Simple Monetary Rules Under Fiscal Dominance

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 937 July 2008 Simple Monetary Rules Under Fiscal Dominance Michael Kumhof, International Monetary Fund Ricardo Nunes, Federal Reserve Board Irina Yakadina, International Monetary Fund NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgement that the writer has had access to unpublished material) should be cleared with the author or authors. RecentIFDPsareavailableontheWebatwww.federalreserve.gov/pubs/ifdp/. ThispapercanbedownloadedwithoutchargefromSocialScienceResearchNetwork electronic library at http://www.ssrn.com/. 1

Simple Monetary Rules Under Fiscal Dominance MichaelKumhof,InternationalMonetaryFund RicardoNunes,Federal ReserveBoard IrinaYakadina,International MonetaryFund July2008 Abstract This paper asks whether an aggressive monetary policy response to inflation is feasible in countries that suffer from fiscal dominance, as long as monetary policy also responds to fiscal variables. We find that if nominal interest rates are allowed to respond to government debt, even aggressive rules that satisfy the Taylor principle can produce unique equilibria. But following such rules results in extremely volatile inflation. This leads to very frequent violationsof the zerolower boundon nominal interest ratesthat make suchrules infeasible. Evenwithintheset of feasiblerulestheoptimal responsetoinflationishighlynegative,and more aggressive inflation fighting is inferior from a welfare point of view. The welfare gain from responding to fiscal variables is minimal compared to the gain from eliminating fiscal dominance. Keywords: Optimalsimplepolicyrules,fiscal dominance. JELClassification: E61,E62 TheauthorsthankJordiGali,MichelJuillardandseminarparticipantsatUniversitatPompeu FabraandtheIMFforhelpfulcomments. Theviewsinthispaperaresolelytheresponsibility of the authors and should not be interpreted as reflecting the views of the IMF, the IMF Executive Board, IMF management, theBoardof Governorsof theFederal ReserveSystem oranyother personassociatedwiththeFederalReserveSystem.

"...Acentralbankchargedwithmaintainingpricestabilitycannotbeindifferentastohowfiscalpolicyisdetermined"(Woodford,2001)"Ideally,wherefiscalpolicythatunderminescentralbankcontrol ofinflationisarealpossibility,thisshouldbeaccountedfor,discussedininflationreports,andreflected incentralbankprojections"(Sims,2005) 1 Introduction Is a monetary authority’s commitment to fighting inflation aggressively a sufficient condition for ensuring price stability? It has long been held that the answer to this question should be negative. The reason is that the central bank’s inflation objective may collide with an inflexible, or dominant, stance of fiscal policy that is unable or unwilling to adjust primary surpluses to stabilize government debt. Fiscal dominance was analyzed by Sargent and Wallace (1981) in an economy with real debt, where an unrealistic inflation objective leads to insufficient seigniorage revenue in the short run that has to be made up by higher seigniorage, and therefore inflation, in the long run. The fiscal theory of the price level of Woodford (1996, 1998, 2001)1 considers an economy with nominal debt, and shows that non-explosivegovernment debt inthefaceof dominant fiscal policycanonlybeguaranteed by ensuring that real interest rates fall when inflation rises.2 This is the opposite of the Taylor (1993) principle for stabilizing inflation, which requires higher real interest rates in response to higher inflation, and which is generally taken to represent the notion of fighting inflation aggressively. The Taylor principle is derived in a standard New Keynesian setup for monetary policy analysis by assuming that the fiscal authority sets lump sum taxes that satisfyabalancedbudgetrequirement. In this paper we focus on inflation targeting under fiscal dominance as in Woodford (2001), motivated by the belief that this framework may be appropriate to describe the 1 Other key contributions to this literature are Cochrane (1998) and Sims (1994). A long listofadditionalreferencesiscontainedinCochrane(1998,2000)andWoodford(2001). 2 This assumption implies that the out of equilibrium present value of budget supluses is notequaltotherealvalueofdebt.Thisdoesnotmeanthatthegovernmentdoesnotcareaboutsatisfyingthe intertemporalbudgetconstraint. Itisthatthelevelofsurplusissetbeforethepricelevelisdetermined. 2

pressuresfacingatleastsomeof thedevelopingcountriesthathaverecentlystartedtoadopt inflation targeting. The reasons for fiscal dominance include some combination of a weak fiscal revenue base, a rudimentary tax collection system that encourages tax evasion, the contingent bailout liabilities attached to weak banking systems, and simple overspending at the federal or regional level. Under such conditions, if the government has issued nominal debt denominated in local currency, fiscal difficulties are often resolved not through an increase in tax revenues but instead through high inflation that erodes the real value of government liabilities.3 The assumptions underlying the policy recommendations of the inflationtargetingliteraturearethereforeclearlynotsatisfied. But the recent literaturehas shownthat thisalone doesnot settle the question of whether fiscal dominanceunambiguouslypreventsacentral bankfrom fightinginflation. Ontheone hand,Loyo(1999)andSims(2005)holdthatalackoffiscaladjustmentcouldmakeinflation targetingcompletelyinfeasible. Butontheotherhand,BenignoandWoodford(2006)argue thatwhileinflationvolatilityishigherunderfiscaldominance,itneednotbeexcessivelyhigh as long as medium term inflation expectations are anchored. To show this they compute a Ramseyoptimal policywherethemonetaryauthorityimplicitlyrespondstofiscalvariables. The result of a Ramsey optimal policy is a set of implied laws of motion for the main macroeconomicvariables,butunfortunatelythereisnoobviousmappingfromsuchapolicy to an implementable policy rule, which for a modern central bank would invariably take the form of an interest rate rule. It is therefore not immediately obvious whether the results of BenignoandWoodford(2006)shouldbeinterpretedasfightinginflationaggressivelyinthe sense of the Taylor principle. Moreover, the Ramsey policymaker is assumed to formulate policies in response to a great deal of information that includes private agents’ behavioral 3 If all of an inflation targeting government’s debt is denominated in foreign currency, the same circumstances would result in a balance of payments crisis, as shown by Kumhof, Li andYan(2007).KumhofandTanner(2007)presentsevidenceonthesizeoflocalcurrencygovernmentdebt markets in developing countries. Daniel (2001) presents a detailed examination of the fiscal determinantsofcurrencycrisis. 3

