Working Paper Monetary aggregates, financial intermediate and the business cycle

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1 econsor Der Open-Access-Publikaionsserver der ZBW Leibniz-Informaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Hong, Hao Working Paper Moneary aggregaes, financial inermediae and he business cycle Cardiff Economics Working Papers, No. E2011/16 Provided in Cooperaion wih: Cardiff Business School, Cardiff Universiy Suggesed Ciaion: Hong, Hao (2011) : Moneary aggregaes, financial inermediae and he business cycle, Cardiff Economics Working Papers, No. E2011/16 This Version is available a: hp://hdl.handle.ne/10419/65767 Nuzungsbedingungen: Die ZBW räum Ihnen als Nuzerin/Nuzer das unengelliche, räumlich unbeschränke und zeilich auf die Dauer des Schuzrechs beschränke einfache Rech ein, das ausgewähle Werk im Rahmen der uner hp:// nachzulesenden vollsändigen Nuzungsbedingungen zu vervielfäligen, mi denen die Nuzerin/der Nuzer sich durch die erse Nuzung einversanden erklär. Terms of use: The ZBW grans you, he user, he non-exclusive righ o use he seleced work free of charge, erriorially unresriced and wihin he ime limi of he erm of he propery righs according o he erms specified a hp:// By he firs use of he seleced work he user agrees and declares o comply wih hese erms of use. zbw Leibniz-Informaionszenrum Wirschaf Leibniz Informaion Cenre for Economics

2 CARDIFF BUSINESS SCHOOL WORKING PAPER SERIES Cardiff Economics Working Papers Hao Hong Moneary aggregaes, financial inermediae and he business cycle E2011/16 Cardiff Business School Cardiff Universiy Colum Drive Cardiff CF10 3EU Unied Kingdom : +44 (0) f: +44 (0) ISSN June 2011 This working paper is produced for discussion purpose only. These working papers are expeced o be published in due course, in revised form, and should no be quoed or cied wihou he auhor s wrien permission. Cardiff Economics Working Papers are available online from: hp:// Enquiries:

3 1 Moneary aggregaes, nancial inermediae and he business cycle Hao Hong Cardi Business School Version: 20/06/2011 This paper explains and evaluaes he ransmissions and e eciveness of moneary policy shock in a simple Cash-in-Advance (CIA) economy wih nancial inermediaes. Lucas-Fuers s (1992) limied paricipaion CIA models are able o explain decreasing nominal ineres raes and increasing real economic aciviy wih moneary expansion hrough limied paricipaion moneary shock and he cos channel of moneary policy. Calvo s (1983) sicky price moneary model examines he real e ecs of money injecions hrough rms price seing behaviour, bu i fails o generae a negaive correlaion beween nominal ineres raes and money growh rae, which has been observed in he daa. This paper employs McCandless (2008) nancial inermediaes CIA model o explain he ransmissions and impacs of moneary shocks. The model does no reques limied paricipaion moneary shock or Keynesian ype of sicky price/wage, o examine he lower nominal ineres rae and increasing real economic aciviy wih moneary expansion. By exending he model wih Sockman s (1981) CIA consrain, i is able o accoun for boh posiive response of consumpion subjec o moneary innovaions, which has been found in Leeper e al. (1996) and he posiive correlaion beween oupu and consumpion which has been observed in he daa. Key Words: Moneary business cycle; nancial inermediae; cash-in-advance model Subjec Classi caion: E44; E52

