A COMPARISON OF EXCHANGE ECONOMIES WITHIN A MONETARY BUSINESS CYCLE

Transcription

1 The Mancheser School Vol 73 No. 4 Special Issue A COMPARISON OF EXCHANGE ECONOMIES WITHIN A MONETARY BUSINESS CYCLE by SZILÁRD BENK Magyar Nemzei Bank, Cenral European Universiy MAX GILLMAN Cardiff Business School, Cenral European Universiy, Economics Insiue of he Hungarian Academy of he Sciences and MICHAL KEJAK* CERGE-EI The paper ses ou a moneary business cycle model wih hree alernaive exchange echnologies: he cash-only, shopping ime and credi producion models. The goods produciviy and money shocks affec all hree models, while he credi model has in addiion a credi produciviy shock. The paper compares he performance of he models in explaining he puzzles of he moneary business cycle heory. The credi model improves he abiliy o explain he procyclic movemen of moneary aggregaes, inflaion and he nominal ineres rae. Inroducion The conribuion of moneary facors o business cycle movemens has been sudied using he general equilibrium approach in he cash-in-advance economies of Cooley and Hansen (989, 995, 998) and he shopping ime model of Gavin and Kydland (999) and Dimar e al. (25). While money supply shocks have been found o have lile effec on business cycles, suppored also in Ireland (24) and Benk e al. (25), here are sill many nominal feaures ha presen a challenge for general equilibrium moneary modeling. For example, inflaion persisence resuls in he model of Dimar e al. (25) hrough he use of Taylor rules of money raher han simple growh rae rules. Liquidiy feaures have no been well explained in he inflaion ax models alhough recen work has brough a rudimenary liquidiy effec ino oherwise sandard exchange-based economies wihou imposing nominal rigidiies; his is hrough he use of a credi producion secor in Li (2). Explaining procyclic moneary aggregaes and inflaion rae move- *The auhors are graeful o Cenral European Universiy and o he World Bank Global Developmen Nework for gran suppor, he hird auhor o he Czech Republic gran 42/2/393. We hank he referees of he journal for very good commens and are also graeful o paricipans a he Norh American Economeric Sociey 25 Meeings, he Sociey for Economic Dynamics 24 Meeings, he CGBCR 24 conference, he GDN 24 workshop in Prague and he RES 25 meeing. Published by Blackwell Publishing Ld, 96 Garsingon Road, Oxford OX4 2DQ, UK, and 35 Main Sree, Malden, MA 248, USA. 542

2 Comparison of Exchange Economies 543 mens has been even more elusive. A procyclic inflaion movemen is found only in Dimar e al. (25) when here is negaive or near-zero feedback from oupu in he Taylor rule, whereas his feedback parameer is ypically esimaed a higher posiive levels. Exending he exchange economy by allowing for he producion of credi as an alernaive o cash, while mainaining a simple money supply growh rule, has found success in oher relaed areas besides he liquidiy effec. These include he modeling of he income velociy of base, M and M2 moneary aggregaes (Gillman and Kejak, 24), he explanaion of he effec of inflaion on growh (Gillman and Nakov, 24; Gillman and Kejak, 25a, 25b) and he specificaion of a role for financial developmen wihin he inflaion growh nexus (Gillman and Harris, 24; Gillman e al., 24). Using he credi producion echnology also has shown promise in explaining oupu movemens during financial deregulaory periods a business cycle frequencies (Benk e al., 25). Here he paper applies he credi producion approach o he business cycle in order o compare his exchange echnology exension o more sandard approaches, he cash-in-advance and shopping ime models. A simple money supply rule is mainained. Velociy is endogenous and he resuls sugges ha he credi producion approach improves he abiliy of he inflaion ax models o explain business cycle movemens. In paricular he paper demonsraes ha he credi producion model can explain procyclic movemens in moneary aggregaes, inflaion and nominal ineres raes while he sandard models canno. Such poenial improvemens make sense inuiively in ha hey resul from exploiaion of an addiional margin, relaive o he sandard cash-inadvance economy. A similar margin exiss in he shopping ime model bu i is rarely exploied here; and shocking he shopping ime is awkward in is raionale. The margin included by he credi approach is he abiliy of he agen o rade-off beween using cash and using credi in exchange, depending on relaive coss. Cash-only models do no have his freedom and shopping ime approaches specify a general ransacions cos ha induces a margin beween using money and using ime for exchange. This money ime rade-off can be described as a broad-brush approach ha he credi approach refines by specifying labor ime ha is used in a diminishing reurns producion funcion for credi services as an alernaive o money in exchange. A disinc advanage of he credi approach relaive o shopping ime is ha he credi producion funcion can be shocked, and calibraed using ime-series daa from he bank secor. For example, he credi shock in a credi producion approach has been idenified robusly in Benk e al. (25). Boh Alvarez e al. (2) and Schaber (23) show condiions under which Taylor ineres rae rules can be equivalen o simple money supply growh rules.

