different speeds of debt stabilisation in emu

8/20/2019 Different Speeds of Debt Stabilisation in EMU

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The macroeconomic impact of dierent speeds of debtstabilisation in EMUCampbell Leith and Simon Wren-Lewis

The potential importance of scal policy in inuencing ination has

recently been highlighted, followingWoodford (1998) under the heading of the !"iscal Theory of the #rice $e%el& ("T#$)' The "iscal Theory has also beenetended to consider the case of independent scal authorities operatingunder a common monetary authority (seeWoodford 1998 upor *+++ergin *+++ -ims 199.)'

The scal theory essentially characterises two regimes / one where thescal authorities act prudently, go%ernment debt does not constitute anelement of net wealth and monetary policy is free to target ination, andanother, where scal insol%ency re0uires surprise ination to deate thenominal %alue of go%ernment debt' n $eith and Wren2$ewis (*++1) we relaa number of assumptions underlying the "iscal Theory of the price le%el by

considering a two2country model in continuous time with o%erlappinggenerations of consumers supplying labour to imperfectly competiti%e rmswhich can only ad3ust their prices infre0uently' #olicy is described by simplelinear feedbac4 rules' We nd that there are two stable policy regimes similarto those in the "iscal Theory5 one where the go%ernment follows a rule whichstabilises its debt and monetary policy is !acti%e& in the sense of $eeper(1991) and another where an imprudent go%ernment re0uires monetarypolicy to be !passi%e&' 6owe%er, unli4e the "iscal Theory, both monetary andscal policy a7ect ination in both regimes'We also obtain the result that it istheoretically possible for one scal authority to partially compensate forsome degree of la scal policy on the part of another monetary union

member, without implying an indenite transfer of wealth from the citiensof that economy to the other'

n this chapter we etend this wor4 by de%eloping a two2country openeconomy model in discrete time, where again each country has o%erlappinggenerations of non2icardian consumers who supply labour to imperfectlycompetiti%e rms which can only change their prices infre0uently'Weeamine the case where the two countries ha%e formed a monetary union,but where the scal authorities remain independent' We allow for a richermenu of monetary and scal policy interaction by dropping the assumptionof lump sum taation and allowing the scal authorities to %ary both tarates (which are distortionary) and go%ernment spending (which feedsdirectly into aggregate demand)' We restrict oursel%es to considering onlythe policy regime in which the scal authorities act to stabilise their owndebt, and where monetary policy is acti%e, as this appears to characterise:;< under the -tability and =rowth #act' We then eamine, through a seriesof policy simulations, how asymmetries in the scal policy responses to debtdise0uilibrium can a7ect the :uropean >entral an4&s ability to controlination'We assume that each scal authority stabilises its own debt


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su?ciently to allow an acti%e monetary policy regime, but as4 what is theappropriate speed of debt stabilisation, and whether stabiliation that is tooslow or too fast in one country will signicantly inuence the other'

The structure of the chapter is as follows' -ection 1 outlines the modeland section * eamines the steady state of the model and linearises the non2

linear model around this steady state' -ection @ then calibrates the model,before assessing the implications of (1) %arying the speed of scalad3ustment to debt dise0uilibrium, (*) asymmetric responses in scal policyto dise0uilibrium in the debt le%els of the independent scal authorities and(@) asymmetries in the etent of nominal inertia across :< member states inthe face of %arious symmetric and asymmetric shoc4s' -ection A concludes'1. The model

Bur model consists of two countries operating under a monetaryunion, where a single monetary authority targets a%erage consumer priceination across the union, but each country&s scal authorities are free topursue independent scal policies' Within each country, o%erlapping

generations of consumers supply labour to imperfectly competiti%e rms'>onsumers in each country do not epect to li%e for e%er, and there are nobe0uests in the model, so the conditions underpinning pure icardiane0ui%alence do not hold' Cs a result the go%ernment&s liabilities (consistingof money and bonds) constitute an element of net wealth and will,therefore, a7ect the real interest rate obser%ed in the model'We alsoassume that the imperfectly competiti%e rms in each economy can onlyreset prices at random inter%als, as under >al%o (198@) contracting' Thecombination of non2icardian consumers and nominal inertia implies thatmonetary and scal policies interact and that both can ha%e real e7ects onthe economy' We now proceed to outline the model in more detail,

considering rst the problem facing indi%idual consumers, beforeaggregating across all consumers' We then turn to the pricingDoutputdecisions of our representati%e rm before detailing the linearisation of themodel re0uired to render it suitable for numerical simulation'1.1 The consumer’s problem

The utility of a typical home consumer, i, is increased through consumption of a basket of consumption goods, cis , holding real money balances, Mis Ps , and suffersdisutility from providing labour services, Ni s . Consumers also face a constant probability of death (1 − γ ), which allows us to write the consumers certainty e!uivalentutility function as,

This specification of utility is identical to that found in "bsfeldt and #ogoff (1$$%). The basket of consumption goods is defined by the following C&' inde appliedacross home and foreign goods,


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'imilarly, the consumer price inde is given by,

'ince there are assumed to be no impediments to trade, the law of one price holds

for each individual good, so that the home price inde can be rewritten as

where p( z ) is the home currency price of good z , p( z ) is the foreign currency price of good z and * ε is the nominal echange rate, which is fied under monetary union.

