Chaper 4 oney and oneary olicy in he Ineremporal Framework We have for he mos par ignored he role of money and hus moneary policy in our sudy so far. This is ecause he main issues we have een considering in paricular, he idea of opimal decision-making y represenaive agens, which lead o he enchmark consumpion-leisure and consumpion-savings opimaliy condiions urn ou o no require explici consideraion of money. Our lack of meaningful inclusion of money is also in par due o he fac ha i has proven somewha difficul o consruc a simple framework for he hree disinc roles ha money plays in modern sociey. For cenuries (or perhaps millienia), hose hree disinc roles have een hough o e: ) A medium of exchange (which circumvens he prolems of arer exchange, which is nearly impossile in developed economies) 2) A uni of accoun (as an example, if you spend U.S. dollars a a U.S. sore, he price ags will e denoed in numers of U.S. dollars, raher han in, say, numers of allpoin pens) 3) A sore of value (if a piece of frui were used o make paymens, one piece of frui would oviously decay very quick, wihin days or weeks a es which implies ha is value erodes quickly; insead, one piece of firous and secure paper ha displays George Washingon s porrai is likely o las for decades) espie he heoreical difficuly of incorporaing he hows and whys of paricular socieies or counries or eras seling on a commonly undersood definiion of money, i is virually enirely aou money around which he divide eween he RBC school of hough and he New Keynesian school of hough emerges. To illusrae he fundamenal difference eween he wo heories and hence he fundamenal spli in modern macroeconomic heory, we need o develop a concep of money marke equilirium, which in urn requires oh money demand and money supply. We will ake a shorcu, u widely-used, approach, which is he money-in-he-uiliy (IU) funcion framework o generae demand for money. Simply pu, he IU approach simply insers (real) money ha is, he purchasing power of moneary unis as an argumen o he represenaive consumer s uiliy funcion. Before geing o he economics of and shor-run and long-run policy recommendaions Spring 204 Sanjay K. Chugh 20
ha emerge from he IU framework, hough, we refresh ourselves on he linkages eween moneary markes and ond markes. Governmen Bond arke You should already e familiar wih he conceps riefly presened in his secion. Bu ecause he connecion eween moneary markes and ond markes is crucial for undersanding how moneary policy operaes, a rief recap seems appropriae. We assume ha he onds are all governmen onds. 03 In convenional imes, he Federal Reserve implemens is policy decisions via open marke purchases or sales of U.S. governmen onds. oreover, we assume all onds are nominal onds, meaning ha each uni of a ond pays ack a fixed amoun of currency. We will speak of a single governmen ond marke wihin a counry, even hough here are many differen ypes of onds issued y governmens, disinguished primarily y heir mauriy lengh and face value. A ond s mauriy lengh is he ime from issuance unil he full value of he ond is repaid o he ond-holder, while a ond s face value is he full value ha is repaid upon mauriy. For example, he U.S. governmen issues onemonh Treasury ills, hree-monh Treasury ills, six-monh Treasury ills, wo-year Treasury noes, hree-year Treasury noes, five-year Treasury noes, and en-year Treasury noes of various face values. 04 Bonds are simply loans, a poin ha is ofen misundersood. Regardless of a ond s mauriy lengh and face value, a governmen ond is simply a loan ha a ond-holder provides o he governmen o e repaid a a laer dae wih ineres. The amoun o e repaid a he pre-specified dae is he ond s face value. Because he face value is no repaid unil some fuure ime period, he amoun ha a ond-holder would e willing o pay in he curren period for a ond of face value FV dollars is somehing less han FV dollars. The reason for his is simply he imediscouning of fuure values. For example, $00 one year from now is likely worh less han $00 o you righ now in oher words, you are likely o e willing o accep somehing less han $00 a his insan in lieu of receiving nohing now and $00 one year from oday. Because of ime-discouning, he period- price (denoed ) of a one-period mauriy ond is relaed o is face value FV + and he nominal ineres rae i, which represens 03 There exis also corporae onds (onds issued y companies) and hence markes for corporae onds, which are imporan markes. However, for sandard, or convenional, moneary policy purposes, i is fairly irrelevan which ypes of onds exis, so we will ignore corporae ond markes. 04 There are also many oher mauriy lenghs of U.S. governmen onds. Spring 204 Sanjay K. Chugh 202
