In January 2016, the newly elected government of Argentina announced a policy of

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1 Monetary Poliy with Delining Defiits: Theory and an Appliation to Reent Argentine Monetary Poliy Rody Manuelli and Juan I. Vizaino The authors study the nature of the optial onetary poliy in a regie of fisal doinane when the onetary authority whih an print oney or issue interest-earning debt is required to finane an exogenous sequene of transfers to the Treasury. They show that the degree of oitent on the part of the onetary authority has a signifiant ipat on the details of the optial poliy. They apply this odel to the reent experiene of Argentina and find that the inflation rate experiened by Argentina during the first year of the onetary progra is lose to the preditions of a weakly tie-onsistent solution. Moreover, onsistent with both versions of their odel full oitent and weak tie onsisteny the Central Bank of Argentina has inreased the ratio of interest-earning debt relative to the onetary base. (JEL E52, E58, E61, E63, E65) Federal Reserve Bank of St. Louis Review, Fourth Quarter 217, 99(4), pp In January 216, the newly eleted governent of Argentina announed a poliy of dereasing governent budget defiits. It also speified what fration of the defiit would have to be finaned by the onetary authority. In the ase of Argentina, this was a signifiant aount. For the year 216, the Central Bank of Argentina (del Bano Central de la Repúblia Argentina, BCRA) was required to transfer to the Treasury approxiately 2 perent of GDP out of a total governent defiit of 4.8 perent of GDP. In addition, the BCRA deided to inrease the onetary base by lose to another 2.5 perent of GDP to inrease the stok of foreign reserves. The Argentine onetary authority finds itself in one of the versions of the eonoy that Sargent and Wallae (1981) studied in the well-known Soe Unpleasant Monetarist Aritheti paper naely, the ase in whih the fisal authority oves first and the onetary authority passively aoodates the fisal deands. However, the proble faed by the BCRA differs fro the proble studied by Sargent and Wallae in that the BCRA an issue interest-earning debt. Thus, the hoie of onetary poliy faed by the BCRA boils down to Rody Manuelli is a professor of eonois at Washington University in St. Louis and a researh fellow at the Federal Reserve Bank of St. Louis. Juan I. Vizaino is a Ph.D. student at Washington University in St. Louis and a researh assoiate at the Federal Reserve Bank of St. Louis. The authors thank Steve Williason and two anonyous referees for their oents. 217, Federal Reserve Bank of St. Louis. The views expressed in this artile are those of the author(s) and do not neessarily reflet the views of the Federal Reserve Syste, the Board of Governors, or the regional Federal Reserve Banks. Artiles ay be reprinted, reprodued, published, distributed, displayed, and transitted in their entirety if opyright notie, author nae(s), and full itation are inluded. Abstrats, synopses, and other derivative works ay be ade only with prior written perission of the Federal Reserve Bank of St. Louis. Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

2 the hoie of the ix between debt and oney, with the understanding that the only tax it an use to servie the debt is the inflation tax. 1 In this artile, we study the poliies that a onetary authority that is faed with suh a teporary fisal doinane situation teporary in the sense that it is required to transfer a delining aount of resoures to the fisal authority should pursue. In a very general sense, this is an optial taxation proble and, like ost probles of this type, the answer depends on the ix of taxes available and the degree of oitent on the part of the poliyakers. In this partiular appliation, the only tax available is the inflation tax, so the proble boils down to the hoie of distortionary inflation taxes over tie. One possibility is to allow the stok of oney to be deterined by the tie path of the expenditures that the entral bank ust finane. Another option is to ontrol the quantity of oney in the eonoy by issuing interest-earning seurities. This allows the entral bank to hoose the tiing of inreases in the oney supply that need not ath the tiing of transfers. We onsider the ase of a entral bank that an issue its own interest-earning seurities of a given aturity and that, in the language of Del Negro and Sis (215), does not have fisal support; that is, it annot assue that the Treasury will reapitalize the bank with genuine resoures if the bank inurs losses in its portfolio. Thus, the only option available to the entral bank is to ollet seigniorage to reain solvent. Unlike the Federal Reserve Syste, other entral banks do issue atively tradable interest-earning bills of different aturities. 2 Moreover, in any ountries, they are held by both finanial and non-finanial institutions. Aording to Gray and Pongsaparn (215), at least one-third of their saple of entral banks issue their own interest-earning seurities, with a edian aturity of one onth but with individual aturities as high as five years. 3 The seond eleent of our study is the teporary nature of the expenditures that the entral bank inurs. As with the ase of interest-earning seurities, there is no obvious analog of this situation in the United States, as the Fed is not required to ake transfers to the Treasury. However, this possibility is oon in eerging ountries, as entral bank finaning is an iportant share of governent revenue and the odel applies to any teporary inrease in spending. For exaple, it inludes not only the situation in whih the entral bank is required to ake teporary transfers to the Treasury but also the ase in whih the entral bank responds to a banking risis by inreasing its liabilities to reapitalize finanial institutions. 4 What is the optial onetary poliy (or, equivalently, optial debt poliy) for a entral bank in the situation that we desribed above and given the available instruents? It turns out that the answer depends on the degree of oitent on the part of the onetary authority as well as on the details of the aount of resoures that the onetary authority has to transfer to the fisal authority, whih we label the defiit. To ake progress understanding optial poliies, we study a very siple eonoy in whih the path of defiits and aro aggregates are known. This is siilar to the eonoy that Uribe (216) studies exept that we investigate only the role of entral bank finaning of a given defiit. We view the defiit as dereasing over tie and eventually reahing zero. If the onetary authority an preoit to any poliy, then a relatively standard optial taxation arguent, 352 Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

