CAE Working Paper # Another Look at Sticky Prices and Output Persistence. Peng-fei Wang and Yi Wen. December 2004

Transcription

1 CAE Working Paper #04-19 Anoher Look a Sicky Prices and Oupu Persisence by Peng-fei Wang and Yi Wen December 2004.

2 Anoher Look a Sicky Prices and Oupu Persisence Peng-fei Wang Deparmen of Economics Cornell Universiy Yi Wen Deparmen of Economics Cornell Universiy (Firs Version: December 31, 2004) Absrac Price rigidiy is he key mechanism for propagaing business cycles in radiional Keynesian heory. Ye he New Keynesian lieraure has failed o show ha sicky prices by iself can effecively propagae business cycles in general equilibrium. This siuaion may be a direc consequence of he noion ha money-in-uiliy (MIU) and cash-in-advance (CIA) are equivalen mechanisms for generaing money demand. They are no. We show ha price rigidiy in fac can (by iself) give rise o a powerful propagaion mechanism of he business cycle under CIA consrain in sandard New Keynesian general equilibrium models. In paricular, we show ha reasonable price sickiness can generae highly persisen, hump-shaped movemens in oupu, invesmen and employmen in response o eiher moneary or non-moneary shocks. Hence, wheher or no price rigidiy is responsible for oupu persisence (and he business cycle in general) is no a heoreical quesion, bu an empirical one.

3 1. Inroducion Sicky prices are he key mechanism assumed in radiional Keynesian heory for propagaing he impac of moneary shocks as well as oher aggregae shocks hroughou he economy. Bu how srong is such a propagaion mechanism is no clear in he radiional heory. The exbook IS-LM model, for example, argues ha aggregae oupu ends o say below he poenial oupu level afer a moneary conracion only as long as prices remain unchanged. Ye a much more sluggish response of oupu o moneary shocks is documened by he empirical lieraure (see, e.g., Sims 1992, Chrisiano e al. 1995, and Srongin 1995, among many ohers). Empirical evidence indicaes ha he deviaion of oupu from is poenial rend seems far more persisen han he esimaed degree of price sickiness would sugges. To demonsrae his persisen effec of sicky prices in a fully-specified new Keynesian dynamic-general-equilibrium model has also proven o be difficul, as recenly sressed by Chari, Kehoe and McGraan (CKM 2000). CKM show ha empirically plausible degree of price rigidiy generaes only a modes degree of oupu persisence in responding o moneary shocks, far from enough o accoun for he esimaed oupu persisence in he U.S. economy. The usefulness of he sicky price assumpion, one of he corner sones in radiional Keynesian heory, is hus under a serious challenge. 1 The persisence problem raised by CKM (2000) along wih ohers has led researchers o explore oher ypes of rigidiies or economic forces, in conjuncion wih sicky prices, o explain he persisen effecs of moneary shocks. For example, Chrisiano, Eichenbaum, Evans (2003) obain more persisen oupu responses o moneary shock by combining boh sicky prices and sicky wages on he nominal side, aided by habi formaion, adjusmen coss, limied paricipaion in money marke and variable capial uilizaion on he real side. Dosey and King (2001) show ha oupu persisence can be improved by feaures such as a more imporan role for produced inpus, variable capaciy uilizaion, and labor supply variabiliy hrough changes in employmen. These elemens ogeher can reduce he elasiciy of marginal cos wih respec o oupu, improving he persisence of oupu. Bergin and Feensra (2000) emphasize ineracions beween inpu-oupu producion srucures and ranslog preferences o improve oupu persisence under sicky prices. Similar resuls based on producion chains can also be found in he work of Huang and Liu (2001). Oher researchers such as Mankiw and Reis (2002), Woodford (2001), Erceg and Levin (2001) have emphasized he imporan 1 For an excellen review of he New Keynesian lieraure, see Clarida, Gali and Gerler (1999). 2