he ineres componen eween period and period +. The relaionship eween hese hree ojecs is FV. i The way his expression is wrien makes i seem ha i defines he price of a ond. Bu a common inerpreaion of his expression is ha i insead defines he nominal ineres rae i, ecause a any poin in ime a ond s face value and he amoun ond demanders are willing o pay are known. Thus, knowledge of and FV + can e hough of as defining i. Algeraically, we can emphasize his relaionship y simply re-arranging he expression aove o isolae for he nominal ineres rae, which is i FV. These wo equaions are oviously equivalen o each oher. We also include hree oher simplifying poins for he sake of ease of he ensuing analysis.. The face value is always equal o FV =, hence we can drop he ime suscrip and he edious-o-wrie FV. 2. In pracice, here are wo main ypes of onds coupon onds and zero-coupon onds. A coupon ond is one ha makes ineres paymens (called coupon paymens) o he ond-holder a specified imes efore a final paymen of he face value a he mauriy dae, while a zero-coupon ond offers no inermediae paymens efore he paymen of he face value a he mauriy dae. For convenience, we will suppose ha all onds are zero-coupon onds ecause i does no maer for eiher he shor-run or long-run analysis. 3. Nominal ond repaymens are always fully repaid on ime. The las poin says he governmen never defauls on is nominal ond oligaions, which, if we zoom in on he U.S. governmen, is rue. Spring 204 Sanjay K. Chugh 203
oney-in-he-uiliy (IU) Funcion and oney emand Now we egin wih he infinie-horizon framework. The paricular financial asse applicaion when we firs considered he infinie-horizon framework was sock-marke pricing. Bu a roader heme ha emerges from he previous analysis is aou asse pricing in general, regardless of he paricular ype of financial asse under consideraion. In he expanded infinie-period framework here, here will e hree disinc ypes of asses: socks, money, and onds. Figure 79 porrays his richer class of financial asses and he iming of evens. ahemaically, we augmen he represenaive consumer s period- uiliy funcion o now include money demand as an argumen in paricular, he demanded quaniy of money, which is he essence of he IU model. Suppose he represenaive consumer s period- uiliy funcion is u c,, in which / is he consumer s demand for real money alances ha is, for he purchasing power ha a given nominal demand holdings provides. Overall, he real money demand argumen is a sand-in for he various roles ha money plays in differen ime periods, as descried earlier. Because of he sujecive discoun facor (0,) (which indeed carries over from our earlier analysis of he infinie-period framework), he lifeime discouned uiliy from he perspecive of he very eginning of period can e saed as 2 2 3 3 uc, uc, uc2, uc2,... 2 3 s s uc s, ; s0 s he second line wries he presen-value lifeime uiliy funcion compacly using he summaion operaor. Spring 204 Sanjay K. Chugh 204
a - B - - Receives nominal income Y Individual opimally chooses real consumpion c and opimally chooses porfolio of asses (a, B, ) for eginning of period + Receives nominal income Y + a B Individual opimally chooses real consumpion c + and opimally chooses porfolio of asses (a +, B +, +) for eginning of period +2 Receives nominal income Y +2 a + B + + Individual opimally chooses real consumpion c +2 and opimally chooses porfolio of asses (a +2, B +2, +2) for eginning of period +3 a +2 B +2 +2 Sar of economic planning horizon eriod eriod + eriod +2 eriod +3 Receives porfolio of asses (a -, B -, -) inclusive of dividend and ineres income Receives opimally-chosen porfolio of asses (a, B, ) inclusive of dividend and ineres income Receives opimally-chosen porfolio of asses (a +, B +, +) inclusive of dividend and ineres income NOTE: Economic planning occurs for he ENTIRE remaining lifeime. Figure 79. Timeline of evens in infinie-period moneary framework. Spring 204 Sanjay K. Chugh 205
