Chaper 5 Moneary-Fiscal Ineracions In his secion, we riefly explore some issues surrounding he ineracions eween moneary policy and fiscal policy. In developed counries, moneary-policy-seing is effecively independen from fiscal-policy-seing, in he sense ha separae auhoriies conrol he wo ypes of policy-making. For example, Federal Reserve policy-makers are no he same as Congressional policy-makers. Even in a counry where insiuional arrangemens seemingly insulae moneary and fiscal policy from each oher, however, he conduc of each has earing on he opimal choices of he oher. Casual oservaion makes his poin seem relaively ovious for example, i is no rare o hear a cenral ank worry aou he implicaions of fiscal deficis for inflaion and is consequences for is own policy-seing. There are poenially very many ways in which moneary and fiscal policy inerac wih each oher. One way in which ineracions eween he wo are hough aou is using game-heoreic ools. In such an approach, fiscal auhoriies and moneary auhoriies are viewed as playing a game agains each oher. Microeconomiss have developed rich game-heoreic ools o analyze various aspecs of such ineracions. Anoher approach o hinking aou moneary-fiscal ineracions in recen years has is grounding in he dynamic equilirium models ha have ecome a saple of macroeconomic heory since he RBC revoluion. The focus on he analysis in his approach is on a governmen udge consrain ha involves oh fiscal and moneary ineracions. We skech he asic idea ehind his second way of considering moneary-fiscal ineracions. Before even eginning, we poin ou ha using he RBC-dynamic-equilirium approach o sudying moneary-fiscal ineracions is in is infancy. The model we ouch on here is likely only he eginning of a large field of research ye o e developed in coming years. In he model, here are wo agens: a fiscal auhoriy ha conrols governmen spending and axes, and a moneary auhoriy ha conrols he money supply. We descrie each agen in urn, and hen examine how and why hey inerac wih each oher, including how which auhoriy ges o se policy firs has an imporan effec on he policy choice of he oher auhoriy. The Fiscal Auhoriy s Budge Consrain To descrie he fiscal auhoriy, all we need do is specify is flow udge consrain. In period, he fiscal auhoriy has a flow udge consrain T T Pg B T P B RCB. (.3) Spring 204 Sanjay K. Chugh 223
From lef o righ, he erms in his expression are: he nominal amoun of governmen spending ( g is he real amoun of spending); he nominal quaniy of governmen onds ha mus e redeemed (i.e., paid ack) in period (which is simply he value of onds ousanding a he eginning of period ); he lump-sum axes colleced y he governmen; he nominal value of new onds sold o he pulic in period (each uni of which has nominal price P ); and nominal receips from he cenral ank, which are he profis earned y he cenral ank and ransferred o he fiscal auhoriy. The noaion used is as we ve developed hroughou he course, excep for he sligh modificaion ha T we denoe using B he oal governmen onds ousanding a he end of period. We assume, as efore, ha he face value of each ond is FV. In developed counries, even hough he moneary auhoriies and fiscal auhoriies are disinc insiuions, profis earned y he cenral ank (from is normal operaions as well as from he ac of prining money, over which he cenral ank has conrol) are urned over o he fiscal auhoriy on a regular asis (on he grounds ha he cenral ank is a non-profi organizaion and is ulimaely charered y he fiscal auhoriy). These profis ha he fiscal auhoriy receives from he moneary auhoriy are capured y he erm in RCB aove. In he aove udge consrain, he lef-hand-side represens oulays for he fiscal auhoriy in period, while he righ-hand-side represens income iems for he fiscal auhoriy in period. The Moneary Auhoriy s Budge Consrain There exiss also a moneary auhoriy (a cenral ank). Is purpose is essenially jus o conrol he nominal supply of money in he economy. In developed counries, he sysem ha has evolved y which a cenral ank changes he money supply in he economy is o conduc open marke operaions, in which he cenral ank rades some of is holdings of governmen (i.e., fiscal-issued) onds