3 544 The Mancheser School Exploiaion of he addiional margin allows for addiional income and subsiuion effecs ha improve he moneary business cycle model s performance during cerain periods. The income effec is imporan when for example here is a posiive credi shock ha also conribues significanly o GDP. Benk e al. (25) demonsrae ha several of hese appear o exis in he USA during he 98s and 99s, and for example ha hese conribued o even bigger increases in GDP during he upswings saring in 982 and 99. The income from he posiive credi shock causes an addiional upward increase in consumpion and money demand no presen in he oher models. And his is he inerpreaion given for he model s abiliy o explain procyclic moneary aggregae (M) movemen. The subsiuion effec is imporan in erms of he use of money versus credi in he purchase of he consumpion baske. Consider ha a posiive shock o he produciviy of he credi secor causes credi use o become less expensive, and induces more credi o be used relaive o cash in exchange. This acs o decrease money demand in he face of an unchanged money supply growh rae. The level effec on money demand causes he price level o jump and he inflaion rae o pulse upwards. Coninuing wih he example of he financial deregulaion of he 98s in he USA, he inflaion rae would have been pulsed upwards from he deregulaory acs even while he money supply growh rae began o fall; he resul would be an inflaion rae ha did no fall as quickly as expeced (by he money supply growh raes) and a endency for a procyclic inflaion rae when he credi shock conribues significanly o oupu changes. This significan effec on oupu would only occur wih relaively large, occasional, credi shocks such as major deregulaions. This ype of subsiuion likewise carries over o explain how he credi model beer explains observed procyclic nominal ineres rae movemens no explained wih he shopping ime or sandard cash-in-advance models. And so he credi model improves upon he abiliy o explain an observed procyclic naure of moneary aggregaes, he inflaion rae and he nominal ineres raes, bu does his mos plausibly during subperiods conaining srong credi shocks. 2 Exchange-based Business Cycle Models Three represenaive agen models are examined: he sandard cash-inadvance, a shopping ime economy and he credi producion economy. Here a nesed model of he hree economies is presened. Wih uiliy over consumpion c and leisure x given by  U = E b ( logc + Y logx) < b < = he consumer faces a minimum of wo shocks in all hree models: an aggregae oupu produciviy shock and a money supply growh rae shock. The ()

4 Comparison of Exchange Economies 545 hird shock inroduced in he credi economy is o he produciviy of credi producion. Curren invesmen i plus he depreciaed capial from he las period comprise he curren capial sock k : k = ( -d) k- + i (2) Oupu y is produced by he agen wih he previous period capial sock k - and curren labor n via a Cobb Douglas consan-reurns-o-scale producion funcion wih he produciviy shock z : z a -a y = e k- n (3) 2 z = jzz- + ez ez ~ N(, se z) < jz < (4) Firms maximize heir profis y - r k - - w n + ( - d)k -, implying he equilibrium real wage rae w and he real gross capial rae of reurn ne of depreciaion d, or r : z a -a w = ( -a) e k- n (5) z a- -a r = ae k- n + -d (6) Curren income from labor, capial and lump-sum ransfers of new money T are spen on consumpion c and capial, yielding he change in money sock M - M -. Wih P he nominal price of he consumpion good, his gives he period budge consrain as wp( -x -lf )+ Prk -+ T -Pc -Pk M -M- (7) The money supply is subjec o a sequence of random nominal ransfers ha saisfy u T = QM- = ( Q* + e -) M- (8) where Q is he random growh rae of money, Q* is he saionary growh rae of money and u is a random auoregressive process given by 2 u = juu- + eu eu ~ N(, se u) < ju < (9) The oher resource consrain allocaes he oal ime endowmen among leisure, labor hours in producing he aggregae oupu and ime spen in exchange aciviy, denoed by l F : n + x + l = () F 2. Exchange An exended cash-in-advance consrain is specified so ha i encompasses hree alernaive exchange echnologies. The general form is b b2 M - + T Pc ( B -B c A l ) () 2 F F