rules and expectations, while in practice policymakers have to set interest rates in response to observableeconomicvariablesandsubject topracticalconstraints. Thequestionof what constitutes an optimal policy therefore needs to be narrowed even further, and we attempt to do so in this paper. Specifically, we ask whether a benevolent monetary authority can substitute for fiscal adjustment if its only available policy instrument is the nominal interest rate,ifthatinterestrateisrestrictedtorespondinalinearfashiontoobservedmacroeconomic variables, and if that interest rate may not hit its zero lower bound excessively often. The spirit of the exercise is similar to Schmitt-Grohe and Uribe’s (2006) analysis of simple and implementablerules. But we add one key innovation. It is based on the observation that, under fiscal dominance,themonetaryauthoritymustbeclearlyawarethatitistheonlyentitycapableof ensuringnotonlypricestabilitybutalsofiscalsolvency. Itisthereforenaturaltosupposethat itwouldtakefiscalvariablessuchasgovernmentdebtintoaccountinformulatingitspolicy, and that this would increase its ability to react aggressively to inflation. We therefore allow the nominal interest rate to respond not only to inflation and output, but also to government spendingortogovernment debt. We then analyze the feasibility and desirability of an aggressive response of the interest rate to inflation by applying three successive criteria. First, we check for determinacy of equilibria. Second, we rule out determinate equilibria that violate the zero lower bound on nominal interest rates too frequently. Third, we rank the remaining equilibria by computing theirwelfareimplications. Equilibrium determinacy under different monetary and fiscal rules was the subject of Leeper’s(1991) seminalcontributionthat will alsoformthebenchmarkof our study. Under a passive fiscal policy the fiscal authority adjusts taxes in order to meet the government budget constraint. In this case determinacy requires an active monetary policy that reacts strongly to inflation to achieve price stability. Under an active fiscal policy the primary surplus does not respond to the level of government debt. Determinacy then requires a 4

passive monetary policy so that inflation can balance the budget, and this prevents price stability from being achieved. All other combinations of fiscal and monetary policies do not lead to a unique equilibrium. Since the New Keynesian literature has assumed that the fiscal authority adjusts taxes appropriately, the usual policy recommendation is to have the monetary authority fight inflation aggressively. More recently Schmitt-Grohe and Uribe (2006) have analyzed the combinations of fiscal and monetary rules that lead to a unique equilibrium when allowing for the more realistic case of distortionary taxation. They also add the zero lower bound criterion in checking for the implementability of different rules. TheirpaperbroadlyconfirmsLeeper’sresults. OurresultsfirstrestatethecasefortheTaylorprincipleintheabsenceoffiscaldominance. We then show that under fiscal dominance it is indeed beneficial to include government spendingorgovernment debt asanargumentinthecentralbank’sinterest raterule,because doing so entails an improvement, albeit very small, in welfare. But the optimal rules have highly negative coefficients on inflation, and an inflation coefficient greater than one is practically impossibleeven when monetary policy responds to fiscal variables. Government spending in the policy rule does not even expand the range of determinate equilibria to include inflation coefficients greater than one. When government debt enters the policy rule, part of the determinacy region does include an inflation feedback coefficient greater than one. But that region displays extremely high inflation volatility, and it is ruled out by the zero lower bound constraint on nominal interest rates. Furthermore, inflation volatility andwelfarelossesaremuchhigherthanunderaRicardianpolicy,andincreasedramatically asthecoefficientoninflationisincreasedawayfromitsoptimalvalue. Our conclusion contains an important message for developing countries’ central banks. This is that fiscal discipline must absolutely be established before committing to inflation targeting. Monetarypolicyalonecannotengineerarescue. The paper is organized as follows. Section 2 describes the model. Section 3 analyzes optimalmonetaryandfiscalpolicywhenfiscalpolicyisnotdominant. Section4determines 5

optimalpolicyunderfiscal dominance. Section5concludes. 6

2 The Model We take as our baseline case the model described in Schmitt-Grohe and Uribe (2004a). This model is simple but retains the necessary ingredients to evaluate fiscal and monetary policy interactions. Namely, monetary policy is non-neutral due to a transactions cost technologyandduetostickygoodspricesinaworldofmonopolisticcompetition. Financial markets are incomplete in that the government can only issue one period nominal bonds.4 The presence of nominal bonds gives the government an incentive to use inflation to make real returns state contingent as described in Chari and Kehoe (1999). In fact, if prices were fully flexible then the real allocations would be the same as if markets were complete. In thismodel,marketincompletenessdoesmatterbecausetherearepriceadjustmentcosts. The costs of changing prices can be motivated by costs of acquiring and processing information (Zbaracki et al. (2005)). For the sake of realism the government can only use distortionary formsoftaxation. Householdsareindexedbyi [0,1],andhavetheutilityfunction ∈ ∞ E βt(ln(ci)+δln(1 hi)) , (1) 0 t t − t=0 X whereci isconsumptionofthecompositegoodandhi islaboreffort. Consumptionisinturn t t anaggregateofimperfectlysubstitutablevarietiesci(j), t η ci = 1 ci(j) 1+ η η dj 1+η , (2) t t µZ0 ¶ sothat costminimizationimpliesthesetofgoodsdemands P (j) η ci(j) = ci t . (3) t t P t µ ¶ Money facilitates consumption purchases, which are subject to a proportional transactions cost s(vi) = Avi +B/vi 2√AB , (4) t t t − 4 MarcetandScott(2001)provideargumentstosupporttheassumptionofincompletemarkets. 7

