Central Bank Review Vol. 13 (May 2013), pp.33-58
ISSN 1303-0701 print 1305-8800 online
© 2013 Central Bank of the Republic of Turkey https://www3.tcmb.gov.tr/cbr/
F
ISCALL
IMITS ANDM
ONETARYP
OLICY Eric M. Leeper∗ABSTRACTEvery economy faces a ``fiscal limit'' that delivers the maximum government debt-GDP ratio that can be sustained without appreciable risk of default or higher inflation. But governments in advanced economies issue substantial nominal debt and nominal debt is a commitment to repay in nominal units. When such economies are approaching their fiscal limits, debt can be devalued through higher current and future inflation rates. The paper develops a simple bond market supply-demand apparatus to explain how fiscal policy can be a source of inflation, while monetary policy merely determines the timing of inflation.
JEL E31, E52, E62, E63
Keywords Monetary-fiscal interactions, Sovereign risk, Fiscal theory
ÖZHer ekonomi, fark edilebilir düzeyde geri ödememe veya daha yüksek enflasyon riski olmadan sürdürebileceği maksimum kamu borcu / milli gelir oranını sağlayacak, bir
“mali sınır”la karşı karşıyadır. Fakat gelişmiş ülkelerde hükümetler önemli miktarda nominal borç ihraç etmektedir ve bu borç nominal birimlerle geri ödeme taahhüdüdür.
Bu ekonomiler kendi mali sınırlarına yaklaştıklarında bu borç, mevcut veya gelecekteki enflasyonun daha yükselmesi ile devalüe edilebilir. Bu çalışma, para politikasının enflasyonun sadece zamanlamasını belirlediği durumda, maliye politikasının enflasyonun nasıl kaynağı olabileceğini açıklamak üzere basit bir tahvil piyasası arz-talep aracı geliştirmektedir.
MALİ LİMİTLER VE PARA POLİTİKASI JEL E31, E52, E62, E63
Anahtar Kelimeler Parasal-mali etkileşimler, Ülke riski, Mali teori
∗ Indiana University, Monash University and NBER ▪ LEEPER: eleeper@indiana.edu.
1. Introdu Fiscal su is now a p tops the lis sovereign d of GDP. C Portugal, Ir immune: F fiscally res understand recession b countries to sluggish ec fiscal auste fiscal balan Every ec debt-GDP r higher infl ability to r activity and an upper maximum generally p the spendin expenditure that put a together, th surpluses c of maximu level of gov
Of cours rates to var for exampl
1 Data are for gr
2 Trabandt and labor tax rates th
uction ustainability prominent w
st with a de debt troubles Countries wi
reland, and rance and th sponsible G
able: the wo both genera o implemen conomic gr erity moves nces.
conomy face ratio that ca lation. For
raise revenu d encourage
bound on level of re prevents tax
ng side, eco es to functio
floor on s hese consid call it smax. um primary vernment de se, economie
ry over time e, will incre
ross government Uhlig (2011) cal hat may exceed re
, once the e worry in adv ebt-GDP rat s are well kn
th ratios be the United he United K Germany.1 T
orldwide fin ated autom nt sizeable f rowth in the
, has preven es a fiscal lim an be sustain both econo ues is limit e tax evasion
revenues.
evenues as rates from r onomies req on, but mos spending th erations imp
The expect surpluses y ebt.
es are subjec e and over s ease the reve
debt as a share o lculate that only evenue-maximizi
34 exclusive co vanced econ tio well ove nown, come
tween 100 a States. Maj Kingdom are These debt r nancial crisi atic budget fiscal stimul ese countrie nted the no mit that deliv
ned without omic and po
ted: tax dis n to create Political co
the elector ising to the p uire some m st societies hat is well
ply a maxim ted discount yields the m
ct to shocks states of the enues that a
f GDP, from Inte very few countri ing levels.
ncern of em nomies, larg
er 200 perce s in with deb and 150 per jor European e in the 80-p run ups are is and the p t deficits a lus package es, exacerba ormal cyclic
vers the max t appreciabl
olitical reas stortions dis Laffer-curve onstraints f
rate's intole peak of the minimum le have adopte
above that mum level ted present v maximum su s that cause e economy.
given tax ra
ernational Moneta ies Denmark and
merging econ e and small ent. Greece, bt over 150 rcent includ n countries percent rang e to a large prolonged an and induced es. But pers ated by pre cal improvem
ximum gove e risk of de sons, govern scourage ec
e effects tha further redu erance of t Laffer curve evel of gove
ed social co minimum.
of primary value of the ustainable r smax and d Good produ ate generate
ary Fund (2012a) Sweden, for exa
nomies, l. Japan whose percent de Italy, are not ge, as is e extent nd deep d many sistently
emature ment in ernment fault or nments' onomic at place uce the taxation
es.2 On ernment ompacts Taken budget stream isk-free discount uctivity, es while
. ample have
simultaneou be a source that restrict might rever a probabili thinking ab will shift a impacts on As a cou probability Devaluation the situatio Outright d obligations control the currency. M as their mo is dominate higher pro governmen A second debt denom monetary p so its value future price latitude to s maintained perspective real value nominal de ensure that This alt discussed b policy has inflation ca
3 Analyses like assuming gover epitomized by A high” with little
4 Sims (2013) p
5 Most economi as in Sargent a
usly raising e of random t the growth rse those ref ity distributi bout fiscal s and alter the the econom untry's level rises that n can occur on in which default entai and is the o eir own cu Members of onetary polic ed by countr obability of nt bonds and
d type of de minated in policy. Nom
e depends b e levels. A support nom d assumptio es on inflatio of governm ebt must be its real valu ternative m because of a
sufficient r annot happ
Ghosh, Kim, Me rnments continue
America's “Fix t supporting analy provides an insigh ists believe that f and Wallace's (19
GDP to red mness: today h of govern forms. The f ion, a featu sustainabilit e shape of t mic decisions l of governm
a country in two way h southern E
ils reneging only type of
rrency or w the Europea cy is control ries not now outright d d raises sover
evaluation is their hom minal debt is
both on expe country tha minal debt ex on of conv
on. With sur ment debt is devalued by ue is consist
eans of de a wide-sprea resolve to k en.5 This a
endoza, Ostry, an to follow past b the Debt” movem ysis.