for money. For example, if he Fed wans o increase he supply of money in circulaion, i uys some governmen onds from he open marke (hence he erm open-marke operaions ), for which i exchanges money, herey increasing he quaniy of money in circulaion. If he Fed wans o decrease he supply of money in circulaion, i does he opposie: i sells some of he governmen onds i holds in is asse holdings o he open marke, in exchange receiving money from he counerparies o he ransacions. The money he Fed hus receives is no longer in circulaion. M Denoe y B he moneary auhoriy s holdings of governmen onds (as disinc from T B aove). The flow udge consrain of he moneary auhoriy is hus M M P B RCB B M M. The lef-hand-side represens oulays of he moneary auhoriy, which consis of purchases of governmen onds (ha is, even he moneary auhoriy mus pay he marke Spring 204 Sanjay K. Chugh 224
price P o purchase onds i is no simply given onds y he fiscal auhoriy) and he profis ha mus e urned over he fiscal auhoriy. The righ-hand-side represens M income for he moneary auhoriy, which consiss of mauring onds B, and he prining of new money, which is he erm M M. As per our usual noaion, M is he quaniy of money ousanding in he economy a he end of period - (equivalenly, a he eginning of period ) and M is he quaniy of money ousanding in he economy a he end of period. Thus, M M is he amoun y which he nominal money supply changes during period. If M M 0, he cenral ank prined money during period, and if M M 0, he cenral ank removed money from circulaion in period. Changes in he money supply show up on a cenral ank s alance shee; as such, hey represen income iems for he cenral ank, which hus need o e accouned for in he udge consrain. From he money auhoriy s udge consrain, i is easy o see ha M M RCB B P B M M is he amoun ha he moneary auhoriy ends up urning over o he fiscal auhoriy. Consolidaed Governmen Budge Consrain Comining he las way of expressing he moneary auhoriy udge consrain wih he fiscal auhoriy udge consrain, we have T T M M Pg B T P B B P B M M. T Nex, define he difference eween he oal ond issue of he fiscal auhoriy ( B ) and M he ond holdings of he moneary auhoriy ( B ) as he quaniy of onds held y he T M privae secor (denoed y B, wihou superscrip). Tha is, B B B is he quaniy of fiscal-issued onds no held y he cenral ank. B represens he ne governmen de held y he privae secor, since ond repaymens y he fiscal auhoriy o he moneary auhoriy do no ener he privae secor. This B is wha we considered when we sudied he MIU model. T M Wih he definiion B B B, he preceding expression can e rearranged o give Pg B T P B M M, which we refer o as he consolidaed governmen udge consrain (consolidaed GBC). This udge consrain links he aciviies of he fiscal auhoriy axing, spending, and issuing onds wih he aciviies of he moneary auhoriy changing he supply of money. The link fundamenally comes hrough he RCB ha he cenral ank is required o urn over o he fiscal auhoriy. Spring 204 Sanjay K. Chugh 225
The consolidaed GBC is a condiion which mus always hold in he economy. I hus makes clear ha fiscal policy and moneary policy mus e consisen wih each oher, an issue o which we now urn. Acive Fiscal Policy/Passive Moneary Policy Suppose ha when period arrives, he fiscal auhoriy is ale o commi o a paricular choice of g, T, and B -- ha is, i picks a paricular cominaion of spending, axes, and de. Suppose furher ha he fiscal auhoriy makes hese choices wihou heed o he consolidaed GBC. Can i simply ignore he consolidaed GBC when choosing is policy? The answer is yes, ecause here is anoher free variale in he consolidaed GBC: he amoun of money ousanding in he economy a he end of period, M, which is under he moneary auhoriy s conrol. Afer commiing o is paricular fiscal policy, he onus is hen on he cenral ank o make he consolidaed GBC hold y prining some appropriae quaniy of money. Recall in he inroducion we said ha game-heoreic conceps are ofen used o sudy moneary-fiscal ineracions. We can apply a game-heoreic idea o he aove scenario: suppose he fiscal auhoriy ges o move firs (i.e., efore he cenral ank) in ha i can choose axes, spending, and de efore he