4 role of imperfec-informaion in helping sicky prices o generae persisen oupu responses o moneary shocks. 2 By adding a large number of building blocks, such as real rigidiies and complex informaion srucures, ino he sandard sicky-price model can obviously improve he model s fi in erms of oupu persisence, bu a he expense of simpliciy. Ofen more han one facors are added o enangle wih nominal rigidiies such ha i becomes hard o disinguish exacly which facor is doing wha in generaing oupu persisence. In addiion, while sicky or imperfec informaion proves o be effecive in giving rise o oupu persisence, he way hey are modeled in he lieraure ofen uses parial equilibrium framework. I is shown recenly by Keen (2004), for example, ha he business cycle implicaions of sicky informaion proposed by Mankiw and Reis (2003) may no be robus in general equilibrium models. 3 This paper akes a sep back and asks wheher a canonical sicky price model wihou any addiional fricions or rigidiies can generae a reasonable degree of oupu persisence. Puing i anoher way, his paper asks why sicky prices by iself may fail o provide a srong propagae mechanism for he business cycle. This is an inriguing quesion because inuiively here is no reason price rigidiy would no lead o oupu persisence, since i could urn i.i.d. shocks ino serially correlaed movemens in he real balance jus as effecively as any oher ypes of real rigidiies. Real balance in urn could affec aggregae spending and producion. Ye despie he exploding lieraure rying o overcome he persisence problem, wha exacly fails he Keynesian sicky price propagaion mechanism in general equilibrium models remains unclear. Chari, Kehoe and McGraan (2000), for example, show he inabiliy of sicky prices in generaing oupu persisence mainly via model simulaions. The reasons behind he failure are less clearly presened when capial is included. We show in his paper ha sicky prices can in fac by iself generae highly persisen oupu movemens, conrary o he findings of he exising lieraure. In paricular, we show ha empirically plausible price sickiness can generae humpshaped oupu responses o moneary shocks in a way very similar o he daa. Thus, 2 The lieraure has also explored he implicaions of sicky wages for oupu persisence. Models based on saggering wages such as hose in Andersen (1998), Erceg (1997), and Huang and Liu (2001) are sill no able o generae sufficien degree of real persisence seen in daa, hough hey do alleviae he problem o some exen. Edge (2002) recenly esablishes condiions under which wage and price saggering are equivalen regarding heir effecs on oupu persisence, hus he persisence problem is similar in boh sicky-wage and sicky-price models. Also see Dosey and King (2004) for he recen new lieraure on sae-dependen pricing in general equilibrium. This lieraure shows ha sae-dependen pricing can have dramaically richer propagaion mechanisms han ime-dependen pricing in generaing oupu and inflaion persisence. Kiley (2002) and Benhabib and Farmer (2000) show ha exernaliies can also give rise o oupu persisence. 3 Erceg and Levin (2001) is an excepion. 3

5 sicky prices are cerainly a useful assumpion in explaining he business cycle as far as heory is concerned. Wheher hey are responsible for he business cycles in he real world, however, is an empirical quesion. The key o undersand our finding is o realize ha money-in-uiliy and cashin-advance are no equivalen mechanisms in generaing money demand. There are wo reasons. Firs, unless consumpion and money ener he uiliy funcion as perfec complemens, money demand and consumpion demand behave very differenly under MIU. Second, even if consumpion and money ener he uiliy funcion as perfec complemens, money demand and aggregae demand remain very differen under MIU, since aggregae demand includes invesmen and governmen spending. OnlyheCIAconsrainmakesipossibleformoneyohaveimporaninfluence on he dynamics of aggregae spending and producion. 4 Hence he reason ha he exising lieraure fails o deec he srong power of sicky prices in propagaing shocks lies in is failure o realize ha he dynamics of money demand and he dynamics of aggregae spending (oupu) inerac differenly depending on how money eners he model. In MIU models, aggregae spending (e.g., C + I + G + NX)are no effecively consrained by money holdings, hence he maximum effec of shocks on aggregae income are always realized in he impac period due o he volaile reacions from invesmen. This implies monoonic impulse responses. When CIA is imposed on aggregae demand, however, he maximum impac of shocks on aggregae income is subdued and posponed because of he cash-in-advance consrain on oal spending. This gives rise o more smoohed oupu responses o shocks. There should be lile surprise ha our findings also conradic a branch of he exising lieraure ha assumes CIA. For example, Yun (1996) sudies a CIA consrained sicky price model and finds ha money shocks have no persisen effecs on oupu. Ellison and Sco (2000) use he same model and demonsrae ha sicky prices no only fail o produce persisen oupu flucuaions bu also generae exremely volaile oupu a very high frequencies. Boh of hese papers, however, assume CIA consrain on consumpion only. When here is capial in he model, ineremporal subsiuion beween curren consumpion and fuure consumpion can be achieved hrough capial accumulaion. In his case, imposing CIA consrain only on consumpion spending is no effecive for generaing persisen oupu, since invesmen becomes very volaile by serving as he buffer for consumpion, and consequenly invesmen will dicae oupu dynamics. Thus, even if consumpion is hump-shaped, oupu is no. This suggess ha invesmen goods mus also be reaed as cash goods in order for oupu (aggregae spending) o display persisence. 4 For example, when boh consumpion and invesmen are subjec o cash-in-advance consrain. 4