htful discussion o fiscal inflations re 981) “unpleasan
35 duce the deb y's governme nment transf
fiscal limit, ure that carr ty.3 Intrinsic the fiscal lim s of private a
ment debt a will devalu s. The first, European co g on some f default ava who issue an Monetary lled by the E w experiencin efault reduc reign risk pr s available to me currency
a commitm ected future at is at its xpansions w ventional m rpluses fixed also fixed a y higher cur
ent with the evaluing ou ad mispercep keep inflatio
article expla
nd Qureshi (2012 behavior. But mo ment, simply app
of and contract be equire that the ce nt monetarist arith
bt-GDP ratio ent might ad fers, while f
then, is not ries importa c randomne mit distribut
agents.
approaches ue its debt
“outright de ountries now
portion of ailable to co debt denom y Union fall European C ng sovereign ces the val remia.
o countries y and who ment to repay e surpluses a
fiscal limit with higher fu monetarist o
d at their upp at its maxim rrent and fu e fiscal limit utstanding d
ption that so on low and ains inflatio
2) treat the fiscal ost public discuss plies Goldilocks
etween the two typ entral bank system thmetic” paper. L
o. Policy its dopt fiscal r future gover a single poi nt implicati ss in the ec tion, with re its fiscal lim
in some f efault”, conn w find them f outstandin ountries who minated in l into this ca entral Bank n debt probl lue of outs who issue n
retain con y in nomina and on curr
no longer future surplu or new Key
per limit, sm mum value.
uture price le .4
debt is not o long as m stable, then on as a me
limit as a point, sion of fiscal sus reasoning “this d
pes of debt deval matically monetiz Leeper and Walk
elf may reforms rnments int: it is ons for conomy esulting mit, the fashion.
nects to mselves.
ng debt o do not
foreign ategory, k, which lems. A tanding nominal ntrol of
al units, ent and has the uses, the
ynesian
max, the Higher evels to t much
onetary n fiscal eans of
derived by tainability, debt is too
uation.
ze the debt, ker (2013).
devaluation increasingly 2. The Fis
Advance challenges.
data helps t 2.1.Fiscal Figure 1 grouping “a sets of coun far more p economies coming ye levels of d cyclically-i standards.
Figure 1. F Projected
Source: Inter
Many co and the Un sizeable fis when unem recession.
describe in detai devalues nomina -10
-8 -6 -4 -2 0 2
1
n and descr y relevant in cal Problem ed economi
Although t to put the m l Developm 1 reports f advanced” a ntries saw f pronounced rose sharpl ears. Emerg debt over th induced fis
Fiscal Deficit
rnational Monetar
ountries, par ited Kingdo scal consoli mployment
il the difference b al government lia 0
Emerging a developing eco
Advanced economies
1980 90 Fiscal Balance
ribes why n advanced e m
ies today f hese challen agnitudes of ments: Now fiscal data and “emergi fiscal deficit for advanc y, and is pr ging econom
he same per scal imbala
ts and Publi
ry Fund (2012b).
rticularly m om, have rea idation prog
rates were
between a fiscal abilities.
and onomies
2000 World
10
36 the notion economies i
face both s nges are wel f the two in and the Fu from the I ing” econom ts increase b ced econom rojected to e mies, in co riod. Amon ances are c
c Debt in Pe
embers of t acted to these
grams. Tho elevated, o
inflation from mo 16 1950 60
Public D
G7
of a fisca in coming de
short-run an ll known, br
perspective uture
Internationa mies separat beginning in mies. Public
exceed 100 ontrast, exp ng advanced
certainly la
ercentages of
the Europea e large imba se consolid or still risin
onetization of deb 20 80 Debt
70 90
Advance economi
Emerging developing e
al limit may ecades.
nd long-run riefly review
.
l Monetary tely. Althoug n 2009, the r
debt in ad percent of G erienced de d economies arge by hi
f GDP: Actu
an Monetary alances by a dations bega ng, from th
bt and a fiscal in 0 20 40 60 80 100 120
16 000 10 ed
es
World g and
conomies
y grow
n fiscal wing the
y Fund, gh both rise was dvanced GDP in eclining s, these istorical
ual and
y Union dopting an even he 2009
flation that
This imm that most c Figure 2 r percentage emerging e at least dou four countr ratios of 60 The dep support eac retiree toda pension sys dependency liabilities”
turn, measu liabilities w pension and Either solu entail subst Figure 2. D Population A
Source: Worl
mediate fisc ountries fac reports dep of popula economies. W uble in these
ries -Germa 0 percent or pendency ra ch retiree. G ay to 1-2/3 stems or oth y ratio tran that a count ures the lon will have to d benefits sy ution is poli
tantial redist Dependency
Aged 15–64
ld Bank (2012).
al problem p ce. World po
endency rat ation aged
Without exc e countries b any, Japan,
higher.
atio is a ga Germany, for
workers in her old-age nslates fairl try possesse ng-run fisca o be funded ystems must
tically diffi tributions of Ratios: Pop
37
pales by com opulations ar
tios -the po 15–64- for ception, dep between now
Korea, and uge of how r example, w n 2050. For
benefits tha ly directly es. And the l l stress that d in the fut t be reforme cult in dem f wealth amo pulation 65
mparison to re projected opulation 6 r a variety
endency rat w and 2050.
d Spain- wi w many wo will go from countries w at are not pr
into the le level of unfu t a country ture with h ed to imply f mocratic soci ong segment and Older
o the loomin to continue 65 and olde
of advanc tios are expe
By that latt ill see depe orkers there m 3-1/3 work
with pay-as- re-funded, a evel of “un funded liabil
faces: eithe higher taxes
far lower lia ieties becau ts of the pop as a Percen
ng crisis e to age.
er as a ed and ected to ter date, endency are to kers per -you-go a higher nfunded ities, in er these or the abilities.
use they pulace.
ntage of
The degr the debt-GD economies.