4 2 1. INTRODUCTION The negaive correlaion beween shor-erm nominal ineres raes and money growh rae is an imporan moneary ransmission channel in boh radiional Keynesian (Tobin, 1947) and monearis (Friedman, 1968 and Cagan, 1972) macroeconomics models. The increasing real aciviy wih moneary expansion also has been recognised as sylise fac of he moneary business cycle. The sandard CIA models wih exible price from Lucas (1982) and Svensson (1985) indicae posiive correlaions beween money injecions and he nominal ineres raes. By a ecing leisure-consumpion subsiuion, he model generaes negaive e ecs on real economic aciviy 1. In conras, sicky price models are able o accoun for posiive correlaions beween moneary aggregaes and real aciviy hrough Calvo s (1983) price seing behaviour, bu i canno explain he negaive correlaion beween nominal ineres raes and money growh rae. Limied paricipaion CIA models were developed by Lucas (1990), and followed by Fuers (1992). Chrisiano and Eichenbaum (1995), and Chrisiano, Eichenbaum and Evan (1997) are able o explain he negaive response of nominal ineres raes, and he posiive response of real aciviy, o moneary innovaion under a exible price framework. Lucas (1990) modi ed sandard cash-in-advance economy by assuming ha households canno adjus heir consumpion-saving porfolio subjec o moneary innovaions o explain liquidiy e ec on nominal ineres rae. Since he supply of governmen bonds has been deermined by he amoun of savings from households before a moneary shock occurs, he money injecions increase he demand for governmen bonds and lower he reurn of bonds. This negaive response of bond rae subjec o moneary expansion has been referred as he liquidiy e ec of money growh rae. However, Chrisiano (1991) argued ha he inroducion of a liquidiy e ec ino he model may no be enough o generae a lower nominal ineres rae. He suggess ha he liquidiy e ec mus be su cienly srong o dominae he anicipaed in aion e ec. This, in urn, depends on he precise relaionship among is variables or he values of is parameers. The real impacs of moneary aggregaes hrough he liquidiy e ec from Fuers (1992), who supposed ha rms have o borrow from he capial marke o pay heir wage bills in advanced. Wih a lower borrowing rae, rms are more willing o increase heir borrowing from he capial marke and employ more labour. Wih a given iniial sock capial, an increasing labour demand raises he aggregae oupu hrough he producion funcion. This allows limied paricipaion CIA models o explain he posiive response of real aciviy o money injecions, wihou sicky price, hrough he cos channel of moneary policy. However, he weakness of his model is ha i fails o examine he increasing consumpion wih money injecions, and i canno generae he posiive correlaion beween oupu and consumpion which been observed in he daa. Chrisiano and Eichenbaum (1995), and Chrisiano, Eichenbaum and Evan (1997) modi ed he CIA consrain, which allows aggregae consumpion o be equal o he nex period of money demand. This modi caion generaes he behaviour of consumpion ha is observed in he daa. This paper employs McCandless (2008) nancial inermediaes CIA model o explain he ransmissions and impacs of moneary innovaion o real aciviy. The model includes wo nominal ineres raes which re ec he price of money a he goods and capial markes, respecively. Alhough his model is able o accoun 1 Cooley and Hansen (1995) referred as he in aion ax e ec of moneary aggregaes on real aciviy

5 3 for he posiive correlaion beween oupu and moneary aggregaes hrough wo nominal ineres raes, i fails o examine he behaviour of consumpion subjec o moneary expansion, such as he response of consumpion o moneary shock and correlaion wih oupu. Afer exending he model wih Sockman s (1981) CIA consrain, which indicaes ha boh consumpion and invesmen have o be purchased by households using real money balance, he model is able o explain he posiive response of consumpion subjec o moneary shock and also he replicae posiive correlaion beween oupu and consumpion in he daa. Sockman s (1981) CIA consrain is crucial o explain he behaviour of consumpion subjec o moneary innovaions. The paper is organised ino seven secions, he rs of which is his inroducion. Secion 2 presens he heoreical dynamic sochasic general equilibrium (DSGE) CIA model wih funcions of nanical inermediae. Secion 3 explains he procedure of model calibraions. Secion 4 discusses how he model s seady sae is a eced by he money growh rae. Secion 5 examines he model s dynamic and ndings. Secion 6 is a conclusion. 2. THE MODEL ECONOMY Figure 1: he srucure of model economy Household consumers U = E M P 1 0 β (ln c + Ψ ln x ) = 0 n = c + Ωi Firms y e w h + r k 1 y z g 1 α g α = ( l ) ( s k 1) R w h b = w h Moneary auhoriy u * T e + Θ 1) M = ( 1 n m R n Financial inermediaes n + T = b T Figure 1 describes he srucure of he model economy. The economy includes four represenaive agens, who are: household consumers, rms, nancial inermediaes, and he moneary auhoriy. I assumes ha money injecions from he moneary auhoriy are received by nancial inermediaes insead of households. Financial inermediaes also receive savings from households, money injecions from he cenral bank in he form of savings funds, and issue loans o rms in he capial marke. Firms have o borrow heir wage paymens from nancial inermediaes before any goods have been produced and pay wages, and capial and loan bills.