6 CIA consrain on invesmen spending serves essenially as a form of dynamic adjusmen coss for invesmen, which is well known for inducing hump-shaped oupu persisence. 5 Noice ha under CIA consrain for aggregae spending, sicky prices can lead o hump-shaped oupu persisence no only under moneary shocks, bu also under non-moneary shocks, such as echnology shocks and preference shocks. The inuiion is exacly he same as above: cash-in-advance pospones he maximum impac of shocks on aggregae demand because agens are forced o ineremporally smooh aggregae spending via real balance accumulaion over ime. A smoohed aggregae demand hus dicaes a smoohed aggregae supply (producion). Thus, heoreically speaking, sicky prices have no rouble generaing oupu persisence. The res of he paper proceeds as follows. Secion 2 demonsraes oupu persisence under CIA in a highly simplified model wihou capial. We show in his model ha sicky prices can give rise o hump-shaped oupu responses o money shocks under CIA consrain, bu no under MIU when consumpion and money are subsiues. Secion 3 sudies a fully specified general equilibrium model wih capial. I is shown ha under eiher moneary or non-moneary shocks, oupu exhibis hump-shaped persisence as long as invesmen goods are reaed as cash goods. Secion 4 concludes he paper wih suggesions for fuure research. 2. The Basic Model 2.1. Households A represenaive household chooses sequences of consumpion, {C } =0, labor supply, {N } =0, and money demand, {M }, osolve subjec o C + M M 1+X X max E 0 β j [log C an ] j=0 + w N + Π and he CIA consrain, C M ;where X is money injecion, P is he aggregae goods price in erms of money, w is he real wage, and Π is he profi income conribued from firms which he household owns. Noice ha, since he curren money holdings, M, ener he CIA consrain, here is no inflaion ax on consumpion. Hump-shaped oupu persisence remains if he inflaion ax effec is allowed. Denoing λ 1 and λ 2 as he Lagrangian mulipliers for he budge consrain and he CIA consrain respecively, he firs order condiions canbesummarizedby 5 See, e.g., Wen (1998b). 5

7 1 C = λ 1 + λ 2 (2.1) a = λ 1 w (2.2) λ 1 = βe λ λ 2. (2.3) Firms The final goods, Y, are produced by a perfecly compeiive firmaccordingohe h R i echnology, Y = 1 0 y (i) σ 1 σ σ di σ 1, where σ > 1 measures he elasiciy of subsiuion among he inermediae goods, y(i). Le p (i) denoe he price of inermediae h i goods i, he demand for inermediae goods is given by y (i) = p(i) σ Y, and he relaionship beween finalgoodspriceandinermediaegoodspricesisgivenby h R = 1 0 p (i) dii 1 σ 1 1 σ. Each inermediae good i is produced by a single monopolisically compeiive firm according o he following echnology, y (i) =n (i). Inermediae good firms face perfecly compeiive facor markes, and are hence price akers in he facor markes. Profis are disribued o household a he end of each ime period. The cos funcion for firm i, can be derived from minimizing w n (i) subjec o n (i) y. Denoing φ as he Lagrangian muliplier, which is also he real marginal cos, he firs order condiion for cos minimizaion is given by w = φ. Consequenly, he real profi inperiod is given by ( p (i) φ )y (i). Following Calvo (1983) in assuming ha each firm has a probabiliy of 1 θ o adjus is monopoly price in each period, hen a firm s ineremporal profi maximizaion problem is o choose he opimal price, p, o maximize X E (βθ) +s p Λ,+s φ +s y,+s (i), (2.4) +s s=0 where Λ,+s h C+s C i 1 is he raio of marginal uiliies aken as exogenous by he firm; and y,+s denoes he firm s oupu level in period + s given is opimal h p i price in period : y,+s (i) = (i) σ P Y+s +s. The firs order condiion for opimal monopoly price implies he following pricing rule: 6