cenral ank chooses he money supply. As we jus saw, he fiscal auhoriy is hen ale o force he moneary auhoriy ino a paricular acion ecause he moneary auhoriy hen mus see o i ha he consolidaed GBC is saisfied. In he language ha has developed in he field, he scenario jus oulined is one in which fiscal policy is acive (ecause i ges o move firs and hus is no consrained in any of is choices) and moneary policy is passive (ecause i moves second and is choice is ound y he consolidaed GBC). Moneary policy here is essenially jus reacive (passive) o fiscal policy. Acive Moneary Policy/Passive Fiscal Policy Suppose he opposie scenario were rue. Suppose i is he moneary auhoriy ha ges o move firs in ha i can se whaever money supply M i wans (moivaed, perhaps, y some inflaion sailizaion goal, le s say). In his case, he fiscal auhoriy mus reac y seing some appropriae cominaion of g, T, and B. Here we say ha moneary policy is acive (ecause i ges o move firs and hus is no consrained in is choice) and fiscal policy is passive (ecause i moves second and one of is choices is ound y he consolidaed GBC.) Spring 204 Sanjay K. Chugh 226
I may seem ha, ecause he fiscal auhoriy has hree insrumens a is disposal (spending, axaion, and de issuance), he fiscal auhoriy is no all ha consrained in is decisions. I is consrained, however, compared o he acive fiscal policy case considered aove. In he acive fiscal policy case, he fiscal auhoriy is ale o choose all hree of he insrumens g, T, and B freely, knowing ha he moneary auhoriy will have o pick up he slack y prining some appropriae quaniy of money. In conras, when moneary policy is acive, he fiscal auhoriy is ale o freely choose only wo ou of he hree insrumens g, T, and B : once i has fixed wo of hem, he hird is pinned down y he consolidaed GBC. The Ineremporal Governmen Budge Consrain To coninue our analysis of fiscal-moneary ineracions, le us urn o he consolidaed GBC aove, which is acually a flow udge consrain, ino he lifeime (or ineremporal) governmen udge consrain, which is he more ypical form of he governmen udge consrain used in analyzing dynamic fiscal-moneary ineracions. In ransforming he flow GBC ino an ineremporal one, we will also along he way inroduce imporan erminology and ideas. Firs, ake he flow GBC aove and divide hrough y he period- price level, which gives B T P B M M g. P P P P M M The las erm on he righ-hand-side,, measures he real resources, in unis of P period- goods, accruing o he governmen from he ac of money creaion: he amoun of money creaed (which could e a negaive numer, in which money was desroyed i.e., ake ou of circulaion) during period is M M, and dividing y P, which has algeraic unis of (ime- dollars/ime- goods), yields he amoun of period- goods he governmen earns y expanding he money supply (or loses if i conracs he money supply). These real resources are known as seignorage revenue, and we will ofen areviae i as sr. Formally, sr M M P. Now coninue re-arranging he GBC: we can move erms around o arrive a B T P B g sr. P P P Spring 204 Sanjay K. Chugh 227
The lef-hand-side is he real amoun of governmen de ha comes due a he sar of period, and he righ-hand-side is he real amoun of (ne) revenue he governmen has. This ne revenue comes from moneary sources (he seignorage revenue) and fiscal sources (he difference eween ax revenue plus proceeds of new ond sales and governmen spending). Defining T / P as real ax collecions in period, and B / P as he real amoun of governmen de ousanding a he end of period, we can express he preceding as B sr g P P This expression is of course simply sill he period- GBC. The period-+ GBC is analogous, B sr g P. P The ojecive of he nex several algeraic rearrangemens we will go hrough is o replace he erm in he period- GBC using he period-+ GBC. Firs, muliply oh sides y P, giving B P sr P Pg P P. Nex, divide oh sides y P o oain B P sr P P g P P. P P P P P The lef-hand-side, y our definiions, is simply. Also, recall, from our earlier sudy of he dynamic models, ha inflaion eween period and + is defined y P P P, which means ha. Using hese definiions in he las P P expression, we have ( ) sr ( ) ( ) g P ( ), which, despie all he manipulaions, is sill jus he period-+ GBC. Finally, we are ready o inser his ino he period- flow GBC from several seps ago; doing so gives us B sr g P ( ) sr ( ) ( ) g P( ) P. Pulling he ( ) erms ogeher, B sr g P ( ) sr gp P, and hen cleverly grouping he seignorage erms ogeher and he fiscal erms ogeher, Spring 204 Sanjay K. Chugh 228