6 4 Households have o divide heir real money balance ino goods marke ransacion and savings which are paid o nancial inermediaes. Therefore, he model includes wo nominal ineres raes, which are: he ineres rae on he savings funds and he ineres rae on rms borrowing. The ineres raes are equal wihou money injecions. Money injecions lower he ineres rae on rms borrowing wih excess demand in he capial marke, and increase he ineres rae on savings funds hrough an expeced in aion e ec. The lower nominal ineres rae a capial marke has posiive e ec on real economic aciviy hrough marginal cos of labour and he increasing saving rae on saving has negaive e ec hrough leisure-consumpion susbiuion Household Consumers Represenaive households maximise heir expeced log uiliy funcion (1), which includes consumpion c and leisure x, wih discoun facor 2 (0; 1), and allocae heir ime endowmen beween leisure and working hours h. U = E 0 1 X =0 (ln c + ln x ) (1) 1 = x + h (2) Aggregae oupu y includes consumpion and invesmen i goods. The nex period s physical capial socks k have o be accumulaed hrough he law of moion equaion, wih a consan quarerly depreciaion rae. y = c + i (3) i = k (1 )k 1 (4) A he beginning of each period, he iniial real money balance is held by households and divided ino he amoun of savings and goods marke ransacion. Households have o deposi heir saving funds ino nancial inermediaes, and receive a gross ineres rae R m. Cash is he only exchange echnology which can be used for goods marke ransacions. Equaion (5) represens he exchange echnology consrain ha is faced by households in he goods marke. The model assumes ha money injecions are received by nancial inermediaes insead of households. This indicaes ha money injecions from he cenral bank do no ener a CIA consrain a he goods marke. Where n represens households savings, P represens price level, and M 1 represens he iniial nominal money sock. M 1 P n = c + i (5) When = 0 he exchange consrain implies ha he real money balance is used o purchase consumpion goods only. When = 1 he exchange echnology consrain represens ha boh consumpion and invesmen goods can be purchased by real money balance, which is indicaed by Sockman s (1981) CIA consrain. The nex period s money holding includes labour w h, capial r k 1, and saving

7 5 incomes R m n. And he expendiures are on consumpion, invesmen, and savings. The lifeime budge consrain which is faced by households is represened in equaion (6). M P = M 1 P + w (1 x ) + r k 1 + R m n n c k + (1 )k 1 (6) Equilibrium condiions of households are represened by equaions (7)-(11), which come from maximising he expeced log uiliy funcion subjec o lifeime and good marke CIA consrains. 1 c = + (7) x c = Rm w (8) 1 + = R m (9) P c E ( R m ) = 1 (10) P +1 c +1 E [ +1 (r ) + (1 ) ] = 1 + (11) Where and represen he shadow price of lifeime and goods marke CIA consrain. Equaion (9) implies ha he marginal cos of money is equal o he saving rae across equilibrium. The Fisher s relaion, which saes ha he nominal ineres rae on he savings fund depends on expeced in aion and curren-fuure consumpion subsiuion, has been indicaed by equaion (10). Clearly, equaion (8) indicaes he nominal ineres rae on he savings fund has a posiive e ec on leisure-consumpion subsiuion. I re ecs ha he expeced in aion e ecs of money growh rae have a negaive impac on real aciviy. Equaion (7) and (9) show ha he marginal uiliy of consumpion depends on he lifeime shadow price and he marginal cos of money. The model s Euler equaion is represened by equaion (11). When = 0 he exchange consrain is represened by equaion (5), his implies a sandard CIA consrain in which consumpion and invesmen are subsiuion goods. The Euler relaionship which is represened by equaion (12) indicaes ha boh he curren and fuure consumpion subsiuion is a eced by he real ineres rae and he movemen of he nominal ineres rae on he savings fund. Moneary injecions raise he nominal ineres rae on savings hrough an expeced in aion e ec. This has a negaive e ec on money holding and lowers consumpion hrough he CIA consrain. c R m E [ c +1 R+1 m (r )] = 1 (12) If = 1 hen he exchange consrain which is represened by equaion (5) indicaes ha Sockman s CIA consrain is applied, which indicaes ha consumpion and invesmen goods are complemenary goods. The Euler relaionship which is represened by equaion (13) indicaes ha subsiuion beween curren and fuure marginal consumpion of uiliy depends on a real ineres rae which is discouned