Settlements not hold a These proj continue to projections depicts. Ye challenges Figure 3. D
Source: Cecc
6 Comparable lo an “alternative p
ree to which DP ratio pro . Those pro s, show that age-related
ections exte o age for de
place in sh es, advanced are tiny com Debt-GDP Pr
chetti, Mohanty, a
ong-term projecti policy scenario” i
h the aging ojections tha ojections, co t with no fis spending c end only to
ecades after harp relief t d economies mpared to th
ojections: Alt
and Zampolli (20
ions by the Congr in which debt exc
38 populations at Figures 3 onstructed b scal reforms
onstant, deb 2040, but p r the projec
the short-ru s face fiscal e fiscal stres ternative Fisc
010).
ressional Budget ceeds 900 percent
s create fisca 3 and 4 repo
by the Bank s or with fis
bt-GDP gro populations
tion period.
un fiscal wo l challenges
ss that loom cal Policy Sce
t Office (2010), w t of GDP.
al stress app ort for 12 ad k for Intern cal reforms ows expone in many co .6 These lon orries that F
today. But ms in the futu
enarios
which extend to 20
pears in dvanced national that do entially.
ountries ng-term igure 1 today's ure.
082, report
Figure 4. D
Note: Legend Source: Cecc
2.2. How W Because at least sinc to know h when they funds. Norw savings fun surplus targ benefits.
But man long-term f with their s a few vigne
• Ital creating so Prime Min governmen votes to cre
• The crisis, with
Debt-GDP Pr
d appears in Figu chetti, Mohanty, a
Will Policy the demogr ce countries how governm
are realized way invests nds. Other c gets with the ny governm fiscal stress.
short-run fis ettes:
lian Prime M ome stability nister Silvio nt. Berluscon eate political e Economist h governmen
rojections: Al
ure 3.
and Zampolli (20
Respond?
raphic shifts implemente ment policie . Some coun oil revenue countries, lik
e aim of usin ments seem
Should we scal challeng Minister M y in Italy's
Berlusconi ni and forme
l gridlock in t (2012) argu nt spending
39 lternative Fis
010).
s that lie in ed extensive es will adju ntries have b es. Australia ke Chile and ng the surplu to be in look at how ges to extrap ario Monti,
fiscal finan i's party wit er comedian n Italy.
ues that Fran about 57 pe
scal Policy Sc
our futures e social safet
ust to the u been buildin
and New Z d Sweden, h
uses to pre- denial abo w those gove
polate into th , who has b nces, steps
thdrew its n Beppe Gri
nce is slowl ercent of GD
cenarios
are unprece ty nets it is d unfunded lia ng sovereign Zealand have have adopte
fund future out the imp ernments are
he future? H been credite down after support of illo acquire ly heading to DP, high and
edented difficult abilities n wealth e forced d fiscal old-age pending coping Here are ed with former Monti's enough oward a d rising
public debt unemploym internationa Euro area.
• For being turne outcome is plans to do 200 percen
• Wit United Kin governmen were annou agencies, w new fiscal r
• Gre resolution i
• Aft States cont fiscal issue contentious in the comi new debt-c nicely sum terribly wr American C
These vi their fiscal decision m implement away from 3. The Fisc
Recent w the simples builds on B fixed capita buys good governmen from the pe
t, a recent l ment rate abo
al competiti rmer Japane ed away fol s, at least in ouble the con nt debt-GDP
th the recen ngdom came nt debt target unced. This who accused
regime.
eece's sovere is in sight.
ter the debt- inue to be u es. Politicia s decisions, ing year, inc eiling fiasco mmed up by rong when Congress” ( gnettes are n
limits anyti makers reaso
the fiscal their fiscal l cal Limit work on sove
st example Bi (2012). T al and a prop
s and make nt purchase a eak of the d
loss of its A ove the Eur veness. A fr ese Prime M llowing a o n part, a reb nsumption t
ratio.
nt marking d e the govern t it had set f s decision t d the govern
eign debt cr ceiling deba unable to fin ans “solved
laying the g cluding man o. America's U.S. Senato the biggest Steinhauer, not conclusi ime soon. Bu
on to doub adjustments limits.
ereign debt d of which c Those pape portional tax es lump-sum and transfers dynamic La
40 AAA rating
o area avera ragile Franc Minister Shin
one-year stin buke of Prim
ax by 2015 down of eco nment's decis
for itself wh triggered fin nment of we risis is in its acle in 2011 nd common g
” the fiscal groundwork dated across s political m
or Joe Manc threat to o 2012).
ive evidence ut they do g bt that their s necessary
default deve omes from rs consider x levied agai m transfers s processes,
ffer curve. B
for French age, and a st ce implies de nzo Abe retu nt in 2006-2 me Minister
to help cop onomic grow
sion to post hen Britain's
nger-waggin eakening th s third year , political p ground on e l cliff by p
for fresh ar s the board s morass and its chin III: “So our America e that major give forward r governme to keep th
elops model- Bi and Lee closed-econ inst labor in
to private an economi Because tha
sovereign d teady erosio eep troubles urns to offic 2007. The e r Yoshihiko e with Japan wth forecast
tpone achiev austerity m ng by credi e credibility and still no arties in the even the mo postponing rtificial fisca spending cut s implication omething ha an economy economies d-looking ec ents will sm heir countri
-based fisca eper (2012),
nomy mode ncome. Gove agents. For ic fiscal limi at peak depe
debt, an on of its for the ce after election Noda's n's over s in the ving the measures it-rating y of the lasting United st basic several al crises ts and a ns were as gone y is the
will hit onomic moothly es well
l limits, , which els with ernment
r given it arises ends on
the state disturbance for the ma present val subject to point.