where vi = P ci/Mi is money velocity, P is the aggregate price level of the composite t t t t t consumptiongood,andMi isnominalmoneyholdings. t Producers are indexed by j [0,1] and are identical to the set of households because ∈ each household is the sole producer of a single variety y (j) of the composite good. These t goodsareproducedwithalineartechnology y (j) = z h (j), (5) t t t where z is productivity and h (j) is labor hired in a competitive labor market. The output t t market is monopolistically competitive, and each producer sets the price of the good it suppliessubjecttoquadraticpriceadjustmentcostsoftheform θ P (j) 2 θ t 1 = (π (j) 1)2 , (6) t 2 P (j) − 2 − t 1 µ − ¶ and taking the level of aggregate demand for its good as given. Aggregate demand consists ofprivateconsumptiondemandc (j)andgovernmentdemandg (j),with t t y (j) = c (j)+g (j) . (7) t t t Aggregateconsumptiondemandisgivenby(3)aggregatedoveralldemandsi: P (j) η t c (j) = c . (8) t t P t µ ¶ Government demands a composite g that consists of the same varieties as the consumption t good, with the same elasticity of substitution, so that government demand for variety j is givenby P (j) η t g (j) = g . (9) t t P t µ ¶ Aggregateoutputisthennaturallygivenby η 1 1+η 1+η y t = y t (j) η dj . (10) µZ0 ¶ Financialassetsincludemoneyandnon-statecontingentoneperiodnominalgovernment bonds held from period t to t + 1, denoted by Bi, with gross nominal interest rate R . A t t borrowingconstraint isimposedtoprevent householdsfromengaginginPonzischemes. 8

Non-financial income accrues to households in the form of net cash flows from their activity as producers and from wage income. The former is given by P (i)y (P (i)/P )η t t t t − W h (i) θ ((P (i)/P (i)) 1)2,andthelatterbyW hi(1 τ ),whereW isthenominal t t − 2 t t − 1 − t t − t t wage(therealwageisdenotedbyw )andτ isthelaborincometaxrate. t t Thehouseholdbudgetconstraint,combiningthepreviousfeatures,isgivenby P ci[1+s(vi)]+Mi +Bi Mi +R Bi (11) t t t t t ≤ t − 1 t − 1 t − 1 P (i) θ P (i) 2 +P t y (i) w h (i) t 1 +(1 τ )P w hi . t P t − t t − 2 P (i) − − t t t t " t t 1 # µ ¶ µ − ¶ The household maximizes (1) subject to (11), (4), (5) and (6). The first-order conditions for this problem are shown in Appendix A. Note that household superscripts and producer indicescanbedroppedintheseconditionsasallagentsfaceidenticaldecisionproblemsand thereforeobtainidenticalsolutionsinequilibrium. Thegovernmentbudgetconstraint isgivenby M +B = M +R B +P g τ P w h . (12) t t t 1 t 1 t 1 t t t t t t − − − − The monetary and fiscal authorities decide on the nominal interest rate and on the labor tax rate R ,τ . The precise form of the rules that determine these two policy instruments is t t { } of course critical for the presence and implications of fiscal dominance. Those rules will thereforebediscussedindetailinthesubsequentsectionsofthepaper. Shock processes are given by the following laws of motion for productivity and government spending: lng = (1 λg)lng +λglng +εg; εg˜N(0,σ2 ) , (13) t − t − 1 t t εg lnz = (1 λz)lnz +λzlnz +εz; εz˜N(0,σ2 ) . (14) t t 1 t t εz − − Calibration follows Schmitt-Grohé and Uribe (2004) and is summarized in Table 1. A baroveravariableindicatesitssteadystatevalue. Thetimeunitisoneyear. 9

β 0.96 A 0.0111 π¯ 1.042 B 0.07524 h ¯ 0.2 λg 0.9 g/y 0.2 σ 0.0302 εg B/(PY) 0.44 λz 0.82 η/(1+η) 1.2 σ 0.0229 εz θ 17.5/4 3 Monetary Policy in a Ricardian World In this section we specify how the monetary authority can implement a desired equilibrium in a world of endogenous taxation that ensures budget balance. The monetary authority is assumed to specify an interest rate rule that responds to deviations of current inflationandoutput fromtheir target values,whilethefiscal authorityisassumed toraiseor lowerlabortaxratesinresponsetodeviations-laggedbyoneyear-ofgovernmentliabilities from a target value.5 This second, fiscal part of the rule ensures long-run government solvency. Inparticular,weconsidertherule:6,7 ln(R /R ) = φRln(π /π )+φRln(y /y ) , (15) t ∗ π t ∗ y t ∗ τ = τ +φτ(a a ) . t ∗ a t 1 ∗ − − wherea = (M +R B )/P aretotallaggedgovernmentliabilities,π andy are t 1 t 1 t 1 t 1 t 1 ∗ ∗ − − − − − inflation and output target values of the monetary authority, and τ and a are tax and asset ∗ ∗ targetvaluesofthefiscalauthority. AsinSchmitt-GroheandUribe(2006),wesetthetarget 5 Thisisbasedontherealisticpremisethatfiscaldecisionsoccurwithaoneyearlag. 6 Another Ricardian rule is sometimes considered in the literature, namely ln(R /R ) = t t 1 φRln(π /π )+φRln(y /y ).Thismaybeeasiertoimplement,asthemonetaryauthor − itydoesnotneed π t ∗ y t t 1 informationonthesteadysta−televelsoftheinterestrateandoutput. However,wehavefoundqualitatively verysimilarresultsbetweenthisruleand(15),andthereforeconcentrateourdiscussiononthelatter. 7 Inflation forecast based rules would replace current inflation by expectations of inflation, but thispresumesthatthemonetaryauthoritycanperfectlyobserveprivateagents’expectations.Inpracticethis could either mean extracting them from surveys or applying econometric techniques to extract them from financial data. As for the former, Nunes (2005) shows why survey expectations maynotreflectactualexpectations.Asforthelatter,inthedevelopingcountriesthatmotivatedthisstudythe datarequiredtousethesetechniquesaregenerallynotavailable. 10