uring every ime period, an opimal realancing amongs he hree asses in he porfolio occurs. This is descried in he period- udge consrain of he consumer, c B Sa Y B ( S ) a, in which, as in he asic asse-pricing framing, is he nominal price of consumpion, S is he nominal price of a one uni of sock in period, and is he nominal dividend per share in period. Noice he iming of he udge consrain: in period, he consumer chooses nominal money holdings o carry ino period +. 05 (And see also Figure 79.) In urn is implied ha he period + flow udge consrain is c B S a Y B ( S ) a, he period +2 flow udge consrain is c B S a Y B ( S ) a, 2 2 2 2 2 2 2 2 2 2 and so on for periods +3, +4, +5,... Opimal Choice The sequenial Lagrange prolem saed in nominal erms is 2 2 3 3 uc, uc, uc2, uc2,... 2 3 Y B ( S ) a c B Sa Y B ( S ) a c B S a 2 2 Y2 B ( S2 2) a 2c2 2B2 2 S2a 2... 05 echanically, we know his ecause i is, raher han, ha appears on he lef-hand-side of he udge consrain, and he lef-hand-side represens oulays in period. Spring 204 Sanjay K. Chugh 206
which should look familiar o you i is simply an exension of he sequenial Lagrange funcion in our earlier sudy of sock-marke pricing. The firs-order condiions wih respec o c, a, B, and u c, 0, S S, 0 are, respecively, 0, and u, 0. 2c The firs condiion saes he usual resul ha he marginal uiliy of consumpion equals he Lagrange muliplier (scaled y he price level ). The second firs-order condiion is our familiar sock-pricing equaion. The hird firs-order condiion is ha on ond holdings. In he fourh firs-order condiion, he / erm arises ecause each individual can choose his/her nominal money holdings, u akes he aggregae price level as given. Because real, no nominal, money demand is he second argumen of he uiliy funcion, he chain rule is required, which generaes he / erm. These four firs-order condiions aken ogeher generae many rich insighs aou linkages eween onds markes and sock markes, eween ond markes and moneary markes, and are he foundaion of possile ideological divides eween wheher or no changes in moneary policy affec eiher shor-run macroeconomic condiions or long-run macroeconomic condiions or oh. The following secions descrie hese insighs in urn. As you will see, we will go ack and forh eween macroeconomic heory and finance heory given he richness of he framework, he inersecion eween he wo apparenly differen srands of hough urns ou o e a very clear inersecion. ricing Kernel and Asse rices elve ack ino a i of finance heory, we can rearrange he firs-order condiion on ond holdings o ge Spring 204 Sanjay K. Chugh 207
. This already sheds a lo of ligh on he inersecion of macro and finance! Recall from our sudy of sock-pricing ha / was defined as he pricing kernel of he economy. Here i is! The price of a nominal ond equals he pricing kernel imes one. 06 Or, saed from he opposie perspecive, he pricing kernel of an economy equals he price of a shor-erm riskless nominal ond. 07 Noe ha he aove expression is of he same general form as he sock-pricing equaion we encounered earlier he price of an asse ( ) depends on a pricing kernel and a fuure payoff (which is simply FV = ). Bonds are hus priced using he general ype of asse-pricing equaion we used o price socks. Coninuing, he firs-order condiion on a gives us S ( S ), which is our usual sock price condiion. From wha we now know, we can alernaively express he sock-price as S ( S ), which explicily demonsraes a crucial linkage eween ond prices and sock prices. Sock prices can hus e said o e keyed (parially) off of onds prices. 06 The one here is simply he payoff of he nominal ond in our model ha is, we assumed ha he face value, hence he payoff, of he ond is FV =. 07 The riskless componen was menioned aove, so we can hink of hese nominal onds as U.S. governmen nominal onds. Spring 204 Sanjay K. Chugh 208