B P sr P ( ) sr g P ( ) g P ( ) P. Recall from he MIU model (or, indeed, any moneary model) he relaion eween he nominal price of a ond and he nominal ineres rae, P ; also recall he Fisher i i equaion, r. These wo facs imply ha, in he las equaion, P ( ) i r. Replacing he P ( ) in he las equaion using his, he period- GBC can e wrien B sr g P P r r r sr g Noice ha in his represenaion of he period- GBC, seignorage revenue, ax revenue, and governmen spending in oh periods and + appear. If we were o susiue ou he erm on he far righ of he las expression using he period-+2 GBC, we would have B sr sr 2 g g 2 P 2 2 sr 2 g P r ( r)( r ) r ( r)( r ) ( r)( r ) afer going hrough a similar se of algeraic rearrangemens. 4 If we hen susiued ou 2 using he period-+3 GBC, and hen coninued successively susiuing ou fuure real ond erms using successive flow GBCs, we would ulimaely arrive a he infinie-period version of he GBC,. B srs s g s P s0 s0( rs) s0( rs), 4 Tedious, yes, u perhaps worhwhile for you o race hrough yourself o convince yourself ha his is in fac correc. Spring 204 Sanjay K. Chugh 229
which, noe well, involves oh an infinie produc and an infinie summaion. 5 The successively growing producs he firs erm of which is, he second erm of r which is, he hird erm of which is, and so on ( r)( r ) ( r)( r )( r2) are discoun facors. 6 We will refer o his las expression as he ineremporal governmen udge consrain, which is an infinie-period version of he flow GBC oained y chaining ogeher all of he flow GBCs from period on ino he infinie fuure. Noe ha he righ-hand-side of he ineremporal GBC is a funcion of all curren (period-) and fuure seignorage revenue (which sems from money creaion, which is in he province of he moneary auhoriy) as well as all curren and fuure primary udge surpluses (which is he difference eween ax collecions and governmen spending and is in he province of he fiscal auhoriy). There are a hos of macroeconomic implicaions of he ineremporal GBC, a few of which we urn o now. In he following, we essenially jus ake alernaive views on he ineremporal GBC, in he sense ha we rea some pars of i as fixed and ask wha oher pars of i mus adjus in order o make i hold wih equaliy. Before proceeding, we define one more noion: a non-ricardian fiscal policy is a policy y he fiscal auhoriy (which, again, conrols axaion and governmen spending) in which he curren and fuure pah of regular fiscal insrumens (i.e., axes and spending) is no adjused o ensure ha he ineremporal GBC holds (or, in he erminology common in his field, o ensure ha ineremporal solvency holds ). Loosely speaking, if he fiscal auhoriy is running a non-ricardian fiscal policy, i does no care aou or pay heed o he needs of ineremporal solvency when seing is curren and fuure policy insrumens. 5 Technically, if you do several seps of he forward susiuions and le ime go o infiniy, you will see P s s ha here is acually anoher erm on he righ-hand-side, lim s s0( rs). A echnical condiion ha mus e imposed in any well-specified dynamic macro model (including ours) is ha his limi is zero, hence he infinie-period GBC aove is correc. This limi eing zero is he infinie-period analog of he resricion from our very simple wo-period model ha A2 0. Wheher in he wo-period case or he infinie-period case here, his so-called No-Ponzi condiion jus saes, essenially, ha he value of asses a he end of he economy are zero (wheher he end e a he end of period 2 or a he end of period infiniy ). Analyzing his No-Ponzi resricion furher is ouside our scope and is eer lef o a more advanced course in macroeconomic heory. 6 Recall from our infinie-period model ha in seady-sae, r, which means r Spring 204 Sanjay K. Chugh 230. Our inerpreaion of was ha i was consumers discoun facor (i.e., a measure of heir impaience). Hence he erminology here.