valuestobeequaltothenon-stochasticsteadystateoftheassociatedRamseyoptimalpolicy problem. Note that we are departing from the most conventional monetary policy analysis becausetaxationisdistortionaryandisalsoanobjectof optimization. We find that the parameter φR does not affect most of our key results in an important y way, and we therefore show most results for the case φR = 0. Where it does have some y effectwecommentaccordingly.8 ThefirstpanelofFigure1,labelled“Determinacy”,shows the equilibrium determinacy analysis. The vertical axis considers different values of the feedbackcoefficientongovernmentliabilitiesφτ whilethehorizontalaxisconsidersdifferent a values of the inflation feedback coefficient φR. White areas signal that the equilibrium π exists and is unique. The figure displays two white regions. One area is associated with a sufficiently large tax response (significantly greater than zero) and a strong response of interest rates to inflation φR (greater than one, the Taylor principle). In this constellation π of parametersthefiscal rule guarantees government solvency while themonetary rulefights inflation aggressively in order to pin down the price level. This confirms the results known fromtheNewKeynesianliteraturewithlumpsumtaxation. Thesecondareacorrespondsto anactivefiscalandpassivemonetarypolicy. In the next panel of Figure 1, labelled “Zero Bound”, we plot in black all rules that are notconsistentwitheitherequilibriumdeterminacyorwiththezerolowerboundonnominal interest rates.9 As in Schmitt-Grohe and Uribe (2006), the zero lower bound constraint is imposedbyrequiringthatEln(R) 2σ . Bycomparingthefirstandsecondpanelonecan R ≥ see that the zero bound does not eliminate many rules. Both in the top left and bottom right regionstherearemanyrulesthatcanleadtoanimplementableequilibrium. The next panel “Welfare” plots welfare contours for combinations of coefficients that satisfy the determinacy and zero lower bound conditions. We compute welfare using a 8 We found it sufficient to consider only three values of φR to characterize the solutions, y namelyφR 0.5,0,0.5 . y ∈{− } 9 ThereaderisreferedtoAppendixBfordetailsonthesecomputations. 11

second order approximation, as explained in detail in Schmitt-Grohe and Uribe (2004b).10 Consider two policy regimes, a reference regime denoted by r, and an alternative regime denoted by a. The welfare loss is defined as the fraction of regime r’s mean consumption that the household would be willing to forego while still being as well off as under regime a. WeconsidertheRamseyallocationtobethereferenceregimeandtheallocationsinduced by the simple rule to be the alternative regime. We observe that the welfare results for an activemonetaryandpassivefiscalpolicyaregenerallysuperiortothoseforactivefiscaland passivemonetarypolicy. Furthermore,welfareincreasesinthedirectionofamoreaggressive monetary response to inflation. The welfare loss of the best rule is 0.02%, and that rule is givenby11 ln(R /R ) = 3ln(π /π ) , (16) t ∗ t ∗ τ = τ +0.36(a a ) . t ∗ t 1 ∗ − − The final panel of Figure 1, labelled “Inflation Volatility”, shows that the welfare results are closely related to the volatility of inflation implied by the chosen policy mix. It shows that an active monetary policy response to inflation stabilizes inflation volatility far better than an active fiscal policy. Furthermore this effect, which works through agents’ inflation expectations,isstrongerforamoreaggressiveresponsetoinflation. For later comparison with fiscal dominance, Figures 2a and 2b show impulse responses foronestandarddeviationshockstoproductivityandgovernmentspending. Weobservethat in a Ricardian world monetary policy responds to inflation in the short run, while tax rates are adjusted very gradually to stabilize debt in the long run. The critical feature of fiscal dominanceisthat taxratesarenotavailablefor thistask. 10 See also Collard and Juillard (2001). The reader is referred to Appendix C for a description ofthewelfarecomputations. 11 We limit our search to inflation coefficients φR 3. A further small welfare improvement π ≤ wouldbeattainablewithevenhigherφR. π 12

4 Monetary Policy under Fiscal Dominance Wemodelfiscaldominancebyassumingthatthetaxrateisexogenousandconstant. With government spending specified as an exogenous stochastic process (13), fiscal instruments are therefore not being used to ensure that the intertemporal budget constraint of the government holds. In such a world the central bank has no choice but to accommodate fiscal shocks. An important question is whether it can still fight inflation aggressively while doing so. The conventional answer is that it cannot, and this is based on using a monetary rule identical to (15) combined with exogenous taxes. But we suggest that a monetaryauthoritythatknowsitistheonlyinstitutioncapableofensuringfiscalsolvency(in additiontopricestability)wouldnotignorefiscalvariablesinsettingitspolicy. Wetherefore allow for monetary rules that may respond not only to inflation and output but also to fiscal variables. We establish whether this improves the performance of interest rate rules under fiscal dominance, and whether such rules may make it possible to respond aggressively to inflation. Specifically, the interest rate rules we consider continue to react to inflation and output. But in addition we consider a response to deviations of either government spending or of government liabilities from their desired levels. Stability and welfare analysis of the same typeasinFigure1isshownforthesetwocasesinFigures3and4. 4.1 Government Spending in the Interest Rate Rule We first consider an interest rate rule that takes into account deviations of government spendingfromaconstant valueg: ln(R /R ) = φRln(π /π )+φRln(y /y )+φRln(g /g) . (17) t ∗ π t ∗ y t ∗ g t Rule (17) posits that if government spending is 1% above its steady state level then the interest rate will be changed by φR basis points. This case is presented in Figure 3. The g mainresultisthatrespondingtogovernmentexpendituresdoesnotincreasethedeterminacy 13