8 X σ (βθ) +s E Λ +s P+sY σ +s φ +s p s=0 =. (2.5) X (σ 1) (βθ) +s E Λ +s P+s σ 1 Y +s s=0 Because all firms ha can adjus heir prices face he same problem, all monopolis firms will se heir prices in he same way as indicaed above. The average price of firms ha do no adjus prices is simply las period s price level, 1. Given ha only a fracion of 1 θ can adjus heir prices in each period, he final good price h i index can hen be wrien as = θp 1 1 σ 1 1 σ +(1 θ)p 1 σ Equilibrium and Aggregaion In equilibrium household s firs order condiions and firms profi maximizaion condiions are saisfied, all markes clear, and he CIA consrain binds. We sudy symmeric equilibrium only. In a symmeric equilibrium, here are only wo ypes of firms, one ha has he chance o adjus price and one ha does no. Since all inermediae good firms face he same marginal cos, heir labor demand is in he same proporion o heir oupu level, regardless hey adjus prices or no. Hence in equilibrium he labor marke clearing condiion is given by N = Z 1 0 ( n(i)di = θ p 1 implying ha he aggregae producion funcion is given by: Y = ( θ p 1 ) σ σ p +(1 θ) Y, (2.6) ) σ σ 1 p +(1 θ) N. (2.7) If a firm ges o adjus is price, is real profi inperiod is given by h p i 1 σ Y h p i σ φ Y, and if a firm does no ge o adjus is price, is profi isgivenby h i p 1 1 σ h i P Y φ Y p 1 σ. The aggregae profi ishusgivenby Π = θp1 σ 1 ( +(1 θ)p (1 σ) P 1 σ Y θ p 1 ) σ σ p +(1 θ) φ Y = Y w N. (2.8) 7

9 The household aggregae income is hen given by w n + Π = Y. The final goods marke clearing condiion is given by C = Y Equilibrium Dynamics The model is solved by log-linearizaion around a zero-inflaion seady sae as in King, Plosser and Rebelo (1988). Using circumflex lower-case leers o denoe percenage deviaions around seady sae, he log-linearized opimal price and he price index are given respecively by ˆp =(1 βθ) P ³ s=0 E ˆφ+s +ˆp +s and ˆp = θˆp 1 +(1 θ)ˆp, which ogeher imply he New Keynesian Phillips relaionship: ˆπ = βe ˆπ +1 + (1 θ)(1 βθ) θ ˆφ, (2.9) where π is he inflaion rae, ˆπ ˆp ˆp 1. The log-linearized aggregae producion funcion is given by ŷ = ˆn, hence around he seady sae he aggregae producion funcion is he same as individual firm s producion funcion. Noice ha he CIA consrain can be expressed as ŷ ŷ 1 = x ˆπ,wherex log X M 1 denoes he growh rae of nominal money sock. We assume ha he moneary auhoriy follows a money growh rule given by x = ρx 1 + ε. The household s firs-order condiions are hus reduced o: (2 β)ŷ 2 ˆφ = β(ˆπ +1 + ˆφ +1 ). Subsiuing ou π in his equaion and in he New Keynesian Phillips curve using he CIA consrain, he sysem of equaions for solving {ŷ, ˆφ } are given by: x +ŷ 1 (1 + β)ŷ = βe (x +1 ŷ +1 )+ which can be arranged more compacly as (1 θ)(1 βθ) θ ˆφ (2.10) 2ŷ 2ˆφ = βŷ +1 βx +1 β ˆφ +1 (2.11) ŷ +1 ŷ ˆφ +1 E x +1 = 1+β β 1 β (1 θ)(1 βθ) βθ 1+ρ xβ β β β 1 β 1 βθ+θ+βθ 2 βθ 1 β ρ x ŷ ŷ 1 ˆφ. The eigenvalues of he Jacobian marix are given by: { 2 β, 1 βθ, θ, ρ}. Noe ha he firs wo of he eigenvalues are larger han uni, hence hey can be uilized o solve 8