5 546 The Mancheser School where B, B 2, b and b 2 are parameers, and à F is a variable, specified in he following special cases. 2.. Cash-only. For he sandard cash-in-advance economy ha uses only cash, le B = and B 2 = Shopping Time. The shopping ime case assumes ha à F is a posiive parameer A F, B =, B 2 =-, b = and b 2 =-; or M + T - Pc AF lf (2) This implies a proporionaliy of he ime spen in shopping o he consumpion velociy of money; or ha l F = A F [c /(M /P )]. While he more general form of he shopping ime funcion is l F = f(c, M /P ), f c >, f M/P <, he paricular specificaion wih proporionaliy o velociy is found in Gavin and Kydland (999) and Lucas (2), jusified because i yields a consan ineres elasiciy of money demand equal o -.5 as in Baumol (952). Given ha ime in exchange aciviy is proporional o velociy, his implies a uniary elasiciy of exchange ime wih respec o velociy; ( l F / V )(V /l F ) = where V c /(M /P ). Or if he elasiciy is defined in erms of he raio of exchange ime o consumpion, where h [ (l F /c )/ V ][V /(l F /c )], hen again h = Credi Producion. Here à F = A F e n, B =, B 2 =, b =-g and b 2 = g, or -g n g M- + T Pc ( -c AFe lf ) (3) I is assumed ha g Œ (, ), A F > and ha he shock n follows an auoregressive process: 2 u = jnn- + en en ~ N(, sen) < jn < (4) Noe ha he credi secor specificaion, supplying only a means of exchange and no ineremporal credi, is parallel o he aggregae oupu secor specificaion in several ways. Firs he credi shock is similar o he produciviy shock above, excep ha he credi shock is a secoral produciviy shock raher han an aggregae shock across all secors. Bu i is sill a shock o he shif parameer of he producion funcion boh in he credi secor case and in he aggregae producion case. To see his, consider leing a Œ (, ] denoe he fracion of consumpion goods ha are purchased wih money. Then c a is he oal amoun purchased wih money and c ( - a ) is he remainder: he oal amoun of goods purchased wih credi. Now consider producing his quaniy of credi used for exchange wih he following producion funcion involving labor ime: c ( - a ) = A F e n (lf /c ) g c, where l F is he labor ime. This can be rewrien as - a = A F e n (lf /c ) g which says ha

6 Comparison of Exchange Economies 547 he share of credi producion is produced wih he labor per uni of consumpion, wih a diminishing marginal produc of normalized labor. Solving for a = - A F e n (lf /c ) g, wriing he exchange consrain as M = a P c and subsiuing for a gives he exchange consrain (3). This clarifies ha he assumpion behind he exchange consrain is simply ha he credi share is produced in a diminishing reurns fashion. And i shows ha he shock affecs he produciviy facor of his producion funcion. The credi producion funcion is also similar o he Cobb Douglas form of he aggregae producion funcion. Wriing i as c ( - a ) = A F e n l g F c -g,i is of he Cobb Douglas form in l F and c. However, jus as American Express offers credi for exchange (no ineremporal loans) wih is sandard card, and jus as American Express akes he oal economic aciviy as a given in is producion of he exchange credi for he economy, so also does our credi producion ake he oal oupu as a given in is producion of he exchange credi. The degree of diminishing reurns depends on he parameer g. Gillman and Kejak (25b) illusrae ha a value of g beween and.5 resuls in a marginal cos of credi producion ha is upward sloping and convex, as in he righ-hand side of a sandard U-shaped marginal cos curve, while values beween.5 and give an upward sloping bu concave marginal cos curve. The values used in he robusness (Secion 5 below) range beween and bu values above.5 are suspec in ha hey yield a marginal cos ha rises a a diminishing rae, unusual if found in he indusrial organizaion lieraure. The baseline value in he simulaions is g =.2, as esimaed in Gillman and Oo (23) from he ime-series esimaion of US money demand ha is derived from a similar credi echnology Comparison. In comparison o he shopping ime case, one key difference is he abiliy o shock he produciviy of he credi producion in a sandard way, in ha i is similar o he shock o any secor or o he aggregae oupu. The oher key difference concerns he elasiciies of hese models o nominal ype changes. Consider ha he exchange ime in he credi model is no proporional o he consumpion velociy of money as i is in he common shopping ime specificaion. Raher he exchange ime o velociy raio rises wih he inflaion rae. This implies a significan difference in he underlying money demand funcion. And a similar difference exiss beween he cash-only and he credi producion economies. Consider he elasiciy of exchange ime relaive o velociy (/a ). While zero in he cash-only case, and one in he shopping ime case, he elasiciy of exchange ime wih respec o velociy is larger han one in he credi producion case. For he credi case, le V c/(m/p) and h [ (l F /c )/ V ][V /(l F /c )]; hen h = (/g )[/(V - )]. If, for example, a =.5 and g =.2, hen V = 2 and h ª 5. This means ha he exchange ime rises much more han proporionally wih increases in he velociy. And his is jus a