By conras, a Ricardian fiscal policy is hen one in which he fiscal auhoriy does pay heed o he ineremporal GBC when seing curren and fuure policy. Under a Ricardian fiscal policy, he fiscal auhoriy views iself as eing consrained y he ineremporal GBC (i.e., i elieves ha is acions mus e consisen wih i), while under a non- Ricardian fiscal policy i does no view iself as eing consrained y he ineremporal GBC. Wheher or he fiscal auhoriy elieves i mus saisfy is udge consrain is likely an issue we canno resolve, ecause in he end, as we will now see, he (ineremporal) governmen udge consrain is saisfied he ie comes in which prices and/or quaniies mus adjus o ensure ha i is saisfied. In all ha follows, he analysis is ased on he ineremporal governmen udge consrain, which we reproduce here for convenience: B srs s g s P s0 s0( rs) s0( rs) A Fiscal Theory of Inflaion Enering period, he nominal de sock B is fixed ha is, i canno e changed (le s assume no defaul) and hence is he nominal de he governmen mus repay a he sar of period. Suppose ha he moneary auhoriy, hrough is conrol of he money supply, is perfecly ale o conrol and commi o a pah hrough ime of seignorage revenue saring from dae onwards. Tha is, suppose he moneary auhoriy is ale o credily commi iself o a sequence of seignorage revenue ino he infinie fuure, ( sr, sr, sr2, sr 3,...). Finally, also suppose ha i is moneary facors ha (effecively) deermine he price level in period, so ha once he cenral ank has announced is moneary policy (which, here, akes he form of he announcemen of is pah of seignorage), he price level P ecomes fixed. Wih hese policy and marke arrangemens in place, fiscal policy, hrough is sequence of curren and fuure primary fiscal surpluses (which, afer all, is wha he sequence of ( g) erms represens) mus e se so as o saisfy he ineremporal governmen udge consrain. Relaing his o he noions developed aove, fiscal policy here can e viewed as passive: any changes in wha he moneary auhoriy is doing in erms of generaing seignorage and/or any changes in he price level P mus e me y a reacion y fiscal auhoriies o ensure ineremporal solvency. On he oher hand, he acive power could reside wih he fiscal auhoriy; he fiscal auhoriy could independenly (in our earlier erminology, acively ) se is pah of ( g). If i is sill he case ha P is deermined y facors oher han he ineremporal Spring 204 Sanjay K. Chugh 23
governmen udge consrain, hen acive fiscal policy requires ha he pah of seignorage revenue adjuss o ensure ineremporal governmen solvency. Noe ha, viewed hrough he lens of he ineremporal governmen udge consrain, i is no necessarily he case ha curren (period-) money creaion mus change if here is a change in period primary fiscal policy, u raher ha curren and/or fuure seignorage generaion mus change. 7 Curren or fuure seignorage generaion which is fuelled y money creaion ulimaely means (higher or lower) inflaion, so long as we elieve ha a quaniy-heoreic link operaes eween money growh and inflaion he cash-in-advance model, o ake one example, uilds in he view ha indeed such a link exiss, a leas in he long run. Hence, wih acive fiscal policy and a fixed period- nominal price level P, he ineremporal governmen udge consrain ariculaes a fiscal heory of inflaion. This is nohing more han a slighly-more careful resaemen of our earlier acive/passive disincions: if he fiscal auhoriy does no alance he governmen udge consrain, hen i falls on he moneary auhoriy o do so. Moneary policy acions, in urn, have consequences for inflaion, u ecause hese acions hemselves were induced y fiscal policy, his is ulimaely a fiscal heory of inflaion, even hough he proximae cause of he inflaion was money creaion. A Fiscal Theory of he Price Level Wha if in he scenario jus oulined of an acive fiscal policy, he moneary auhoriy did no link? Wha if insead, he cenral ank was srong enough/credile enough/commied enough o is own independen moneary policy (presumaly guided y some welfare maximizaion ideas in he ackground) ha i refuses o e induced o money creaion/desrucion y fiscal policies. The ineremporal governmen udge consrain mus e saisfied