Let stmax
function of shocks tha distribution
where qt,tmax
the econom spending po Research policy beha more by th obligations modeled, s the fiscal li
bt∗, the gov governmen
Productiv of uncertain revenue-ma grow as a and policy transfers ca the debt pr reforms. B decisions, transfers gr rates will r approach i distribution economy.
Figure 5
of the eco es and priva aximum sus lue of max random dis
xzt denote f all the exog at hit the e n of the real
1xzt1 is th my is zt an olicies that d h on sovereig avior make he governm . The politi o we treat t imit distribu vernment de nt raises taxe vity and go nty. Good p aximizing le share of th
can shift b apture the f rojections in ecause curr transfers flu row for an rise toward its fiscal lim n also chang 5 reports th
onomy, the ate agents' op
stainable go ximum prim sturbances, “
e the maxim genous shoc
economy at value of gov
B∗zt
∑
T
he one-perio nd the disc deliver the m
gn debt defa clear that t ment's willing
cal calculus the effective ution in (1).
efaults in so es to meet its vernment tr productivity evel of tax r e economy, between the
fiscal implic n Figures 3
ent governm uctuate betw extended pe the peak o mit. But the ge with the he cumulativ
41 joint dist ptimal decis overnment d mary surplus
“maximum mum prima cks to the ec t t, the fi vernment de
∑
Tt
qt,TmaxzTs
od real disc count factor maximum su aults and obs the decision gness, than s behind the e fiscal limit . If the valu ome well-spe
s debt obliga ransfers poli shocks rais rates. Transf , depending
two types cation of ag and 4, whil ments canno ween the st eriod, gover f the Laffer e position a
non-policy ve probabili
tribution of sion rules in debt, equali ses, smax. I debt” is a ary surplus onomy, zt. iscal limit ebt, B∗zt, sTmaxzT
count factor r is evaluat urplus in stat
servation of n to default n its ability, e default dec
t, bt∗, as a ue of outstan
ecified mann ations.
icies can be se taxable in fers program the prevail of transfers ging populat le stable tran ot commit fu table and un rnment debt r curve and
and shape and policy ity distribut
f the funda nduce a distr ing the disc In an envir
distribution in period Conditiona is defined given by
r when the ted at the t
te zt. f actual gove t on debt is to honor i cision is no random dra nding debt e
ner. Otherw e important ncome and s ms may be st ling policy
policies. G tions that un nsfers reflec future govern
nstable regi t will increa d the econom
of the fisca shocks that tions for the
amental ribution counted onment n, not a
t as a l on the
as the
state of tax and ernment
driven its debt t easily w from exceeds wise, the sources shift the table or regime, Growing nderlies ct fiscal nments' mes. If ase, tax my will al limit hit the e fiscal (1)
limit from conditional low and h portends fu fiscal limit.
the fiscal li when produ
Figure 5. F
Source: Bi an
The righ with the pr can suppor breaching t many adva maximum s countries a the limit.
In a com triggers shi understandi merely illu across coun economy's when it is a governmen
7 Examples of c
m an examp l on three al high. Produ uture values . A debt-GD imit of abou uctivity is hi Fiscal Limit D
nd Leeper (2012)
ht panel of th evailing tran rt a much h
the fiscal lim anced econ surpluses, sh are now exp mplete econo
ifts in agent ings about h ustrates the untries and a structure. I at its fiscal l nt debt.
complete models
ple economy lternative va uctivity shoc s of similar DP ratio of 2 ut 20 percen
igh, and 80 p Distribution fo
).
he figure rep nsfers regim igher level mit. Unstab nomies, dra hifting the li periencing g
omic model ts' expectati how policies
fiscal limi across time In what fol imit and opt
include Bi (2012
42 y. The left alues of prod
cks are per size and in 200 percent t when prod percent whe or Example E
ports how th me. When tra of debt with le transfers amatically l
imit to the le enerate non l, the endog ions and dec s will chang
t. Limits in , as they d lows, I sho ts to allow in
2), Bi and Leeper
t panel plo ductivity in rsistent, so nduces subst
implies a pr ductivity is a en productiv
Economy
he fiscal limi ansfers are s thout signifi growth, lik lowers the
eft: debt lev n-trivial prob
genous fisca cisions that ge at the fisc n actual eco depend on m ow how an
nflation to d
(2012), and the p
ts the distr period t: a the curren tantial shifts robability of average, 10 vity is low.
it distributio stable, the ec
icant probab ke that proje present va vels like thos babilities of al limit distr depend on cal limit.7 F onomies wi many details economy o devalue outs
papers in footnote
ribution average, t value s in the f hitting percent
on shifts conomy bility of ected in alue of se some f hitting ribution agents' Figure 5
ill vary s of an operates
tanding
e 17.
4. Inflation The conv can affect buy gover Excessive m which Sarg fiscal limit primary sur governmen generates in
Missing denominate inflation th called the “ of derision for over 20 new Keyne having bee to all econo under the c that render Friedman's phenomeno It turns o can also be Understand governmen budget con Because th economic m model.
