shor run and sill imply a nearly invarian shadow value. Togeher, hese wo observaions sugges ha i is reasonable o rea he shadow value of suffiienly long-lived durables as roughly onsan in he fae of a moneary disurbane (or indeed any shor-lived shok). Thus, for a long-lived durable, and for plausible half-lives of prie rigidiy we an ake D D and q q. 7 7 The idealized durable goods seing also allows us o simplify he uiliy sruure. In he households objeive funion, he marginal uiliy of onsumpion U C,+j is in priniple a funion of boh non-durables C and durables D. However, sine he peren hanges in D are negligible, we an wrie U C,+j = u(c,d ) u(c, D) C so he marginal uiliy of non-durable onsumpion is approimaely a funion of C alone. C 15
Impliaions. There are several imporan onsequenes for he equilibrium in he low-depreiaion limi. irs, regardless of prie rigidiy in he durable and/or non-durable seor, he labor supply urve (5) implies ha, for suffiienly ransiory shoks, equilibrium employmen is governed only by hanges in he real produ wage in he durable goods seor. Using (5) and q q we have ψ n N 1 η W q. P Sine q is approimaely, onsan, movemens in N are deermined solely by hanges in he real produ wage W /P. Considerhefle-prie equilibrium. In his ase, he nominal prie of new durable goods will simply be he desired markup μ over he nominal marginal os. Tha is, P = μ MC so ha m =(μ ) 1. We an hen use he approimae relaionship above ogeher wih he nominal marginal os of durables (18) o ge an epression for he fleible prie employmen level. We hen have (μ ) 1 = MC,le P,le ψ n 1 N le η q f N le. Z or, using he form of f ( ), in log deviaions near he zero inflaion seady sae, Ñ le 1 1 η + α Z (28) This is a single equaion in he variables N le and Z. Thus, he effiien aggregae employmen level is governed solely by he produiviy disurbane in he durable goods seor. (This resul is reminisen of a similar resul in Kimball [1994].) Seond, nondurable onsumpion (and produion) moves one-for-one wih hanges in he real relaive prie of nondurables / durables. Using ondiion (4) and q q we have U C, P q. P Third, he equilibrium nominal ineres rae is a dire refleion of epeed inflaion in he durable goods seor. Tha is, for durable goods pries, here is a pure isher effe. To see his, noe ha he Euler equaion for he durable good requires P q =(1+i ) βe q +1. P+1 16
Again, beause he shoks are assumed o be shor-lived, we an use q q +1 q o immediaely ge 1 1 βe 1+i 1+π +1 So, o a firs order approimaion E π +1 βĩ. This relaionship shows ha a moneary poliy rule for seing he nominal ineres rae i is anamoun o a rule ha speifies a arge for durable goods inflaion. Using he epression for he nominal marginal os of durables (18) ogeher wih he labor supply ondiion (5) we an wrie he real marginal os for he durable good m as m ψ nn 1 η q f (N ). Z Again, using he form for f ( ) ogeher wih (26) and (28) we an epress he real marginal os in he durable goods seor as a funion of he oupu gap Ŷ, fm ζŷ, α 1 where ζ = + 1 η 1 α (he real rigidiy derivaive emphasized by Ball and Romer 1990). Subsiuing his epression ino he Phillips urve for he durable goods seor (24) we have π λ ζŷ + βe π +1 + u. (29) Noie ha only he prie rigidiy of he durable good maers for influening he oupu gap. 8 In he absene of a os-push shok in he durables seor (u =0), his version of he Phillips urve implies ha o sabilize he oupu gap (or equivalenly o sabilize employmen), i is neessary and suffiien o sabilize inflaion in he durable goods seor π.this is a speial insane of a divine oinidene for durable goods (see Blanhard and Galí, 2007). 8 BHK (2008) analyzed a speial ase in whih pries for long-lived durable goods were perfely fleible. They showed ha in ha ase, moneary poliy was approimaely neural. The model here eends his resul and shows ha if durable goods have siky pries, hen i is only he prie rigidiy for he durable goods ha maers for he dynamis of aggregae oupu and employmen. 17