regionforφR comparedtotheconventionalcaseofφR = 0,asmonetarypolicystillhastobe π g passive, φR < 1. The zero lower bound restriction onnominal interest rates imposes further π restrictions on the implementable range of feedback coefficients, specifically the coefficient ongovernmentspendingcannotbetoolargeinabsolutevalue. Thebestruleintheclass(17) isdescribedby ln(R /R ) = 0.84ln(π /π ) 0.5ln(y /y )+0.22ln(g /g) . (18) t ∗ t ∗ t ∗ t − − We find that the welfare losses associated with this rule are very much larger than for the Ricardiancase,at0.202%versus0.02%. Allowingforanon-zerocoefficientongovernment spending is beneficial, but only slightly so, as under the restriction φR = 0 welfare losses g can be shown to rise to 0.210%. The third panel of Figure 3 shows that maximizing welfare calls for a highly negative coefficient on inflation, and that attempting a more aggressive inflationresponseleadstolowerwelfare. ThereasoncanbeseeninthefinalpanelofFigure 3,whichshowsthatinflationvolatilityincreasesasφR israisedaboveitsoptimalvalue. This π not only leads to more volatile nominal interest rates and therefore violations of the zero lowerboundconstraint,butalsotomorevariablerealinterestratesandoutput,whichcauses welfare losses. The Taylor principle in this case is not even consistent with determinacy, not to mention the zero lower bound or welfare considerations. We now turn to another argument of the policy rule that holds more promise in expanding the monetary authority’s options,governmentliabilities. 4.2 Government Liabilities in the Interest Rate Rule We consider an interest rate rule that responds to deviations of inflation and output from their target values, as before, and to deviations of government debt (scaled by steady state GDP) from its target value. Since the monetary authority faces no policy implementation lags, we will assume that the interest rate rule reacts to the current level of government 14

liabilities: ln(R /R ) = φRln(π /π )+φRln(y /y )+φR(a a )/y . (19) t ∗ π t ∗ y t ∗ a t ∗ ∗ − The rule (19) assumes that if the ratio of government liabilities to output is 1 percentage pointhigherthantarget,thentheinterestratewillberaisedbyφRbasispoints. Doesthisrule, a whichisconsideredinFigure4,allowforanaggressiveresponsetoinflation? Atfirstsightit looksalotmorepromisingthanFigure3. Moststrikingly,aslongassolvencyisguaranteed by lowering interest rates sufficiently in response to excessive government liabilities, it is now possible to reach the region of determinacy even with an aggressive response to inflation. Butthisisanillusion,astheanalysisofthezerolowerboundconditiononnominal interest rates shows. All coefficient combinations that include an aggressive response to inflationviolatethelowerbound,whichmakesthisruleimpossibletoimplementinpractice. For instance, if the coefficient on inflation were 1.5 and that on liabilities were -0.2, then the standard deviation of interest rates would be 4.1. Such volatility implies that interest rates would have to be higher than 8.2% on average to satisfy the lower bound condition, while in our economy the average interest rate is 3.8%. It is true that many developing economiesexperiencehighinflationandconsequentlyhighnominalinterestrates. However, if a successful inflation targeting regime were to be implemented in developing countries theninflationandnominal interestrateswouldbelower. Thebest ruleinthisclassis ln(R /R ) = 1.5ln(π /π ) 0.08(a a )/y . (20) t ∗ t ∗ t ∗ ∗ − − − Similarto(17),wefindthatincludinggovernmentliabilitiesintheruledoesleadtoaslightly better performance, with welfare losses droppingfrom0.210%under therestrictionφR = 0 a to 0.204% for (20).12 Maximizing welfare again calls for a highly negative coefficient on inflation, and even pushing in the direction of a rule satisfying the Taylor principle, without actuallygettingthere,isdetrimental. Thesewelfareresultsarecloselyrelatedtotheimplied 12 Thismakeslittledifferencetotheoptimalbehaviorofmonetarypolicy.UndertherestrictionφR =0the a optimalcoefficientoninflationchangestoφR = 1.26. π − 15

inflation volatilities of each regime, shown in the last panel of Figure 4. Under a Ricardian regimeinflationvolatility is 0.08for theoptimal rule(16). Under fiscal dominance inflation volatility is very much higher, about 1.5 when the optimal rule is implemented. Moreover, the volatility of inflation increases dramatically as a more aggressive inflation response is attempted. The implied volatility of the real interest rate and therefore of real variables explainswhywelfaredeterioratesinthisattempt. Finally, Figures 5a and 5b present the impulse responses for technology and government spending shocks under rule (20). The crucial difference to the Ricardian case is that under fiscaldominancetheinterestrateratherthanthetaxratehastobeusedtostabilizedebt,and this stabilization takes place over a much shorter time horizon. As a result nominal and real interestratesaremuchmorevolatile. TheresponseofthedebttoGDPratioineachexample istheoppositeoftheRicardiancase. Figure5ashowsthatapositiveproductivityshockleadstoanincreaseinthepublicdebt, rather than a fall as in Figure 2a. Under a Ricardian policy debt is used as a shock absorber. This means that higher productivity, which reduces marginal cost and therefore inflation, is allowed to reduce the real interest rate, thereby boosting demand and reinforcing the direct effect of higherproductivityonthereal wage. Theresult isanincreaseintaxrevenue that, combined with the lower real interest rate, reduces debt. The economy subsequently benefits from this debt reduction through a reduction of the distortionary labor tax rate, which gradually returns debt to its long run value. But under fiscal dominance tax rates cannot fall to pass on the beneficial tax revenue effects of higher productivity. If there is an unexpected increase in productivity, debt must therefore increase immediately through a surprisedecreaseintherateofinflationthatisaboutfivetimeslargerthanunderaRicardian policy. The reason is that lower inflation leads to an increase in the real interest rate that furtherreducesdemandandthereforemarginalcost. Thehigherrealinterestratecausesdebt to rise for two interrelated reasons. First, it directly increases the real cost of servicing the debt. Second, it reduces demand for output and thus for labor, which reduces tax revenue 16