10 he sysem forward o deermine {ŷ, ˆφ } as funcions of he sae {ŷ 1,x }.Clearly, he oher wo smaller roos, {θ, ρ}, deermine he propagaion mechanism of oupu. The decision rule of oupu akes he form: ŷ = θŷ 1 + αx (2.12) where α is he elasiciy of oupu wih respec o money growh shocks. Clearly, he persisence of oupu is deermined joinly by he degree of price sickiness, θ, and he persisence of shocks. If moneary shocks are AR(1), for example, hen oupu follows AR(2): ŷ =(θ + ρ)ŷ θρŷ 1 + αε, (2.13) which implies a hump-shaped impulse response funcion. Suppose ha he average price sickiness is abou four quarers in he economy, he probabiliy of no adjusing prices is hen θ = Given ha money growh shocks have auocorrelaion of ρ =0.6, as is commonly assumed in he lieraure (e.g., CKM 2000), 6 hen he degree of oupu persisence implied by he model maches he conrac muliplier of he U.S. economy esimaed by Chari, Kehoe and McGraan (2000) almos exacly. The maximum impac of a money injecion on oupu is delayed for hree quarers afer he shock. The simulaed impulse responses of oupu are graphed in Figure 1 (op window). 6 Also see our calibraion using pos-war daa in he nex secion. 9

11 Fig. 1. Impulse Response of Oupu o Money Shock When money demand seps from MIU insead, under sandard assumpions regarding he elasiciy of subsiuion beween consumpion and money, no humpshaped oupu persisence can be generaed from he model. To demonsrae, le he household solve: subjec o C + M max E 0 X j=0 β j log C + η log M an M 1+X +w N +Π. Le all parameers ake he same values as in he previous CIA model. The boom window in Figure 1 shows ha oupu does no have hump-shaped persisence. Hence, oupu exhibis hump-shaped persisence under sicky prices only if money can have a srong influence on oal spending, such as in he case of CIA. 7 7 In models wihou capial, CKM (2000) argue ha perfec subsiuabiliy beween consumpion and leisure is crucial for generaing oupu persisence under he Taylor (1980) ype of price 10

12 The inuiion is ha cash-in-advance forces agens o ineremporally subsiue away curren spending for fuure spending via real balance accumulaion, which smoohs demand and hence producion. In oher words, when money has only an uiliy (income) effec, as is he case in MIU models, i generaes is maximum impac on aggregae spending insananeously, hence no allowing he impac o be buil up hrough ime via ineremporal subsiuion beween curren spending and fuure spending. Under CIA consrain, money serves o sore real purchasing power under price sickiness. In order o increase spending, agens mus increase cash holdings. Thus he iniial impac of money injecion on demand is subdued, delayed, and ransmied ino he fuure. This effec coninues o hold in more general models wih capial, as he following secion shows The Full Model 3.1. Households The represenaive household chooses consumpion (C), hours (N), capial sock (K), money demand (M), and bond holdings (B) osolves: max E 0 X =0 " β Θ log C a N 1+γ # 1+γ (3.1) subjec o C +[K +1 (1 δ)k ]+ M + B /R p = M 1 + B 1 + X p +r K +w N +Π G (3.2) C + K +1 (1 δ)k M p (3.3) where r and w denoe real renal rae and real wage rae ha prevail in compeiive facor markes; R denoes nominal reurns o bonds, δ denoes he depreciaion rae of capial. A he end of each period, he household receives wages from hours worked, renal paymens from capial lending, and nominal bonds reurns as well as rigidiy. Here we find ha his requiremen is no necessary under he Calvo (1983) ype of price rigidiy. See Kiley (2002) for discussions regarding he differences beween he Taylor ype and he Calvo (1983) ype of price rigidiies. 8 Technically speaking, he sable roo, θ, in he CIA model drives from he real balance due o price sickiness. Hence his roo should show up in boh he CIA model and he MIU model. However, a crucial difference beween he wo models is ha he real balance dicaes aggregae demand only in he CIA model bu no in he MIU model. Consequenly, lagged oupu, y 1, shows up as an endogenous sae variable in he CIA model bu no in he MIU model. 11