The consumer can hold her financial wealth in the form of domestic government bonds, D, foreign bonds, F , and money balances, M . 'ince there is a common monetary policy, domestic and foreign bonds earn the same nominal return, it , and domesticconsumers receive a share in the profits of domestic firms. +t is assumed that theconsumer receives a premium from perfectly competitive insurance companies in return

for their financial assets should they die. This effectively raises the rate of return fromholding financial assets by 1 γ . The consumer also receives labour income of Wt Ni t anda share of the profits from all the imperfectly competitive firms in the economy, πt . Theconsumers labour and profit income is taed at a rate τt . Therefore, the consumers budget constraint, in nominal terms, is given by

-eflating the flow constraint by Pt

where rt is the eante real interest rate. The parameters φ and φ measure the proportionof domestic and foreign bonds, respectively, which are nominal. Therefore, when φ / φ/ 0 all financial wealth is fully indeed such that the epost real interest rate enoyed byholders of the financial asset is e!uivalent to the eante real interest rate they epected.2hen φ / φ / 1 all debt is nominal and surprise inflation can erode the real value of nominal financial wealth by decreasing the epost real interest rate relative to the eanterate as under the 3T45. +n our policy simulations we shall assume that the economy wasinitially in steady state before an unanticipated shock moved the economy away from thissteady state. 2e shall then track the response of the economy to this shock under differentdescriptions of monetary and fiscal policy. 6s a result, when the shock hits the economyit is possible for eante real rates to differ from epost real rates. 7owever, for theremainder of the simulation, owing to the pooling of risks due to finite lives and


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stochastic price setting, the economy behaves as if it is operating under perfect foresight.Therefore we can drop the distinction between eante and epost real rates in periodsother than the initial period, t , in which the shock hits. The consumer then has tomaimise utility, (8'1), sub3ect to her budget constraint, (8'E), alongwith the usual sol%ency conditions' The %arious rst order conditions

this implies are gi%en below'"irstly, there is the usual consumption :uler e0uation

The optimisation also yields a money demand e0uation

where the demand for money balances is increasing in the le%el of consumption, but decreasing in the nominal interest rate, whichrepresents the opportunity costs of holding nancial wealth in the formof money rather than bonds' The indi%idual&s optimal labour supply

decision will satisfy

such that it is increasing in realwages, but decreasing in consumptionaswor4ers attempt to substitute leisure for consumption'


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1'1'1 Aggregating across individual consumers. y assuming that eachcohort is of sie 1 when born, a cohort of age s will ha%e a sie

γ s

' Therefore the total sie of the population is ∑s=0

∞

γ s=

1

1−γ '

We will also assume that the probability of death and initial

cohort sie are identical across the two countries' Cs a result, byeamining a%erage per capita %alues of %ariables we can stillcompare aggregate le%els of %ariables across countries' Therefore the relationship between aggregate per capita laboursupply and consumption in all cohorts@ is gi%en as,

While the money demand e0uation is gi%en by,

The aggregate (per capita) consumption e0uation is,

where we ha%e used the national accounting identity to replacewage and prot income with output, yt ' Gotice that future labourand prot income is discounted at an interest rate which ismar4ed up by a factor which reects the probability of death' This mar42up is critical in o%erturning the results of the standardicardian eperiment of decit nanced ta cuts in our model'>onsumers discount the future ta increases that a ta cut2induced decit implies more hea%ily than the decit accumulates


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interest' Cs a result a ta cut increases discounted human wealthand thereby, ceteris paribus, increases consumption'n the foreign country there will be corresponding e0uations forlabour supply,

money demand,

and consumption,

1.2 The rm!s problemWe now turn the problem facing the rm' Cs consumers are able topool the ris4s associated with asymmetric price setting on the part of indi%idual rms, the representati%e rm&s ob3ecti%e is to maimise the

discounted %alue of its prots using the ris42free interest rate' Therefore we dene the real prots of the home rm, producing good " , as

assume that rms are sub3ect to the constraints implied by >al%ocontracts, i'e' in each period only a proportion of rms (1 / #) are ableto change prices and each rm does not 4now if it will be part of thatgroup' Cs a result there is an intertemporal dimension to the rm&spricingDoutput decision' -uppose the rm is able to change its price

this period, then its ob3ecti%e function for determining that optimalprice is gi%en by,


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"or simplicity it is assumed that the rm&s production technology islinear, y ( " )t H $( " )t ' The >:- form of the utility function implies thatthe ith home consumer&s demand for product " is gi%en by

while the ith foreign consumer will demand

ntegrating demands across consumers, noting that ### holds for theaggregate consumer price le%els and assuming that the homego%ernment allocates its spending in the same pattern as homeconsumers implies that world demand for product " is gi%en by,

where y ( " ), c, cI, g, and gI are dened as real per capita %ariables' Therm&s (per capita) demand for labour will be e0ui%alent to e0uation(8'**)'


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The home output price inde, p(h) is dened as

where K pt is the price set in accordance with e0uation (8'*A) bythose home producers that were able to change prices in that

period, while a%erage home output (relati%e to home population)is gi%en by

and the aggregate consumer price le%el is gi%en by

=i%en the linear production technology, per capita demand forlabour is obtained by summing across the n home rms,

1.% The government "inally, we consider the go%ernments of both economies' The homego%ernment&s budget constraint, in nominal terms, is gi%en by

that is domestic go%ernment bonds are held either by home consumers(&t ) or by foreign consumers (' L t )' The go%ernment nancesspending by issuing money and taing home output at the rate ( t '

The corresponding foreign go%ernment&s budget constraint isgi%en by

where the interest paid on this debt may or may not be indeed toination'We shall discuss the formulation of both monetary and scalpolicy below'

1.) *lobal mar+et clearing conditionsn our two2country model there are also global mar4et clearingconditions for the goods and asset mar4ets' n the goods mar4et it

implies the following condition

while e0uilibrium in the asset mar4et implies that the sum of pri%atenancial assets in the two economies e0uals the sum of publicliabilities,