8 6 by he marginal cos of money. According o equaions (7) and (13), he behaviour of consumpion subjec o money injecions depends on he real ineres rae and he marginal cos of money. Moneary expansion increases he marginal cos of money hrough an in aion e ec of he money growh rae, and has a negaive e ec on consumpion. Real ineres raes rise wih money injecions as oupu increases, and have a posiive e ec on consumpion. Therefore, consumpion increases wih money injecions as he real ineres rae dominaes he expeced in aion e ec. c E [ ( r )] = 1 (13) c +1 R m Financial Inermediaes The funcion of nancial inermediaes is followed Fuers (1992) and McCandless (2008) ha money injecions are received by nancial inermediaes insead of households. The cash ow consrain which has been faced by nancial inermediaes is represened by equaion (14). n + T = b (14) Where T sands for money injecions from he cenral bank, and b denoes he demand of he capial marke. By assuming ha nancial inermediaes have zero pro, he gross reurn of he saving fund which is received by households is equal o he income of nancial inermediaes from he capial marke; his is indicaed by equaion (15). R m n = R b (15) Where R m represens he nominal ineres rae on savings, and R sands for he nominal ineres rae on borrowing a he capial marke. The money injecions from he cenral bank which are received by nancial inermediaes increase he loan able funds for he capial marke. They have a negaive e ec on he borrowing rae in order o increase he loan able money supply of he capial marke. This indicaes ha here is a lower nominal ineres rae on he capial marke wih moneary expansion Firms Aggregae oupu is produced by represenaive rms hrough he Cobb-Douglas producion funcion; wih labour, capial sock, and exogenous echnology. The shares of labour and capial are 1 and, respecively. y = e z h 1 k 1 (16) The exogenous Toal Facors Produciviy (TFP) is assumed o follow an AR (1) process wih auoregressive parameer z, and srucure shock " z. z = z z 1 + " z (17) Following Fuers s (1992) assumpion, goods producing rms are he only borrowers a he capial marke and hey have o borrow cash from capial marke for wage paymen before any goods have been produced. This creaes an addiional CIA consrain which is faced by rms a capial marke, represened by equaion

9 7 (18). Therefore, a lower nominal ineres rae on borrowing wih moneary expansion reduces he marginal cos of labour and encourages rms o employ more labour and raise aggregae oupu. This has been referred o in he lieraure as he cos channel of moneary policy. b = w h (18) The aggregae incomes of rms include capial marke borrowing and goods marke sales. The capial marke income is used o pay wages. Goods marke income is used for rening capial and borrowing paymens. Equaion (19) indicaes ha a lifeime budge consrain has been faced by rms. Represenaive rms maximise heir producion funcion subjec o heir lifeime budge and capial marke CIA consrain o obain he marginal cos of labour and capial, which are indicaed by equaions (20) and (21). R w h + r k 1 = y (19) R w = (1 ) y h (20) r = y k 1 (21) Where w and r represens he real wage and real ineres rae, respecively. Equaion (20) indicaes ha he marginal cos of labour is varied wih he borrowing rae a he capial marke. This furher implies ha an increasing borrowing rae has a negaive e ec on labour demand, while a decreasing borrowing rae has a posiive e ec on labour demand. In conras o a sandard CIA model, here is a gap beween household labour income and rms labour coss in his model. The gap, which is given by (R 1)w h, can be considered as a nancial fricion wih money injecions. I allows he borrowing rae o be varied wih money injecions. Moneary expansion a ecs real economic aciviy hrough he labour demand equaion as he marginal coss of labour are varied wih he nominal ineres rae on borrowing Moneary Policy The moneary policy ha has been implemened by he cenral bank hrough he money supply rule is represened by equaion (22). M = M 1 + T (22) Moneary expansion has been represened by equaion (23). I indicaes ha money injecions from he cenral bank depend on seady-sae money growh rae, moneary shock e u, and he iniial money sock. T = ( + e u 1)M 1 (23) The deviaion of he money growh rae was assumed o follow AR (1) process, wih auoregressive parameers m and srucure shock " m. u = m u 1 + " m (24)