13 profis Π from all firms he household owns, and pays a lump sum ax o governmen in he amoun of G. If consumpion is he only cash goods, hen our model reduces o ha of Yun (1996) and Ellison and Sco (2000). 9 Denoing he Lagrangian mulipliers for (3.2) and (3.3) as λ 1 and λ 2 respecively, he firs order condiions wih respec o {C,N,K +1,M,B } can be summarized by Θ = λ 1 + λ 2 (3.4) C an γ = λ 1 w (3.5) λ 1 + λ 2 = β(1 δ)e (λ λ 2+1 )+βe λ 1+1 r +1 (3.6) λ 1 = βe λ λ 2 (3.7) +1 λ 1 = βe λ 1+1 (3.8) R Firms The final good secor is he same as described previously. Hence he demand of inermediae goods is given by y(i) = Y, and he price index for final goods i σ is given by P = h p(i) P h R 1 0 p(i)1 σ dii 1 1 σ. The producion echnology for inermediae good i is given by y(i) =Ak(i) α n(i) 1 α,where0< α < 1andA denoes aggregae echnology shocks o produciviy. The cos funcion of firm i is derived by minimizing rk(i)+wn(i) subjec o Ak(i) α n(i) 1 α y. Thefirs order condiions are given by r = φα y(i) y(i) k(i),w = φ(1 α) n(i),whereφ denoes he real marginal cos. Given he producion funcion, he real marginal cos can be wrien as φ = 1 µ α µ 1 α r w. (3.9) A α 1 α 9 CIA consrain on boh consumpion and invesmen has been widely used in he lieraure. For example, see Sockman (1981), Abel (1985), Fuers (1992), among many ohers. Sockman (1981) conribues o he lieraure by showing crucial differences i may make by subjecing invesmen goods o he CIA consrain. Fuers (1992) sudies he liquidiy effec of moneary shocks by subjecing firms o CIA consrain regarding invesmen finance and wage paymens. Carsrom and Fuers (2001) show ha here can be a large difference for moneary policy wheher invesmen is subjeced o cash-in-advanced or no. Also see Wang and Yip (1992), and Gong and Zou (2002) for discussions on he implicaions of subjecing invesmen o CIA consrain. 12

14 Noe ha, since he oal cos equals φ y (i), he marginal cos equals average cos. Le he probabiliy of price adjusmen in each period for any inermediae firm be 1 θ, a firm s opimal price is again o choose p o maximize P h E s=0 (βθ) +s p ih Λ p i σ,+s +s φ +s P Y+s +s, which yields he same pricing rule as before: p = X σ (βθ) +s E Λ +s P+sY σ +s φ +s s=0 X (σ 1) (βθ) +s E Λ +s P+s σ 1 Y +s s=0 (3.10) 3.3. Aggregaion A each poin of ime, firms ha have he chance o adjus prices have differen facor demand as well as differen oupu and profis from hose who do no adjus prices. Aggregaion needs o ake his ino consideraion. In a symmeric equilibrium, here are only wo ypes of firms. Uilizing he facor demand funcions for each ype of firms, he aggregae capial sock and employmen can be shown o be: N = Z 1 K = k (i)di = α φ ( Y θ 0 r Z 1 n(i)di =(1 α) φ ( Y θ 0 w p 1 p 1 ) σ σ p +(1 θ) Hence he aggregae producion funcion can be expressed as Y = A K α N 1 α θp σ 1 (3.11) ) σ σ p +(1 θ). (3.12) P σ +(1 θ)p σ. (3.13) Noice ha near he seady sae, he aggregae producion funcion will be independen of prices. The aggregae profi can be shown o be Π = Z θ P 1 0 φ P 1 σ Y di + Z 1 θ P P σ φ Y di = Y w N r K. (3.14) Hence he equilibrium marke clearing condiions and resource consrains are given by: 13

15 C + G + K +1 (1 δ)k = Y (3.15) M = M 1 + X (3.16) B = B 1 = 0 (3.17) C + K +1 (1 δ)k = M (3.18) The opimal pricing rule in (3.10) in conjuncion wih he law of moion of he aggregae price index, = h θp 1 σ 1 +(1 θ)p 1 σ i 1 1 σ, leads o he same relaionship for he dynamics of inflaion around he seady sae as before: ˆπ = βe ˆπ +1 + (1 θ)(1 βθ) θ ˆφ, excep ha he marginal cos funcion is now differen Seady Sae and Calibraion In a zero-inflaion seady sae, i can be shown ha he following relaionships hold: φ = σ 1 (3.19) σ K Y = φ βα (2 β)[1 β(1 δ)]. (3.20) Noice ha, compared o a sandard RBC model in which K Y = βα 1 β(1 δ),hereare wo disorions on he seady sae capial-oupu raio in he sicky price model. Firs, monopolisic compeiion gives rise o a markup of 1 φ φ % > 0, which approaches zero only if he elasiciy of subsiuion σ (i.e., φ 1). A posiive markup implies a lower seady sae capial-oupu raio. Second, due o he fac ha money is needed o faciliae ransacions, an inflaion axisimposedonin- vesmen reurns, which lowers he seady sae capial-oupu raion by a facor of (2 β). If β =1,hiseffecs disappears. 10 The exogenous shocks are assumed o be ohorgonal o each oher and follow AR(1) processes in log: x = ρ x x 1 + ε x log A = ρ A log A 1 + ε A log Θ = ρ Θ log Θ 1 + ε Θ log G = ρ g log G 1 + ε g 10 See Sockman (1981) for more discussions on his issue. 14