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n both cases the usual closed economy identities do not hold, as oneeconomy can be a net eporter to the other and can also hold netforeign nancial assets'

2. Linearising the model around a symmetric steady staten order to get the model into a tractable form for conducting policy

simulations we need to linearise it (the innite forward2loo4ingsummations implied by the rm&s pricing decisions cannot be dealt with ina non2linear framewor4, e%en if we underta4e numerical simulations)' nthis section we detail the steady state of our model, before log2linearisingthe dynamic e0uations around this steady state'2.1 The symmetrical steady state o, the model

n this section we deri%e the steady state of our model, as this will bethe base around which we log2linearise our model before conducting anumber of numerical policy simulations' The optimal price in steadystate, which is the same as that which would be set under eibleprices, is gi%en by

Cs MNthe rms in the economy lose mar4et power and tend towardsa state of perfect competition' >ombining this with the labour supplycondition (8'1*), the linear production function and the nationalaccounting identity in a symmetrical steady2state, y H c O g, yields thefollowing e0uilibrium output,

To highlight the suboptimal le%el of output arising due to ta distortionsand imperfect competition, consider a bene%olent social planner whomaimies indi%idual utility by choosing c (ta4ing g as gi%en) in thefollowing ob3ecti%e function

This yields a higher steady2state output le%el which remo%es thedistortions due to imperfect competition and non2lump2sum taation,

f we normalise the ed nominal echange rate to one, the steady2state consumption function becomes

the domestic go%ernment&s budget constraint in steady2state is


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and money demand is gi%en by

Gote that in this symmetrical e0uilibrium, with ### due to free trade, itwill also be the case that the real %alue of debt held o%erseas will bethe same in both countries, ' L D H '/ ' This fact, combined withe0uations (8'@A)/(8'@9), will determine the steady2state %alue of realassets in the model, along with the e0uilibrium real interest rate' -inceconsumers are not innitely li%ed, the real interest rate is not identicalto consumers& rate of time preference, but will be a7ected by theoutstanding stoc4 of go%ernment liabilities, since these liabilitiesconstitute consumers& net wealth'

2.2 Linearising the model around the steady state

We now proceed to log2linearise the model around this symmetricalsteady state' To illustrate this consider the labour supply e0uation

$og2di7erentiation of this epression yields

where a hatted %ariable denotes the percentage de%iation from steady

state,^ X t =

d X t ∨ x− x

X .T ' This approach can be applied to all the

e0uations in our model' Get, consider the epression for the log2linearised optimal price set by a home rm

-ubstituting for the log2linearised denition of consumer prices, Pt H1* P p(h)t O 1* ( P p( , )t ), and 0uasi2di7erencing yields


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-ubstituting the linearised labour supply function into this epressionyields

This is the same as the usual Gew Jeynesian #hillips cur%e, ecept thatthere now eists a terms2of2trade e7ect in addition to the usualaggregate demand e7ect' There is also a distinction between theinationary impact of an increase in consumption (which will raise both

P ct and P yt , ceteris paribus) and an increase in eports or go%ernmentspending (which will raise P yt alone, ceteris paribus) which is notpresent in the usual Gew Jeynesian #hillips cur%e' The reason for thisdistinction is that wor4ers need to be compensated in the form of higher wages to supply the higher output, but in the case of anincrease in consumption wor4ers re0uire additional compensation asthey ha%e an increased desire to substitute leisure for consumption' This distinction will turn out to be critical in dening the scal policyresponse re0uired to eliminate the inationary conse0uences of debtdise0uilibrium following a shoc4' "inally, increasing taation will beinationary owing to the detrimental e7ects this has on labour supply'

C similar epression can be deri%ed in terms of foreign output prices5


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where use was made of the fact that real interest rates (dened asnominal rates relati%e to consumer price ination) are the same acrossall countries under :;< gi%en the free trade in consumer goods'Gow we turn to the consumption function, (8'11), where log2

linearisation yields

where Pht is discounted human wealth, after ta, which e%ol%esaccording to

There are similar linearised e0uations for foreign consumption

with an associated denition of human wealth


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-ince this is an open economy, the go%ernment&s budget constraint isnot synonymous with those of consumers, whose holdings of nancialwealth e%ol%e according to

while in the foreign economy the e%olution of pri%ate holdings of nancial wealth follows

The output of rms in the domestic economy is go%erned by thelinearised %ersion of e0uation (8'**)

and for foreign rms

There are also the two global mar4et2clearing conditions' "irstly, forgoods across the two economies,

and, secondly, for assets across the two economies,

2.2.1 &escribing monetary and scal policy Cll that remains is to complete our description of monetary andscal policy' Bur model contains a number of features whichsuggest goals for policyma4ers / for eample, the distortions dueto imperfect competition and taation create incenti%es forpolicyma4ers to boost output abo%e its steady2state le%el, whilethe nominal inertia generated by o%erlapping >al%o contractssuggests that a low (ideally ero) and constant rate of ination is