andleadstoaprimarydeficit. Buttherealinterestratedropisquicklyreversedwhilehigher productivity continues for some time, thereby turning the primary deficit into a primary surplus. Atthatpointgovernmentdebtstartstoapproachitslongrunlevelfromabove. Figure 5b shows that an increase in government spending leads to a fall in the public debt, rather than an increase as in Figure 2b. Under a Ricardian policy higher government spendingistranslated,withoutanyincreaseininflation,intohigherdebtthatissubsequently repaidverygraduallythroughhighertaxes. Butunderfiscaldominancetaxratescannotrise to deal with a higher debt level. If there is an unexpected increase in spending, debt must therefore be eroded immediately with surprise and very sizeable inflation that is allowed to reducetherealinterestrate,therebyloweringtherealcostofservicingthedebt. Inaddition, thecombinationofhighergovernmentspendingandalowerrealinterestrateboostsdemand for output and thus for labor, which in turn increases tax revenue and leads to a primary surplus. Butbecausetherealinterestratedropisquicklyreversedwhileelevatedgovernment spending continues for some time, this almost immediately turns into a primary deficit. At that pointgovernmentdebtstartstoapproachitslongrunlevelfrombelow. The impulse responses for a government spending shock in Figure 5b look qualitatively similar to those reported in Benigno and Woodford (2006) in their discussion of the exogenoustaxationcase. Ourpolicyrule(20)maythereforebeonesimplewaytoimplement the target criterion they have in mind. It implements their prescription that inflation expectationsmustbefirmlyanchored,inthesensethatwhileinflationismuchmorevolatile than in the Ricardian case, it also quickly returns to its long run value. The importance of this prescription stems from the fact that it requires less inflation to maintain intertemporal solvency, because with rapid but anchored movements in inflation the endogenous response of output and therefore of tax revenue is stronger and moves debt in the same direction as inflation. Butinpractice,asshowninalargeempiricalliteraturecoveringmanydifferentcountries, a firm anchoring of inflation expectations has only been successfully implemented in cases 17

wheremonetarypolicyrespondsaggressivelytoinflation. Yetaswehaveseen,thisisneither a feasible nor a desirable alternative in a world of fiscal dominance. This poses a severe problem for policymakers, because it seems very doubtful that the public would interpret a monetary rule with a very negative inflation coefficient as providing a firm anchor for inflation. The inclusion of fiscal variables in the monetary rule makes very little difference to these results, either in terms of the optimal inflation coefficient or in terms of welfare outcomes. The welfare gains from removing fiscal dominance altogether are an order of magnitude greater than the gains from targeting fiscal variables through nominal interest rates. 5 Conclusions This paper has considered optimal monetary policy when the fiscal authority is unable, or unwilling, to control tax revenues and spending. Weak taxation systems, tax evasion, banking crises or overspending are some of the factors that can undermine the control of fiscal deficits in developing economies. The paper shows that under such circumstances the usual prescription of the inflation targeting literature, a more than proportional interest rate response to inflation innovations known as the Taylor principle, becomes impractical and undesirable. Theoptimalcoefficientoninflationisinvariablyhighlynegative. It hasnotbeenclearfromtheliteraturewhetherthissituationcanberescuedbyacentral bankthatadaptsitselftofiscaldominancebyconditioningitsactionsonfiscalvariablessuch as government spending or government debt. This paper directly addresses that question. It finds that responding to government spending does not even expand the set of inflation coefficientsthatgiverisetouniqueequilibria. Respondingtodebtismorepromisingbecause the set of unique equilibria is expanded and allows for an aggressive response to inflation. However, an interest rate rule that tackles fiscal dominance by responding to debt and that simultaneously satisfies the Taylor principle is not a robust solution. First, volatility of all 18

variables is extremely high when an aggressive response to inflation is attempted. Second, andasadirectconsequence,policiesthatfollowtheTaylorprinciplealwaysviolatethezero lower bound on nominal interest rates. Third, and also as a direct consequence of volatility, welfareconsiderationscall forahighlynegativecoefficientoninflation. There is one positive result, which is that under fiscal dominance it does make sense for the central bank to include fiscal variables in its policy rule, because doing so improves welfare. But that improvement is trivial compared to what could be accomplished by removingfiscaldominancealtogether. Onlysolidfiscalfundamentalsallowforbothabenign outcome in terms of welfare and for the ability to fight inflation aggressively. Fiscal reform in developing countries is therefore an indispensable step before implementing inflation targetingregimes. 19