3 as desribed in Uribe (216), iplies that the entral bank should use a ixture of onetary injetions and debt to finane the required transfers. The basi idea is to sooth tax distortions in this ase, the distortions assoiated with the inflation tax and to use interest-earning debt to finane the differene between the delining transfers and the revenue fro the inflation tax. This is an extension of the tax-soothing arguent in Barro (1979) and the priniples of finaning of governent spending in Luas and Stokey (1983). The optial poliy is suh that, even after the entral bank is no longer required to finane a defiit, it hooses to inflate so that it an servie the existing debt, and the present disounted value of the revenue fro the inflation tax is equal to the present disounted value of the required transfers. The assuption that the onetary authority is able to oit to positive inflation in the presene of zero defiits is soewhat probleati sine the entral bank has an inentive to ipleent a one-tie open arket operation issuing non-interest-earning oney to buy the interest-earning debt. In the absene of oitent, and depending on the stok of debt, suh an open arket operation an potentially result in a jup in the prie level, but it allows the onetary authority to ipleent a zero inflation poliy fro then on. We label poliies that ipose that inflation be zero when the defiit is zero as weakly tie-onsistent poliies. We show that weakly tie-onsistent poliies ipose tight restritions on the aount of debt that an be issued. In partiular, they iply that the total value of noinal assets relative to output annot exeed the ratio of oney to output under zero inflation. Our notion of weak tie onsisteny aounts to requiring standard tie onsisteny only when the fisal situation is suh that the onetary authority does not have to ake any ore transfers to the Treasury. As is well known in an eonoy with noinally denoinated debt, a tie-onsistent poliy is suh that it engineers a large inflation as soon as possible to iniize the real value of the debt. We do not find suh an extree version of tie onsisteny a useful way of thinking about poliy, sine it ignores other onsequenes of suh an extree poliy. Thus, weak tie onsisteny is a oproise that assues that all eonoi partiipants private setor and governent alike understand that the governent will be restritive about the poliies that an be ipleented in the future. We use this odel to study the optial onetary poliy for Argentina, taking as given the path of the defiit. We find that, onsistent with both solutions, the Argentine onetary authority inreased the debt-to-oney ratio over the first year of the progra. The key differene between the oitent and the weakly tie-onsistent solutions are the ipliations for the inflation rate. The oitent solution estiates an average inflation rate of 2.6 perent, while the weakly tie-onsistent solution predits a value lose to 25 perent. The reent Argentine experiene 33 perent inflation in the first year of the progra and a arket expetation of 2 perent for the seond year appears to be uh loser to the latter than to the forer. The work ost losely related to ours in addition to Uribe (216) is that by Díaz- Giénez et al. (28), where it is also shown that tie onsisteny liits the ability of the onetary authority to ipleent optial poliies. The key differene with our artile is that the path of defiits is not dereasing and that there is oordination between the fisal and onetary authorities, whih iplies that taxes other than the inflation tax are used to finane Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

4 the servie of the debt. Martin (213) has a thorough disussion of optial poliies in eonoies with different fritions. He restrits hiself to the ase in whih bonds have payoffs in real ters. In the ontext of New Keynesian odels, Leeper, Capbell, and Ding (216) disuss optial onetary and debt poliy iposing tie onsisteny. For a reent survey of onetary odels and optial poliies, see Canzoneri, Cuby, and Diba (211). There is a large literature that reognizes the fisal diension of onetary poliy. See, for exaple, Bassetto and Messer (213), Berriel and Bhattarai (29), Cao (217), and Del Negro and Sis (215). MODEL We study the siplest eonoy that an be used to explore the role of lak of oitent. We take an off-the-shelf odel siilar to that used by Uribe (216). We assue that output, y, and governent spending, g, are onstant. This iplies that, in equilibriu, onsuption is onstant as well. The fisal authority piks a sequene τ t of taxes, and it deands fro the onetary authority transfers x t = g τ t. We view x t as a dereasing funtion of tie with the property that x t = for all t T. It is onvenient to separately desribe the budget onstraint for the onetary authority and the rest of the governent (whih we label the Treasury ). 5 The Treasury s budget onstraint is &B t T + P t x t + P t τ t = i t B t T + P t g, where a dot over a variable indiates the tie derivative. The inoe side of this onstraint inludes the soures of funds: bond issuane, Ḃ tt ; tax revenues, P t τ t ; and transfers fro the onetary authority, P t x t. The expenditure side is the su of interest payents, i t B tt, and governent purhases, P t g. The onetary authority s budget onstraint is &M t + & B t M = i t B t M + P t x t. The expenditure side of this onstraint inludes transfers to the Treasury, P t x t, and interest payents on the debt it has issued, i t B tm. The only soures of funds are inreases in the oney supply, Ṁ t defined as the onetary base: urreny in irulation plus non-interest-earning reserves and interest-earning debt, Ḃ tm. The notation akes it lear that in the eonoy under study there is interest-earning debt issued by the Treasury, B tt, whih has to be distinguished fro debt issued by the entral bank, B tm, sine the latter is baked only by future inreases in the real value of the oney stok (seigniorage) beause we restrit P t x t to be nonnegative. Putting together these two budget onstraints, we arrive at the onsolidated budgetary restrition for the governent given by 354 Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

5 &M t + B & T t + B & M t + P t τ t = i t B T M ( t + B t )+ P t g. Given our fous in this artile the optial hoie by the onetary authority on how to finane the transfer P t x t this onsolidated budget onstraint plays a inor role. We assue that there is a representative dynasty that has preferenes over onsuption and real oney balanes given by U = e ρt u( t )+ v( t ) dt, where t is onsuption at tie t and t = M t /P t is real oney balanes. 6 The funtions u and v are assued stritly onave and twie ontinuously differentiable. The private setor budget onstraint is given by &M t + B & T t + B & M t = i t B T M ( t + B t )+ P t y P t P t τ t. On the inoe side, the representative dynasty earns interest at the noinal rate i t on its holdings of Treasury-issued debt, B tt, as well as the stok of onetary authority-issued debt, B tm. In addition, the representative agent earns inoe, spends resoures purhasing onsuption, and pays taxes (if τ t <, the onsuer reeives a transfer). In what follows, the key relationship is aong real oney balanes, onsuption, and the noinal interest rate. It an be shown that the representative agent s deand for real oney balanes satisfies (1) where = i t, v t u t t = M t P t. We assue that output is fixed and that governent spending is onstant. This iplies that private onsuption is onstant and, hene, that the real interest rate is equal to the disount fator. In equilibriu, the interest rate is i t = ρ +π t, whih is the standard Fisherian result. The onetary authority understands the tradeoff between inflation and real oney balanes as aptured by equation (1), whih an be ore onveniently written as (2) v t u = ρ +π t. As entioned before, the budget onstraint of the onetary authority (not the onsolidated governent budget onstraint) is given by Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