10 Compeiive Equilibrium Compeiive equilibrium of his economy consiss of a se of feasible allocaions {y, c, k, M, h, n, x }, a se of prices{r, w, R m, R }, exogenous shocks{z, u }, and aggregae oucomes, such ha: Given r, w, R m, allocaion c, k, M, x, n, solves he households problem; Given r, w, R, allocaion h, k, y, solves he rms problem; The goods, labour, and money marke are clear; 3. CALIBRATION The procedure of calibraing deep srucure parameers is o map he model economy ino he observed feaures of daa. This means ha he seady-sae value of he variables can be implied by he deep srucure parameers. Wih given deep srucure parameers, he model s seady-sae can generae grea raios which can be observed direcly from daa. Table 1 concludes he behaviour of echnology and moneary shocks. Seadysae echnology shock has o be normalised equal o one. Auoregressive process and variaion of echnology shock follows Cooley and Hansen (1995), which has a persisence parameer of 0.95 and a variance of srucure shock of 0.7%. The persisence and variance of money growh rae will be esimaed from following he M1 money growh rae regression, wih ime duraion from 1959Q4 o 2009Q4. The resuls indicae ha here is a 1.2% money growh rae per quarer a seadysae, wih a persisence of This compares wih Cooley and Hansen (1995) who had seady-sae money growh raes of 1.3%, wih a persisence of I also compares wih Benk, Gillman and Kejak (2005) who found a 1.23% seadysae money growh rae, wih a persisence of The variance of moneary shock from M1 regression is 0.9%, which is also close o he resuls of Cooley and Hansen (1995) and Benk, Gillman and Kejak (2005), which are 0.89% and 0.1%, respecively. log M = 0: :64 log M 1 (0:0009) (0:0545) Table 1 also summarises he base line deep srucure parameers, which can be implied from wo groups of U.S daa. Firsly, he daa se from Gomme and Ruper (2007) wih duraion from 1948 Q1 o 2004 Q2 indicaes ha he quarerly depreciaion rae is 0.024, which compares wih he resuls of Cooley and Hansen (1995) which found ha. I also indicaes ha he invesmen-oupu raio is Wih a given depreciaion rae and invesmen oupu raio, he seady-sae capial-oupu raio is going o be There are wo sources of income for households, which are: labour and capial income. Capial and labour income shares are calibraed in he model by using U.S daa from 1950 Q1 o 2009Q4. The daa implies ha he share of wage income is equal o 0.6, and which compares wih he resuls of Cooley and Hansen (1995) which were ha. Wih a capial share of 0.4, a depreciaion rae 0.024, and a capial-oupu raio of 10.8, he model implies ha he real ineres rae is equal o before depreciaion rae. Since he quarerly seady-sae in aion is equal o he money growh rae, he seady-sae Euler equaion implies ha he preference parameer is equal o U.S daa also indicaes ha he seady-sae working hours from he goods producing secor and leisure are 1/3 and 2/3, respecively.

11 9 This requires deep srucure parameers which are equal o Wih Sockman s (1981) CIA consrain, he model s Euler equaion and grea raios imply ha is equal o 0.988, and ha is equal o Table 1: Baseline parameers Preferences 0.987/0.988 Discoun facor wih/wihou Sockman CIA consrain 1.58/1.59 Leisure weigh wih/wihou Sockman CIAconsrain Goods Producion 0.4 Capial share in goods secor Capial sock depreciaion rae e z 1 Good secor produciviy parameer Moneary auhoriy 1.2% Quarerly money growh rae Shocks processes Auocorrelaionparameers z 0.95 Goods secor produciviy m 0.64 Money growh rae Sandard Deviaion of Shock Innovaions z 0.7% Goods secor produciviy m 0.9% Money growh rae Table 2: Targe values ss 1.2% Quarerly in aion rae i ss =y ss 0.26 Invesmen-oupu raio k ss =y ss 10.7 Capial-oupu raio x ss 2/3 Leisure 4. MONETARY TRANSMISSIONS AND REAL ACTIVITIES AT STEADY-STATE This par of paper discusses moneary properies of model a saionary sae wih varying money growh rae. Firs of all, he in aion e ec of he money growh rae a a saionary-sae is given by equaion (25), which indicaes a posiive correlaion beween he nominal ineres rae on saving and he rae of in aion. By combining he households and rms seady-sae CIA consrain, equaion (26) and (27) re ecs a negaive relaionship beween borrowing and in aion raes a a saionary-sae. In oher words, he saionary sae money growh rae is posiively correlaed wih he saving rae, and negaively correlaed wih he borrowing rae a capial marke. R m ss = ss (25) R ss = 1 ss c ss (mss m ss c ss ) (26) R ss = 1 ss y ss (mss m ss y ss ) (27)