4.3 A Useful Speial Case To gain insigh ino he behavior of he model, we ne onsider an insane of he model ha permis an approimae analyial soluion. The speial ase requires boh δ and r near 0 as well as large prie rigidiy. We assume ha he sruural shoks are shor-lived and so presen only ransiory hanges o he equilibrium. These assumpions imply ha we are onsidering a ase of an ideal durable as disussed above and ensure ha we an use he approimaions q q and D D in onsruing he equilibrium. To furher simplify he analysis, we impose he addiional assumpion ha ρ = σ whih implies ha he marginal uiliy of non-durable onsumpion is simply U C, = C 1 σ. TheTaylorruleweonsiderlimisaenionoinflaion raes in he wo seors. Tha is, we resri moneary poliy o reaion funions of he form i =ī + φ π, π + φ π,π (30) where φ π, and φ π, are he moneary auhoriies reaions o hanges in inflaion in he wo seors separaely. 4.3.1 Equilibrium The New Keynesian Phillips Curve for he durable seor is given by equaion (29). To find he approimae Phillips Curve for he non-durable goods seor we use (18) o wrie he real marginal os of non-durables as m = m Z Z P P m Z qc 1 σ Z where he approimaion uses he inraemporal effiieny ondiion (4) ogeher wih q q. We an now wrie he New Keynesian Phillips Curve for he durable seor as 9 1 π = λ σ C + Z Z + 1 µ 1 1 α η + α Ŷ + βe π +1 + u (31) 9 In he le-prie equilibrium m = m =1so C le 1 σ q Z Z he non-durables Phillips Curves in erms of only he gaps Ĉ and Ŷ π = λ 1 σ Ĉ + 1 1 α µ 1 η + α Ŷ + βe π +1 + u andhus,weanequivalenlyepress 18
The sysem is now redued o he wo approimae Phillips Curves (29) and (31), he wo Euler equaions (7) and (8), and he Taylor rule (30). The log-linear versions of hese las ondiions are ĩ = φ π, π + φ π, π 1 σ C = βĩ 1 h i σ E C +1 E π +1 and, again using he approimaion q q 0=βĩ E π +1. This sysem of five equaions is sill ompliaed by he presene of he epeaion erms above. To suppress his ompleiy we assume ha he shoks are suffiienly ransiory so ha we an rea E π +1 = E π +1 =0. 10 Using he las wo ondiions, we immediaely have C ĩ 0 in equilibrium. This onlusion may seem unusual bu i aually has a fairly dire inerpreaion in he one of radiional IS/LM models. The near onsany of q is similar o a perfely elasi IS-urve. As a resul, hanges in moneary poliy have no effe on he real ineres rae. If fuure inflaion epeaions are anhored by long-run faors hen he nominal ineres rae will be unhanged. Sine here are no hanges in he nominal ineres rae in equilibrium we have π = φ π, φ π, π. Assuming ha he Taylor Rule oeffiiens are boh posiive, his ondiion implies perfely negaively orrelaed inflaion raes aross seors regardless of seoral prie rigidiy and he ype of shoks. Addiionally, only he relaive response o inflaion (i.e. he raio φ π, )maers φ π, for he equilibrium. Solving for he oupu gap and inflaion in erms of he sruural shoks gives he approimae equilibrium. Proposiion 2. or he model desribed in his seion wih long-lived durables ( δ, r 0) suffiienly shor-lived shoks, σ = ρ, and zero measuremen error ( V m Y =0), he 10 This assumpion has wo pars. irs, we assume ha produiviy and os-push shoks are unorrelaed (have no persisene). Seond, we ignore he relaive prie beween he wo seors as a sae variable. Sine inflaion raes are quie small in equilibrium, he laer assumpion is reasonable for shor-lived shoks. We disuss he auray of his approimaion below. 19