The ig-picure, finance-heoreic, lesson o ake away here is ha asse-pricing equaions invarialy have he same general form, regardless of wha specific ype of asse is eing considered. Tha general form is price of asse in curren period = (pricing kernel) x (asse-appropriae fuure reurns) Fisher Equaion We can oain he exac Fisher equaion as an implicaion of opimal choices in his model, raher han as a relaionship which we so far have seemingly assumed o e rue. To see his, egin wih he las expression, S ( S ). ivide his expression hrough y he nominal price level (which is disinc from he nominal price of a ond ), o ge S ( S ). Nex, on he righ-hand-side, muliply and divide y / (which is of course jus muliplying y one, which is always a valid operaion o conduc ) o arrive a S ( S ). The real price of sock purchased in period is S / (ecause i is divided y he curren price level), while he real payoff in period + of he sock purchased in period + is ( S )/ (ecause i is divided y he fuure price level). The period-(+) real payoff divided y he period- real price is defined as he real reurn on he asse ha is, i is he ojec we have hereofore een calling he real ineres rae. 08 Leing r denoe he real ineres rae eween period and period +, we herefore have ha 08 Socks are considered o e real asses ecause heir payoff is generally no fixed in currency erms, whereas onds are considered o e nominal asses ecause heir payoff is generally fixed in currency erms (non-indexed onds, a leas). Spring 204 Sanjay K. Chugh 209
( S )/ r. S / Wih his, we can wrie he previous expression as ( r ). Only one more sep remains in oaining he exac Fisher relaion from firs principles. To finish he algera, noe ha, y consrucion and ased on our definiions, / i, and /. The previous expression can hus e re-wrien as i ( r)( ), which is he exac Fisher relaion. The economic inuiion ehind he Fisher equaion is ha i links he reurns availale on nominal asses (nominal onds) and he reurns availale on real asses (socks). The linkage is hrough inflaion; once he nominal reurns of onds are adjused y inflaion, heir reurns on nominal onds are exacly equal o he reurns on socks, provided financial markes are operaing well. This ype of idea ha, once reurns are convered ino comparale unis, hey are equalized when markes are ehaving raionally goes y he erminology of noarirage in finance heory. No-arirage relaionships are key uilding locks of more advanced finance heory; we defer richer consideraion of issues semming from such relaionships o a more advanced course on finance heory. The exac Fisher equaion emerges naurally in any model feauring oh nominal asses and any ype of real asse, no jus socks. This rings us ack full circle o our iniial sudy of he wo-period consumpion-savings model, in which we assered he exac Fisher equaion. Nominal Ineres Raes and oney emand Nex, le s consider how he nominal ineres rae i affecs macroeconomic condiions. So far, we have no exploied he informaion conained in he firs-order condiions wih respec o consumpion or money holdings, u now we finally will. Spring 204 Sanjay K. Chugh 20
Spring 204 Sanjay K. Chugh 2 Rewrie he firs-order condiion on nominal money holdings from aove as 2, u c. We know from he firs-order condiion on ond holdings ha ; insering his in he previous expression gives 2, u c. ividing hrough y, 2, u c. Nex, we can use he firs-order condiion on consumpion o replace he erm on he lef-hand-side, giving us 2,, u c u c. The erm on he lef-hand-side now is jus he RS eween real money demand and consumpion i.e., i is he raio of he marginal uiliy of (real) money o he marginal uiliy of consumpion. As for he righ-hand-side of his expression, ecause /( ) i, i can e saed as 2,, u c i u c. One final algeraic simplificaion gives us he consumpion-money opimaliy condiion
u2 c, i i u c,, which saes ha he RS eween period- real money and period- consumpion equals a funcion of he nominal ineres rae a he represenaive agen s opimal choice. This opimaliy condiion is compleely analogous o he consumpion-leisure opimaliy condiion and he consumpion-savings opimaliy condiion wih which we have ecome familiar. The consumpion-money opimaliy condiion saes ha when consumers are making heir opimal choices, hey choose consumpion and real money holdings in such a way as o equae heir RS eween consumpion and money demand o a funcion of he nominal ineres rae. Excep for inerpreaion, he indifference-curve/udge consrain diagram in Figure 80 ough o look familiar y now. consumpion slope = -i/(+i) opimal choice / Figure 80. Consumpion-money demand opimaliy condiion. Also, as in, say, he consumpion-leisure analysis, we can ranslae he opimal choices for any paricular nominal ineres rae i in he indifference curve/udge consrain diagram in Figure 80 o a marke diagram. Figure 8 races he quaniy of money demanded as a funcion of is price i. To ge from Figure 80 o Figure 8, conduc he Spring 204 Sanjay K. Chugh 22