4.1. A Sim To focus and the inf simply ass quantity of
8 Early develop Cochrane (1998 arguments again
n as a Mea ventional pe inflation on rnment bon money grow gent and Wa
t, where it i rpluses. The nt debt the c
nflation.
from this co ed in nomi hat is unrela
“fiscal theor by macroec 0 years, it rem
esian explan n distilled in omics stude carpet by m r it irreleva
aphorism t on.”
out that the e presented ding how f nt debt is nom nstraints, ass
ese relations model the fis
mple Model s on how m flation rate, sume that th
f output go
pments of the f 8). Two example nst it are Buiter (2
ans of Deva erception am nly if the cen nds or to
wth is Caga allace (1981 is unwilling ere is no disp central bank onventional inal terms, ated to expli ry of the pric conomists. A mains a bit m nations of in
nto basic su ents. Those maintaining ant. This co
that “inflatio fiscal theory in a form t fiscal policy
minal requir set-pricing r ships are co scal theory i
monetary and , we abstrac he economy oods, Y. W
fiscal theory incl es of authors wh 2002) and Gali (2
43 luation mong macroe
ntral bank s finance gov n's (1956) e ) connected g or unable
pute among k creates a c view is the then there icit debt mo ce level,” is Although the mystical to n nflation, in upply and de explanations strong assu onventional on is alway y explanatio that is comp y can dete res only a fe relations, an mpletely ge is ubiquitous
d fiscal poli ct from pro y is endow We further
lude Leeper (19 ho ridicule the f 2013).
economists systematical vernment p explanation d directly to to stabilize economists channel by w
fact that if is a new onetization.
frequently t e fiscal theo
non-speciali contrast, ar emand analy
s typically s umptions abo
view is ful ys and every on of price-l mprehensible ermine the ew key econ
nd market-c eneric they a s and potent
icies determ oduction and wed each pe simplify by
991), Sims (1994 fiscal theory with
is that fiscal lly prints mo purchases d
of hyperinf fiscal policy e debt by ad that by mon which fiscal
government channel for This new c treated as an ory has been ists.8 Monet re well unde yses that are sweep fiscal out fiscal b lly consisten ywhere a m
level determ to non-spe price level nomic relatio clearing con
apply in any tially obtains
mine the pric d employme eriod with y abstractin
4), Woodford (1 hout offering any
l policy oney to directly.
flations, y at the djusting netizing l policy t debt is r fiscal channel,
n object around tarist or erstood, e taught l policy ehavior nt with onetary mination cialists.
l when onships:
nditions.
y formal s in any
ce level ent and a fixed g from
1995), and y coherent
money: ins interest rate
Househo available th in period t one-period t 1, sells nominal go non-zero ne dollars in e these bond along the average ma when these long b
Optimal
Pt is the p The first short-term rate; it ensu nominal an relationship short-bond opportuniti
making it interest rate
The fisca
9 Abstracting fr or Gali (2008), things a bit, but
stead, we tre e, R.9 olds make a
hree assets:
t 1, sells a nominal go at price Ps overnment b et supply. A each period ds as a portf
maturity st aturity of the 1all bonds bonds is 1 choices by t
price level, expression nominal int ures that the nd real bond p that links
prices. This ies between
clear that i e, the centra al authority
rom money is con and with most fo does not alter the
eat the centr consumptio a real one-p at price qt,t
overnment b
st Rt−1in t bonds, Bm t, As in Woodf t j 1for folio of bon tructure giv e portfolio: w
are consols
− −1. the househo
Pst 1R Pm t Ps
so Pt/Pt1
(2), is the terest rate t ere are no un
ds. The sec the price of s term struct short- and lo
Pm t
∑
j0
in its setting al bank deter
chooses the
nsistent with the ormal models at c e key messages, a
44 ral bank as c
n-savings de period bond,
1 in period bond, Bst, th t, and is also , that sell at ford (2001), r each j ≥ 0 nds at all po ven byT−
when 0 that pay $1 olds yield tw
t Et Pt
Pt
stEt1 Pm
is the inve e usual Fi to expected nexploited a cond express f long bonds
ture relation ong-term no
∑
jEt
i0 j
R g of an exp rmines the pr e current lev
new Keynesian central banks. Br as Leeper and Wa
choosing a s ecision each , bt, that pa d t, and is in hat pays 1 u o in zero ne
t price Pm t
long bonds 0with 0 ≤ ossible matu
t1. Chang 0 all bonds 1 every perio wo asset-prici
t
1qt,t1
m t1
erse of the g isher relatio inflation an arbitrage opp sion (3), is s to the entir nship, which ominal bond
R1ti
pected path rice of long- vel of the pri
literature in, for ringing money in alker (2013) show
short-term n h period. The
ays 1 unit o n zero net su
unit of curr t supply; lon
t in t and s sold at t p
≤ 1. We in urities with w
ging var are one-per od. The dura
ing relations
gross inflatio on connecti nd the real portunities b the term st re expected h rules out ar ds, implies th
h of the sho -term bonds imary (exclu
example, Woodf nto the analysis c w.
nominal ey have f goods upply; a ency in ng-term d are in pay j nterpret weights ries the riod and
ation of s
on rate.
