Lecture II: Fiscal and Monetary Theories of Inflation

Transcription

1 Lecure II: Fiscal and Moneary Theories of Inflaion 1

2 Fiscal-Moneary Policy Links 2 Two Polar Regimes Ricardian Regime: Fiscal policy adjuss o ensure governmen s solvency (IBC). Moneary policy ses ineres raes and/or money supply consisen wih inflaion objecive. Non-Ricardian Regime: Fiscal policy ses g and inconsisenly wih wih IBC. The price level adjuss so as o ensure ha IBC holds. case of fiscal dominance : moneary policy ypically can only choose beween inflaion now vs. inflaion laer.

3 Fiscal-Moneary Policy Links 3 Basic governmen accouning wih cenral bank Take Eq. (I.16) and add cenral bank receips (RBC): B G T R B RBC T P 1 T 1 1.: G R B B T RBC P 1 T T 1 1 (I.23) Cenral bank ransfer o Treasury Where he subscrip T accouns for oal governmen bonds.

4 Fiscal-Moneary Policy Links 4 Cenral Bank Accouning: Typical Cenral Bank Balance Shee Asses Liabiliies Inernaional Reserves ("NFA") Ne Domesic Asses ("NDA") High Powered Money ("H" or "M") Divide by p only if everyhing is expressed in real erms R B B RBC ( M M ) / p 1 M M (I.24) Change in Governmen bond holdings in he hands of he cenral bank (cenral bank financing of Treasury) Cenral bank finances is spending wih issuance of high powered money

5 Fiscal-Moneary Policy Links 5 Governmen bond holdings in he hands of households is of course oal governmen bond issuance less he sock of governmen bonds siing in he cenral bank balance shee (under he iem NDA ). Hence: T M B B B Solving (I.24) for RBC, plugging ino (I.23) and using he above, we end up wih he consolidaed budge for he governmen (i.e. Treasury + Cenral Bank): B G T R B ( M M ) / p P : G T R B B ( M M ) / p P (I.25)

6 Fiscal-Moneary Policy Links 6 Eq. (I.25) says ha he consolidaed governmen s primary defici can now be financed wih eiher ne bond issuance (i.e. discouned of ineres paymens) o he households plus money issuance he so-called seignorage financing. Clearly, bond financing can be expensive: he governmen has o pay ineres rae r on is bond issuance. And we have seen in Figure 4, ha r can be high!

7 Fiscal-Moneary Policy Links 7 Bu his doesn mean (as we will see more shorly) ha seignorage financing is no cosly! To sar examining his, re-wrie (I.25) as: p M M G T R B B P p p 1 p 1 M R B B R M 1 m p 1 p m Real reurn on money balances R 1 p p 1 Real money balance

8 Fiscal-Moneary Policy Links 8 Prima-facie, even wihou aking ino accoun oher (allocaive) coss of price insabiliy, he above eq. shows ha money financing can be cosly. m E.g. if here is deflaion (i.e. p>p+1), R 1 he rae of p 1 reurn paid on money can be high. p So, money financing is no so rivially on a purely accouning basis!

9 Money, Deficis and Inflaion in General Equilibrium 9 This raises he fundamenal quesion of why people hold money. And anoher, no less ricky quesion, of wha is money. In his lecure, we shall confine ourselves o he former quesion. Under complee markes, fia money can only be a sore of value ha, in he limi (i.e. T->, imposing he ransversaliy condiion), is valueless.

10 Money, Deficis and Inflaion in General Equilibrium 10 So, moivaing money holdings would require some fricion. Here we will review a model in which holding money saves ransacions coss shopping ime The model follows L-S, chaper 24. This basic se-up will be used o discuss various fiscalmoneary models of inflaion.

11 Money, Deficis and Inflaion in General Equilibrium 11 Uiliy: Consrains: 0 u( c, l ) b m m c y b 1 1 R p p leisure 1 l where is shopping ime ( s in L-S bu we use lile dela o avoid using s which we used before for fiscal surplus). As before: endownmen economy wih no uncerainy.