6 &M t + & B t M = i t B t M + P t x t, whih in real ters is & t + & b t M = ρb t M + x t π t t, where and seigniorage is b M t = B M t, P t s t = & t +π t t. OPTIMAL MONETARY POLICY Optial Poliy Under Full Coitent In this setion we study the optial onetary poliy without iposing any restritions on the onetary authority other than those required to satisfy the budget onstraint in equilibriu. Sine output (and onsuption) are fixed, the optial onetary poliy is the solution to the following proble: (3) ax { b M t, t } subjet to e ρt v( t )dt, (4) & t + b & M t = ρb M v t + x t t u ρ and the appropriate transversality ondition. The optial onetary poliy (see Uribe, 216) is suarized in the following result. t Proposition 1 (Optial Poliy Under Coitent [Uribe, 216]). The optial poliy is haraterized by a onstant level of real oney balanes,, and a onstant inflation rate, π, given by where is hosen so that and a debt poliy given by (See the appendix.) e ρt v u π = v u ρ, x t b M t = e ρt t e ρs v x s u ρ dt = b M +, ds +b M Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

7 Under the optial poliy with oitent, inflation is onstant and the stok of debt initially inreases and then dereases and it onverges to zero as t. Weakly Tie-Consistent Optial Poliy Manuelli and Vizaino The optial poliy with oitent is suh that, after tie T, the inflation tax is used to finane repayent of prinipal and interest on the debt issued by the onetary authority. This poliy is not weakly tie onsistent. To see this, onsider what happens at tie T. Let the stok of oney at that tie be denoted M T and the stok of bonds (in noinal ters) B TM. The proble faed by the entral bank is to hoose onetary poliy to solve the ontinuation proble. Forally, the proble is subjet to equation (4), whih is ax { b M t, t } T ρ t T e v( t )dt, & t + b & M t = ρb M v t + x t t u ρ t, and subjet to a given initial aount of total liabilities of the entral bank, M T + B T. Proposition 2 (Optial Poliy After Tie T). Assue that the entral bank annot issue negative debt; then the optial onetary poliy engineers an open arket operation so that the resulting stoks of oney and bonds are and the prie level is M T = M T + B T P T = M T, * where * is suh that the optial inflation rate is zero; that is, (See the appendix.) v * u = ρ. When the entral bank is not required to finane any ore defiits, there is no longer any optial taxation arguent that requires any soothing of distortions over tie and the eonoy reverts to the (onstrained) first best. The optial onetary poliy solves a finite- horizon version of the previous proble, with the additional terinal ondition that the stok of entral bank liabilities at tie T ust be equal to the level of real oney balanes under zero inflation. This ondition aounts to a restrition that the prie level annot jup at tie T. This is one of the priniples of honest governent as defined by Auernheier (1974). Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

8 The proble faed by the onetary authority is given by subjet to and subjet to ax { t } T e ρt v( t )dt, &b M t = ρb M v t + x t t u ρ t T +b T M = *. Proposition 3 (Optial Poliy until T). The optial poliy is suh that real oney balanes are onstant and they satisfy (See the appendix.) v ( ) ρ M T = ( u 1 e ρt +b )+ e ρt x t dt e ρt *. Let R t be the ratio of interest earnings bonds to real oney balanes. Thus, R t = b M t. t Given that the optial level of real oney balanes is, it follows that R t = e ρt M t ( +b )+ e ρs v ( ) x s u ( ) ds. Sine we are interested in the ase in whih defiits are delining, the ter v x s u is initially positive and turns negative as t T. Thus, R t is initially inreasing and then dereasing. Inflation is given by v π = u ρ whih is dereasing in real oney balanes. The key ipliation of the weak tie-onsisteny requireent is that the value of the stok of liabilities of the onetary authority annot exeed the level of the deand for oney under zero inflation., 358 Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

9 ARGENTINE MONETARY POLICY THROUGH THE LENS OF THE MODEL In this setion, we briefly desribe the reent onetary poliy followed by the BCRA, alibrate the odel, and study the ipliations under both oitent and weak tie onsisteny for the Argentine experiene. Reent Argentine Monetary Poliy Manuelli and Vizaino The Institutional Fraework. The BCRA s harter speifies that its ission is to proote within the fraework of its powers and the poliies set by the National Governent onetary and finanial stability, eployent, and eonoi developent with soial equality (BCRA n.d.; ephasis added). 7 The BCRA board inluding its president and vie presidents is appointed by the exeutive branh with Senate agreeent, and it an be reoved by the branh if a speial oission of Congress agrees. In pratie, it has not been diffiult for the branh to replae the authorities of the entral bank and, for pratial purposes, the BCRA is not independent. 8 The BCRA issues interest-earning seurities as of this writing the only type is denoinated Lebas (Letras del Bano Central) with aturities that range fro 28 to 273 days. These entral bank bills and repos are used to ondut open arket operations to regulate the quantity of oney. The BCRA also operates a disount window and anages the reserves of foreign urreny. When the Argentine onetary authority transfers resoures to the Treasury, it inreases the liability side of its balane sheet by the aount of the transfers (an inrease in the onetary base) and, siultaneously, it inreases the asset side by viewing the transfer as a loan labeled transitory advanes. Aording to urrent legislation, these transitory advanes are apped at the ax of 12 perent of the onetary base or 1 perent of annual governent revenue. These loans have a duration of a year, but ontinuous inreases in the onetary base allow for indefinite renewals and inreases in the stok. In fat, they are never repaid. 9 Sine the BCRA has the ability to issue its own interest-earning debt, it an ondut an open arket operation in this seurity ondut an aution to absorb soe or all of the inrease in the oney supply. To illustrate the ehanis, onsider the following exaple: Suppose the BCRA wants to ake a one-tie transfer to the Treasury in the aount Z. This reates an inrease in the liability side of its balane sheet (an inrease in the onetary base) equal to Z. On the asset side, the transitory advanes aount is inreased by Z. If the entral bank does not want to hange the oney supply, this would be the end of the story. Consider now the ase in whih the entral bank for whatever reason deides that the onetary base should be only Z/2. Then, to absorb liquidity, it autions off interest-earning seurities in the aount Z/2. After a period say, a year the entral bank inreases the oney supply to pay off the interest-earning bills. Thus, after one period, the oney supply and the liabilities of the entral bank equals Z + (Z/2) i. On the asset side, it is standard for the entral bank to give the rest of the governent a new loan in the aount Z. Thus, the Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