approimae equilibrium is given by he following equaions (i.) π = λ S Z + λ S Z + S u λ λ S u (ii.) (iii.) where S = Ŷ = π = λ S Z + λ S Z + S u λ λ S u 1 α ½ α S Z 1 + + S Z + 1 λ (1 S ) u 1 ¾ λ S u η φ π, λ φ π, λ +φ π, λ and S =1 S. To hek he auray of he approimaions q q and D D, Table1ompareshe impa responses implied by he approimaions in Proposiion 2 o he ea (linearized) responses for several realisi depreiaion raes. The able repors he impa reaion of employmen, he oupu gap, and durable and non-durable inflaion o he wo produiviy shoks and he wo os-push shoks. While he approimaion does fairly well for small values of δ, i gradually breaks down as δ rises. (See Table 2 for he parameer values used o ompue his speial ase.) I is sraigh-forward o find epressions for he approimae varianes of he model variables in he speial ase. These alulaion are fairly edious and so we summarize he epressions for he variane of aggregae inflaion Π = N N π + N N π, seoral inflaion raes and he variane of he oupu gap in he following orollary. Corollary. The unondiional varianes of aggregae inflaion, seoral inflaion and he oupu gap are given by (i.) i µ N V h Π = N λ S N 2 N λ S Ψ (32) (ii.) V [ π ]=(λ S ) 2 Ψ and V [ π ]=(λ S ) 2 Ψ (iii.) where Ψ V Ã i V hŷ = h i Z + V 1 α 1 η + α! 2 ( (S ) 2 Ψ + h i Z + 1 2 V [u λ ]+ 1 2 V [u λ ]. µ ) 2 1 λ (S S ) V [u ] 20
Noie ha beause he inflaion raes are perfely negaively orrelaed in equilibrium, he variane of aggregae inflaion is no simply he share-weighed average of seoral inflaion varianes. Table 1 inludes a omparison of he sandard deviaion of inflaion and he oupu gap implied by he Corollary above wih he ea sandard deviaions. Again, he approimaion does a fairly good job, pariularly for low depreiaion raes. 4.3.2 The Opimal Taylor Rule in he Speial Case We are now in a posiion o onsider he opimal Taylor Rule for he speial ase above. or eposiional purposes we will assume ha he objeive of he moneary auhoriy akes he simple ad ho form i i L = V hŷ + W π V h Π (33) where W π gives he weigh of inflaion relaive o oupu sabilizaion in he moneary auhoriy s objeive. As in Woodford [2003] we epress he objeive as a imeless one in whih he moneary auhoriy does no inorporae he iniial posiion of he eonomy bu raher simply hooses a poliy o minimize he unondiional weighed variane in (33). The following proposiion provides an epression for he opimal Taylor Rule oeffiien. Proposiion 3. or he speial ase wih long-lived durables ( δ, r 0) suffiienly shor-lived shoks, σ = ρ, and zero measuremen error, he opimal Taylor Rule requires φ π, φ π, = λ λ Ã ζ 2 ζ 2 V[u λ ] Ψ + N N λ W π N N λ + N ζ 2 V[u λ ] + N Ψ N λ W N π N λ + N λ N λ! N where ζ = 1 α 1 +α. η The epression in Proposiion 3 offers several insighs ino he opimal poliy. irs, onsider he speial ase in whih he moneary auhoriy ares only abou sabilizing inflaion, ha is, W π. Sine seoral inflaion raes are negaively orrelaed, aggregae inflaion variane an be ompleely eliminaed in he model by hoosing Taylor Rule oeffiiens in proporion o he size of eah seor, ha is, φ π, = N φ π, N. In his ase, i is easy o show ha i he squared erm in (32) is zero so V h Π =0. This migh be viewed as he mos naural way for a moneary auhoriy o rea o inflaion in differen seors. Inuiively, larger seors reeive greaer weigh han smaller seors. Seond, suppose ha W π so he moneary auhoriy values boh oupu and inflaion 21
sabiliy bu ha here are no os push shoks (V [u ]=V[u ]=0). In his ase, he opimal raio of Taylor oeffiiens is φ π, φ π, = 1 λ Ã ζ 2 N W N N π N λ + N λ N! + N N. This Taylor rule plaes more emphasis on durable goods inflaion relaive o he seoral weighs. The deviaion from seoral weighs N N depends posiively on ζ and negaively on λ and negaively on he average prie rigidiy parameers N N λ + N N λ. Third, if W π =0so ha he enral bank ares only abou oupu sabilizaion, hen he opimal raio of he Taylor oeffiiens is µ φ π, = λ φ π, λ (λ ) 2 Ψ V [u ] 1. Noe firs ha he definiion of he aggregae variane parameer Ψ implies ha (λ ) 2 Ψ > V[u ] 1. As V [u ] 0 he enral bank opimally responds infiniely srongly o durable goods inflaion. The os push shoks in he durable goods seor are he only impedimen o ahieving omplee oupu sabilizaion. In he absene of hese os push