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optimal for minimising the distortions the mispricing of thesecontracts can generate (see =oodfriend and Jing 199. for adiscussion of this point)' Therefore, in describing monetarypolicyweassume that the independent :> ignores the inationarybias created by the distortions described abo%e and implements

its mandate to pursue its ination target by following a simpleinterest rate rule' -pecically, we assume that the commonmonetary policy in%ol%es setting real interest rates to target thea%erage rate of output price ination across the two economies, sothat,

and the target for ination, consistent with minimising thedistortions due to mispricing, is ero' $og2linearising this Taylor2type rule for monetary policy gi%es,

n contrast, the scal authorities set the %alues of their tainstruments Ptt and P gt independently / although one authoritymay see4 to ad3ust policy in light of the policy actions of the other'6ere there are a number of factors moti%ating the beha%iour of these scal policyma4ers' "or eample the distortionary nature of taation in this model gi%es them an incenti%e to smooth taes asin arro (19.9)' The institutional constraint implied by the #act for-tability and =rowth also implies that such scal authorities will beforced to use these scal policy instruments to rein in !ecessi%e&

le%els of decits and go%ernment debt as dened by the pact'-ince the model of ta smoothing applies o%er an innite horion,the short2run decits it could imply could easily conict with thedetail of the -tability #act' Cdditionally, for reasons of credibility,go%ernments may ha%e to react to decits more 0uic4ly than pureta smoothing considerations would imply' Ct the same time,general models of optimal scal policy, with 0uadratic lossfunctions detailing the etent to which go%ernments areconstrained in their ability to raise taation and cut go%ernmentspending, typically generate simple linear feedbac4 rulesoperating from debt to scal policy instruments (see $oc4wood,

#hilippopoulos and -nell 199F, for eample)' We therefore assumethat the home go%ernment ad3usts the ta rate relati%e to itssteady2state %alue in an attempt to stabilise the debt stoc4' Thiscan be thought of as a rule of thumb capturing all the abo%efactors and, in particular, enabling the scal authority to a%oid thecosts associated with breaching the constraints implied by the#act for -tability and =rowth' This gi%es rise to the followingtaation feedbac4 rule in the domestic economy5


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in the foreign economy'We also consider the case where the feedbac4 rules operating ontaation are replaced with similar feedbac4 rules operating ongo%ernment spending in the domestic and foreign economies5

n our analysis, we consider e0uilibria in which the debt of eachscal authority is stable' n contrast, other authors (e'g' ergin*+++ Woodford 1998) ha%e allowed one scal authority to borrowindenitely from the other, in which case it is only the aggregate

budget constraint that matters' These alternati%e assumptions arediscussed in >anoneri, >umby and iba (*++1)'

This completes our description of the economy which consists of #hillips cur%e relationships for output prices in both economies(e0uations (8'AF) and (8'A.)), consumption (e0uations (8'E1) and(8'E@)) with the associated e0uations of motion for human wealth(e0uations (8'E*) and (8'EA)) and nancial wealth (e0uations(8'EE) and (8'EF))' There are also e0uations describing thee%olution of each go%ernment&s liabilities (e0uations (8'A9) and(8'E+)) and the output in each economy (e0uations (8'E.) and(8'E8))' "inally, there are the global goods and asset mar4etclearing conditions (e0uations (8'E9) and (8'F+)) as well as thepolicy rules describing the common monetary policy (e0uation(8'F*)) and the scal feedbac4 rules for taation ((8'F@) and(8'FA)) and go%ernment spending ((8'FE) and (8'FF))'

3. Interactions beteen monetary and !scal policy under EMU


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n this section we begin by discussing our choice of parameters beforeassessing, through the use of simulations, the policy implications of di7erent degrees of scal rectitude under a common monetary policy'%.1 Calibration

n parameterising the model, we assume a 0uarterly data period,

and the parameters we choose are gi%en in table 8'1, along with thesteady2state %alues these imply' The %alue of the elasticity of demand facing our imperfectly

competiti%e rms, , comes from the econometricwor4 of otembergandWoodford (1998)' The 0uarterly discount factor of 1D1O+.++. isslightly higher than that found in other studies (such asJollman 1998or otemberg andWoodford 1998, for eample)' The reason for this isthat these studies assume innitely li%ed consumers so that theirassumed %alue of 1D1O+.++.E is e0ui%alent to an annual real interestrate of around @Q' -ince the eistence of nite li%es in our modelraises the real rate of interest abo%e consumers& rate of time

preference, this slightly lower rate of time preference is consistent withthe same e0uilibrium real interest rate commonly found in theliterature'

The 0 parameter is the probability of sur%i%al for our consumersand it implies an a%erage wor4ing life for consumersDwor4ers in ourmodel of thirty years' Crguably this is a not implausible measure of a%erage time spent in employment, although it admittedly implies ahigh probability of death if the model is ta4en literally' Ge%ertheless,such a parameter %alue is necessary to generate a plausible steady2state %alue of go%ernment debt relati%e to =#' This mar42up o%er aliteral probability of death can be 3ustied as reecting uncertainty not

formally captured in our model' "or eample, "aru0ee, $aton and-ymans4y (199.) show that not raising the probability of death in thisway implies near2icardian consumption beha%iour' They then showthat etending the model to allow for non2monotonic lifetime earningsproles e7ecti%ely raises the interest rate mar42up in the e0uation foraggregate human wealth in a manner consistent with our calibratedparameter'

( is our basic rate of income ta and is set at *EQ' The parameter is chosen to normalise the le%el of output to 1 to easecomparison of the steady2state le%els of other %ariables' Theparameter # measures the probability that a rm will not be able to

reset its price in the net 0uarter' Therefore, 1D1R# measures thea%erage length of time between price changes' C %alue of @ / A meansthat it ta4es, on a%erage, one year for rms to reset prices' This gureis consistent with the econometric wor4, using euro2area data, of =ali,=ertler and $Sope2-alido (*++1) and $eith and ;alley (*++1)'"inally, we assume, that the parameter go%erning the importance of money in utility approaches ero, implying that the economyapproaches its cashless limit as inWoodford (199E)' This simplies our