somehow. Bu how, if neiher auhoriy reacs o make i hold? The answer lies in he marke-deermined price level P. In our aove discussion of he fiscal heory of inflaion, we ook he sand ha P is deermined y facors oher han he ineremporal governmen udge consrain. Bu if neiher regular fiscal policy nor moneary policy adjuss appropriaely, hen i mus e ha P (which, afer all, is no se in sone a he eginning of period unless prices are compleely sicky ) adjuss o saisfy he ineremporal udge consrain, for a given B. 8 7 If i is no he case ha curren-period seignorage changes, i mus e ha he governmen de posiion eween and + asors he change u of course, as in any ineremporal udge consrain, inermediae asse posiions do no appear, only iniial asse posiions. 8 There is anoher opion, of course, one alluded o aove: i could e ha he governmen reneges on he promised B, i.e., i could e ha he governmen defauls on (par of) is nominal de. Such an Spring 204 Sanjay K. Chugh 232
To make he discussion a i more concree, suppose ha, relaive o is original plans for he sequence of ( s gs) s0, he fiscal auhoriy decides o lower ( g) u leaves ( s gs) s (noe carefully he ime indexes here!) unchanged. Tha is, suppose he governmen decides o lower he primary fiscal surplus in period, u leave all fuure surpluses unchanged. Now also suppose ha he independen cenral ank remains commied o is plan for he money sock, which means i will no e induced o deviae from is plan for he sequence sr, s 0,,2,...,. s The governmen canno/does no defaul on is nominal de repaymen oligaion B. The only way, hen, for he ineremporal GBC o hold is for he period- price level P o rise; i mus rise ecause he righ-hand-side of he ineremporal GBC has fallen (due o he reduced primary fiscal surplus in period ), which requires ha he lef-hand-side falls, oo. Wih B fixed, his requires a rise in he price level in he curren period. This mechanism, y which a change in fiscal policy ranslaes ino a direc change in P is ermed he fiscal heory of he price level. We migh wan o say ha in his case a change in fiscal policy resuled in inflaion ecause i caused a rise in P. Viewed his way, seems o e lile difference eween he fiscal heory of he price level and he fiscal heory of inflaion. The disincion is sule, ye imporan. Under he fiscal heory of he price level, any shock (i.e., a change in fiscal policy unanicipaed y markes) ranslaes immediaely and fully ino a one-ime change in he nominal price level. If fiscal policy never changes again, here need e no fuure unanicipaed changed in he nominal price level. On he oher hand, under he fiscal heory of inflaion, he period- price level has nohing o do wih fiscal policy from period- onwards; insead, a change in curren or fuure fiscal policy ranslaes ino a change in money creaion a some ime in he presen or fuure, implying addiional inflaion in he fuure. In some sense, he fiscal heory of inflaion and he fiscal heory of he price level are he polar opposie heories. The former effecively saes ha surprise changes in fiscal policy leads only o fuure changes in inflaion, u curren inflaion is unaffeced. The laer effecively saes ha surprise changes in fiscal policy leads only o changes in curren inflaion, u fuure inflaion is unaffeced. In realiy, one migh (proaly naurally) expec ha fiscal pressures are relieved hrough oh channels ha surprise changes in fiscal policy lead o changes in oh curren and fuure inflaion. Such a division of fiscal pressure on nominal prices ino curren pressure versus fuure pressure is in pracice hard o disenangle, and, indeed, proaly plays ou in differen ways in differen counries and in differen ime periods. I is good o undersand, hough, he adjusmen may in fac e a very relevan one o consider for developing counries, in which de defauls are no ha uncommon. For he governmen of a counry such as he Unied Saes, however, which has never defauled on is de, his siuaion may e less relevan a descripion of realiy. Spring 204 Sanjay K. Chugh 233
underlying ensions presen; he ensions are ariculaed in he fiscal heory of inflaion and he fiscal heory of he price level. Spring 204 Sanjay K. Chugh 234