10 transitory-advanes aount still has a balane equal to Z. Sine the BCRA has funded this investent in a zero-interest governent loan with a ix of oney (that pays no interest) and entral bank bills (that earn a positive interest), the result is an operational loss. This loss redues bank apital and has to be opensated for soehow. The details of how this is done vary aross the world. In soe ases, entral banks siply ativate losses. In other ases, the Treasury issues a non-negotiable zero-interest long-duration (e.g., over 5 years) bond that is used to reapitalize the bank. 1 In the ase of Argentina, the BCRA also has foreign exhange reserves aong its assets, and it revalues the aording to standard aounting praties. This reates a paper profit that has suffied to opensate for the losses on the BCRA s investent portfolio. Reent Developents Even though a disussion of the onetary poliy of Argentina is beyond the sope of this artile, 11 it is useful Table 1 Transfers to the Treasury to douent the agnitude of the transfers that the BCRA has ade (and ontinues to ake) to the Treasury. In Year Perentage of GDP ters of the odel desribed before, the transfer orresponds to what we labeled P t x t.the size of the transfers 25.5 sine 24 is shown in Table In the past few years, BCRA finaning of defiits has 27.5 been very large. The soure of this finaning has been twofold First, in the period until 21-15, about half of the transfers were finaned by selling assets. Basially, the BCRA used part of its stok of foreign urreny reserves to finane the Treasury. The other half onsisted of transfers This poliy has resulted in generally high and variable inflation. Figure 1 shows the relationship between inflation and seigniorage for the period Although the traditional Laffer-urve-type pattern does not eerge for the saple period under study, the resoures obtained via seigniorage are learly non-negligible, averaging 2 perent of GDP, for an average annualized SOURCE: BCRA. inflation rate lose to 21 perent. The figure shows a relatively high degree of instability in the deand for oney, whih iplies that the sae inflation rate is assoiated with a wide range of seigniorage values. The ore reent onetary experiene is suarized in Table 2. The base of the inflation tax the onetary base flutuates around 8 perent of GDP, while in the reent past inflation has averaged about 33 perent. 14 This iplies that revenue fro seigniorage has been approxiately 2 perent of GDP. As entioned before, during the year 216, the BCRA transferred to the Treasury approxiately 2 perent of GDP and purhased foreign urreny reserves aounting to 2.6 perent of GDP Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

11 Figure 1 Inflation and Seigniorage in Argentina (24-16) Seigniorage (perent of GDP) Inflation (onth-over-onth perent) SOURCE: BCRA, Instituto Naional de Estadístia y Censos, and provinial statistial institutes. Table 2 Money and Inflation Conept Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 M/Y B/M Inflation NOTE: M/Y, oney-to-output ratio. B/M, BCRA s debt-to-output ratio. SOURCE: BCRA, Instituto Naional de Estadístia y Censos, and provinial statistial institutes. Over the past year, the BCRA has been inreasingly relying on interest-earning debt as an alternative to outright inreases in the onetary base. Table 2 shows that there has been an inrease in the ratio of entral bank debt to oney over the past two years and, in partiular, sine the beginning of the new onetary progra in 216. During 216, the ratio of interestearning debt to the onetary base has inreased fro 67 perent to alost 9 perent. We now develop a quantitative version of the odel that is suitable for studying optial onetary poliy in the ontext of the Argentine situation. Theoretial Restritions We assue that 1 γ v( ) = z y 1 γ,u( ) ( y + ay = )1 γ 1 γ, Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

12 where is oney deand relative to output and is the ratio of onsuption to output, while α is a preferene shifter that aptures inial levels of onsuption. 16 Following Luas and Niolini (213), we take that the relevant onept of transations deand for oney is M1. The deand for oney,, satisfies = ( +α )( zi) 1/γ. This speifiation iplies that seigniorage is given by = z s 1 +α γ r, where is the onetary base (the base of the inflation tax). If the ratio of 1 / is denoted 1 + ζ, then define With this notation, seigniorage is s K z 1+ζ +α γ = K( ) γ r., where fro now on denotes the stok of the onetary base. Sine we use seigniorage to estiate the relevant paraeters, it is lear that we an only identify K and not its individual oponents. For the tie path of the defiit, we assue the following funtional for: Let x t = ψ ψ T t 1te κ t T. t >T T ˆx = e ρt x t dt. Given our hoie of funtional fors, the optial level of oney balanes in the oitent ase,, is the solution to (5) K 1 γ = ρ( w + ˆx ). Fro Proposition 3, real oney balanes under weak tie onsisteny, w, satisfy where * is the solution to K 1 γ ρ w = ( 1 e w ρt + ˆx e ρt * ), K( * ) γ = ρ. 362 Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