12 10 Wih a sandard CIA consrain, he model s saionary sae Euler relaion, which is represened by equaion (28), indicaes ha he real ineres rae is independen of he rae of in aion and leads o grea raios such as invesmen oupu, consumpion oupu and capial oupu raios, which are independen o he rae of in aion or he moneary growh rae. Wih Sockman s (1981) CIA consrain, he model s saionary sae Euler relaion, which is implied by equaion (29), indicaes ha he real ineres rae varies wih in aion or money growh rae, and leads boh real price and grea raios o vary wih he money growh rae. This re- ecs he hird moneary ransmission channel a saionary-sae, which has been called a real ineres rae e ec of he money growh rae. yss k ss = rss = (28) yss k ss = rss = ( ) ss Since he rms wage bill varies wih he lending rae, boh leisure-consumpion and leisure-labour subsiuions are a eced by he saving rae, and he borrowing and real ineres raes. The e ecs of saving, borrowing, and real ineres raes on leisure-consumpion and leisure-labour subsiuions a a saionary sae will be considered as in aion, liquidiy, and real ineres rae e ecs of he money growh rae. Wih a sandard CIA consrain, he real ineres rae e ec is zero because real prices are independen of he money growh rae. Furhermore, he negaive e ec of moneary aggregaes on leisure-labour subsiuion hrough saving rae is dominaed by posiive e ec of money growh rae hrough borrowing rae, equaion (31) indicaes lower leisure-labour raio wih money growh rae, which means increasing labour supply. Equaion (32) indicaes lower capial-labour raio wih money growh rae due o borrowing rae channel. This is he opposie of he Tobin e ec (1965), where increases in he seady-sae money growh rae will also increase he capial-labour raio. And consisen wih Sockman (1981) argumen, where i needed he Sockman CIA consrain and he model does no. I is increase capial sock hrough equaion (32) and raises he aggregae oupu hrough Cobb-Douglas producion funcion; he level of invesmen wih he law of moion equaion. Wih a Sockman CIA consrain, equaion (30)-(32) indicaes ha he money growh rae has a negaive e ec on leisure-labour subsiuion hrough he borrowing rae; posiive e ec hrough saving rae and he real ineres rae. If a negaive e ec from he borrowing rae is dominaed by he posiive e ec from he saving and real ineres rae, hen he model concludes ha here is an increase in leisure and a decrease labour supply wih he moneary aggregaes. This is lower capial socks wih equaion (32) and aggregae oupu hrough producion funcion. x ss h ss = (29) i ss = yss r ss (30) Rm ssr ss c ss (1 )y ss (31) k ss h ss = Rss w ss (1 )r ss (32)

13 11 In conclusion, he nancial inermediae CIA model wih sandard consrain indicaes boh a real ineres rae and grea raios which are independen o he money growh rae a saionary-sae. By assuming ha rms borrow funds from he capial marke o pay he wage bill in advance, real wages are varied wih he borrowing rae and his leads o a leisure-labour subsiuion which is a eced by boh he saving rae from Fisher relaion and by he bond rae from he wage equaion. A rising saionary sae money growh rae will increase he goods secor labour demand, he capial sock, and he level of real aciviies. Therefore, he model generaes he posiive e ec of he money growh rae on real aciviy a saionary-sae. By exending he model wih Sockman s (1981) CIA consrain, he model indicaes ha boh he real ineres rae and he consumpion-oupu raio are increased wih he saionary sae money growh rae. This leads leisure-labour subsiuion o a ec he saving rae, bond rae, and consumpion-oupu raio. Increasing he saionary sae money growh rae will lower he level of real aciviies since he posiive e ec of liquidiy e ec is dominaed by negaive e ecs of saving rae and real ineres rae. Therefore, he model wih sockman consrain generaes he negaive e ec of he money growh rae on real aciviy a saionary-sae. 5. THE MODEL S DYNAMIC AND SIMULATION This par of he paper analyses he dynamic behaviour of moneary ransmissions, discusses he e eciveness of moneary policy shock on real economic aciviy hrough various moneary ransmission channels, and evaluaes he e eciveness of he model economy wih business cycle facs The E ecs on Nominal Ineres Raes The e eciveness of moneary aggregaes on nominal ineres raes is invesigaed hrough he cenralised economy as follows. The represenaive agens problem under a cenralised economy can be considered as maximising he expeced uiliy subjec o lifeime, goods marke CIA consrains, and capial marke CIA consrains. max E 0 1 X =0 (ln c + ln x ) + ( m 1 + r k 1 + w (1 x ) + (R m 1)n m c k (R 1)b + (1 )k 1 + ( m 1 n c ) + (b w (1 x )) n : (R m 1) = (33) b : (R 1) = (34) m : E ( ) = (35) Fisher relaions on nominal ineres raes for he borrowing and saving funds have been represened by following equaions, where = (R R m ) :

14 R = ( ) + ( + ) E ( ) (36) R m + = E ( ) Clearly, here is only an in aion e ec on he saving rae and he liquidiy e ec on he borrowing rae depends on. Wih equaion (14) and (15), he borrowing rae is less han he saving rae wih posiive money injecions from he cenral bank, which implies ha he liquidiy e ec erm is negaive. This is because he value of cash in he capial marke is less han he value of cash in he goods marke as money injecions are received by nancial inermediaes and loaned o rms in he capial marke. (37) 5.2. Moneary Transmissions and Real E ecs Figure 2: Variables response o a 1% posiive echnology shock Figures 2 and 3 re ec he moneary ransmissions and real variables response o 1% posiive echnology and moneary shocks in he model economy, boh wih and wihou a Sockman CIA consrain. A negaive response of in aion o echnology shock re ecs he couner-cycle behaviour of he price level. Real economic aciviies are increased wih a echnology shock. The moneary ransmissions which include savings and borrowing raes have a posiive response o a echnology shock. The responses of velociy o a echnology shock re ec he relaionship beween he exchange echnology consrain and he quaniy heory of money. The Sockman ype of exchange echnology consrain implies ha velociy does no move wih a echnology shock due o he e eciveness of echnology shock on oupu which is 12