12 Money, Deficis and Inflaion in General Equilibrium 12 Shopping-ime ransacion echnology: m 1 l H c, 1 p m 1 / p c So, we can now se up he Lagrangian and solve i: m b m m u( c, l ) y b c 1 l H c, 0 p R p p

13 Money, Deficis and Inflaion in General Equilibrium 13 FOC wih respec o c, l, b, m 1 1 yield: R 1 uc( ) ul ( ) Hc( ) u ( 1) u ( 1) H ( 1) c l c (I.26) R R R m H m p / () (I.27) R R m uc() R ul() Hc( ) Hm/ p( ) 0 (1.28) (Homework: Provide he inuiion for all hese expressions)

14 14 Money, Deficis and Inflaion in General Equilibrium Applying he implici funcion heorem o he above yields: m p 1 F( c, R / R ) m 1 Recalling ha R and R, i hus follows ha: m p p (1 i ) p / p 1 where F 0, F 0. c i m 1 F( c, Rm / R ) (, ) F c i p (I.29) Thus his micro founded model delivers he familiar money demand ( LM curve) funcion.

15 Money, Deficis and Inflaion in General Equilibrium 15 As we did in he discussion of he Ricardian equivalence in our firs lecure, now inroduce he governmen. Recall he budge consrain in (I.25): G T R B B ( M M ) / p P Where M is money supply. Equaing M o money demand m in (I.26) and assuming exogenous sequences for governmen spending and axaion, and iniial asse holdings, we can solve he model.

16 Money, Deficis and Inflaion in General Equilibrium 16 Le s characerize he saionary equilibrium of his economy. P { G g, T, B} Le be se by he governmen, inheried from he pas (all small caps denoe equilibria). c g y Le he resource consrain be ; and le Rß=1. { B, M } 0 0 The equilibrium is given by a price sysem so ha for c, M, B 1, he household opimal problem and he governmen budge consrain are saisfied. Equilibrium Rm (1-inflaion rae) and po are hen pinned-down.

17 Money, Deficis and Inflaion in General Equilibrium 17 We seek an equilibrium for which X=X, where X is any of exogenous or endogenous variables in equilibrium. As shown in L-S (eq ), his equilibrium delivers he following expression linking he fiscal posiion and he rae of inflaion, p+1/p in saionary equilibrium: P ( R 1) g B f ( Rm )(1 Rm ) R (I.30) Overall Governmen Defici Seignorage financing

18 Money, Deficis and Inflaion in General Equilibrium 18 m 1 1 Noe ha f( Rm ) and ha 1Rm. p p p 1 p We can hus decompose oal seignorage financing as he produc of he inflaion ax base componen and he inflaion rae componen. Imporan: noe from above ha he inflaion ax base is dependen on he inflaion rae: rising inflaion lowers money demand m+1! Hence, here is poenial for muliple equilibria!

19 Money, Deficis and Inflaion in General Equilibrium 19 Illusraion of he relaionship beween defici and inflaion, he seignorage Laffer curve (L-S, ): i) Pu funcional forms in u and H o compue f(rm)=f(c,rm/r) ii) Se o pin-down R=1/. iii) Se c o pin down l=1-c. iv) Se coefficien of risk aversion s and he (inverse of) he leisure elasiciy coefficien (a). v) Then plo Rm=1-(gross)inflaion rae agains he defici. Homework: do i for various s. Then, fix s2 and change 0.9

20 Money, Deficis and Inflaion in General Equilibrium 20 Using his model s saionary equilibrium soluion we can now Effecs of an increase in Mo To see his, consider he soluion a =0: M p 0 0 f ( R ) ( g P B ) B / R m 0 0 where f ( R ) m / p m 1

21 Money, Deficis and Inflaion in General Equilibrium 21 Using his model s saionary equilibrium soluion we can now sudy he effec of various policy experimens Effecs of an increase in Mo, all else consan To see his, consider he soluion a =0: M p 0 0 P ( R1) f ( Rm ) ( g B0 ) R (I.31) where f ( R ) m / p m 1

22 Money, Deficis and Inflaion in General Equilibrium 22 P ( R 1) Since ( g B0 ) will no change, from (I.30) i mus also be ha Rm will R no change. Hence, Mo/Po will no change DMo=DPo. So, here is concomian jump in he price level as M increases

23 Money, Deficis and Inflaion in General Equilibrium 23 Using his model s saionary equilibrium soluion we can now sudy he effec of various policy experimens Effecs of a persisen fiscal defici From (I.30) and he seignorage Laffer curve, i is clear ha a permanen increase in he fiscal defici will increase (1-Rm), i.e. he seady-sae inflaion rae, if one is on he righ side of he Laffer curve. However, here may be an equilibrium ha he ax base increases, so he bigger defici is financed wih higher M/P.