13 The level of real oney balanes under the weakly tie-onsistent solution is ρ (6) w = K 1 e ρt the iplied inflation rate is and the ratio of the two inflation rates is ρ w + ˆx e ρt K π w = K w γ ρ, w + ˆx e ρt K π w ρ = π ( 1 e ρt ) w + ˆx 1/γ To suarize, the optial level of real oney balanes in the oitent and weakly tie-onsistent versions of the optial onetary poliy solve equations (5) and (6), respetively. Fro a qualitative perspetive, inreases in the present value of entral bank liabilities, w + xˆ, not only inrease the inflation rates in eah of the two senarios (as ore seigniorage is needed to finane the interest on the liabilities of the onetary authority) but also inrease the gap between the inflation rates in the oitent and weakly tie-onsistent solutions. An inrease in the deand for oney, as easured by an inrease in K, dereases inflation in both regies, but ore so in the weakly tie-onsistent ase, as it lifts up the deand for real oney balanes under zero inflation. 17 Finally, inreases in the tie horizon redue π w /π. Calibration We use onthly data 18 to estiate the following regression by nonlinear least squares (NLLS): s t = K γ t r t + ε t, where s t is seigniorage in period t, defined as the hange in the onetary base relative to the flow of output; t is the onetary base; and ε t is an error ter. We assue that r = ρ =.4. Sine onetary poliy in Argentina has been extreely variable with long periods in whih finanial institutions were fored to hold reserves in relatively large proportions, we use onthly data for 25-15, a period with a relatively ore stable onetary poliy regie. One ajor disadvantage of using onthly data for Argentina (see Burdisso, Blano, and Sardi, 21) is that seasonal flutuations are large. In our odel, these seasonal flutuations translate diretly into seasonal hanges in the seigniorage. We address this issue by seasonally adjust- 1/γ γ γ γ, Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

14 Figure 2 Tie Path of the Defiit Defiit (perent of GDP) De 215 De 216 De 217 De 218 De 219 SOURCE: Authors alulations. ing both the seigniorage and the real oney balanes series. For our purpose, the ritial oeffiient to estiate is γ. Our estiated value is γ = 3, with a robust standard error equal to (1.3). 19 This iplies that the sei-elastiity of the deand for oney is.33. The literature has not arrived at a onsensus value for the sei-elastiity of the deand for oney with respet to the interest rate. The estiates of Mogliani, Urga, and Winograd (29), Gay (25), and Baso, D Aoto, and Garegnani (212) suggest a value between 1.24 and Kiguel and Neueyer (1995) find a uh lower elastiity equal to.5. Uribe (216) uses the Kiguel and Neueyer (1995) results to estiate a sei-elastiity of.13. Our estiate is on the low side but not out of line with other estiates of the deand for oney as reported in Canzoneri, Cuby, and Diba (211). 2 Finally, to pin down the sale paraeter K, we use average real oney balanes relative to output during the year 215 ( =.86) and the noinal interest rate on tie deposits (i =.22). The estiate is K = i γ =.14. This iplies that real oney balanes under zero inflation (relative to output) equal.15, a large but not unreasonable value. We now desribe how we selet the paraeters for the tie path of the defiit. First, sine we assue that the defiit is zero in T = 4, it follows that ψ ψ 1 4 =. 364 Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

15 Figure 3 Coitent: Debt-to-Monetary Base Ratio Debt-to-Monetary Base Ratio De 215 De 216 De 217 De 218 De 219 SOURCE: Authors alulations. To alibrate the other two paraeters (κ,ψ 1 ), we assue that the average defiit during the first year of the progra is 4.6 perent of GDP and during the seond year is 2 perent of output. The value that we assue for the first year is based on an estiate of the transfer the BCRA agreed to give to the Treasury (about 2 perent of output) and the inrease in the stok of foreign reserves (whih aounts to 2.6 perent of GDP). 21,22 Thus, κ,ψ 1 solve ψ 1 ( 4 + ( 4 ) e 3κ 2 ψ 1 4 e 3κ + 4 2e 2κ 2 =.46 =.2. The solution is κ =.24 and ψ 1 =.155. Given our estiates, the present disounted value of the defiit whih we denoted xˆ in the previous setion is 6.9 perent of GDP. 23 Taking Deeber 215 as the starting point, the path of the defiit is shown in Figure 2. As required by the theory, we ipose that the initial value of the liabilities of the entral bank equal the existing stok in Deeber 215, whih was approxiately 14 perent of output. Ipliations of the Model and the Experiene of Argentina Our quantitative odel iplies that in the full oitent ase, the onetary base is about 13 perent of output and the average annual inflation rate is 2.6 perent. The debt of the entral bank inreases onotonially until id-218. The initial value is 1.5 perent of GDP in Deeber 215; it reahes a axiu of 9.5 perent of GDP by id-218. In order to better opare with the situation in Argentina, Figure 3 displays the tie path of the ratio of entral bank debt relative to the (onstant under the optial poliy) onetary base. Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

16 Figure 4 Weak Tie Consisteny: Debt-to-Monetary Base Ratio Debt-to-Monetary Base Ratio De 215 De 216 De 217 De 218 De 219 SOURCE: Authors alulations. The debt-to-onetary base ratio inreases fro its initial level of around.12 up to around.75 by id-217 and starts dereasing afterward. What is the optial poliy if the onetary authority annot preoit to positive inflation with zero defiits? In this ase (weak tie onsisteny), the optial level of the onetary base is lower than under full oitent and equals 7.9 perent of output. The onsequene is a uh higher average inflation of 24.7 perent. Weak tie onsisteny iplies that the optial poliy is to retire the debt the only option if revenue fro inflation is going to be zero at the end of the positive defiit period. Thus, the optial poliy alls for a large open arket operation at tie T. The tie path of the debt-to-onetary base ratio is displayed in Figure 4. This version of the optial poliy iplies that in id-217 the debt-to-onetary base ratio peaks at about 16 perent, signifiantly higher that under the full-oitent solution. How should one evaluate the reent onetary poliy of the BCRA in light of the optial onetary poliy the odel presribes given the fisal doinane regie in Argentina? Based on the odel, Argentine onetary poliy has not been optial. The odel predits for both the oitent and the weakly tie-onsistent solutions that inflation ust be onstant over the period of the progra. The inflation rate in Argentina during the first year was dereasing. However, it is interesting to explore whih of the two senarios (oitent or weak tie onsisteny) ore losely resebles the Argentine experiene during 216. To this end, we onsider two indiators: (i) the ratio of interest-earning debt to oney and (ii) the inflation rate. The intuition fro the optial taxation exerise is that the BCRA should be using debt inreasingly during this period for two related reasons. First, the defiit is viewed only as te- 366 Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