7 548 The Mancheser School sandard feaure of a producion funcion wih a diminishing marginal produc in each of is facors. To see his, consider a sandard Cobb Douglas producion funcion of oupu, say Y, ha depends on a labor quaniy L and capial K, as in Y = L g K -g. Then he elasiciy of he raio of labor o capial wih respec o he raio of capial o oupu, denoed by h, compares direcly o h, he labor elasiciy of velociy as defined above; his Cobb Douglas elasiciy can be found o be equal o h =-/g. Wih g =.2, h ª-5, similar o h ª 5 when V = 2 (he difference in signs resuls because he credi oupu is - a and no a ). These elasiciy resuls in he producion funcions reflec he same hing: ha he marginal cos curve is posiively sloped and rising a an increasing rae. Increasingly more labor ime is used because of increasing marginal coss of producion. So he elasiciy resul in he credi producion funcion is a naural consequence of using a sandard microeconomic relaion and is no found in he sandard shopping ime and cash-only models. The consequence of he credi specificaion can be pu in erms of income and subsiuion effecs. There can be significan income effecs from using an increasing amoun of ime in banking, as he inflaion rae increases. Cash-only has no such real resource use in avoiding inflaion and shopping ime has wha migh be called a uniary elasic cos. During he business cycle, a significan posiive credi produciviy shock can free up a measurable amoun of ime and have a significan income effec on he credi model. The subsiuion effec can be saed in erms of he ineres elasiciy of money demand. The cash-only model has a very sluggish ineres elasiciy of money ha rises slighly in magniude as he inflaion rae goes up; i does no allow for exchange ime o be used as an alernaive o money; and herefore he consumer has no alernaive by which o buy goods and only slighly subsiues away from money as inflaion rises. The shopping ime model has a consan ineres elasiciy similar o he Baumol (952) model ha resuls from is assumpion of a uniary ime elasiciy wih respec o velociy. And he credi, or banking ime, model produces an ineres elasiciy ha rises in magniude wih he inflaion rae in a way very similar o he Cagan (956) model; 2 his is a resul of using a more sandard producion funcion. These differing subsiuion effecs can influence business cycle resuls if here is a large shock ha significanly affecs he use of money versus is credi alernaive in he credi model. The only exchange alernaive in he cash-only model is leisure, no ypically subjec o shocks; in he shopping ime model, he exchange alernaives are leisure or shopping ime, also no ypically shocked. And noe ha, a high raes of inflaion, he elasiciy ends o be higher in he credi model han in boh he cash-only and shopping ime (depending on calibraions) and he subsiuion effec would hen be sig- 2 See Gillman and Kejak (22).

8 Comparison of Exchange Economies 549 nificanly greaer and he effec of a shock larger, such as one ha possibly may have occurred during he moderaely high US inflaion of he early 98s when deregulaion began. 2.2 Equilibrium The consumer s exchange consrain can alernaively be wrien in he nesed model as M + T - apc (5) where a = cash-only = AF lf shopping ime g n Ê l F ˆ = -A (6) Fe credi producion Ë c or, expressed in erms of l F, in each of hese cases, gives ha lf = cash-only = AF a shopping ime n g = [( -a) ( AF e )] c credi producion (7) This formulaion summarizes he nesed model developed above and is convenien for defining he equilibrium and for calibraion. The consumer chooses consumpion, leisure, capial sock, he fracion of goods bough wih money, ime spen in exchange aciviy and he money balances over ime, {c, x, k, a, l F, M } =, o maximize lifeime uiliy () subjec o he budge consrain (7), he cash-in-advance consrain (5) and he exchange echnology given in equaion (7) for he hree cases: Ï Ê M- + T ˆ L = EÂ b Ì( c + x)+ - ac Ó l log Y log Ë P = È M- + T M + m w( -x -l )+ rk + -c -k - (8) Î Í F - P P A compeiive equilibrium for his economy consiss of a se of allocaions {c, x, l, n, l F, k, a, M } =, a se of prices {w, r } =, exogenous shock processes {z, n, u } =, a money supply process and iniial condiions k - and M - such ha, given he prices, shocks and governmen ransfers, he allocaions solve he consumer s uiliy maximizaion problem, solve he firm s profi maximizaion problem and make he goods, labor and money markes clear. In a saionary deerminisic seady sae we use he ransformaion p = P /M (and also denoe real money balances by m = M /P ). There is no uncer-

9 55 The Mancheser School ainy and ime indices can be dropped, denoing by an aserisk he seadysae values and by R* = r*(q* + ) he seady-sae ineres rae facor. 2.3 Log-linearizaion and Calibraion The firs-order condiions and log-linearizaion of he model, following Uhlig (995), are presened in Appendix A. This uses he firs-order Taylor approximaion of he log variables around he seady sae and replaces all equaions by approximaions which are linear funcions in he log-deviaions of he variables. For example, he variable x is replaced wih x = x*( + ˆx ), where ˆx is he percenage deviaion (log-deviaion) from he seady sae, or x ª dlogx, and x* is he seady-sae value of he variable x. The baseline calibraion uses sandard values ha are found in he lieraure. For he more novel credi secor parameer A F, is value is se o.422 which follows from seing g =.2 (as esimaed in Gillman and Oo (23)). The able in Appendix A2 presens he values used in all hree models. 3 Impulse Responses Figures 3 show he impulse responses for he credi model o goods produciviy shocks, money shocks and he addiional credi produciviy shock. The impulse responses of he cash-only and shopping ime models o goods produciviy and money shocks are similar o hose of he credi model, wih he excepions menioned below. 3. Goods Produciviy Shock Across he hree models, a posiive goods produciviy shock (Fig. ) causes more oupu, consumpion, capial, labor, real wages, real ineres rae and real money, and lower leisure and prices. Shopping ime falls slighly while banking ime falls a lo, as labor ime is more valuable. 3.2 Money Shock Across he hree models, a posiive shock o he nominal money supply growh rae (Fig. 2) causes an increase in capial, real wages and prices, and a decrease in oupu, consumpion, labor, he real ineres rae and real money. Leisure falls in he shopping ime model bu increases in he cashonly and credi models. A he same ime, he exchange ime in he credi model rises by some -fold more han he shopping ime. Also consumpion falls srongly in he cash-only model, less so in he credi model, and hardly a all in he shopping ime model. The cash-only and credi models show he ypical goods o leisure subsiuion, bu he shopping ime model does no. This can be inerpreed as he shopping ime model having oo much