15 13 re eced by real money demand. The sandard ype of exchange echnology consrain indicaes ha only he e eciveness of echnology shock on consumpion is re eced on real money demand. Because he oupu increases more han consumpion wih a echnology shock, he quaniy heory of money requess a velociy increase wih oupu. Figure 3: Variables response o a 1% posiive moneary shock For he model wih a sandard CIA consrain, he posiive response of he saving rae o moneary expansion re ecs he expeced in aion e ec of money growh rae. This has been referred o by Cooley and Hansen (1995) as an in aion ax e ec and i has a negaive e ec on real economic aciviy. Since he money injecions are received by nancial inermediaes insead of households, and have o be loaned o rms for wage paymens in he capial marke, i creaes excess demand in he capial marke. Since he supply of he capial marke is deermined by real aciviy (which is rms wage bills) nancial inermediaes have o lower he borrowing rae in order o allow he exra savings funds o be loaned o rms a he capial marke. I leads negaive response of he borrowing rae subjec o moneary expansion and has a posiive e ec on real aciviy hrough he marginal cos of labour. In oher words, here are wo moneary ransmission channels when he sandard CIA model is exended wih funcion of nancial inermediaes, which are: saving and borrowing raes. The money injecions increase leisure, decrease he labour supply, and have a negaive e ec on real aciviy hrough he saving rae channel. They decrease he leisure, increase labour demand, and have a posiive e ec on oupu hrough he borrowing rae channel. Figure 3 concludes ha boh employmen and oupu are increased wih moneary expansion because he posiive e ec from he borrowing rae dominaes he negaive e ec from he saving rae. The model wihou Sockman CIA consrain fails o generae he behaviour of consumpion subjec o moneary shock since he consumpion is decreased insead of increased wih moneary expansion. This indicaes ha he posiive e ec from

16 14 he borrowing rae canno dominae he negaive e ec from he saving rae on consumpion. Beside he borrowing and saving raes, he model wih a Sockman CIA consrain inroduces an addiional moneary ransmission channel hrough he real ineres rae in he Euler equaion, and has posiive e ecs on real aciviy, paricularly on consumpion. This allows he model o overcome he weakness on consumpion behaviour. Figure 3 shows ha he consumpion does increase wih moneary expansion since he posiive e ec from borrowing rae is able o dominae he negaive e ec from he saving rae, wih a lower subsiuion rae 2 of consumpion due o he Sockman CIA consrain. The velociy has negaive response o moneary shock since money demand increases more han aggregae oupu. Therefore, he CIA model which employs he Sockman CIA consrain, and assumes ha money injecions are received by nancial inermediaes insead of households, is able o examine he behaviour of real aciviy subjec o moneary expansion hrough he cos channel of moneary policy under a exible price framework, wihou a limied paricipaion moneary shock Business Cycle Facs Table 4 describes conemporaneous correlaions wih aggregae oupu from he log derended ime series daa wih duraion from 1959Q1 o 2004Q2. I also summarises he simulaed economy saisics wih boh echnology and moneary shocks. The saisics of simulaion are compued from an ari cial ime series consiss of 182 periods wih 50,000 imes simulaions. In order o compare hese resuls wih real daa saisics, i has o be aken logged and derended by a Hodrick-Presco ler. When a sandard CIA consrain is applied (where = 0), he moneary innovaion is able o generae a posiive correlaion beween he nominal ineres rae and oupu; however, i fails o replicae he posiive correlaion beween aggregae oupu and consumpion. Therefore, i does no imply he consumpion behaviours which have been observed in he daa. By exending he model wih Sockman s (1981) consrain (where = 1), he model is able o overcome he weakness of he model economy (i.e. consumpion behaviour canno explained) and is able o replicae he posiive correlaion beween oupu and consumpion. Table 4: Conemporaneous correlaions wih aggregae oupu Daa = 0 = 1 Oupu 1:00 1:00 1:00 Consumpion 0:79 0:11 0:91 Invesmen 0:92 0:89 0:99 Employmen 0:82 0:81 0:80 Treasury bill rae 0:24 0:47 0:38 6. CONCLUSION This paper inegraes he CIA economy wih he funcion of nancial inermediaes, and allows money injecions o be received by nancial inermediaes insead 2 The subsiuion rae refers o he real ineres rae discouned by saving rae, which is indicaed by he model s Euler equaion.