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analysis without distorting our results, and can be 3ustied asseigniorage re%enues are relati%ely unimportant for :; economies)'

Cll that remains is to choose the policy feedbac4 parameters forthe monetary and scal policy rules' We assume that the coe?cient onecess ination, m, is +'E as this is widely used in studies of interestrate reaction function (see Taylor 199@, for eample), and is often agood guide to the actual conduct of monetary policy' Cdopting a

positi%e %alue for m implies that monetary policy is !acti%e& in thesense of $eeper (1991)' n $eith and Wren2$ewis (*++1) we show thatan !acti%e& monetary policy of this sort must be supported by scalpolicies in which scal instruments are ad3usted so as to stabilise thedomestic stoc4 of go%ernment debt in the long run' n that paper wealso show that it is possible for a strong scal reaction to debtdise0uilibrium in one economy to compensate for a relati%ely wea4scal response in the other'

We also identify a policy regime where the scal authorities donot act to stabilie their respecti%e debt stoc4s, but re0uire themonetary authorities to abandon their !acti%e& targeting of ination and

utilise their monetary instruments to ensure debt stability' While thispolicy regime may be of historical interest, we would argue that thecurrent policy arrangements underpinning :;< put us clearly in the!acti%e& policy regime' The conditions implied by the #act for -tabilityand =rowth more than satisfy the scal sol%ency conditions identiedin $eith and Wren2$ewis (*++1)' $eith and Wren2$ewis (*+++) alsoclearly showed, in the closed economy contet, that scal policieswhich support an !acti%e& monetary policy were preferable to usingmonetary policy to stabilie debt as this tended to prolong anydise0uilibrium following shoc4s to the economy' "or these reasons wefocus on the conduct of policy in a policy regime where monetary

policy !acti%ely& targets ination and scal policy will ensure scalsol%ency in the long run' 6owe%er, as we show, this still lea%essignicant room for manoeu%re, as a far wea4er response to scaldise0uilibrium than is implied by the -tability #act would still beconsistent with saddlepath stability in our dynamic model' Bur netsection therefore in%estigates the optimal speed of response to debtdise0uilibrium'

%.2 Simulations


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n this section we eamine simulations of the calibrated %ersionof our model to consider how 0uic4ly the authorities in each countryshould stabilise debt' s rapid scal feedbac4 better than slowdebtstabilisationU f one country stabilies at an inappropriate rate, howdoes this inuence the other economyU

%.2.1 Symmetric economies shoc+s and policiesWerst consider the symmetric case, where both countrieschoose the same %alue for the , parameter' "or a symmetricshoc4, the two2country model acts as a single economy' We thenconsider what happens if one country adopts scal feedbac4 thatis !too slow&, or if the countries& ination responses di7er' n eachcase we consider both feedbac4 on go%ernment spending andthrough taes, as their implications are 0uite di7erent' The rst shoc4 we consider is an autocorrelated consumption

shoc45 there is a positi%e shift in consumption in the rst period of 1Q, which dies out in a uniform way o%er the net four periods'

(>onsumption remains endogenous throughout, so the rise inconsumption in the rst period may not be 1Q, because of changes to wealth or interest rates, for eample')

n the case where scal feedbac4 operates through go%ernmentspending, there is a clear benchmar4 case for the %alue of the , parameter' n our model, the only dynamic %ariables whosecurrent %alues inuence the future are asset stoc4s' Cconsumption shoc4 will result in changes in the le%el of personalnancial wealth, which will inuence consumption and laboursupply after the shoc4 has passed' The only other direct inuencethat changes in wealth will ha%e is through scal feedbac4, where

changes in go%ernment debt will inuence go%ernment spending'f the inationary impact of the latter eactly o7sets the former,ination will be unchanged after the consumption shoc4 haspassed'

6owe%er, ination stabilisation is not e0ui%alent to outputstabilisation, because labour supply is endogenous' Wor4ersdemand higher wages when they are as4ed to supply additionallabour to produce more output' 6owe%er, when the source of demand for the higher output is their own consumption then theywill also re0uire further wage increases as they see4 to substituteconsumption of goods for leisure (see the #hillips cur%e which

embodies this labour supply beha%iour, e0uation (8'AF))' Therefore, to stabilise ination after the shoc4 is o%er, anyo7setting change in go%ernment spending has to eceed thechange in consumption in order to eliminate the inationary wagedemands of wor4ers' "rom e0uation (8'E1) we see that in the log2linearised model the direct impact of nancial wealth onconsumption is gi%en by


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Cs noted abo%e, any fall in go%ernment spending must eceed theincrease in consumption to lea%e ination unchanged' Burassumption of 0uadratic disutility of labour supply implies that thepercentage reduction in output must e0ual the percentage rise inconsumption to eliminate the inationary impact of thedise0uilibrium in nancial wealth (see e0uation 8'E+)' f weconsider only the direct nancial wealth e7ect (see e0uation(8'F.)), then the %alue of the feedbac4 parameter , whichachie%es this is

=i%en that the steady2state %alues of model %ariables are afunction of model parameters and the go%ernment&s choice of ta

rates and go%ernment spending, this epression re%eals that the!matching& parameter is also a non2linear function of theseparameters and policy choices' 6owe%er, e%aluating this functionusing plausible parameter %alues conrms the intuition that whenconsumers are near icardian and policy choices in combinationwith model parameters

ensure that the e0uilibrium debt stoc4 is not too large, then the%alue of , implied by this function is fairly small' n other words,when debt dise0uilibrium has little impact on consumption, then