10 Comparison of Exchange Economies 55 Percen deviaion from seady sae.5.5 oupu capial consumpion Years afer shock Percen deviaion from seady sae real money share of cash inflaion price~ Years afer shock Percen deviaion from seady sae labor leisure banking ime Years afer shock Percen deviaion from seady sae real wage w/r real reurn Years afer shock Fig. Impulse Responses o Per Cen Produciviy Shock; Credi Model subsiuion owards exchange ime a low inflaion raes, because of he consan -.5 ineres elasiciy of money; he credi model in conras has a nearzero ineres elasiciy of money a very low inflaion raes. The credi model s inelasic money demand a low inflaion raes causes more subsiuion from goods o leisure Credi Produciviy Shock The hird shock (Fig. 3) appears only in he credi model, giving i poenially more explanaory power hrough his addiional dimension. Here he key difference, wih a posiive credi produciviy shock, is ha while consumpion and oupu rise, so do prices. In comparison, for a money shock, consumpion and oupu fall as prices rise, in all hree models. This is he reason why he addiional shock allows for a beer explanaion of procyclic inflaion. And his feaure makes sense: an increase in credi produciviy during say financial deregulaion causes more banking and less money use, wih he same money supply growh rae; hus more inflaion. If he credi 3 See also how Lucas (2) conrass he consan ineres elasiciy funcion versus he consan semi-ineres elasiciy funcion a low inflaion raes.

11 552 The Mancheser School Percen deviaion from seady sae capial oupu consumpion Years afer shock Percen deviaion from seady sae inflaion price~ share of cash real money Years afer shock Percen deviaion from seady sae.5.5. leisure labor Years afer shock Percen deviaion from seady sae banking ime Percen deviaion from seady sae x w/r real wage real reurn Years afer shock Years afer shock Fig. 2 Impulse Responses o Per Cen Money Supply Shock; Credi Model shock also leads o a posiive GDP impulse, hen inflaion moves up a he same ime as GDP. This is a feaure found in US pos-war daa, and as elaboraed upon nex, he impulse responses show ha neiher he goods produciviy or he money shock yields such procyclic inflaion. 4 Puzzles Table firs ses ou he acual cyclical behavior of he pos-war US economy over he 959:I 2:IV period. This updaes he facs presened in Cooley and Hansen (995). I shows he sandard deviaions and he crosscorrelaions wih real GDP and wih M growh for real and nominal variables.

12 Comparison of Exchange Economies 553 Percen deviaion from seady sae 5 x 3 5 consumpion oupu capial Years afer shock Percen deviaion from seady sae.5 price~ inflaion real money share of cash Years afer shock Percen deviaion from seady sae banking ime labor leisure Years afer shock Percen deviaion from seady sae x 3 real reurn real wage w/r Years afer shock Fig. 3 Impulse Responses o Per Cen Credi Produciviy Shock; Credi Model 4. Simulaions Simulaions were conduced for all hree models, in order o see how hey perform compared wih he puzzles in he lieraure; only he credi model simulaions are presened in Table 2. This able presens he resuls of simulaing he credi model economy 5 imes, each simulaion being 68 periods long, o mach he number of observaions underlying he US saisics repored in Table. Each simulaed ime series is filered wih he Hodrick Presco filer; he sandard deviaions of he key variables are repored as well as heir cross-correlaion wih oupu. A comparison wih he acual cross-correlaions in Table shows noeworhy feaures. While he credi model does no capure he acual oupu correlaion wih banking hours, i does do raher well wih he inflaion rae and he nominal ineres rae. The acual daa show a posiive correlaion of fuure oupu wih inflaion and nominal ineres raes, and a negaive correlaion wih lagged oupu wih inflaion and nominal ineres raes. The credi model simulaion shows a similar paern alhough i is no exacly in phase wih acual daa. For example, he acual daa show a posiive curren oupu correlaion, and in he simulaion he correlaion urns posiive only wih he one-period-ahead oupu.