following hough experimen: successively lower he nominal ineres rae i in Figure 80. Along he money demand axis, i seems o e he case ha successively increases. If his is rue, his generaes he clear downward-sloping porion of he money demand funcion in he money-marke space of Figure 8. Coninuing he hough experimen, suppose i is exremely small for example, i = 0.025. I is apparen from he consumpion-money opimaliy condiion ha he udge line is exremely fla. If i were o hi exacly zero or urn sricly negaive, he opimaliy condiion would make no sense a all. Because of he sric equaliy sign in he consumpion-money opimaliy condiion, i would imply ha he RS eween consumpion and real money demand was negaive, which violaes (a leas 99.9999% of he ime ) asic microeconomic principles. Casual inspecion of Figure 80, which has he usually shaped indifference curves ha are sricly convex o he origin, also visually confirms his. i S S (pos-grea Recession) ZLB region / Figure 8. The money marke. oney demand ( ) increases as nominal ineres rae i decreases. Nominal ineres raes can never fall elow zero. Hence emerges he zero lower ound (ZLB) resricion on nominal ineres raes, which saes exacly wha we concluded: nominal ineres raes can never fall elow zero. The ZLB resricion is clear in money marke space in Figure 8. Spring 204 Sanjay K. Chugh 23
Funcional Form for references To faciliae oh he shor-run and long-run moneary policy analyze, as well as o formalize wha was casually concluded immediaely aove, le s specialize our uiliy funcion o uc, lnc ln. This funcional form displays sricly convex o he origin indifference curves in he indifference curve space of Figure 80. And none of he policy conclusions we reach elow depend on his paricular funcional form, u i allows for ease of algeraic manipulaions o come. The marginal uiliy funcions associaed wih his uiliy form are oviously u c, and u2 c,. 09 This means ha he period- c / consumpion-money opimaliy condiion can e wrien as c i, / i which is diagrammale in Figure 80. Or, recasing i in money-marke space, i i c, which is diagrammale in Figure 8. Wih all of his now in place, we are ready o examine wo long-sanding quesions in moneary analysis, one a shor-run issue, he oher a long-run issue. Boh he long-run and shor-run issues cener around he quesion of wheher or no moneary policy is neural. oneary policy is said o e neural wih respec o he economy if changes in moneary policy do no affec real aggregae oucomes in he economy. Symmerically, moneary policy is said o e non-neural wih respec o he economy if changes in moneary policy do affec real aggregae oucomes in he economy. 09 Verify his for yourself. Also noe well ha here is no use of he chain rule here he chain rule was already used o oain he consumpion-money opimaliy condiion, irrespecive of he precise uiliy funcional form. Spring 204 Sanjay K. Chugh 24
oneary olicy I: The Shor-Run To consider neuraliy vs. non-neuraliy in he shor run, we firs have o define more rigorously wha he shor run is, and hen look a he ordering of evens wihin ha shor run. A naural inerpreaion of shor run in our muli-period model is one period of ime, which we lael period. Wha aou he ordering of evens wihin ha one period of ime? Figure 82 zooms in on period and diagrams one example. The wo main aspecs around which he shor-run neuraliy deae revolves are wheher or no an unexpeced change in Federal Reserve moneary has occurred and he fac ha money markes almos universally clear quickly. 