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go%ernment spending does not need to be ad3usted by much too7set the direct inationary impact of debt dise0uilibrium' This %alue of , is, howe%er, only an upper bound on the matchingparameter' Cs the change in go%ernment spending has to eceedthe changes in consumption arising from changes in consumers&

holding of nancial wealth, output also changes and this feedsbac4 onto consumption through human wealth' This is the indirecte7ect of debt dise0uilibrium on consumption and, %ia laboursupply decisions, ination' t turns out that, for our centralparameter set, a %alue of , of +'E is close to the gure that allowsscal policy to o7set the e7ects of debt on ination'A This impliesa decrease in go%ernment spending of +'EQ for e%ery 1Q ecessdebt' We call this the !matching case&' n an important sense, thisis the only %alue of the feedbac4 parameter which is consistentwith the :>&s ination target, because only with this degree of scal feedbac4 will ination be at target after any shoc4'

"igure 8'1 shows the path of go%ernment debt following thisdemand shoc4, and compares the matching case with two moreaggressi%e scal stabiliation

parameters, , H 1 and , H *'E


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stays below base throughout when , V1, reecting lower sa%ingscorresponding to the positi%e consumption shoc4, the decline insa%ings is muted by additional income coming from higher interestrates on the eisting debt stoc4' These e7ects are important5 if themonetary policy response was more aggressi%e, or if the ination

response more rapid, or debt was indeed (see below), then it is0uite possible for debt to rise after a period or two as higher debtinterest payments dominate the e%olution of go%ernment debt'Cs we would epect, the most aggressi%e scal feedbac4 leads tolarge shortterm changes in go%ernment spending' "igure 8'* plotsoutput in these three simulations' Cfter the initial period, outputdise0uilibrium is signicantly higher with aggressi%e feedbac4,because lower sa%ings and debt generate higher le%els

of public spending' (There is a one2period lag in scal feedbac4, sogo%ernment spending does not change in the rst period of theshoc4') Table 8'* gi%es the change in ination in these three cases o%erthe rst two years' The di7erences in ination are smaller than

gure 8'* would suggest, for two reasons' "irst, the inationaryimpact of higher go%ernment spending is half that of higherconsumption, owing to the labour supply responses of wor4ers(see discussion abo%e)' -econd, under the more relaed scalfeedbac4, go%ernment spending and output are higher in themedium term' Cs ination cumulates future ecess demand withdiscounting, this has some impact on short2term ination'Clthough di7erences are small, ination is higher with aggressi%escal feedbac4, reecting higher ecess demand' The initialincrease in output of around +'EQ is translated into an initialincrease in the annual ination rate of around 1'@Q' i7erences inination would be larger if monetary policy were less acti%e' "oreample, if m H +'* rather than +'E, then the impact gure forination would be 1'81Q with , H *, and 1'FEQ with , H +'E'>hoosing the slower, matching feedbac4 parameter thereforeproduces less output dise0uilibrium, slightly better ination controlin the short run, and eliminates ination dise0uilibrium after theshoc4 is o%er' The implication that the go%ernment&s scal


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correction should be slow reects the etent of consumptionsmoothing implied by our intertemporal model' t conrms andetends results obtained for a closed economy in $eith and Wren2$ewis (*+++)'f scal feedbac4 wor4s through taation rather than go%ernment

spending, then there is no e0ui%alent !matching& case, becausestabilisationwor4s through consumption' >onsumers will smooththe impact of ta changes, which means that these changes ha%elittle demand impact' 6owe%er, in the model ta changes alsoinuence labour supply, so that lower taes will raise output andreduce ination through this route' Cs a result, ta cuts aimed atrestoring debt e0uilibrium will ha%e a benecial supply2side e7ect'Cs table 8'@ shows, more aggressi%e scal feedbac4 produceslower ination and higher output dise0uilibrium, but thedi7erences are not large'

We now consider a supply shoc4, in the form of a one2yearination shoc4, such that, ceteris paribus, ination would be 1Qhigher in the rst 0uarter, +'.EQ in the second 0uarter etc' Withnon2indeed debt, this shoc4 initially reduces the real %alue of


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debt (because of higher ination), but subse0uently debt is higherbecause of lower ta receipts and higher interest rates'Cs debt falls initially, go%ernment spending initially rises, but thenis cut in an e7ort to reduce higher debt' The more aggressi%e thescal feedbac4, the larger the initial rise, and subse0uent

reduction in go%ernment spending (gure 8'@)' "igure 8'A showsthe conse0uences for output'

The more aggressi%e scal feedbac4 initially reduces the fall inoutput, but after the rst year output is lower' The net impact onination is small (as ination depends on cumulated future ecessdemand), but it is marginally higher under the more aggressi%efeedbac4' Bn impact ination is +'.1Q higher when , H +'E, but+'.@Q higher if , H 1'

f feedbac4 occurs through taation, we get a similar pattern inta rates (an initial cut, followed by subse0uent increases), butconsumers smooth their e7ect' The net result is that consumptionand output dise0uilibrium is smaller when feedbac4 is moreaggressi%e, and so ination is also slightly better initially (+'FEQon impact when , H 1, and +'F.Q when , H +'E)' 6owe%er,ination becomes slightly higher under the more aggressi%e scalpolicy after a few 0uarters, because higher taes reduce laboursupply, adding to inationary pressures' These results suggest that the optimal degree of scal feedbac4

depends critically on whether feedbac4 occurs throughgo%ernment spending or through taes'F When taes are used,there is a case for rapid feedbac4 (as in the scal stability pact),