Appendix A. First Order Conditions Let the multiplier of the budget constraint (11) be given by Λ , and let λ = Λ P . t t t t Denote real money balances by m = M /P . Finally, use the fact that the equilibrium t t t is symmetric, with P (i) = P i. Then we have the following conditions for government t t ∀ debt,consumption,laborsupply,moneydemand,andpricesetting: R t λ = βE λ , (A.1) t t t+1 π t+1 µ ¶ 1 2Ac = λ 1+ t 2√AB , (A.2) t c m − t t µ ¶ δ = λ w (1 τ ) , (A.3) t t t 1 h − t − 1 Ac2 2 m = t , (A.4) t B +1 1 Ã − Rt ! η w θ βθ λ t t+1 y 1 = π (π 1) E π (π 1) . (A.5) t t t t t+1 t+1 − 1+η z 1+η − − 1+η λ − t t µ ¶ µ ¶ Appendix B. Determinacy and Zero Lower Bound Computations ThepicturesinFigures1,3and4arecomputedusing101pointsbothforthecoefficients on the horizontal and on the vertical axis. The coefficient φR is assumed to belong to the y set 0.5,0,0.5 . Hence, for each rule we consider a grid of 30603 points. The welfare {− } evaluations may be inaccurate for points near the indeterminacy regions. To overcome this problem we only compute welfare for points lying in the interior of the unique equilibrium area. The statistics referred to in the paper were computed through 500 simulations of 100 periods. All computationshavebeendonewiththeDYNAREtoolkit. 20

Appendix C. Welfare Computations FollowingtheBellmanequationonecandefine: VF = U +βE VF , (21) t t t t+1 whereU isperiodutilityandVF islife-timeutility. Conditionalwelfareisthevalueoflifet t time utility taking into account that the initial starting point is a predetermined level. This value can beobtained from the a second order approximation to the policy function of VF . t Withthepolicyfunctionathand,conditionalwelfarecanbeobtainedbypluggingtheinitial steadystateintothepolicyfunctionofVF . Itiscommontoconsider theinitialsteadystate t tobethenon-stochasticsteadystate. We conduct welfare comparisons of different rules. Consider the reference policy, denoted by r, and an alternative policy denoted by a. We have taken the reference policy tobetheRamseypolicy. Theconditional welfareofthereferenceregimeis ∞ VFr = E βtU(cr,hr) , (22) 0 0 t t t=0 X where cr and hr denote consumption and hours of work in the reference regime. Similarly, t t conditionalwelfareinthealternativeregimeis ∞ VFa = E βtU(ca,ha) . (23) 0 0 t t t=0 X We denote by λ the welfare cost of following the alternative regime. It is defined as the fractionof regimer’sconsumptionthat thehouseholdwouldbewillingtolosetobeaswell offunderregimeaasregimer: ∞ VFa = E βtU((1+λ)cr,hr) . (24) 0 0 t t t=0 X For thespecificutilityfunctionconsidered,theexpressioncanberearrangedas 1 VFa = VFr + ln(1+λ) , (25) 0 0 1 β − 21

where λ is defined as an implicit function, which we will approximate up to second order. Following Schmitt-Grohe and Uribe (2004b), we introduce a parameter σ that scales the variance of the exogenous stochastic processes g and z . Totally differentiating equation t t (25) twice with respect to σ we can obtain λ , which is the only term different from zero σσ in the second order approximation around the non-stochastic steady state. It easily follows that σ2 λ = (1 β)(VFa VFr ) , (26) − σσ − σσ 2 orequivalently σ2 λ = (1 β)(VFa VFr) . (27) − 0 − 0 2 22

Bibliography Benigno,P.andWoodford,M.(2006),“OptimalInflationTargetingunderAlternativeFiscal Regimes”,NBERWorkingPapers,Number 12158. Chari, V.V. and Kehoe, P.J. (1999), “Optimal Fiscal and Monetary Policy”, Chapter 26 in Taylor,J.B.andWoodford,M.,eds.,HandbookofMacroeconomics,Volume1C,Elsevier. Cochrane, J.H. (1998), “A Frictionless View of US Inflation”, NBER Macroeconomics Annual,13,323-384. Cochrane, J.H. (2000), “Money as Stock: Price Level Determination with No Money Demand”,NBERWorkingPapers,Number7498. Collard,F.andJuillard,M.(2001),“AccuracyofStochasticPerturbationMethods: TheCase ofAssetPricingModels”,JournalofEconomicDynamicsandControl,25(6-7),979-999. Daniel,Betty(2001),"AFiscalTheoryofCurrencyCrises,"InternationalEconomicReview, vol.42(4),pages969-88. Kumhof, M., Li, S. and Yan, I. (2007), “Balance of Payments Crises under Inflation Targeting”,JournalofInternationalEconomics,72(1),242-264. Kumhof,M.andTanner,E.(2007),“GovernmentDebt: AKeyRoleinFinancialIntermediation”,inA.Velasco(ed.),FestschriftinHonorof GuillermoA.Calvo(forthcoming). Leeper, E. (1991), “Equilibrium under Active and Passive Monetary and Fiscal Policies”, Journal of MonetaryEconomics,27(2),129-147. Loyo, E. (1999), “Tight Money Paradox on the Loose: A Fiscalist Hyperinflation”, Manuscript,KennedySchoolof Government. Marcet, A. and Scott, A. (2001), “Debt and Deficit Fluctuations and the Structure of Bond Markets”,C.E.P.R.DiscussionPapers,Number3029. Nunes, R.C. (2005), “Inflation Dynamics: The Role of Expectations”, Manuscript, UniversitatPompeuFabra. Sargent, T.J. and Wallace, N. (1981), Some Unpleasant Monetary Arithmetic, Fedreal ResearveBankofMinneapolisQuaterlyReview,Fall,1-17. Schmitt-Grohe, S. and Uribe, M. (2004a), “Optimal Fiscal and Monetary Policy Under StickyPrices”,Journalof EconomicTheory,114,198-230. Schmitt-Grohe, S. and Uribe, M. (2004b), “Solving Dynamic General Equilibrium Models UsingaSecond-OrderApproximationtothePolicyFunction”,JournalofEconomicDynamicsandControl,28(4),755-775. Schmitt-Grohe,S.andUribe,M.(2006),“OptimalSimpleandImplementableMonetaryand 23