17 porary. Seond, beause of the deision to inrease the stok of foreign reserves during 216, it is frontloaded. Both versions of the odel oitent and weak tie onsisteny presribe that the debt-to-oney ratio should have inreased during 216. This is onsistent with the evidene. The quantitative odel iplies that the debt-to-oney ratio at the end of the first year of the progra should be between 47 perent (under oitent) and 133 perent (if the poliy is weakly tie onsistent). The orresponding value for Argentina is 89 perent, roughly in the iddle of the two estiates. Given the sipliity of the odel, it does not see that using this indiator an deterine the degree of oitent ipliit in the reent poliy. The two versions of the odel differ signifiantly in ters of their ipliations for the inflation rate. Under oitent, the inflation rate is estiated to be less than 3 perent (average for the duration of the progra), while the weakly tie-onsistent solution estiates inflation to be uh higher, lose to 25 perent. The reent Argentine experiene sees to be uh loser to the latter. As entioned before, the inflation rate during the first year of the progra was 33 perent and the arket expetations for the seond year are around 2 perent. 24 Even if the BCRA sueeds in signifiantly lowering inflation during the rest of the progra, it appears that the atual poliy is better approxiated by the weakly tie-onsistent solution. In a reent paper, Uribe (216) uses a siilar odel to analyze the Argentine experiene. He studies only the full-oitent solution and inludes in his analysis a uh larger lass of governent debt, as he is interested in how to finane the overall defiit and not just the fration that ust be finaned by the entral bank. 25 His estiates of the deand for oney are different fro ours, as he assues that sei-elastiity with respet to the interest rate is signifiantly lower than ours. He onludes that the inflation rate assoiated with the optial poliy is slightly below 5 perent and the onsolidated governent s debt-to-gdp ratio peaks above 4 perent. We view the ore liited sope of our analysis that inludes only the liabilities of the entral bank as a ore appropriate use of the odel. A oparison with the evidene suggests that this is the ase. At the end of 216, the total liabilities of the BCRA aounted to 16.2 perent of GDP. Given our estiate of the present value of the defiit for the reaining three years of the progra xˆ for the ontinuation is 2.6 perent of output the weakly tie-onsistent version of the odel iplies that the average inflation rate will be lose to 18 perent. There are two fores that influene the inflation estiate. On the one hand, the present disounted value of the defiit is substantially saller (2.6 perent vs. 6.9 perent), refleting the frontloaded path of the defiit. This redues required inflation. On the other hand, the stok of liabilities is higher (16.2 perent vs. 14 perent), and this requires a higher inflation rate. In a sense, our estiate is onsistent with the view that inflation should be dereasing in Argentina but viewed as an average over the life of the progra it is higher than the offiial foreasts. 26 CONCLUDING COMMENTS This artile shows that the quantitative ipliations of the optial onetary poliy under fisal doinane depend on the assued ability of the onetary authority to oit. Under Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

18 full oitent, a standard optial taxation arguent shows that the onetary authority should issue both bonds and oney. When the entral bank annot oit to a poliy of positive inflation when the defiit is zero, then the ability to sooth the distortion assoiated with the inflation tax is redued and there is a tight ap assoiated with the axiu aount of debt that the onetary authority an issue. The odel, alibrated to apture the basi details of the reent onetary poliy of Argentina, iplies that the Argentine onetary authority has followed a poliy that, to a first rough approxiation, results in an inflation rate that is lose to that iplied by the optial poliy under weak oitent. However, the atual poliy deviates fro the optial in that the inflation rate is not onstant. To what extent do the issues we disussed in this artile apply to the United States? It is iportant to note the differenes in institutional setups between the type of entral bank that we analyzed the Central Bank of Argentina and the Federal Reserve Syste. First, and ost iportant, the Federal Reserve Syste is truly independent and, therefore, it does not have to agree to finane the rest of the governent at a pre-speified level. 27 Seond, the Fed does not issue longer-ter interest-earning seurities and, hene, does not fae the prospet of raising seigniorage to servie the debt. 28 Are there lessons for the ondut of onetary poliy in the United States that an be drawn fro this exerise? The answer is a qualified yes. The Fed, just like the BCRA, an issue a seurity reunerated reserves that an be used to drain liquidity fro the syste. Are there possible senarios that the Fed ould fae that reseble the one analyzed in this artile? Ignoring soe legal issues, the Fed ould find itself in a situation in whih it has to transfer resoures to the finanial syste, for exaple, during a banking risis. In this ase, the Fed an hoose to inrease the oney supply in the for of non-interest bearing reserves to absorb part of the inrease by paying interest on soe portion of total reserves. This would oe lose to issuing interest-earning seurities to partially absorb exess liquidity. This type of arrangeent is different fro the urrent situation in whih all reserves reeive the sae return. We view reating two types of reserves as the siplest way of reating a bond that, in this exaple, would be held only by finanial institutions. There is a sense in whih the ativities of the Fed sine 28, when it inreased its holdings of assets, ould fit in this fraework. Ignoring for now the quality of the assets in the Fed s portfolio (that were ostly high-quality ortgage-baked seurities and Treasuries), one ould argue that the ideas we disussed in this artile ight apply to a entral bank that aquires private setor assets if, subsequently, the arket value of those assets drops signifiantly. In that ase, the situation is analogous to the Fed aking a one-tie transfer to the private setor, whih is lose to what we disussed. n 368 Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