16 where x log X M 1 denoes money growh rae. The model is calibraed a quarerly frequency. We choose he ime discouning facor β = 0.99, he rae of capial depreciaion δ = 0.025, he capial elasiciy of oupu α = 0.3, he seady-sae governmen spending o oupu raio G Y =0.2, he inverse labor supply elasiciy γ = 0 (Hansen s indivisible labor), and he elasiciy of subsiuion parameer σ = 10 (implying a markup of abou 10%). 11 We se he shock persisence parameers ρ A = ρ Θ = ρ g =0, 9. These parameer values are quie sandard in he lieraure. To calibrae money growh shocks, we esimae an AR(1) model for he growh rae of moneary base (M0) in he U.S. (1950:1-2003:4), and we obain ρ x =0.6 and σ εx = Impulse Response and Empirical Evaluaion The model is solved by log-linearizaion around he zero-inflaion seady-sae. The impulse responses of oupu, consumpion, invesmen and employmen o a onesandard-deviaion shock o money growh are graphed in Figure 2. Several feaures are worh noicing in Figure 2. Firs, a moneary growh shock can cause significan increases in economic aciviy. On impac, invesmen increases by 2.6 percen and oupu increases by 0.56 percen, while consumpion increases by only 0.06 percen. The overall sandard deviaion of invesmen is abou four imes ha of oupu, and he overall sandard deviaion of consumpion is abou half ha of oupu. These differen magniudes sugges ha moneary shocks can explain one of he mos prominen business cycle facs emphasized by he real business cycle lieraure; namely, ha consumpion is less volaile han oupu and ha invesmen is more volaile han oupu. 11 The resuls are no sensiive o his parameer. For example, similar resuls obain even when he markup is zero. 15

17 Fig. 2. Impulse Responses o Money Shock Second and mos srikingly, he impulse responses of oupu (Y ), employmen (N) andinvesmen(i) are all hump-shaped, wih a peak response reached around he hird quarer afer he shock. This suggess a richer propagaion mechanism of he model han a sandard RBC model or a sicky-price model wih money-in-uiliy. This richer propagaion mechanism induced by sicky prices and he CIA consrain enables he model o mach he observed oupu persisence in he U.S. economy quie well. For example, if we esimae an ARMA process for he logarihm of real GDP of he Unied Saes (1950:1-2003:4) wih a quadraic ime rend, hen he fied equaion is log(y )=1.3log(y 1 ) 0.37 log(y 1 )+v, (4.1) where he sandard deviaion of he residual is σ v = Using his esimaed sandard deviaion o shock he U.S. oupu, Figure 3 (lef window) shows ha he 12 CKM (2000) obain similar esimaes. 16

18 shape of he impulse response funcion of he U.S. oupu looks very much like ha implied by he model (where he sandard deviaion of money shock in he model is σ εx =0.006), excep ha he volailiy of he model oupu is only abou one hird imes ha of he daa oupu. Chari, Kehoe, and McGraan (2000) propose o measure he persisence of oupu by is half life. The half-life of oupu in he model is 9, while ha in he daa is 10. Ellision and Sco (2000) show ha sicky price models canno explain he business cycle since hey end o generae oo much variaions in oupu a he high frequencies bu no enough variaions a he business cycle frequencies. Here we show ha his conclusion does no hold if invesmen spending is subjec o cashin-advance consrain. The righ-hand side window in Figure 3 shows ha he power specrum of oupu growh in he model maches ha in he daa quie closely in erms of variance disribuion across frequencies. In erms of oal variance, however, he model (based on he calibraed money growh shocks) explains only abou 16% of he daa Inroducing capaciy uilizaion could improve he model in his regard. 17