13 554 The Mancheser School Table Cyclical Behavior of he US Economy: 959:I 2:IV Cross-correlaion of oupu wih Variable SD % Corr. wih M growh x(-5) x(-4) x(-3) x(-2) x(-) x x(+) x(+2) x(+3) x(+4) x(+5) Oupu Consumpion Invesmen Banking hours Real wage Prices (CPI) Inflaion Money (M) Money growh Real money Ineres rae (TBill) Cons. velociy Income velociy

14 Comparison of Exchange Economies 555 Table 2 Sandard Deviaions in Per Cen and Correlaions wih Oupu of he Simulaed Economy (Hodrick Presco Filered Series) Cross-correlaion of oupu wih Variable SD % Corr. wih M growh x(-5) x(-4) x(-3) x(-2) x(-) x x(+) x(+2) x(+3) x(+4) x(+5) Oupu Consumpion Invesmen Capial Banking hours Share of cash Real wage Leisure Labor Prices Inflaion Real reurn Money Money growh Real money Ineres rae Wage rae Cons. velociy Income velociy

15 556 The Mancheser School 4.2 Explanaion of Puzzles wih Simulaions across Models The various puzzles from Cooley and Hansen (989, 995, 998) and Gavin and Kydland (999) are enumeraed in Table 3 and organized ino credi effecs and inflaion ax effecs caegories (Table 3). Columns 2 4 summarize he exen o which he hree models, credi, cash-only and shopping ime respecively, are able o explain puzzles when faced wih join produciviy and money shocks. Columns 5 8 show when he credi shock is also acive, applying only o he credi model. Firs noe ha, when subjec o join produciviy and money shocks, he credi model generaes he procyclic moneary aggregaes and he money oupu phase shif, as found in he acual daa. These facs are no replicaed by he wo alernaive models wih he join shocks. This shows an advanage of he credi model using sandard shocks. Credi shocks alone (column 5) generae procyclic moneary aggregaes and income velociy as well as he phase shif beween money and oupu, as seen in he daa. This simulaion also replicaes he procyclic inflaion and nominal ineres rae, wih values very close o he daa. The oher models canno mach he daa here. Column 8 presens resuls of he credi model wih all hree shocks, as in he simulaions presened in Table 2. Here he inflaion procyclic movemen wih curren oupu is los, bu as noed above he simulaion sill maches he correlaion of inflaion wih one-periodahead oupu. Wha emerges primarily from his comparison wih he puzzles is ha he credi shock can be imporan in explaining inflaion movemens. Pu differenly, when he economy is in a period during which he credi shock is imporan, such as banking deregulaion, he procyclic inflaion movemen can be explained in his way. 5 Sensiiviy and Robusness I is imporan ha he simulaions prove robus o variaions in key parameers, in paricular he degree of diminishing reurns in credi producion, g, he produciviy shif parameer in credi producion, A F, and he inflaion rae level. For he g values of.2 (he baseline calibraion),.3,.5,.6 and.8, wo of he mos imporan cases are examined: he credi-shock-only case and he case when he economy is faced wih all hree shocks. When faced wih credi shocks only, he procyclicaliy of moneary aggregaes remains unchanged under all g values excep for he larges value.8. The procyclic naures of income velociy, inflaion and nominal ineres rae are exremely robus; he correlaion coefficiens remain approximaely consan under all values of g. The same robusness is found in he phase shif beween oupu and money. When subjec o all hree shocks, he economy demonsraes he

16 Comparison of Exchange Economies 557 Table 3 The Exen o Which Produciviy, Money or Credi Shocks Can Explain he Moneary Puzzles () (2) (3) (4) (5) (6) (7) (8) Credi model CIA model SHT model Credi model wih credi shocks PR + M PR + M PR + M CR PR + CR CR + M CR + PR + M Facs and puzzles shocks shocks shocks shock shocks shocks shocks A. Credi. Moneary aggregaes are procyclical (+.7; +.33 in CH, Yes No No YES YES No Yes 995) Phase shif in he correlaion beween oupu and money Yes No No YES No Yes Yes = lagged money is correlaed wih presen oupu 3. Posiive correlaion beween oupu and inflaion No No No YES No No No (+.38) Posiive correlaion beween oupu and nominal ineres No No No YES No No No rae (+.35) B. Inflaion ax. Income velociy is procyclical (+.5) Yes Yes Yes Yes Yes No YES Negaive correlaion beween money growh and oupu YES YES Yes N/A N/A Yes Yes (-.3) Negaive correlaion beween money growh and hours YES YES Yes N/A N/A Yes Yes (-.5 in CH, 995) Negaive correlaion beween money growh and Yes Yes YES N/A N/A Yes YES consumpion (-. in CH (998) bu.2 in CH (995); here) 5. Negaive correlaion beween oupu and prices Yes Yes Yes No Yes Yes Yes (-.5) CH, Cooley and Hansen; CIA, cash-in-advance; SHT, shopping ime; PR, produciviy; M, money; CR, credi; N/A, no available; Yes indicaes ha he shock explains he puzzle; YES indicaes he bes explanaory power of he differen models for a given puzzle.