0 Figure 82 conains oh of hese aspecs. Suppose ha a moneary policy shock has occurred. For he sake of concreeness, suppose he money supply in period,, unexpecedly urns ou o e larger han S markes had earlier (earlier wihin he shor-run period, o e more precise, and as Figure 82 shows) anicipaed. The moivaion is likely mean o oos aggregae demand. Regardless of policy moivaion, y definiion of money marke equilirium, S mus e rue, regardless of wheher a policy shock has occurred. In urn, he (equilirium) money demand funcion (ased on he paricular funcional form descried aove) requires ha i i c. For his expression o hold wih equaliy, a nominal money supply shock requires ha adjuss or c adjuss or i adjuss, or any cominaion hereof. Noice ha whaever i is 0 The vasly liquid and coninuously operaing money marke funds (which direcly corresponds o he money marke in our analysis) had failed o clear only hree imes in heir 37-year hisory up unil he 2008 financial crisis. Noe ha in equilirium, we drop he S and superscrips ecause he very definiion of equilirium is ha supply = demand. Spring 204 Sanjay K. Chugh 25
ha adjuss o mainain money-marke equilirium, i all occurs in he shor run. Tha is, all of hese prices and quaniies are daed period. To simplify he analysis, and ecause i has een empirically rue in he U.S. from lae 2008 unil a leas 204, suppose he shor-erm nominal rae is i = 0. In erms of Figure 8, he economy has hi he zero lower ound. The unanicipaed moneary simulus hen has o effec eiher nominal prices in he shor run or consumpion quaniy demand c in he shor run, or oh. Le s pain he wo polar exreme cases, firs he sric Keynesian sicky price view, and hen he sric RBC flexile price view. Spring 204 Sanjay K. Chugh 26
a - B - (equilirium) - Consumers make opimal choices of c and nominal money demand, aking as given some expecaion aou S Federal Reserve mees and deermines acual S of economy. If differen from expeced S, a money shock has occurred Regardless of wheher or no money shock occurred, period- consumpion-money opimaliy condiion mus sill hold. Thus = = S mus occur o ensure a moneary marke B equilirium. (equilirium) eriod Quesion: if moneary policy shock occurred, wha prices or quaniies adjus during period o ensure consumpion-money opimaliy condiion holds? Figure 82. Timing of evens wihin a given period. Second half of imeline emphasizes ha money-marke equilirium is achieved in every period ime of ime. Spring 204 Sanjay K. Chugh 27
In he sric Keynesian case, nominal prices do no adjus in he shor run. Thus, feeling flush wih unexpecedly large quaniies of cash, consumers will raise heir demand for goods in he shor run. oneary simulus has succeeded in ha real quaniy demanded has increased, a leas in he shor run. oneary policy is hus non-neural in he Keynesian school of hough. In he sric flexile-price RBC case, nominal prices adjus very quickly. rovided ha very quickly is shorer han he lengh of period, he unexpeced increase in consumpion demand is quickly neuralized -- he erminology is no coincidenal y a rapid increase in. In his case, all moneary simulus has creaed is a urs of inflaion. oneary policy is hus neural in he RBC school of hough. Figure 83 illusraes hese wo exreme cases from he perspecive of he period- goods marke. The aggregae goods demand funcion necessarily shifs ouwards due o an unexpeced increase in he nominal supply he (equilirium) money demand expression i i c shows his. AS (in RBC view) AS (in Keynesian view) * A pos-policy shock A pre-policy shock G Figure 83. Following a posiive shock o moneary policy, aggregae demand shifs ouwards. Wheher or no his leads o a emporary increase in equilirium G depends enirely on he shape of he shor-run aggregae supply funcion. Spring 204 Sanjay K. Chugh 28
For macro-relevan lenghs of period (which is ypically quarerly ecause G accouns are compiled and referenced for he January arch quarer, April June quarer, he July Sepemer quarer, and he Ocoer ecemer quarer), daa suggess ha an empirically-relevan slope of aggregae supply is sricly posiive so, somewhere eween he exremely fla Keynesian AS funcion and he exremely verical RBC-syle AS funcion. For modern macroeconomiss, his hen egs he quesion: wha are he microeconomic reasons for parial nominal price sickiness? We sidesep his issue for now, and reurn o i laer in he more advanced New Keynesian Theory secion of he ook. For he remainder of he analysis here, we consider he effecs of moneary policy in he long run. oneary olicy II: The Long-Run We have een considering an infinie-period framework. As we were ale o do in our earlier, simpler, infinie-period model asen money, i is useful o consider seady-saes. In our explicily moneary model here, considering he seady-sae will sarkly reveal a relaionship imporan o all of moneary heory, a relaionship eween inflaion and he rae of growh of he nominal money supply of he economy. This way of hinking aou inflaion commonly goes under he name of monearism or he quaniy heory of money. 