shoks, he enral bank an ahieve is goals simply by argeing durable goods inflaion. If insead V [u ] hen he opimal response plaes less and less weigh on he durable goods seor. In he more realisi ase in whih he varianes of boh os-push shoks beome arbirarily large, he raio φ π, approahes λ (a resul reminisen of Aoki 2001). φ π, λ These limiing resuls are naural in ligh of he lose onneion beween inflaion sabilizaion and oupu sabilizaion. In he limiing speial ase onsidered here, he moneary auhoriy opimally reas more o durable goods inflaion if i ares more abou sabilizing he oupu gap and/or if he variane of durable goods os-push shoks is lowered. In onras, if he variane of durable goods os push shoks is high, i is opimally o rea o seoral inflaioninaordanewih heirshareingdp. Of ourse, hese resuls depend riially on being in he low-depreiaion (i.e., ideal durable) limi and he oher assumpions underlying Proposiions 2 and 3. To hek he auray of he prediions, we alulae he impa responses o seoral produiviy shoks Z and Z, and o seoral os-push shoks u and u for he speial ase for several differen depreiaion raes. Table 1 repors he varianes of employmen, he oupu gap, durable goods inflaion and non-durable goods inflaion, as well as he raio of opimal Taylor rule 22
oeffiiens for boh he approimaion (he firs olumn) and he ea numerial soluions. Aording o he able, he approimaion is surprisingly aurae for low depreiaion raes. 4.4 Quaniaive Analysis In his seion we use alibraed versions of he DSGE model o analyze he performane of differen Taylor rules. We begin by speifying a baseline alibraion of he model and hen ompue he opimal Taylor rule assoiaed wih various model speifiaions. An opimal Taylor rule maimizes a given rierion funion subje o he onsrain ha moneary poliy adhere o a speifiaion in he family given by (23). 11 In his seion, moivaed in par by he resuls in he speial ase above, we impose an addiional resriion on he rule. The speial ase above showed ha he equilibrium depended only on he raio of he Taylor oeffiiens φ π,. This resul approimaely arries over o many parameri seings and, in φ π, suh ases, leads o numerial insabiliy of he opimal Taylor rule oeffiiens. We plae addiional limiaions on he Taylor rule by furher resriing he family o i =ī + φ Y Y m + Φ Π (w π +(1 w ) π ) (34) where Φ Π is a fied number whih normalizes he enral bank s reaion o a measure of inflaion (below we sele φ Π =2). In erms of he earlier analysis, he raio of he oeffiiens is simply φ π, = w φ π, 1 w. If he weighs w and (1 w ) are equal o he share of durable goods produion and non-durable goods produion in he eonomy, hen his rule reas o sandard aggregae inflaion. or fied φ Π, he opimal Taylor rule in his seup is one in whih φ Y and he weigh w maimize he objeive funion. 4.4.1 Baseline Calibraion We alibrae he model for ease of eposiion of our resuls raher han for empirial plausibiliy and illusrae he robusness of he onlusions. We se he annual ime disoun rae o imply a subjeive ime disoun faor of wo peren. The ineremporal elasiiy of subsiuion (σ) is 0.5. This is somewha higher han onvenional esimaes (e.g., Hall 1988) bu lower han log uiliy. The rish labor supply elasiiy (η) is se o 1.0. We se he elasiiy of subsiuion beween durable and non-durable onsumpion (ρ) of0.8andwehoosehe 11 See Boehm and House [2014] and he referenes herein for addiional disussion of opimal Taylor Rules. 23