24 Money, Deficis and Inflaion in General Equilibrium 24 Fiscal Requiremen for Price Sabiliy Seing 1-Rm=0 in (I.30), clearly requires he overall (no he primary!) fiscal defici o be zero. Wih R given, his of course has implicaions for he required primary defici oo: P ( R 1) g B 0 R R1 r. : ( g) B B R (1 r)

25 Money, Deficis and Inflaion in General Equilibrium 25 Limis o wha Moneary Policy Can Do ( Unpleasan Monearis Arihmeics ) P Suppose ha g rises. Then from (I.30) permanen inflaion 1-Rm will rise. The cenral bank hen ries o miigae he impac on Po, engaging ino open marke operaions: buy high-powered money (reducing M in =1) and selling bonds (increasing B). M p M P ( g 0 B0) B / R p Effec is ambiguous: a bes lower po bu higher B (due o ineres paymens on deb) increases 1-Rm

26 Money, Deficis and Inflaion in General Equilibrium 26 Opimum Quaniy of Money ( Friedman rule ) The idea is ha reducing shopping ime increases welfare. Hence moneary policy should saiae households wih money. 1 Since Rm (1, ), he Friedman rule implies ha he opporuniy cos of holding money should be as low as possible. Here i is herefore bound by he reurn on (safe) bonds. So, Rm R.

27 Money, Deficis and Inflaion in General Equilibrium 27 To see wha implicaions his has for nominal ineres seing (e.g. he insrumen conrolled by cenral banks), recall: Rm p / p 1 R 1 r 1 i E (1 R ) i R m m (I.32) R wih, his implies ha. m R i 0 This is he well-known Friedman rule.

28 Money, Deficis and Inflaion in General Equilibrium 28 The Fiscal Theory of he Price Level Recall ha in solving he model B (he real value of public deb) is deermined by he governmen and, given g,, R, Bo and Mo, inflaion (1-Rm) and Po are hen deermined. Under he FTPL, B is endogenous: while he governmen can decide on nominal deb, he price level will adjus o as o make B consisen wih he iner-emporal budge consrain. Again, we can use eqs. (I.30) & (I.31) o see how i works.

29 Money, Deficis and Inflaion in General Equilibrium 29 Re-arrange (I.30) o wrie: B R 1 [ P g f ( Rm )(1 Rm )] R1 R P R B [ g ] f ( Rm)(1 Rm) R1 R1 P R B R [ g ] f ( Rm )(1 Rm ) R So, given g,, R, R, one can pin down real public deb, B. m

30 Money, Deficis and Inflaion in General Equilibrium 30 So, he exra requiremen here is ha policy can deermine seignorage (1-Rm) or, equivalenly, given (I.32), o peg he nominal ineres rae i. Once his is done and, wih Bo and Mo given, he price level is pinned down by compuing po from re-arranging (I.31): M0 B 0 R g R f R m R m p0 0 0 ( ) ( )(1 )

31 Money, Deficis and Inflaion in General Equilibrium 31 Noe also ha he pah of money supply also ges deermined using: M 1 f Rm p 0 ( ) Given Mo, hen, Mo, M1, is now deermined. So, once he price level is pinned down by he fiscal heory of he price level, he pah of money supply is now also endogenously deermined. A corollary is ha one does no need money for he price level o be deermined.

32 Money, Deficis and Inflaion in General Equilibrium 32 So, we currenly have wo differen fiscal heories of inflaion! The earlier Sargen and Wallace one shows ha he inflaion rae adjuss o he overall fiscal defici (g-+rb) in saionary equilibrium. So, fiscal policy is dominan. The price level (po, p1,..) is pinned down by money supply: as we saw, his is he so-called Ricardian regime. Moneary policy can only influence he iming of inflaion (now vs. fuure), bu no long-run inflaion. So, no rue inflaion argeing under fiscal dominance.