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although the benets are minor' f debt stabilisation occursthrough go%ernment spending, then dise0uilibrium after the shoc4is o%er is

minimised by choosing feedbac4 that matches the response of consumers to changes in wealth, which probably implies slowscal feedbac4' The danger of rapid feedbac4 is clearest followinga demand shoc4, where the demand impact of scal correctionintensies the destabilising e7ects of the shoc4' These conclusions are not critically dependent on our assumption

that no debt is indeed' The path of debt following a consumptionshoc4 when all debt is indeed is shown in gure 8'E'We choosethe !matching& %alue of the feedbac4 parameter'

When debt is indeed, its %alue is not automatically reduced bysurprise ination' Bn the other hand, higher interest rates increasedebt interest payments, which adds to the debt stoc4, so that afterthe initial period debt is higher, despite the positi%e shoc4 tosa%ings' 6owe%er, our earlier conclusions about the ad%antages of the matching case o%er faster scal feedbac4 remain, because the

matching parameter eliminates the ination conse0uences of anydebt dise0uilibrium, whate%er its sign' n the case of an inationshoc4, debt is now higher throughout as a result of higher interestrates' When scal feedbac4 occurs through go%ernment spending,the larger fall in output under more aggressi%e scal feedbac4 isbrought forward' When taes are used, ination is still lower onimpact when feedbac4 is more aggressi%e, but the inationary


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impact of higher ta rates noted abo%e is also brought forward, soination is higher after the third 0uarter'

%.2.2 Symmetric economies and policies but asymmetric shoc+sn ourmodel the pattern of demand across goods is the same for

both countries& consumers' Cs a result, an asymmetric demandshoc4 (consumers sa%e less in country one but not in country two)does not lead to any change in a%erage preferences acrossindi%idual goods' 6owe%er, the shoc4 in%ol%es not only an increasein consumers& demand for goods in country one, but also theirdemand for leisure' Therefore, while output rises in country two due

to higher demand for their products, there is an o7setting fall inlabour supply in country one, with the net result that output incountry one hardly changes' Ct the same time the real echangerate appreciates for country one to reduce global demand for theirproducts in line with the reduced labour supply'

Cn asymmetric shoc4 also means that consumers& wealth andgo%ernment debt no longer mo%e together' >onsumers in countryone nance their higher consumption mainly by borrowing fromconsumers in country two, rather than borrowing from theirowngo%ernment' n any one country, therefore, it no longer ma4essense for scal feedbac4 to try to match the response of consumers

to changes in wealth, because debt and wealth follow 0uite di7erentpaths' "igure 8'F shows the impact of an asymmetric shoc4 onination in both countries when go%ernment spending is used tostabilise debt' The impact of changing the degree of scal feedbac4is %ery small, as was the case for a symmetric shoc4' Bnce again,ination is %ery slightly lower with slower scal feedbac4'i7erences generated by alternati%e scal policies are dominatedby di7erences between countries' n both cases, ination is initially


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higher incountry one (the source of the shoc4), but it also declinesmore rapidly there' The real echange rate initially appreciates incountry one, because output is higher in country two' C similarconclusion applies when feedbac4 occurs through taation, and foran asymmetric ination shoc4'

@'*'@ Symmetric economies and shoc+s but asymmetric policies-uppose both countries face the same shoc4, but their speed of scal correction di7ers' This is a critical eperiment in assessing theappropriateness of the scal stability pact' mplicit in the pact&sformulation is the idea that la scal control in one country couldimpose costs on the other, and could 3eopardise the ability of themonetary authorities to control ination' Bur analysis in relatedwor4 ($eith and Wren2$ewis *++1) showed that this was the case if one country applied little or no control o%er its public debt'6owe%er, does the same apply if debt control is slow rather thannon2eistentU

n the case of a demand shoc4 and scal feedbac4 throughgo%ernment spending, di7erent speeds of ad3ustment ha%e littledi7erential e7ect on each country' n particular, the real echangerate is unchanged' This is because go%ernment spending is spreade0ually across demand for each good, and consumers areindi7erent between each country&s debt' The only conse0uence of one country reducing its speed of scal feedbac4 is that it lowersthe a%erage speed of correction for both countries' Cs we sawabo%e, with this shoc4 slow ad3ustment is preferable (the !matching&case)' Cs a result, the country ad3usting 0uic4ly imposes costs(albeit small) on the country ad3usting slowly ;uch the same

applies in the case of a supply shoc4'When scal feedbac4 occurs through taation, then results are

more interesting, because di7erences in taation between countriesgenerate di7erences in supply and the real echange rate' n thecase of a demand shoc4, debt falls and so the scal authoritiesreduce ta rates' -uppose feedbac4 in country one is !fast& ( , H 1),and in country two !slow& (, H +'E)' The more rapid fall in taes incountry one leads to greater labour supply in the short run, andhigher output' To sell the additional output, country one&s realechange rate initially depreciates, but this is re%ersed after a fewyears when country two&s taes become lower relati%e to country

one'-lower ad3ustment in country two lowers the a%erage speed of

ad3ustment, and we saw in the case of symmetrical policies that itwas preferable to ad3ust taes 0uic4ly rather than slowly for ademand shoc4' Cs a result, slow ad3ustment in country two raisesination in country one relati%e to the case where both countriesad3ust 0uic4ly' 6owe%er, the di7erences are tiny5 ination at an


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annual rate is about +'+1Q higher in country one as a result of slowad3ustment in country two'