weigh on nondurable onsumpion (ψ )oimply C =.75. The elasiiy in he wo seors Y aggregaors (ε) is 7. The apial share parameer (α) is 0.35. We hoose he Calvo parameers θ and θ o imply a 6-monh half-life of nominal rigidiy. The persisene of he produiviy and os-push shoks is se o 0.5 annually. Measuremen error shoks have no persisene. Innovaions of he produiviy shoks are assumed o have an annual sandard deviaion of 1 peren. The annual sandard deviaions of ospush shoks are 0.1. Hene, he baseline alibraion plaes subsanially greaer weigh on produiviy shoks han he os-push shoks. We onsider several differen depreiaion raes (δ). The baseline depreiaion rae is se o 0.05 annually. This is somewha lower han he sandard alibraion of 10 peren annually bu somewha higher han he depreiaion rae for sruures. See raumeni [1998] for a deailed disussion of he various depreiaion raes orresponding o a wide variey of goods in he eonomy. The baseline alibraion is summarized in Table 2. 4.4.2 Numerial Illusraions Table 3 shows he opimal weigh on durables inflaion w and he opimal response o he oupu gap φ Y for differen alibraions and welfare objeives. Calibraion (i) is he baseline seing. The remaining alibraions (labeled (ii.),... (vi.) in he able) have parameer values equal o he baseline alibraion eep for a single parameri variaion. Calibraion (ii) feaures subsanially less measuremen error in he oupu gap han in he baseline alibraion. Speifially, we se he (annual) sandard deviaion of measuremen error o 0.25 raher han 1.00. Calibraion (iii) has a high annual depreiaion rae (δ =0.20). Calibraions (iv) and (v) have asymmeri prie rigidiy aross seors; (iv) has a half-life of prie rigidiy in he non-durables seor of 1 quarer while (v) has he reverse (a half-life of durable good prie rigidiy of 1 quarer). Calibraion (vi) has an annual sandard deviaion of he os-push shok innovaions of 0.2 raher han 0.1. In he baseline alibraion, w always eeeds a quarer he weigh durable goods inflaion reeives in overall CPI inflaion. Imporanly, w eeeds a quarer regardless of he objeive. When he enral bank ares equally abou inflaion and he oupu gap i is opimal o plae a weigh of almos 72 peren on durable goods inflaion. Under he assumpion ha he enral bank minimizes he uiliy-based loss funion, w is sill abou 0.50. Ineresingly, i is opimal o plae subsanial weigh on durables inflaion even if he enral bank does no value low oupu volailiy. When he enral bank only values oupu sabiliy a weigh of 24
almos 80 peren is opimal. The remaining olumns of Table 3 illusrae oher alibraions. Perhaps no surprisingly, if measuremen error is fairly small, he enral bank responds sronger o he oupu gap (alibraion ii.). In his ase w falls somewha bu sill remains well above one quarer. Some of his differene is due o he subsiuabiliy beween responding o he oupu gap and responding o durables inflaion. Refleing on he previous disussion in Seion 4.1, in he absene of srong os push shoks, oupu sabilizaion and sabilizaion of he durable goods seor are idenial. As a resul, if he oupu gap is poorly measured, i is preferable o avoid srong responses o he gap and o insead arge durables inflaion. Calibraion (iii.) shows ha he resuls oninue o hold even when he depreiaion rae is as large as 20 peren annually. While w barely hanges relaive o he baseline alibraion, i falls o one quarer as he depreiaion rae approahes one. igure 1 shows he opimal weigh w for he four differen welfare objeives in Table 3. The figure shows ha for low depreiaion raes, he enral bank reas more o durable goods inflaion relaive o is share in GDP (he dashed line a 0.25 in he figure). No surprisingly, as he depreiaion rae approahes 1.00, he weigh on durable goods inflaion approahes is share in GDP 0.25. Columns (iv.), (v.), and (vi.) show ha our resuls oninue o hold for asymmeri seoral prie rigidiy or when he os-push shoks have a greaer variane han in he baseline alibraion. igures 2 o 5 show impulse response funions. We onras hree Taylor rules: (a) a Taylor rule in whih he oeffiiens are hosen o maimize he ad-ho objeive wih W π =1, (b) a Taylor rule whih is opimal for he uiliy-based objeive, and () a Taylor rule ha uses he weigh w =0.25 as CPI inflaion would sugges and an oupu gap response ha isopimalforhead-hoobjeivewihw π =1. Aross all four figures, he Taylor rule ha is opimal for he uiliy-based objeive (full blak line) produes he smalles inflaion responses. In onras, he Taylor rule ha is opimal for he ad-ho objeive (dashed line) leads o he smalles oupu gap. The Taylor rule wih sub-opimal oeffiien w =0.25 produes a subsanially larger oupu gap eep for he os-push shok in he durables seor. 25