19 Fig. 3. Oupu Dynamics of Model and Daa The inuiion for he persisen oupu effec of sicky prices in he full model wih capial is similar o ha in he basic model wihou capial. Cash-in-advance acs o smooh aggregae spending across ime, since by requiring cash, he maximum impac of shocks on demand (and hence supply) is posponed unil enough real balance is accumulaed. Thus he CIA consrain serves essenially like an ineremporal form of adjusmen cos, which is well know for generaing hump-shaped oupu dynamics. However, if only consumpion goods is subjec o CIA, oupu canno have enough persisence since shocks can immediaely impac on invesmen spending, which will dicaes aggregae demand and supply, making oupu very volaile a he high frequencies (see, e.g., Ellison and Sco 2000). Given ha consumpion can be smoohed via capial accumulaion, i can be shown ha CIA consrain on invesmen goods alone is enough o generae hump-shaped oupu 18

20 persisence under moneary shocks. 14 In addiion, sicky prices under CIA consrain can also effecively propagae non-moneary shocks. Figure 4 plos he impulse responses of oupu and employmen o one sandard deviaion echnology shocks and preference shocks respecively. I shows ha non-moneary shocks can also generae hump-shaped oupu persisence in he model (windows A and C). This feaure of he model is worh emphasizing since i is well known ha sandard RBC models lack an endogenous propagaion mechanism o explain he hump-shaped, rend revering oupu response o ransiory shocks (Cogley and Nason, 1995, Wason, 1993). Here i is shown ha sicky prices can do he job. 15 One more feaure of he model o noice is ha employmen responds negaively o echnology shocks (see Window D in figure 4). Because sicky prices and CIA consrain render aggregae demand rigid in he shor run, higher oal facor produciviy hus induces cos-minimizing firms o lower employmen. This negaive effec of echnology shocks on employmen as a resul of sicky prices has been empirically documened and explained by Gali (1999). However, in a money-in-uiliy general equilibrium model, echnology shocks generae posiive employmen even if prices are sicky, since invesmen can increase o absorb he shocks. 14 Inflaion in he model behaves like an AR(1) process, indicaing cerain degree of persisence, bu no hump-shaped persisence. Hence he model canno explain he well known fac ha inflaion lags oupu. However, is volailiy relaive o oupu maches he U.S. daa quie well. For he issue of inflaion persisence and is relaion o oupu, see Fuhrer and Moor (1995), Ireland (2003), Mankiw and Reis (2003), Wang and Wen (2004), among ohers. 15 For oher mechanisms ha can also generae hump-shaped oupu dynamics, see Wen (1998a,b,c) and Benhabib and Wen (2004). 19

21 Fig. 4. Effecs of Non-Moneary Shocks 5. Conclusion In his paper, we showed ha sicky prices can generae srong oupu persisence if money eners he economy via cash-in-advance consrain insead of via moneyin-uiliy. In paricular, we showed ha reaing invesmen goods as cash goods is crucial for sicky price models wih capial o generae hump-shaped oupu persisence. Empirically calibraed moneary shocks seem capable of explaining a broad range of business cycle facs a leas as well as echnology shocks. Hence wheher sicky prices and moneary shocks are responsible for he business cycle is no a heoreical quesion, bu raher an empirical one. Given ha muliple mechanisms, such as habi formaion in leisure (Wen 1998a), ime-o-build (Wen 1998b, which differs from Kydland and Presco 1982), capaciy uilizaion under increasing reurns o scale (Benhabib and Wen 2004, and Wen 1998c), facor hoarding and employmen adjusmen coss (Wen 2004), among many ohers, can give rise o hump-shaped oupu persisence, i would be ineresing o empirically es which mechanism 20

22 is he main culpri in propagaing he business cycle in he real world. Bills and Klenow (2003), for example, find some empirical evidence agains he sicky price propagaion mechanism of moneary shocks. Baharad and Eden (2004) find ha he saggered price seing assumpion is no favored by a micro daa. Wang and Wen (2004) show ha endogenous moneary policy, raher han sicky prices, are more likely o be responsible for inflaion dynamics in he U.S. Also, economic flucuaions in he 1970s and 1980s during he oil crises periods may provide an ineresing laboraory o es he moneary heory of he business cycle. Some promising iniial researches along his line can be found in Roemberg and Woodford (1996), Bernanke e al. (1997), Finn (2000), Barsky and Kilian (2001), Hamilon and Herrera (2004), and Aguiar-Conraria and Wen (2004), among ohers. 21

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