ing the interest between tructure path of rbitrage hat
ort-term . usive of
ford (2013) omplicates
(2) (3)
(4)
interest pay must cover must satisfy
Because thi constraint h
Notice that constraint i link betwee tomorrow:
logic into t calls the ``b
where qt,T
value of ou expected d nothing m governmen cash flows meeting int value from developing
Combini constraint ( period t
By this ver Pm tBm t/Pt, surpluses fr is the pres outstanding
yments) bu r the princip y the govern
P is budget co holds in peri P t the new d in period t
en the debt Bm t and s the indefinit bond valuati
T is the T − utstanding g discounted p more than nt bonds: the . A govern terest payme m expected g the demand ing the bond (5), yields a
Pm
P rsion of the b depends on from period
sent value g bonds. Ex
dget surplu pal and inte nment's budg
Pm tBm t
Pt st
onstraint also iod t 1 Pm t1Bm t1
Pt1 debt sold in
1because t the govern
st1 must b te future lea ion equation
1 Pm t Pt
− t-period government present value
a conventi e value of an ment bond's ents on the d
surpluses, d for govern d valuation e
an expressio
m tBm t
Pt Et
∑
T
bond valuati n the expec t 1onwar of expected xpressions
45 s, st, and n erest on ou get constrain
t 1 P P o holds in ev
st1 1 n period t,
it must be s nment sells
e related to ads to an ex n''
Bm t−1 Et
discount fac bonds the l e of all futu ional asset n asset depen
s “cash flow debt. Becau
condition ( ment bonds equation (7) on for the m
∑
Tt1
qt−1,TsT
ion equation cted discoun rd, abbreviat d surpluses, (7) and (8)
new bond s utstanding d
nt in period
m tBm t−1
Pt
very time pe
Pm t1Bm
Pt1 Bm t, enters erviced, so t today and
each other.
xpression tha
t
∑
Tt
qt,TsT
ctor with qt left side of ure primary t-pricing re nds on its e ws” are futu use governm
(7) is a cr .
, with the go market valu
≡ EtPVSt
n, the value nted present ted as EtPV , the greate ) emerge a
sales, Bm t. ebt. These
t
eriod, an ana
t
s the govern there is a ne
the surplus . Extrapolati at Cochrane
t,t ≡ 1. The (7) must eq y surpluses.
elation appl xpected disc ure surpluse ment debt der
ritical step overnment's
e of bonds
1
of bonds so t value of p VSt1. The
er is the v after imposin
It also choices
alogous
nment's ecessary it runs ing this (2011)
market qual the This is lied to counted es after rives its toward budget sold in
ld at t, primary e higher alue of ng that (5)
(6)
(7)
(8)
private age the restricti real interest Because demand fun
Two determ higher the p surpluses, Demand al of bonds, th is associate the inflatio in currency current and
Bond sup past, and eq must be to 4.2. Determ
Entire te when there for econom future surp might still fluctuations discretionar that are exo of primary Economic form expe behavior is Sargent and
10 Three aspect money. First, un depends explicit and, therefore, nominal return t introduces a sca bond demand (b
ents make op ion that gov t rate.
(8) embed nction for no
minants of price level t EtPVSt1 so rises whe hrough the t ed with a hig
n rate.10 Be y, rather th d future price
pply is perfe quilibrium p satisfy the g mining the P extbooks are e is no fiscal mic or politi luses whene l adjust su s in real ry changes ogenous to th
surpluses, agents unde ectations ov s consistent w
d Wallace (1
ts of the demand nlike fiat money, tly on expected f
are protected fr to bonds and driv ale variable like i but see Canzoneri
ptimal asset- vernment de ds private a
ominal gove Bmtd P the nomina today, Pt, o
, the grea en the price term structu gher path of ecause nomi han in good
e levels.
ectly inelast prices, the su government
Price Level e written ab l limit, so w ical reasons ever the rea urpluses for
economic in surpluse he model. F
st, as an erstand the ver future s
with an econ 1981).
d for nominal bon bonds are “back fiscal policies. Se rom fully anticip ves down the nom
ncome or wealth i, Cumby, and Di
46 -demand dec ebt-GDP mu
agents' opti ernment bon
Pt
PmtEtPVS al demand f or the higher ater is the of bonds to ure relation ( f the short-te inal governm ds, bond de tic. Given po upply of bo budget cons
bout how th we focus on t , the fiscal l value of o r reasons o
activity m es or surplu For our purpo n exogenous nature of th surpluses. T nomy that h
nds are distingui ed” by future sur cond, unlike fiat pated inflation. H minal price of bo into money dem ba (2011) for a d
cisions, whi ust grow at imal choice nds St1
for bonds a r the expect nominal d oday, Pm t, f
(4), and the erm nomina ment bonds emand depe olicies, debt onds in perio straint (5).
he price lev the opposite authority ca outstanding d other than might indu uses might c oses, we can and possib he randomn This assum has hit its fis
ished from the ty rpluses and, there
money, bonds pa Higher anticipat onds. Third, trans mand, which is ab description of liqu
ich include a a rate less t es, it consti
are immedia ted present v
emand for falls. A low
Fisher relat al interest ra promise to ends positiv t inherited fr od t is wha
vel gets dete e case: suppo
annot raise debt rises (f debt-stabil uce automa change for n treat the se
ly random p ness, so are mption about scal limit, ju
ypical demand fo efore, the demand ay positive nomin ted inflation driv sactions demand bsent in this speci uidity demand for
and and han the itutes a
ate. The value of bonds.
er price tion (2), ate or of pay off vely on
rom the atever it
ermined ose that (lower) falls). It ization:
atic or reasons equence process.
able to t fiscal ust as in
or nominal d for bonds nal interest ves up the
for money ification of r bonds).