33 Money, Deficis and Inflaion in General Equilibrium 33 New Fiscal Theory of he Price Level (Cochrane, Sims, Woodford), he seady-sae inflaion rae is chosen by policy (e.g. by nominal ineres rae pegging); for a given nominal deb, inflaion will hen increase or reduce real deb. Then wih inflaion and real deb deermined, po is pinneddown. Under FTPL, he iner-emporal budge consrain holds only a he equilibrium value of he price level. Under radiional Sargen-Wallace heory, i holds for all P.

34 Money, Deficis and Inflaion in General Equilibrium 34 Since we only observe equilibrium oucomes, i is virually impossible o disinguish empirically he wo heories. One advanage of he new fiscal heory of he price level is o rule ou muliple equilibria in he radiional heory arising from he he righ hand side of (I.30): f(rm)(1-rm). The exra resricion ha seignorage (or is inverse 1-Rm) is se by policy (i.e. nominal ineres peg) akes care of mulipliciy: Po, P1, ec. can be uniquely obained.

35 Cagan s Inflaion Model 35 Milon Friedman: Inflaion is always and everywhere a moneary phenomenon Hisorically, high and hyper-inflaions have always been associaed wih rapid growh of base money. Cagan (1956) is a classic sudy of 8 hyperinflaions (defined as π>50% per monh) ha ook place beween 1920 and Those hyperinflaions were associaed wih major macro disrupions such as he financing of war expenses.

36 Cagan s Inflaion Model 36 As mos hings in economics, here is considerable conroversy on wha was he cause/ulimae driving force of hose inflaionary ouburss. Some say seignorage financing (e.g. due o war-relaed fiscal burdens and disrupions in naional ax collecion sysems). Ohers emphasized he exchange rae (reporedly he view of much conemporary commenaors on he German hyper inflaion of ). Eiher way, inflaion was highly correlaed wih money growh.

37 Cagan s Inflaion Model 37 From Franco, 2013

38 Cagan s Inflaion Model 38 From Franco, 2013

39 Cagan s Inflaion Model 39 Cagan s main pioneering conribuion was sudy he role of inflaion expecaions in he inflaionary process. As we shall see, he modeled expecaions in an adapaive way. And concluded ha, indeed, money growh was he culpri. Bu again, in fundamenal-based models of inflaion, a he roo of rapid money growh is he exisence of non-rivial public deficis.

40 Cagan s Inflaion Model 40 From Fischer, Sahay, and Végh, 2002

41 Cagan s Inflaion Model 41 Le s now ake a look a he Cagan model [We shall follow closely Wash (2010, secion 4.4] Following Cagan, he seing is in coninuous raher han discree ime: f g rb D h. H H H PY (I.35) rae of Inflaion ax base money growh

42 Cagan s Inflaion Model 42 Now recall he money demand funcion in (I.29): m p 1 F( c, R / R ) m where c=y+g in a closed endownmen economy (i.e. wihou oupu being deermined by invesmen). Cagan noed ha he peculiar naure of high/hiper-inflaions is ha R and Dy are abou sable viz prices. So, he above becomes: m 1 FR ( m ) p

43 Cagan s Inflaion Model 43 Cagan s novely: demand for base money (H) as a raio o nominal GDP (=PY) becomes a funcion of expeced inflaion: h e exp( a ) (I.35) (I.35) ino (I.34): f e D exp( a )

44 Cagan s Inflaion Model 44 Saionary Equilibrium dh 0.: (I.37) real income growh and e (I.38) Hence: f ( ) D e a (I.39)

45 Cagan s Inflaion Model 45 Solving for ϴ gives he rae of money growh consisen wih raising Δf of seignorage revenues. (I.39) gives he condiion for max seignorage revenues: 1 a For money growh raes above ha, he inflaion ax base conracs faser wih money growh so overall seignorage falls.