2 Le s coninue o use he uiliy funcion uc, lnc ln, u, jus like in he consideraion of shor-run effecs aove, none of he conclusions we reach depend on his paricular funcional form. For he sake of no having o urn ack many pages, recall ha he money demand expression is 2 One of he mos-ofen quoed sayings y he lae ilon Friedman, he 976 Noel laureae in economics, is ha inflaion is everywhere and always a moneary phenomenon, which has commonly een inerpreed o mean ha i is he acions of he cenral ank of an economy (in paricular, how he cenral ank manages he money supply of an economy) ha alone deermine he rae of inflaion in he economy. As we are aou o see, precisely speaking, only in he seady sae (i.e., in he long run or on average ) is inflaion a purely moneary phenomenon. Spring 204 Sanjay K. Chugh 29
i i c. A compleely analogous condiion holds in period - (or period -2, or period +, ec.): i i c. Le s comine hese ime- and ime-(-) versions of he consumpion-money opimaliy condiion y dividing he former y he laer; doing so gives us / c i i. / c i i Reorganizing erms a i, we have c i i. c i i From our usual definiion of inflaion, we have ha. Now define he growh rae of nominal money in an analogous way. Specifically, define as he growh rae of he nominal money sock of he economy eween period - and period. As an example, if he nominal money supply does no change eween period - and period, he nominal money growh rae is 0. Using our definiions of he inflaion rae and he money growh rae aove, we can rewrie i as c i i. c i i Now le s consider he seady-sae. Recall our definiion of a seady-sae as a sae of he economy in which all real variales sele down o consan values over ime, u nominal variales need no do so. Le s make he laer par of his concep a i more precise han we did earlier: i is only nominal level variales ha need no sele down o consan values in he long run. For example, he nominal price level of he economy need no sele down o a consan value in he long run. The same is rue of he level of he nominal money supply of he economy. Spring 204 Sanjay K. Chugh 220
On he oher hand, nominal growh rae variales do sele down o consan values in he long run. Tha is, he growh rae of a nominal variale is considered o e a real variale. oreover, ineres raes, regardless of real or nominal, also sele down o consan values in he seady-sae. Applying his more precise concep of a seady-sae o he previous expression aove, we see ha all of he variales conained in i sele down o consan values in he long-run: ha is, c c c, i i i,, and. Imposing hese seady-sae values and canceling erms, we oain or, more simply,,. (.2) Expression (.2) capures he essence of he monearis school of hough wihin macroeconomics, saing ha (in he long run i.e., in he seady sae) he inflaion rae of he economy is governed y he rae of growh of he money supply. The rae of growh of he money supply is conrolled y an economy s cenral ank ecause i is ulimaely he economy s sole (legal) supplier of money. The higher is he growh rae of money in an economy, he higher is (in he long-run) he economy s inflaion rae. Hence, moneary policy is non-neural in he long-run. This long-run monearis perspecive is universally acceped y modern-day RBC-oriened macroeconomiss and modern-day New-Keynesian-oriened macroeconomiss oh camps acknowledge ha in he long run, nominal prices do adjus. 3 The neuraliy deae is enirely aou he shor-run. We will nex examine even furher he causes and consequences of moneary policy in oh he shor run and he long run, wih a special focus on he ineracions eween moneary policy and fiscal policy. This monearis linkage will e in he ackground of many of he causes and effecs we discuss here. 3 This view apparenly would no have een shared y Keynes himself, o whom he famous phrase In he long run, we re all dead! is ariued. Spring 204 Sanjay K. Chugh 22
Spring 204 Sanjay K. Chugh 222