17 558 The Mancheser School same robusness. Moreover, when g increases, he correlaion coefficiens of he money growh wih oupu and hours worked move closer owards heir observed values. The only excepion is he correlaion of oupu wih moneary aggregaes, which, a higher g values, becomes acyclical or slighly counercyclical. For he produciviy parameers (A F ) of.6,.,.4,.7 and 2., when only credi shocks operae in he economy, he model remains robus under various produciviy parameers wih one excepion: a low produciviy he nominal money supply becomes slighly counercyclical. Under join produciviy, money and credi shocks he sysem proves o be robus; however, jus as wih varying g values, moneary aggregaes display a raher acyclical paern, alhough he shif in he correlaion coefficien is almos negligible. Under various inflaion raes (-4, -2,, 2, 5,, 2, per cen), he resuls are robus wih all of he shock processes. The excepion is he behavior of nominal money supply under credi shocks, which urns ou o be procyclic only a moderae inflaion raes bu counercyclical a deflaionary or hyperinflaion raes. 6 Discussion The impulse responses show ha he shopping ime model has differences such as is leisure decrease when he money supply growh rae is shocked upwards. This feaure is no found in he oher wo models and i appears o be relaed o he assumpion of is exchange ime moving proporionally wih velociy. This may creae a lesser performance of he shopping ime model o explain he inflaion ax puzzles. For example, he credi model wih goods produciviy and money shocks seems beer a explaining procyclic moneary aggregaes. However, he performance differences among he hree models are somewha marginal in comparison wih he advanage of having he addiional credi shock in he credi model. This gives he procyclic aggregae movemens found in he daa and can generae procyclic inflaion rae movemens. A relaed ype of shopping ime shock can be added o he shopping ime framework, as Dimar e al. (25) show, bu his has less inuiion in ha he specificaion of he shopping ime funcion is no linked o any microfoundaions oher han a fixed ineres elasiciy of money demand. The advanage of he credi model is ha he addiional credi produciviy shock helps o capure subsiuion away from money use during imporan financial secor innovaion periods, and o generae income effecs in erms of saved ime in banking. The inflaion movemens are no persisen in he credi model, however, when using he simple money supply growh rule, and his makes he overall model s performance wih all hree shocks sill inconsisen wih observed inflaion oupu conemporaneous correlaion. Bu since he credi-shock-

18 Comparison of Exchange Economies 559 only model gives he righ magniude and posiive sign for he inflaion correlaion, an increase in inflaion persisence such as from a Taylor feedback rule as in Dimar e al. (25) may lead o overall improvemen. Anoher area for improvemen in he model is liquidiy effecs. Cooley and Hansen (995, 998) modify cash-in-advance economies wih nominal rigidiies and he non-neuraliies so inroduced cause larger velociy and ineres rae volailiy ha are closer o he facs. However, he inflaion ax models of Secion 2 beer fi for example he negaive correlaion beween curren oupu and he price level. And he nominal rigidiy models poorly explain real variable movemens, and do no capure money growh, inflaion and ineres rae correlaions. A credi approach may sill be useful for he liquidiy problem if cash ransfers can be injeced firs ino he credi secor wih a subsequen increase in he supply of credi before he inflaion rae increases. 7 Conclusion The paper analyzes hree differen models of exchange echnology wihin a business cycle framework. The firs wo are he sandard cash-only and shopping ime models and he hird is a credi model ha is a sochasic version of he Gillman and Kejak (25b) economy. The credi model allows for an addiional shock o he usual goods produciviy and money shocks. I is found ha his addiion allows he co-movemen of moneary aggregaes, inflaion and he nominal ineres rae wih oupu a differen poins in he phase of he business cycle o be capured beer han oher models. Impulse responses confirm his feaure in he credi model ha is no available in he cash-only and sandard shopping ime models. The paper hus is able o argue ha he credi producion approach is an exension ha, based in a microfoundaions-linked calibraion, improves he performance of he moneary business cycle model. The conribuion represens a sep ha allows he general equilibrium business cycle o accoun for imporan changes in banking and for he more sandard inflaion ax effecs. Appendix A Firs-order Condiions and Log-linearizaion The firs-order condiions wih respec o c, x, k, a, M are - a -la -mw Ê ˆ - m = c Ë n AFe Y - mw = x - m + be( m + r + )= g (A) (A2) (A3)

19 56 The Mancheser School - lc + mwc -m + b Ê l E P Ë These can be simplified o w* a* R* - = Ê- ˆ g A Ë A x a R w a A Y c = + ( -)+ ( - ) * * * * F w* r* = b F Ê - a ˆ A Ë e A e n n g F F + m P F ˆ = ( g )- ( g )- = g (A4) (A5) (A6) (A7) (A8) The log-linearized sysem of equilibrium condiions includes he consumer s firsorder condiions ( l* a* c* + m* c* ) cˆ * * *ˆ * * * ˆ * * * ˆ + l a c a + m w lfw + m w lflf + l* a* c* l ˆ * * * * ˆ + ( m w lf* + m c ) m = xˆ ˆ + m + wˆ = - mˆ + ˆ Em+ + Er ˆ+ = - l ˆ + m ˆ + ˆ + ( -g) ˆ -( -g) ˆ w lf c - n = Ê ˆ - m ˆ l* + ˆ + Á ˆ * = Ë l* + m* l m l* + m* mˆ ˆ p E p u he firm s equilibrium condiions - wˆ + z + akˆ - anˆ = - - rˆ + [ -b( -d) ] z + ( a -)[ -b( -d) ] kˆ + ( -a) [ -b( -d) ] nˆ = - - yˆ + + ˆ z ak- + ( -a) nˆ = and he resource and money marke consrains (A9) (A) (A) (A2) (A3) (A4) (A5) (A6) - ˆ a* lf + aˆ + cˆ - = g( a* - ) g n ll *ˆ F F + x* xˆ + n* nˆ = pˆ + aˆ + cˆ = -w* n*ˆ w -w* n*ˆ n -r* k*ˆ r - r* k*ˆ k + c*ˆ c + k* k ˆ = - pˆ - pˆ - pˆ + u = - (A7) (A8) (A9) (A2) (A2) Equaions (A9) (A2), ogeher wih he hree shock processes for goods produciviy, money supply and credi produciviy, form he complee recursive sysem of linear sochasic difference equaions in he endogenous sae variable ˆk,