46 Cagan s Inflaion Model 46 Money Supply-Inflaion Relaionship in Cagan s Model (aken from Wash, 2010)

47 Cagan s Inflaion Model 47 This figure says ha wih zero money growh,θ=0, here is no seignorage (cf. eq. I.39). In his case, inflaion is acually negaive if μ>0 from I.37. Holding μ consan (jusifiable in he shor run under high inflaions, as discussed), hen he 45 degree line plos he one o one relaionship beween money growh and inflaion. Poins A and D are wo possible soluions: boh are seady sae inflaion raes consisen wih a given defici.

48 Cagan s Inflaion Model 48 Given Δ, wheher he economy is in a high- vs. low inflaion equilibrium will depend on form of expecaions adjusmen As menioned, Cagan assumes adapaive expecaions: e. e e ( ) The equaion ha closes he model is obained by differeniaing (I.35): h.: e e e exp( ) exp( ). h h a a a. e a Inflaion forecas error (I.40) (I.41)

49 Cagan s Inflaion Model 49 (I.40) and (I.41) are a differenial equaion sysem in h/ h and e Firs, use (I.41) o subsiue ou expeced inflaion in (I.40) and solve for acual inflaion o obain:. e e ( a ) a 1a (I.42) This shows ha equilibrium inflaion will be a negaive funcion of expeced inflaion for a given real money growh θ-μ. Inuiion: as lower e rises, he inflaion ax base shrinks requiring o re-esablish he lower inflaion equilibrium.

50 Cagan s Inflaion Model 50 Then solve for changes in expeced inflaion:. e e e ( ) k 1a 1a (I.43) This equaion delivers he condiion for a non-explosive, lower inflaion equilibrium: if a 1 he coefficien will be posiive (assuming ϴ>μ) implying ha changes in expeced inflaion will be dampened as expeced inflaion ges higher. If a 1, hen he equilibrium is explosive.

51 Cagan s Inflaion Model 51 This explosive equilibrium can occur if money demand is (negaively) oo sensiive o expeced inflaion and/or expeced inflaion is oo sensiive o he gap beween acual and expeced inflaion. This is inuiive, if money demand is oo elasic o expeced inflaion, hen he inflaion ax base is lower. So, for a given fiscal defici, from equaion I.35 one can see ha faser money growh will be needed. So, inflaion will rise, ha will fuel higher inflaion expecaion, lowering he inflaion ax based, hus calling for more inflaion, ec. This vicious circle is ofen observed in hyper-inflaions.

52 Cagan s Inflaion Model 52 Noe, however, ha if you are no in his perverse equilibrium, hen adapaive expecaions allows some freeriding in defici financing. This is because expeced inflaion lags behind acual inflaion, so he demand for money will no be as low (i.e. he inflaion ax base will be higher), allowing a given defici o be financed wih lower inflaion. The downside is ha reducing inflaion akes longer: you can cu he defici bu agens expeced inflaion will converge only gradually o he new waned inflaion rae.

53 Cagan s Inflaion Model 53 Limiaions and Exensions of he Cagan Model In pracice, expecaions are arguably far more forward-looking: he feedback beween expeced and acual inflaion is closer o zero on average: lile scope for fooling agens and sysemaic free riding in defici financing via seignorage. Avoiding he explosive inflaion equilibrium can be achieved by credible policies which dampen inflaion expecaions. Sill here may be perverse feedbacks beween fiscal deficis and money growh. E.g. he so-called Keynes-Tanzi effec: real revenue loss due o lags in ax collecion (axi becomes cheaper han bus).

54 Cagan s Inflaion Model 54 There is more o his money-fiscal feedback han he Keynes-Tanzi effec. For insance, ax drag: as inflaion rises, if he ax sysem is no indexed, people move ino higher ax brackes, hus raising revenues. G can also be corroded by inflaion (e.g. delay in paying suppliers). So, overall he effec of inflaion on public deficis is ambiguous (see C-T, 2005 for a fuller discussion)

55 Cagan s Inflaion Model 55 Some boom-line: The reverse effecs of inflaion on he general governmen balance seem weak. Hence i is reasonable o assume ha in economies where he cenral bank is no insiuionally srong he causaliy ends o run in he direcion of fiscal deficis o inflaion, raher han he oher way around. In his case, money supply is sill he fuel, bu he ulimae driving force comes from fiscal imbalances.