19 APPENDIX Proofs Proof of Proposition 1. The Hailtonian of the proble is H C = v( )+ λ ρb M v + x u where as a atter of notation we define &b M = z. ρ z + λ b ( z), The first-order onditions assoiated with the axiu proble are λ = λ b v &λ = ρλ v ( )+ λ u &λ b = ρλ b ρλ. ρ v ( ) u ( ) It follows that λ. b = λ. = and real oney balanes are given by v ( ) = λ u ( ) v ( ) u ( ) v Thus, real oney balanes and the inflation rate are onstant. The governent budget onstraint iplies that the real stok of entral bank debt evolves aording to &b M t = ρb M v t + x t u ρ., and the solution that satisfies the transversality ondition is suh that b M t = e ρt t e ρs v x s u ρ ds + ( b M + ). In partiular, the aount of debt issued by the onetary authority at t = is e ρt v u ρ x t dt = b M +. Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

20 Proof of Proposition 2. The Hailtonian for the entral bank s axiization proble is H P = v( )+ λ ρb M v + x u ρ z + λ b ( z), whih is siilar to the one for the oitent ase. The sae arguent then shows that real oney balanes are onstant and, under the poliy that onetized the debt, inflation an be hosen so that T v u ρ t T e but sine x t = for all t T, then = *. ρ x t dt =, Proof of Proposition 3. An arguent siilar to the previous proposition shows that the optial is onstant. Then entral bank debt is given by b M t + = e ρt M t ( +b )+ e ρs v x s u ds. Iposing the terinal ondition T + b T M = *, we get the result. Estiation One issue with nonlinear least-squares estiation is that, in soe ases, estiates are very sensitive to the initially hosen paraeters. For the estiation proedure, we provide an initial value for the oney deand shifter K onsistent with the average real oney balanes relative to output during the year 215 ( =.86) and the noinal interest rate on tie deposits (i =.22). We obtain K =.14. In the ase of γ, we provide as an initialization point a set of values in the ranges suggested by the oney-deand estiation literature (fro.5 to 2). In all ases, we obtain K =.18 (.585) and γ = 2.97 (1.32), where the heteroskedastiity- and autoorrelation-onsistent standard errors are reported in parentheses. Although the estiate for K is not statistially signifiant, a joint signifiane test suggests that the estiated oeffiients are statistially signifiant at the 1 perent level. For the quantitative siulation, given that for K the onfidene interval of the estiation suggests a wide range of possible values, we alibrate it in suh a way so that it athes its average value for Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

21 Estiates of the Deand for Money There are a nuber of estiates of the deand for oney in Argentina. The different estiates vary in ters of their overage, the notion of oney, and how they handle dynai adjustent. These are the results fro a ursory review of the literature: 1. Mogliani, Urga, and Winograd (29) find the following: In their estiation of the long-run deand for oney allowing for strutural breaks (and using M1 as the notion of oney), real oney balanes display a unit elastiity with respet to inoe, while the sei-elastiity with respet to the interest rate is Kiguel and Neueyer (1995) define oney as M1 and also estiate the deand for oney in different subperiods. They find that the oeffiient of inoe is not signifiantly different fro zero, and their estiates of the sei-elastiity with respet to the interest rate range fro.2 to Gay (25) estiates the deand for oney (but does not say what he eans by oney) and he uses as his right-hand-side variable ln(i t /(1 + i t )). To turn his estiate into a sei-elastiity requires taking a stand on the value of i t. If Gay s estiated oeffiient is denoted β, then the sei-elastiity is β. ( 1+i t )i t If we assue that i t =.1, then the resulting sei-elastiity is (taking an average of his estiates) 2.79, while if the interest rate is 2 perent (i t =.2) the estiate is Baso, D Aoto, and Garegnani (212) estiate that the inoe elastiity of the deand for oney is slightly above 1 (although it is not lear whether it an be rejeted that it is equal to 1) and the interest sei-elastiity is 1.8. It is not surprising that sine Argentine onetary poliy has been very unstable over the last half entury, with several episodes of hyperinflation, it is not possible to find robust estiates of the deand for oney. In this artile, we use soe inforation about the seielastiity of the deand for oney fro the existing studies and opleent it with a very siple statistial odel to obtain a reasonable paraeterization of the relevant funtions that allows us to ake progress in understanding the reent experiene. Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

22 The Evolution of Debt Levels Here we report the ipliations of the two versions of the odel for the ratio of entral bank debt to GDP. Figure A1 Coitent: Debt-to-GDP Ratio Central Bank s Debt (perent of GDP) De 215 De 216 De 217 De 218 De 219 SOURCE: Authors alulations. Figure A2 Weak Tie Consisteny: Debt-to-GDP Ratio Central Bank s Debt (perent of GDP) De 215 De 216 De 217 De 218 De 219 SOURCE: Authors alulations. 372 Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW

23 NOTES Manuelli and Vizaino 1 It is ipossible to deterine why, if issuing bonds is part of the optial poliy, the fisal authority hooses to delegate this to the onetary authority. The first-best optial poliy is one in whih the ix of all taxes inluding the inflation tax is pinned down and the onsolidated governent budget onstraint deterines the evolution of the publi debt. The analysis of the institutional arrangeents that give rise to this situation is beyond the sope of this artile. 2 The Federal Reserve Syste also issues a bill-like seurity beause reserves earn interest. However, these seurities are like allable bonds beause the holders an turn the into oney on deand. 3 Nyawata (212, Table 2) inludes data on axial aturities. In soe ases, the upper bound is very long. Thailand s entral bank an issue 2-year bonds, while the Arenian onetary authority an issue 15-year bonds. 4 Gray and Pongsaparn (215) ite the ase of the entral bank of Chile, whih in the early 198s issued a large aount of debt to sterilize inreases in the oney supply assoiated with bailouts of doesti banks. Stella and Lonnberg (28) provide other exaples. 5 See Bassetto and Messer (213) and Berriel and Bhattarai (29) for exaples of analyses that distinguish between the two budget onstraints to keep trak of onetary and fisal interations. 6 Effetively we are onsolidating households and the non-governental private setor. Thus, we view t as the real value of the onetary base, inluding the portion held by oerial banks. 7 The original in Spanish is El bano tiene por finalidad proover, en la edida de sus faultades y en el aro de las polítias estableidas por el gobierno naional, la estabilidad onetaria, la estabilidad finaniera, el epleo y el desarrollo eonóio on equidad soial. 8 Even though by statute the president s andate lasts six years, the edian duration of a andate over the past 3 years has been less than 9 onths. It has been standard for inoing Treasury inisters to hoose their own BCRA president. In any ases in whih the BCRA president s and the Treasury s positions do not agree, the onflit is solved by the reoval of the authorities of the BCRA. For exaple, in 212 the BCRA president was reoved after he refused to use international reserves to honor debts. 9 The law allows for doubling of the liits when eonoi onditions warrant suh a hange. This flexibility has been used in the reent past. 1 For exaple, the governent of Honduras transferred a bond that, in noinal ters, inreased the apital of the entral bank by 1.1 perent of GDP in However, Stella and Lonnberg (28) estiate that the arket value of that bond was.6 perent of GDP. 11 See BCRA (216 or the ost reent version) for ore inforation about the urrent ondut of onetary poliy in Argentina. 12 Seigniorage is oputed as the year-over-year differene in the onetary base relative to the average noinal GDP in those 12 onths. Inflation is easured as the 12-onth average of the onth-over-onth inflation rate over the sae period. 13 The Laffer urve shows the relationship between tax rates (inflation) and the aount of tax revenue (seigniorage) olleted by governents. Traditionally, it exhibits an inverse u-shaped pattern. 14 The value for the first quarter of 216 is soewhat isleading, as the new governent eliinated soe prie ontrols that resulted in easured pries those entering the prie index athing up to arket-learing pries. 15 Taking into aount transfers to the Treasury only, the BCRA transferred to the Treasury the equivalent of 2. perent of GDP in 216 and has oitted to transfer 1.5 perent of GDP in y + vy We experiented with a forulation that has a iniu level of oney balanes given by v( ) = z 1 γ, 1 γ but the estiate of v was not signifiant. 17 In May 216, the BCRA announed an inrease in the andatory reserve requireents of the finanial syste that roughly orresponds to a 4 perent inrease in the deand for oney, whih in our ase orresponds to a 12 perent inrease in K. Federal Reserve Bank of St. Louis REVIEW Fourth Quarter

24 18 Using onthly data requires a onthly easure of private onsuption and GDP. We onstrut these series by perforing a ubi spline interpolation of their quarterly ounterparts. 19 The appendix desribes the estiation proedure. 2 In the appendix, we report the results of several reent studies of the deand for oney in Argentina. 21 The BCRA also inherited another liability in the for of underpried exhange rate futures. Thus, our estiate is probably an understateent of the true initial ost. 22 As entioned before, the previous adinistration used a signifiant portion of the foreign exhange reserves to fund Treasury operations. Thus, we assue that the inrease in reserves brings the to the level that the BCRA onsiders adequate. Sine the doesti real interest rate in Argentina is signifiantly higher than the return on its foreign urreny holdings, we ignore this soure of inoe and take the buildup of reserves as akin to an expenditure that earns no return and, hene, is part of P t x t. 23 This iplies that, in the last two years of the progra, the average annual defiit is.6 perent and.1 perent of GDP, respetively, whih is probably on the low end. 24 The latest available version of the BCRA s Market Expetations Survey (REM) orresponds to January It does not appear that Uribe takes into aount in his alulations the expenditures assoiated with the purhase of foreign reserves. 26 The results of the odel have to be taken as an approxiation. There are at least two diensions that an aount for the differene in foreasts. First, the path of the defiit relative to GDP is best viewed as rando. Seond, the BCRA has indiated that the long-run inflation rate is 5 perent, rather than zero as we assued. 27 In the past few years, the Fed has ade substantial transfers to the Treasury as a result of the profits assoiated with the anageent of its portfolio. However, these were not legally andated transfers and it is unlear to us what would happen if the Fed starts inurring losses on its portfolio. 28 In the extree ase of losses in its asset portfolio, the Fed an hoose to pay no interest on reserves and, hene, annot tehnially be required to inrease the oney supply in response to developents in its portfolio. REFERENCES Auernheier, L. The Honest Governent s Guide to the Revenue fro the Creation of Money. Journal of Politial Eonoy, 1974, 82(3), pp ; Bano Central de la Repúblia Argentina (Central Bank of Argentina). Charter of the Central Bank of the Argentine Republi. N.d.; Bano Central de la Repúblia Argentina (Central Bank of Argentina). Infore de Objetivos y Planes respeto del desarrollo de la polítia onetaria, abiaria, finaniera y reditiia para el año 217 (Annual Targets and Progras Report of the Central Bank of Argentina, 217). Deeber 216, pp Barro, Robert J. On the Deterination of the Publi Debt. Journal of Politial Eonoy, 1979, 87(6), pp ; Baso, E.; D Aato, L. and Garegnani, L. The Inforation Value of Money for Foreasting Purposes: The Cases of Argentina and Chile. Working Paper, Central Bank of Argentina, 212. Bassetto, M. and Messer, T. Fisal Consequenes of Paying Interest on Reserves. Fisal Studies, 213, 34(4), pp ; Berriel, T. and Bhattarai, S. Monetary Poliy and Central Bank Balane Sheet Conerns. B.E. Journal of Maroeonois, 29, 9(1), pp. 1-31; Burdisso, T.; Blano, E. and Sardi, M. Seasonal Adjustent and Loal Calendar Effets in Argentina s Monetary Aggregate. Central Bank of Argentina Ensayos Eonóios, June 21. Canzoneri, M.; Cuby, R. and Diba, B. The Interation Between Monetary and Fisal Poliy, in B.M. Friedan and M. Woodford, eds., Handbook of Monetary Eonois. Volue 3B. The Netherlands: North-Holland, 211, pp Fourth Quarter 217 Federal Reserve Bank of St. Louis REVIEW