5 Conlusion Inflaion argeing has beome a sandard operaing proedure for many modern enral banks. In par his emphasis is moivaed by modern New Keynesian heory whih argues ha here is a dire onneion beween inflaion sabilizaion and oupu sabilizaion. The divine oinidene says ha oupu sabilizaion and inflaion sabilizaion are equivalen. However, mos of he analysis providing he basi raionale for inflaion argeing is based on models wih a single good and hus a single rae of inflaion. Compared o he volume of work fousing on one-good models, muh less aenion has been devoed o he sudy of whih inflaion rae enral banks should arge when here are non-rivial differenes in inflaion aross seors. This sudy onsiders wheher durable goods inflaion should be overweighed relaive o is share in GDP. We find ha ofen i is indeed preferable o plae greaer emphasis on sabilizing durable goods inflaion. Durable goods have muh higher ineres elasiiies of demand han non-durables and hus should be muh more sensiive o ineres rae hanges (and hus he speifiaion of he Taylor rule). In a limiing ase, we obain a divine oinidene for durable goods inflaion. In he absene of os-push shoks in he durable goods seor, sabilizing inflaion in he durable goods seor is anamoun o sabilizing aggregae oupu and employmen. These resuls sugges ha greaer emphasis should be plaed on auraely measuring and monioring durable goods prie hanges over he moneary business yle. 26
Referenes Aoki, K. 2001. Opimal Moneary Poliy Responses o Relaive-prie Changes, Journal of Moneary Eonomis, 48, pp. 55-80. Balke, N.S., and Wynne, M.A. 2007. The Relaive Prie Effes of Moneary Shoks. Journal of Maroeonomis, 29, pp. 19-36. Ball, L. and Romer, D. 1990. Real Rigidiies and he Non-Neuraliy of Money. Review of Eonomi Sudies, vol. 57. Barsky, R.; House, C. and Kimball, M. 2007. Siky-Prie Models and Durable Goods, Amerian Eonomi Review 97 (June), pp. 984-998. Barsky, R.; House, C. and Kimball, M. 2003. Do leible Durable Goods Pries Undermine Siky Prie Models?, NBER working paper No. W9832. Bils, M and Klenow, P. 2004. Some Evidene on he Imporane of Siky Pries. Journal of Poliial Eonomy, 112, pp. 947-985. Bils, M.; Klenow, P. and Malin, B. 2012. Tesing for Keynesian Labor Demand, NBER Maroeonomis Annual 2012,D.Aemoglu,J.ParkerandM.Woodford(Eds.),Cambridge, MA: MIT Press, pp. 311-349. Blanhard, Olivier and Galí, Jordi 2007. "Real Wage Rigidiies and he New Keynesian Model," Journal of Money, Credi and Banking, 39, pp. 35-65. Bodensein, M; Ereg, C.J. and Guerrieri, L. 2008. Opimal moneary poliy wih disin ore and headline inflaion raes, Journal of Moneary Eonomis, 55, pp. S18-S33. Boehm, C. and House, C. 2014. Opimal Taylor Rules in New Keynesian Models, Naional Bureau of Eonomi Researh, NBER working paper No. 20237. Bils, M.; Klenow, P. and Malin, B. Tesing for Keynesian Labor Demand NBER Maroeonomis Annual 2012, D. Aemoglu, J. Parker and M. Woodford eds., Cambridge, MA: MIT Press, 311-349. Boivin, J.; Giannoni, M.P., and Mihov, I. 2009. Siky Pries and Moneary Poliy: Evidene from Disaggregaed US Daa. Amerian Eonomi Review, 99, pp. 350-384. Carlsrom, C and uers, T. 2006. Co-Movemen in Siky Prie Models wih Durable Goods. ederal Reserve Bank of Cleveland Working Paper No. 06-14. Carlsrom, C.T.; uers, T.S., and Ghironi,. 2006. Does i Maer (for Equilibrium Deerminay) Wha Prie Inde he Cenral Bank Targes? Journal of Eonomi Theory, 128, pp. 214-231. Carvalho, C. 2006. Heerogeneiy in Prie Sikiness and he Real Effes of Moneary Shoks. The B.E. Journal of Maroeonomis (roniers), 2, pp. 1-56. 27