(9)
When su if monetar unconstrain become wo must accom stabilization longer adju do the adju real value o bank choos fiscal limit are consis determines We can Algebraical monetary p by the term Pm t. Fisca surplus, s of real bon sequences i (7), determ determines Graphica determines The govern budget con slopes upw paths of ex and the equ
11 Sargent and W emphasis is on terms of debt v defined broadly inflation---so pr
urpluses are ry policy w ned fashion orthless. Fo mmodate the
n. In terms usts to stabil usting: curre of debt is co ses the seque monetary p stent with
.11
now deter lly, the equ policy annou m structure r al policy ann
sTTt . In thi nds, qT,T1
imply the ex mines Pt. T Bm t. This ally, interac
the price l nment supp nstraint. Dem ward when th xpected inter uilibrium pri
Wallace's (1981) generating suffic valuation equation y adjust to stabi rice level changes
unresponsiv were to co n, governme or governme e exogenou of the deb lize debt, so nt and expe onsistent wit
ence of shor policy is con
the expect rmine the e
uilibrium g unces a path relation (3) o nounces a p
is model, th
Tt , is exog xpected pres The governm
solution me ction of su
evel at t. F plies bonds mand for bon he current pr rest rates an ice level is
unpleasant arithm cient inflation tax
n (8) , EtPV
ilize debt. Sarge s cannot revalue d
47 ve to the stat ontinue to ent debt wo ent debt to
s surpluses bt valuation
some comb cted price le th expected rt-term nomi nstrained to ted surplus equilibrium gets determi for the poli or (4) determ path for its p
e real intere genous. The sent value o ment's flow thod repeats upply and Figure 6 des inelastically nds comes fr
rice level is nd surpluses
P1.
metic setup also c x revenues---seign
St1 includes ent and Wallace debt.
te of govern pursue its ould grow
retain value by taking o equation ( bination of
evels chang surpluses. B inal interest
choose inte ses that th
process fo ined recurs icy instrume mines the p policy instru est rate and,
e real intere of surpluses w budget co s every perio demand fo scribes bond y, Bs, in o rom behavio on the verti , nominal b
constrains moneta niorage---to “bac s seigniorage rev e treat debt as
nment indebt objectives exponential e, monetary on the role 8), EtPVS Pt and Pm
e to ensure Because the rates, Rt erest-rate pa
e fiscal au or the price sively. At d ent,RTTt ,
rice of bond ument, the p therefore, th est rate and
and, by exp onstraint at
od.
or nominal d-market be order to sat oral relation ical axis. Fo ond demand
ary policy choice ck” the outstandin venues, so future
real---perfectly i
tedness, in an lly and y policy of debt
t1 no
m t must that the
central
, at the ths that uthority e level.
date t, which, ds at t, primary he price surplus pression t, (5),
bonds ehavior.
tisfy its (9) and or given d is B1d
es, but their ng debt. In e surpluses indexed to
Figure 6.
Note: Supply
When bo price, lowe primary sur B2d: investo initial equil demand fo bonds; low the price le bonds dem to be consis
We now examine so 4.3. Some To make
“today” (pe economy t making the Monetary a
Moneta Fis
Bond Marke
y, , is inelastic
ond supply er expected rpluses pivo ors demand librium pric r bonds. Bo wer aggregat
evel falls, d manded. The stent with th w use suppl ome specific
Examples e the analy eriod t) an today and w
e real disc and fiscal po ary Policy :
cal Policy :
et Equilibrium
and demand is
and demand path of real ots the deman
more nomin ce level, P1
ond holders te demand f demanders s
price level he bond valu ly and dem economic e
ysis more c d the “futur we hold out ount factor olicies take s sets a const chooses a c
48 m
d are drawn l interest rat nd for bond nal bonds a , after the s substitute for goods dr
slide down falls until th uation equati mand for no
events.
oncrete, we re” (all peri tput and go r constant a simple forms tant short inte constant surpl
, as in expres
n as in Figu tes, or highe ds down to th at any given shift in dem
from buyin rives down B2d, reduci he market v ion in (8).
ominal gov
e can separ iods after t overnment p
also: qt,T s
erest rate, RT lus, sT s fo
ssion (9).
re 6, a lowe er expected he demand f price level.
mand there is g goods to the price le ing the quan value of bon
vernment bo
rate dynami ). We consi purchases co
q for all
R for T ≥ or T ≥ t 1,
er bond path of function . At the s excess buying evel. As ntity of ds rises onds to
ics into ider the onstant, T t.
≥ t
but st ≠ s
Monetary p policy hold differ from By pegg inflation,
Constant di present valu
and the bon
We can use
Collecting equilibrium inflation rat 1) a lo inflation wi
2) a lo 3) a hi 4) a lo interest rate
5) low 4.3.1. Bon
Suppose taxes today 7, this shift at its fiscal
policy just p ds future su m that fixed v ging the no
F, and the p
iscount fact ue of surplu
nd valuation
e (11) and (1
the model m price lev
te) arises fro ower path f ill be lower) onger averag igher initial ower path es) wer current o
d-Financed that to resp y and financ fts bond supp
limit, futur
pegs the sho urpluses fixe
value.
ominal inte price of long
T F
Pm T R− ors and con uses in (8) to EtPV n equation, (7
1 Pm t Pt
13) to solve Pt l's implicati
el (14), a om
for short-ter )
ge maturity o debt level for real dis or future prim
d Tax Cut pond to an ces the result
ply to the ri e surpluses
49 ort-term nom ed at s, but erest rate, m
g bonds
qR for
1− for
nstant future o
VSt1 1− 7), to
Bmt−1 st
for the equil RR− B
st ions, based higher curr rm nominal of governme
scount facto mary surplus
economic d ting deficit w ght (from B do not chan
minal interes t allows the
monetary p
T ≥ t 1
r T ≥ t
surpluses r q
− qs
q
1− qs librium pric Bm t−1
1−qq s d on the e
rent price l interest ra ent bonds
ors (or a hi ses
downturn, th with new bo B1s to B2s
).
nge, so EtP
st rate at R e current sur
policy pegs
educe the ex
e level
expression level (and ates (though
igher path f
he governme ond sales. In With the ec VSt1 rem
. Fiscal rplus to future
xpected
for the current h future
for real
ent cuts n figure conomy mains at (10)
(11)
(12)
(13)
(14)
its initial v do not expe their tax cu economy, h so the pric holders to until all the to P2 in fi B1/P1 B2
Figure 7.