"or a supply shoc4 and feedbac4 through taes, it is clearest toloo4 at the case of fully indeed debt, because then taes risethroughout following the

increase in interest rates' (ecall that when debt is not indeed,taes initially fall because ination reduces the real %alue of debt')Cs taes rise more rapidly in country one compared to country two,then country one&s labour supply falls by more and output isrelati%ely lower in country one than in country two' 6owe%er,

consumption in country two is higher as a result of its slower scalreaction compared to the symmetric case, and this supports outputin country one' Cs a result, slowad3ustment in country two initiallyraises output in country one, but then output falls in country onerelati%e to the symmetric policy case' The net impact on ination incountry one is therefore small5 on impact it is +'FEQ compared to+'FAQ with symmetric policies' The gures are identical for countrytwo'

"or both countries, therefore, there is a %ery small cost in termsof higher ination as a result of slower ad3ustment in country two' nterms of a%erage ination across both countries this is eactly what

we would epect, gi%en our results earlier5 the interesting point isthat the ination eperiences of both countries are %ery similardespite asymmetric policies (gure 8'.)' n terms of output, countrytwo clearly gains through slower scal ad3ustment, but country oneis not ob%iouslyworse o7 than itwould ha%e been under symmetricpolicies' These results therefore pro%ide some 0ualied support forthe scal stability pact5 there is a temptation to ad3ust slowly, thecosts of which are spread across the union'


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6owe%er, the support is 0ualied for many reasons' t does notapply if scal ad3ustment ta4es place through go%ernment spending/ in this case the rapid scal ad3ustment implicit in the #act appearsun3ustied' enets are only

noticeable for supply rather than demand shoc4s, and e%en then theyare %ery small'

%.2.) Asymmetric economies symmetric policies and shoc+s-o far we ha%e assumed that the two countries ha%e an identical

structure' Bne of the most fre0uently analysed cases where

structure di7ers is where one country is more sluggish in its inationresponse' ndeed go%ernments in some countries in the :< ha%emade a point of pressing their :< partners to underta4e labourmar4et and other structural reforms in an attempt to ma4e mar4etsthere less rigid'

>onsider the symmetrical demand shoc4 analysed abo%e, wherescal feedbac4 occurs through go%ernment spending, and wechoose the matching %alue of , (, H+'E)' -uppose price inertia incountry two is less than in country one' n our model inertia in bothgoods and labour mar4ets is captured by the alpha parameter' -ofar we ha%e assumed # H +'.E in both countries, which implies that

three20uarters of prices remain ed each 0uarter' -uppose nowthat # H +'E in country two, but remains at +'.E in country one'

This di7erence in ination responsi%eness leads to 0uite di7erentbeha%ior in each country, e%en though the shoc4 is symmetric'"igure 8'8 loo4s at output in each country, and also plots the casewhere # H +'.E in both countries'


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nation tends to increase more rapidly in country two, whichleads to a depreciation in country one' Cs a result, output rises morerapidly in country one, but actually falls in country two' Thedi7erences in ination between the

two countries are less mar4ed, as gure 8'9 shows' The fact thatdi7erences in # inuence output much more than ination in partreects the high demand elasticity we ha%e assumed ( H 8)' -mallmo%ements in the real echange rate generate large di7erences inoutput'

The mar4ed di7erences in output between the two countries leadto %ery di7erent proles in go%ernment debt' Cfter ination erodesdebt in both countries, debt in country two is soon higher than base,while in country one it always stays below base' Ct rst sight thismight suggest that country two should reduce its debtdise0uilibrium more rapidly than country one' 6owe%er, our resultsabo%e suggest that rapid debt correction is not ob%iously desirable' This is conrmed by %arious simulation eperiments not reportedhere5 increasing the relati%e speed of scal feedbac4 in country twodoes not lead to any clear benets in terms of ination or output foreither country' Bne issue that would be worth pursuing in furtherresearch is whether asymmetric economic structures mightgenerate a role for a countercyclical scal policy'

". #onclusionn this chapter we constructed a two2country model which contained a

number of features which bro4e the distinction between icardian andnon2icardian policies highlighted by the "iscal Theory of the #rice $e%el(Woodford 1998)' -pecically, our two economies featured o%erlappinggenerations of consumers who did not epect to li%e for e%er / as a result


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the go%ernment&s liabilities (money and bonds) constitute an element of net wealth and their le%el will a7ect real interest rates in our economies' These consumers then supplied labour to imperfectly competiti%e rmswho sold their output at home and abroad' These imperfectly competiti%erms could ad3ust their prices only at random inter%als' The combination

of non2icardian consumers and the nominal inertia facing imperfectlycompetiti%e rms implied that both monetary and scal policy could ha%ereal and nominal e7ects in both countries'

Bur policy simulations then analysed a situation where both countrieshad formed a currency union, where an independent central ban4 followeda common rule for monetary policy which sought to target the a%eragerate of ination across the two economies, but where the two scalauthorities remained free to pursue independent scal policies' Throughthese simulations we sought to disco%er whether there is a case for rapidor slow stabilisation of debt stoc4s, and whether it might be 3ustiable toimpose fast ad3ustment on both countries'We ha%e shown that the answer

depends critically on whether changes in spending or taes are used tostabilise debt' f scal feedbac4 occurs through go%ernment spending,then there is a strong case for choosing feedbac4 that matches and o7setsthe pri%ate sector&s response to additional debt' This matching case isli4ely to in%ol%e slow ad3ustment, and both countries ha%e an incenti%e toadopt this policy' f feedbac4 occurs through taation, then there arecircumstances where an indi%idual country has an incenti%e to ad3ustslowly, with inationary costs for the union, but these costs are small'"inally we show that the conse0uences of structural di7erences betweencountries may be much more signicant than di7erences in scal policy'

different speeds of debt stabilisation in emu

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