FiscalRules”,Journal ofMonetaryEconomics(forthcoming). Sims, C.A. (1994), “A Simple Model for the Study of the Determination of the Price Level andtheInteractionof MonetaryandFiscalPolicy”, EconomicTheory,4,381-399. Sims, C. (2005), “Limits to Inflation Targeting”, in: B. Bernanke and M. Woodford, eds., TheInflationTargetingDebate,Chicago: UniversityofChicagoPress. Woodford, M. (1996), “Control of the Public Debt: A Requirement for Price Stability?”, NBERWorkingPaper,Number 5684. Woodford,M.(1998),“PublicDebtandthePriceLevel”,Manuscript,PrincetonUniversity. Woodford, M. (2001), “Fiscal Requirements for Price Stability”, NBER Working Paper, Number8072. 24

Determinacy ZeroLowerBound −0.92 −0.92 −0.92 −0.92 −0.92 −0.2−0.23 −0.2 −0.23 −0.2−0.23 −0.2 −0.23 −0.23 −0.23−0.92 −0.23 −0.2 −0.08 −0.03−−0.00.82 −0.08 −0.03 Coefficient on Inflation seitilibaiL no tneiciffeoC −1.5 0 1.5 −3 1 3 Welfare 0.34 1.25 2 2 1.25 1.25 2 2 1.250.56 1.25 0.56 2 2.86 2.86 2.86 2.86 2 2.86 2.86 Coefficient on Inflation seitilibaiL no tneiciffeoC −1.5 0 1.5 −3 1 3 InflationVolatility Figure1: RicardianFiscalPolicyandtheTaylorRule 25

Productivity Government Spending Real Wage 1 2 2 1 0 1 0 −1 0 0 10 20 0 10 20 0 10 20 Nominal Interest Rate Tax Rate Labor 0 0 0.2 −0.2 0 −0.1 −0.2 −0.4 −0.2 0 10 20 0 10 20 0 10 20 Inflation Tax Revenue Output 0 2 1.5 −0.05 1 −0.1 0.5 1 0 −0.15 −0.5 0 0 10 20 0 10 20 0 10 20 Real Interest Rate Debt to GDP Ratio Consumption 0 0 2 −0.1 −1 −0.2 −2 1 −0.3 −3 0 0 10 20 0 10 20 0 10 20 Figure2a: ProductivityShockunderRicardianFiscalPolicy 26

Productivity Government Spending Real Wage 1 3 0 −0.002 2 0 −0.004 1 −0.006 −1 0 0 10 20 0 10 20 0 10 20 Nominal Interest Rate Tax Rate Labor 0 0.3 0.4 0.2 0.2 −0.02 0.1 0 −0.2 −0.04 0 0 10 20 0 10 20 0 10 20 Inflation Tax Revenue Output 0 0.4 −0.005 0.5 0.2 0 −0.01 −0.2 0 0 10 20 0 10 20 0 10 20 Real Interest Rate Debt to GDP Ratio Consumption 0 0 4 −0.01 2 −0.2 −0.02 0 0 10 20 0 10 20 0 10 20 Figure2b: GovernmentSpendingShockunderRicardianFiscalPolicy 27

Determinacy ZeroLowerBound −0.21 −0.28 −0.41 −−00..4218 −0.41 Coefficient on Inflation gnidnepS tnemnrevoG no tneiciffeoC 0 1 11..7923 0.05 0 1 .0 . 5 72 1.93 1.702.05 −2 1 Coefficient on Inflation Welfare gnidnepS tnemnrevoG no tneiciffeoC −1 0 1 −3 1 3 InflationVolatility Figure3: FiscalDominanceandInterestRateFeedbacktoGovernmentSpending 28

Determinacy ZeroLowerBound −−00..43 22− − 0. 0 25 .25 −0.32 −0.42 −−00.3.422−0.25 −0.25 − − 0. 0 3 . 2 42 Coefficient on Inflation seitilibaiL no tneiciffeoC −1 2.224.5 1.82 1.82 2.24 2.5 1.54 1.82 2.22.45 0 1.541.82 2.22.45 1 −3 1 3 Coefficient on Inflation Welfare seitilibaiL no tneiciffeoC −1 0 1 −3 1 3 InflationVolatility Figure4: FiscalDominanceandInterestRateFeedbacktoGovernmentLiabilities 29

Productivity Government Spending Real Wage 1 2 1 0 0.5 1 0 0 −1 −0.5 0 10 20 0 10 20 0 10 20 Nominal Interest Rate Tax Rate Labor 1 0 1 0.5 0 −1 0 −2 −1 0 10 20 0 10 20 0 10 20 Inflation Tax Revenue Output 0 1 1 −0.2 0 −0.4 −1 0.5 −0.6 −2 −0.8 −3 0 0 10 20 0 10 20 0 10 20 Real Interest Rate Debt to GDP Ratio Consumption 1.5 1 1.5 1 1 0.5 0.5 0.5 0 0 0 0 10 20 0 10 20 0 10 20 Figure5a: ProductivityShockunderFiscalDominance 30

Productivity Government Spending Real Wage 1 3 3 2 2 0 1 1 −1 0 0 0 10 20 0 10 20 0 10 20 Nominal Interest Rate Tax Rate Labor 1 0 2 −0.5 0 1 −1 −1 0 0 10 20 0 10 20 0 10 20 Inflation Tax Revenue Output 6 1 4 2 0.5 2 1 0 0 0 0 10 20 0 10 20 0 10 20 Real Interest Rate Debt to GDP Ratio Consumption 0 0 −0.5 2 −2 −1 1 −1.5 −4 0 0 10 20 0 10 20 0 10 20 Figure5b: GovernmentSpendingShockunderFiscalDominance 31