17 of households. I is, herefore, able o explain he ransmission and real impacs of moneary aggregaes wihou sicky price/wage and limied paricipaion moneary shock. For he model wih a sandard CIA consrain, money injecions increase he saving rae hrough an expeced in aion e ec, and have a negaive e ec on labour supply. A he same ime, i lowers he borrowing rae a he capial marke and has a posiive e ec on labour demand hrough he marginal cos of labour. Since he posiive e ec on labour demand dominaes he negaive e ec on labour supply, employmen rises wih moneary expansion and increases oupu hrough he producion funcion. However, he model wih a sandard CIA consrain is unable o explain he behaviour of consumpion because consumpion has a negaive response o moneary shock, and here is a negaive correlaion beween consumpion and oupu. By replacing he sandard CIA consrain wih a Sockman consrain, he model s Euler equaion indicaes ha he subsiuion of curren and fuure marginal uiliy of consumpion is a eced by he real ineres rae discouned by saving rae. This means ha he real ineres rae is a eced by he money growh rae hrough Euler equaion, and inroduces a posiive e ec of moneary expansion on real ineres rae wih an increasing saving rae. This has been considered as a hird moneary e eciveness channel (which is referred o as a real ineres rae e ec in his chaper). An increasing real ineres rae wih a posiive moneary shock has a posiive e ec on consumpion. When combined wih a lower borrowing rae a he capial marke, hey are able o dominae he expeced in aion e ec on consumpion and replicae he consumpion behaviour which has been observed in he daa. Sockman s (1981) CIA consrain plays a major rule o obain a posiive response of consumpion o moneary expansion, and a posiive correlaion beween oupu and consumpion is observed in he daa. In a word, he paper employs McCandless (2008) working capial CIA model by replacing moneary ransacions services wih Sockman s (1981) CIA consrain, which exchanges he echnology used for boh consumpion and invesmen, o explain he real e ecs of moneary shock and he moneary ransmission mechanism. The model does no reques limied paricipaion moneary shock from Lucas (1990), bu i does assume ha money injecions are received by nancial inermediaes insead of households o generae he real impacs of moneary aggregaes. The model wih sandard CIA consrain which from McCandless (2008) canno explain he behaviour of consumpion and generae negaive correlaion beween consumpion and oupu. The paper employs he Sockman CIA consrain o explain he cyclical behaviour of consumpion and velociy. I generaes a posiive response of consumpion and a negaive response of velociy o moneary innovaion, and a posiive correlaion beween oupu and consumpion. The nancial inermediae CIA model wih Sockman s (1981) consrain no only generaes he posiive response of oupu, consumpion, and invesmen o moneary expansion bu also he negaive response of he nominal ineres rae o moneary shock. I is able o explain boh moneary ransmissions and he impacs of moneary shock o real aciviy wihou limied paricipaion moneary shock and sicky price/wage seing. 15

18 16 REFERENCES [1] Cagan, P., (1972) The Channels of Moneary E ecs on Ineres Raes, Columbia Universiy Press, New York [2] Chrisiano, L.J., (1991) Modelling he liquidiy e ec of a money shock, Quarerly review, Federal Reserve Bank of Minneapolis, 15, 3-34 [3] Chrisiano, L.J., Eichenbaum, M., (1995) Liquidiy e ecs, moneary policy and he business cycle, Journal of Money, Credi and Banking 27, [4] Chrisiano, L.J., Eichenbaum, M., Evans, C.L., (1997) Sicky prices and limied paricipaion models: a comparison, European Economic Review 41, [5] Thomas F Cooley and Gary D Hansen (1995) Money and Business Cycle, in Froniers of Business Cycle Research (T. F. Cooley, Ed.), Princeon Universiy Press [6] Fuers, Timohy S (1992) Liquidiy, loanable funds and real aciviy, Journal of Moneary Economics 29, 3-24 [7] Friedman, Milon (1968) The role of moneary policy, American Economic Review, 58:1, 1-19 [8] Lucas, Rober E (1990) Liquidiy and ineres rae, Journal of Economic Theory 50, [9] George McCandless (2008) The ABDs of RBCs: An Inroducion o Dynamic Macroeconomic Models, Harvard Universiy Press [10] Alan C. Sockman (1981) Anicipaed in aion and he capial sock in a cash in advance economy, Journal of Moneary Economics 8, [11] James, Tobin ( ) Liquidiy preference and moneary policy, Review of Economics and Saisics 29:2, ; 30:4, [12] Tobin, J (1965) Money and economic growh, Economerica, 33(4)(Par2),

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