Note: Bond-f rate and, ther and the real q
But this behaves. T the interest change from from the v present val increase in
12 Conventional exactly offsettin amount of the th
alue in equa ect any subs ut into high higher aggre ces of good
increase the e new bond figure 7, whe
2/P2.12 Bond-Finan
financed tax cut to refore, bond price quantity of bonds
analysis is n The outcome
t-rate peg a m the value value in (10) lue of surplu prices occur
l new Keynesian ng increase in the he increase in bon
ation (12). P sequent tax i er consump egate deman ds begin to eir nominal issuances ha ere the real v
ced Tax Cut
oday. Bond suppl es unchanged, th s is unchanged:
not complete e in figure 7 at the initial e in Equatio ). The fixed uses ensure rs today.
n analyses posit e present value of nd supply, ensurin
50 Private agen
increases, fe tion of good nd does not
rise. A hig bond holdi ave been abs value of out
ly shifts to the rig ere is no shift in
⁄
⁄
e without sp 7 assumes th l R, so that on (11) and d bond pric
bond dema
Ricardian fiscal f future taxes. Th ng that the equilib
nts who rece eel wealthier ds and serv bring forth gher price l dings, a proc
sorbed and t tstanding deb
gth. If central ban bond demand th
pecifying ho hat the cent t the price d future infla
e together w and does no
behavior, so a t his pivots bond de
brium price level
eive the tax r and try to vices. In this greater prod level induce cess that co the price lev bt has not ch
k keeps nominal he price level rise
ow monetary tral bank ma of bonds d ation is unc with an unc ot shift and
tax cut today eng emand down by e l remains at P1
cut and convert s model duction, es bond ontinues vel rises hanged:
interest es to
y policy aintains oes not changed changed the full
genders an exactly the .
But an fiscally-ind interest rat expected in pivots dow current inf inflation, by fiscal inflat
Figure 8. B
Note: Bond-f rate in respo attenuating s
At the f economy, w expressions inflation
For a given inflation (P appears gra
13Figure 9 is
inflation-ta duced increa te. A highe nflation. Low
n to B2d
, as flation. Alth
y adjusting t tion.
Bond-Finance
financed tax cut t onse to higher inf ome of the increa
fiscal limit, while monet s (10) and (
n value of Pt) is assoc aphically in
s drawn using
argeting ce ase in curren
r path for wer Pm t in in figure 8.
hough mone the nominal
ed Tax Cut
today. Bond supp flation today, bon ase in inflation to
fiscal poli tary policy d (14) to revea
t 1−
the right si ciated with l
figure 9.13
g the following
51
entral bank nt inflation
R reduces ncreases nom
Higher bon etary policy interest rate
ply shifts to the ri nd prices fall and
day. Instead, infl
icy determin determines it
al the tradeo
qF Bm t st de of (15), lower future
g parameter ch
k is likely by raising t bond prices minal bond d nd demand at y cannot el e it can dete
igth. If central ba d demand for no lation is pushed in
nes the tota ts timing. T off between
t−1/Pt−1
1−qq s it is clear e inflation (
hoices: q . 9
to react the nominal s today and demand, so d ttenuates the liminate the rmine the tim
ank raises nomina minal bonds shif nto the future.
al inflation o see this, c n current and
that higher (F). This t
9804 ( 2% r
to the l policy d raises demand e rise in e fiscal ming of
al interest fts down,
in the ombine d future
current tradeoff
real rate),
(15)
4.3.2. Low Demand the future b through fut real interes rates have they were terms of th
qt,t1, that raising the raises the v to B2d
in F Figure 9. T
Note: Given lower is futur
Persisten experiencin governmen paper highl begin to ris a return t intrinsically signal a mo aggregate d Bm t−1/Pt−1
14 Discount fact
Real Intere for bonds w backing of b ture primary st rates that
been negati for the dec he model, n discount sur
present va value of gov Figure 10 to Trade of Betw
a level of real deb ure inflation, a
ntly low rea ng a pick-up nt debt of re lights is at w se until real i to normalcy y difficult to ove by inve demand and
0. 5, and bas tors cannot excee
est Rates will also shi bonds. That y surpluses, b
serve to di ive in the U ade of the negative real rpluses in te alue of any vernment de reduce the c ween Current
bt and present val a tradeoff that var
al rates ma p in inflation ecent years.
work in the U interest rate y in the w o predict. In estors out of
inflation.
seline current and ed unity forever in
52 ift with chan
backing dep but it also de iscount surp United States
1970s and t l interest rat emporarily g given strea ebt and pivo current price t and Future
lue of surpluses in ries with the aver
ay explain w n despite the
If the fiscal United State s have return world econo n the face o f treasuries,
d future inflation n a dynamically e
nges in inve pends on fis
epends on th pluses. Shor
s for more the first hal tes make th greater than am of future ots down the
e level.
Inflation
n (15), the higher rage maturity of g
why the Un massive ex l inflation m es, then infla rned to more omy remain of a fiscal lim
with the res
of 2% . efficient equilibri
estors' belief cal policy b he expected rt-term real than four y lf of the 20 he discount unity, subst e surpluses.
e demand fr
r is inflation today government debt.
nited States xpansion in n mechanism t
ation is not l e normal lev ns elusive mit, normal sulting incre
um.
fs about ehavior path of interest ears, as 000s. In factors, antially
14 This om B1d
y, , the
is not nominal
hat this ikely to els. But and is cy may eases in