20 Comparison of Exchange Economies 56 exogenous sae variables z, n, u, endogenous conrol variables ĉ, ˆx, ˆn, ˆl F, â, ŵ, ˆr, ŷ, ˆp, p and shadow prices ˆl, ˆm. A2 Calibraion Credi Cash only Shopping ime a d b A F.422 N/A.34 Y Q g.2 N/A N/A j z s z j n.95 N/A N/A s n.75 N/A N/A j u s u... c x n l F.49.8 a w r... p y k m N/A, no available. References Alvarez, A., Lucas, R. E., Jr and Weber, W. E. (2). Ineres Raes and Inflaion, American Economic Review, Vol. 9, No. 2, pp Baumol, W. (952). The Transacions Demand for Cash: an Invenory-heoreic Approach, Quarerly Journal of Economics, Vol. 66, pp Benk, S., Gillman, M. and Kejak, M. (25). Credi Shocks in he Financial Deregulaory Era: No he Usual Suspecs, Review of Economic Dynamics, forhcoming. Cagan, P. (956). The Moneary Dynamics of Hyperinflaion, in M. Friedman (ed.), Sudies in he Quaniy Theory of Money, Chicago, IL, Universiy of Chicago Press, pp Cooley, T. and Hansen, G. (989). The Inflaion Tax in a Real Business Cycle Model, American Economic Review, Vol. 79, No. 4, pp Cooley, T. and Hansen, G. (995). Money and he Business Cycle, in T. Cooley (ed.), Froniers of Business Cycle Research, Princeon, NJ, Princeon Universiy Press, pp Cooley, T. and Hansen, G. (998). The Role of Moneary Shocks in Equilibrium Business Cycle Theory: Three Examples, European Economic Review, Vol. 42, pp

21 562 The Mancheser School Dimar, R., Gavin, W. and Kydland, F. (25). Inflaion Persisence and Flexible Prices, Inernaional Economic Review, Vol. 46, No., pp Gavin, W. and Kydland, F. (999). Endogenous Money Supply and he Business Cycle, Review of Economic Dynamics, Vol. 2, pp Gillman, M. and Harris, M. (24). Inflaion, Financial Developmen and Endogenous Growh, Working Paper 24-4, Monash Universiy. Gillman, M. and Kejak, M. (22). Modeling he Effec of Inflaion: Growh, Levels, and Tobin, in D. Levine (ed.), Proceedings of he 22 Norh American Summer Meeings of he Economeric Sociey: Money. hp:// proceedings/money.hm Gillman, M. and Kejak, M. (24). The Demand for Bank Reserves and Oher Moneary Aggregaes, Economic Inquiry, Vol. 42, No. 3, pp Gillman, M. and Kejak, M. (25a). Conrasing Models of he Effec of Inflaion on Growh, Journal of Economic Surveys, Vol. 9, No., pp Gillman, M. and Kejak, M. (25b). Inflaion and Balanced-pah Growh wih Alernaive Paymen Mechanisms, Economic Journal, Vol. 5, No. 5, pp Gillman, M. and Nakov, A. (24). Causaliy of he Inflaion Growh Mirror in Accession Counries, Economics of Transiion, Vol. 2, No. 4, pp Gillman, M. and Oo, G. (23). Money Demand in a Banking Time Economy, Discussion Paper 254, Hamburg Insiue of Inernaional Economics, Hamburg. Gillman, M., Harris, M. and Máyás, L. (24). Inflaion and Growh: Explaining a Negaive Effec, Empirical Economics, Vol. 29, No., pp Ireland, P. (24). Money s Role in he Moneary Business Cycle, Journal of Money, Credi and Banking, Vol. 36, No. 6, pp Li, V. (2). Household Credi and he Moneary Transmission Mechanism, Journal of Money, Credi and Banking, Vol. 32, No. 3, pp Lucas, R. E., Jr (2). Inflaion and Welfare, Economerica, Vol. 68, No. 2, pp Schaber, A. (23). On he Equivalence of Money Growh and Ineres Rae Policy, Working Paper 23/6, Deparmen of Economics, Universiy of Glasgow. Uhlig, H. (995). A Toolki for Analyzing Nonlinear Dynamic Sochasic Models Easily, Discussion Paper, Insiue for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis.