Debt spillovers in a monetary union: A novel rationale for central bank independence

Campoy-Miñarro, Juan C.; Negrete, Juan Carlos Article Debt spillovers in a monetary union: A novel rationale for central bank independence Economics: The Open-Access, Open-Assessment Journal Provided in Cooperation with: De Gruyter Brill Suggested Citation: Campoy-Miñarro, Juan C.; Negrete, Juan Carlos (2022) : Debt spillovers in a monetary union: A novel rationale for central bank independence, Economics: The Open-Access, Open-Assessment Journal, ISSN 1864-6042, De Gruyter, Berlin, Vol. 16, Iss. 1, pp. 123-136, https://doi.org/10.1515/econ-2022-0017 This Version is available at: https://hdl.handle.net/10419/306057 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Research Article Juan Cristóbal Campoy and Juan Carlos Negrete* Debt Spillovers in a Monetary Union: A Novel Rationale for Central Bank Independence https://doi.org/10.1515/econ-2022-0017 received August 19, 2021; accepted January 06, 2022 Abstract: Central bank independence has been championed on the grounds that it avoids political business cycles, the time-inconsistency problem of discretionary monetary policy, and political conflicts. However, after the financial crisis, central banks have resorted to unconventional monetary policies and embraced additional tasks, making monetary authorities more exposed to political interference. This new reality has put into question the long-lasting consensus on the desirability of central bank independence. We add to this debate a new argument in support of that independence, namely, it internalizes the fiscal spillovers that arise in a monetary union, which is not a full fiscal union. Keywords: Central Bank design, monetary union, fiscal policies, international fiscal spillovers JEL classification: E52, E58 1 Introduction Over the last few decades, central banks across the advanced economies have been granted statutory independence from governments. However, in spite of a longlasting academic consensus on the benefits of delegating monetary policy to independent central banks, this trend may reverse because of the new challenges that monetary authorities are currently facing. After the global financial crisis, two important issues have emerged regarding central banks. On the one hand, they have acquired a more prominent role in financial regulation (Berger & Kibbmer, 2013; Smets, 2014)and have engaged in macroprudential policies (Ueda & Valencia, 2014). These developments have weakened the state control over its financial policies. On the other hand, a second set of concerns is related to central banks’responses to the new scenario where interest rates have approached or even reached the lower bound. Monetary authorities have embarked on unconventional monetary policies such as the provision of liquidity to the financial sector and the so-called quantitative easing, namely, the purchase of assets on a large scale. Some observers have raised the concern that the more a central bank becomes involved in such multiple (and less measurable)objectives and policy instruments, the more they become exposed to political interference (Blejer & Wachtel, 2020; Dell’Ariccia, Rabanal, & Sandri, 2018; Taylor, 2016). Specially, the focus of attention has been placed on that unconventional policy, which allegedly could undermine the independence and credibility of the monetary authorities, particularly if purchases of sovereign debt are viewed primarily as a means of facilitating fiscal deficits or if purchases of risky assets lead to capital losses (Cochrane & Taylor, 2016). The COVID-19 pandemic has exacerbated these issues. Central banks in most countries have even expanded the monetary tools used during the global financial crisis to support the economy and ease financing constraints in the medium term (see Dall’Orto, Vonessen, Fehlker, & Arnold 2020). The dramatic increase in government spending and debt, not seen since war times, has been followed by unprecedented purchases by central banks of those sovereign bonds. Since this unconventional monetary policy has greater distributional effects than traditional interest rate policy, central bank independence has been criticized on the grounds that these measures should not be taken by unelected officials because they are not accountable to the voters.¹ In fact, there has been an increase in the political Juan Cristóbal Campoy: Department of Economics Analysis, Universidad de Murcia, Facultad de Economía y Empresa, Campus de Espinardo, 30100, Espinardo, Murcia, Spain, e-mail: [email protected], tel: +34-868883822; fax: +34-868883758  * Corresponding author: Juan Carlos Negrete, Department of Economics Analysis, Universidad de Murcia, Facultad de Economía y Empresa, Campus de Espinardo, 30100, Espinardo, Murcia, Spain, e-mail: [email protected], tel: +34-868883760; fax: +34-868883758  1When the central bank decides to increase liquidity by buying assets, it is making decisions whose direct beneficiaries are more restricted than when it simply uses conventional monetary tools Economics 2022; 16: 123–136 Open Access. © 2022 Juan Cristóbal Campoy and Juan Carlos Negrete, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. pressures to make monetary authorities less independent from governments (Claeys & Domínguez, 2020; Mersch, 2017). Besides, some international institutions such as the IMF are compelling developing countries to delegate monetary policy to independent central banks as a precondition for loans. In this sense, it could be argued that the aim of such reforms is to make central bankers adopt those international institutions’preferences, namely, to make monetary authorities dependent from them. Having said that, Rau-Goehring, Reinsberg, and Kern (2020)claim that this conditionality has advantages because central bank independence is a signal device for investors, minimizes the risks of government abuse of disbursed funds, and establishes a politically insulated veto player within the borrowing country to constrain excess credit creation. All these recent developments have given rise to a regained interest in the topic of central banks and in the debate on whether they should be independent. The aim of this article is to enter this debate and put forward a novel argument in support of central bank independence in a monetary union, when the common central bank carries out unconventional monetary policy in the form of buying national public debts. In their seminal article, Alesina and Tabellini (2008) showed that it is optimal for society to delegate certain types of activities to independent institutions, while others are better left in the hands of elected politicians. Regarding central banks, the traditional argument to delegate their functions to independent institutions has rested on countering inflationary biases that may occur for the political pressure to boost output for electoral reasons (Hibbs, 1977; Nordhaus, 1975; Rogoff& Sibert, 1988)and for the timeinconsistency problem of monetary policy making (Barro & Gordon, 1983; Kydland & Prescott, 1977; Rogoff, 1985; Svensson, 1997; Walsh, 1995).² In addition, other studies show that governments may also choose to delegate monetary policy in order to detach it from political debates and power struggles (see De Haan & Eijffinger, 2016; Fernández-Albertos, 2015 for recent reviews). All this literature has showed that it is optimal for the society to delegate monetary policy to well-designed independent institutions. Our article puts forward a new argument in support of central bank independence, namely, it is a credible commitment to internalize the externalities that arise in a monetary union when national governments expect that part of its debt will be bought by the common central bank which, in doing so, creates a risk pool. As a consequence, there is a prisoner’s dilemma kind of situation. To wit, national fiscal authorities, will be tempted to spend beyond the limit which is optimal from the point of view of the whole union’s joint welfare, because each government will not bear all the risk of its spending. In the absence of a fiscal union that prevents excessive budget deficits, a central bank less willing to buy bonds than governments is a commitment device to achieve more fiscal discipline. In this sense, we show that it is optimal to delegate monetary policy to an independent and conservative (or “hawkish”)central bank, that is, one whose monetary policy is less expansionary than the one carried out by government-dependent monetary authorities. The novelty of our study is that it shows that there is a role for granting independence to central banks even in the absence of the aforementioned issues considered in this literature, namely, business cycles, time inconsistency problem, and political economy conflicts. On the other hand, since we obtain this result in a setup where all the member countries in the union are homogeneous, we respond to a criticism that the European Central Bank (ECB)has frequently faced, which argues that the reason why this monetary institution is so conservative is that it only reflects the preferences of the core countries in the European Monetary Union (EMU)and not those of the periphery countries. That is, the argument goes, the common central bank has been designed by the former with the aim of undemocratically imposing their preferences on the latter (Holtfrerich, 2008). In this sense, our article shows that having a hawkish central bank in a monetary union need not be interpreted as such an unbalanced result of a conflict of interests among heterogeneous member states. For instance, if all countries in the EMU shared Germany’s preferences, the common central bank should be more conservative than Germany. Our analysis also puts into question another common criticism faced by the ECB, namely, its tendency to be less expansionary than the FED (Pronobis, 2014). It has been argued that this behavior is not optimal, unless the Eurozone and the United States had different preferences (the former being less willing to let their central bank buy governments debt). However, we show that, even if  (Mishkin, 2013). On the other hand, it has been argued that quantitative easing has increased the value of financial assets, making their owners better-off. Besides, Lagarde (2020), president of the ECB, has acknowledged the possibility of employing its various asset purchase programs to combat climate change, which is an issue that allegedly should also be dealt with by an agency dependent from the government. 2Bernanke (2005), former president of the Federal Reserve, labeled the articles by Barro & Gordon (1983), Kydland & Prescott (1977), Rogoff(1985), and Walsh (1995)as the most influential papers in monetary policy in the previous 25 years. 124 Juan Cristóbal Campoy and Juan Carlos Negrete such differences in preferences did not exist, the fiscal externalities that the ECB faces imply that it should be more conservative than the FED. Our article shows that, because of the debt spillovers, there exists a trade-offbetween the optimal degree of fiscal discipline in the EMU and the optimal degree of conservatism of the ECB. In doing so, it rationalizes the evolution of monetary and fiscal institutions in the Euro zone. To wit, during the Great Recession, as more legislation was being introduced to support fiscal discipline in the union (The Six Pack in 2011 and The Fiscal Compact and Two Pack in 2013), monetary policy became more expansionary, carrying out quantitative easing. This process has culminated and been made more explicit with the recent official statement of the ECB’s Governing Council, which has set its inflation goal to 2% and has allowed room toovershootitwhenneeded(“ECB’s Governing Council approves its new monetary policy strategy,”July 8th 2021). This is a significant change from the previous target of “below, but close to, 2%.”However, the unconventional monetary policy of the ECB started to be implemented with a lag with respect to the FED because the EMU is still further away than the United States from being a fully fledged fiscal union. This fact also explains why the ECB will continue to be less dovish than the FED, which announced in 2020, after its own review, a policy of average inflation targeting, which implies that inflation will automatically overshoot its 2% objective after periods of undershooting it. Our article is related to the literature on central bank design pioneered by Rogoff(1985), Svensson (1997), and Walsh (1995). However, we extend the closed-economy framework used in this literature and consider a monetary union with fiscal externalities. In this sense, our article is also related with the vast and fast expanding literature that studies the interactions among national fiscal institutions within a monetary union (see Beetsma & Giuliodori, 2010; Foresti, 2018 for recent reviews and the references therein).³ However, in contrast with these articles, our article focuses on how the optimal design of the monetary institutions interacts with the implementation of fiscal policy, when the common central bank carries out unconventional monetary policy. The remainder of this article is organized as follows. Section 2 presents the model. Section 3 characterizes the first best, which serves as a benchmark scenario. Section 4 analyzes the case where the central bank is government dependent and shows the existence of negative fiscal externalities. Section 5 considers a fiscal union. Section 6 shows the role of an independent central bank. Section 7 analyzes the possibility of having an independent central bank in a fiscal union. Section 8 concludes. Finally, the proofs of some of the results are gathered in the Appendix. 2 The Model We consider a monetary union, which is made up of two symmetric countries, 1 and 2. The working of the economy is given by the following equations: =++gtbm, iii i (1) ()=−+++ L αg g βt δb γp, iSiii 2222 (2) =+ p mm, 12 (3) where =i1,2 and > α βδgγ,,,, 0 . Expression (1)is country i’sbudgetconstraint.Governmentspending ()g i can be financed by taxes ( ) ti, public debt in the hands of the public ()b i andpublicdebtboughtbythecommoncentralbank ()mi. The monetary authorities need not buy sovereign debt directly from the governments, which is forbidden by law in some cases (e.g., the EMU), but in the secondary market.⁴ Equation (2)is country i’s loss function, which is assumed to be shared by the government and the public. That is, the government is “benevolent.”This function shows that its citizens dislike deviations, from target levels, of government spending, taxes, debt in the hands of the public, and bonds bought by the central bank (quantitative easing). Those target levels are normalized to zero, except for the case of government spending ( ) >g0 .Thefirst term of this equation takes account of the fact that there is a welfare loss when government spending is below a social target (this target has increased because of the COVID-19 pandemic). To close this gap, public expenditure has to increase. However, the three  3The COVID pandemic has sparked renewed interest in those interactions (see, e.g., Chadha, Corrado, Meaning, & Schuler, 2021; Panetta, 2021).  4It is assumed that the budget constraint of member countries includes only one period. As Buiter (2014)has pointed out, when a central bank engages in quantitate easing it exchanges government debt for money, which is a non-redeemable liability. This relaxes the intertemporal government budget constraint. However, extending our model to an intertemporal setting with a present value budget constraint (see Woodford, 1998)would not change the qualitative results. The reason is that in such a model, the international fiscal policy spillovers would still exist. Debt Spillovers in a Monetary Union: A Novel Rationale for Central Bank Independence 125 means that can be used to finance it create distortions, which are referred to by the three last terms in equation (2):(i)taxes change incentives and have a negative effect on output; (ii)public debt in the hands of the private sector imply increases in future distortionary taxes and higher interest rates;⁵and (iii)central bank bond purchases are not free lunch either. To wit, when the monetary authorities buy government debt, they create a “pooled risk,” p , measured in equation (3),⁶since it implies that individual countries’risks are passed to the whole union because of the following. On the one hand, as the money supply grows, the risk of future inflation increases. On the other hand, if one member country defaults on its debt, the central bank incurs losses, because the latter’s assets fall in value, making worse offnot only the defaulting country but also the rest of the states in the union, since ownership of the central bank is shared by all members. That type of risk pooling is clearly referred to by The Economist (2012), which claimed that the quantitative easing policy of the ECB means that it “will be buying low-graded peripheralgovernment bonds, redistributing risks across Europe. The Bundesbank has two fundamental worries about the ECB buying government bonds. First, it exposes taxpayers in northern countries to risks that belong to those in southern states, but does so opaquely within the Eurosystem rather than openly. Second, it takes monetary policy too close to the realm of fiscal policy and thus compromises the ECB’s independence.”All this would mean that, when the ECB buys sovereign debt, the member countries would be sharing risks. In fact, as Weidmann (2020)has claimed, government bond purchases in a monetary union, which is not a fiscal union involve the fundamental risk of mutualizing sovereign liability risks. Furthermore, Giavazzi and Tabellini (2016)also point out that this risk pooling exists because thanks to it being a pool, the interest on the debt of the periphery countries has fallen.⁷ Notice that the model sets aside the aforementioned issues considered in this literature to grant independence to central banks. That is, on the one hand, in our setting, monetary surprises cannot increase output, which avoids the traditional time-inconsistency problem in monetary policy (Barro & Gordon, 1983; Kydland & Prescott, 1977; Rogoff, 1985; Svensson, 1997; Walsh, 1995), and, on the other hand, our assumption that governments are benevolent rules out the possibility of conflicts of interests that could give rise to political business cycles (Hibbs, 1977; Nordhaus, 1975; Rogoff& Sibert, 1988)or the need to detach monetary from political debates and power struggles (De Haan & Eijffinger, 2016; Fernández-Albertos, 2015 for recent reviews). In this sense, the novelty of our article is that, even without taking into account those issues, it shows that it is optimal to delegate monetary policy to an independent and conservative central bank. The model also illustrates the trade-offs faced by the economic authorities in the context of the present COVID pandemic, where governments have dramatically increased their spending not only to stabilize output but also to provide support to those most impacted by the crisis (first term of the loss function in equation (2)). This expenditure has to be financed by (i)distortionary current taxes (second term);(ii)by public debt in the hands of the public, which increases interest rates and implies future distortionary taxes (third term);or(iii)by sovereign debt bought by the common central bank, which creates a risk pool (fourth term). Our framework takes into account the new challenges that monetary policy is currently facing. Even after the Great Recession, conventional monetary policy had run out of tools because interest rates had approached or even reached the zero bound limit. As a consequence, to take the economy out of recession, governments have had to incur massive budget deficits. The role of monetary  5As Beetsma and Giuliodori (2010)have pointed out, a national fiscal expansion pushes up the long-run interest rate discouraging investment. This concern has also been expressed by central bankers. For example, Lagarde (2020)has stated that “monetary policy has to minimise any ‘crowding-out’effects that might create negative spillovers for households and firms. Otherwise, increasing fiscal interventions could put upward pressure on market interest rates and crowd out private investors, with a detrimental effect on private demand.” 6The use of quadratic loss functions as the one in equation (2)is standard in the literature on the interactions between fiscal and monetary policies. The inclusion of the first three terms in the loss function is commoninthisliterature(see Beetsma & Giuliodori, 2010; Foresti, 2018). We introduce a new term (the fourth one)to take into account the strategic effects of quantitative easing. On the other hand, Dixit and Lambertini (2003)and Woodford (2003, ch. 6)have shown that this type of function can be built on microeconomic foundations, since they can be derived starting from a representative agent that maximizes a utility function. Furthermore, Blinder (1998),formervice-president of the FED, has stated that economic authorities use their policy instruments so that variations in the economic variables are relatively small and, for changes of this size, any convex objective function can be assumed to be approximately quadratic. Therefore, positive or negative deviations from the policy targets can be considered as losses that are represented with a loss function of this type.  7An alternative risk pooling setting would be the case where Eurobonds are issued. However, including it would not alter the main conclusions because the negative spillovers would also exist in that scenario. 126 Juan Cristóbal Campoy and Juan Carlos Negrete policy has been to accommodate this fiscal expansion so that interest rate do not increase. This narrative has become even less contested with the COVID-19 pandemic. 3 Benchmark Scenario: The First Best We assume that each government’s aim is to minimize the loss of its own country, that its policy actions are not motivated by electoral or partisan objectives and there are no political economy conflicts. These particular issues are set aside in our analysis since they have been studied extensively in the literature (Hibbs, 1977; Nordhaus, 1975; Rogoff& Sibert, 1988). We begin by obtaining the values of the policy variables ( ) gtbm,, itii,, which minimize the joint social loss of the countries in the union. In the rest of this article, we study whether those first-best values can be obtained with different institutions. Solving (1)for bi and substituting it together with equation (2)in equation (3), one can rewrite the country’s loss function as follows: () ( ) () =−++−− ++ L αg g βt δg t m γm m , iSiiiii ij 22 2 2(4) where =ij,1,2 ; ≠ij . Then, the first best is obtained by solving the following problem: (( ) ( ) ()) { }∑−++−− ++ =αg g βt δg t m γm m Min . gtm iiiiii ij ,, 1 2 22 2 2 iii (5) From the first-order conditions (and taking into account expression (1)for bi ),onefinds the firstbestvaluesforthe policy variables ( ) gtbm,, itii,: () =++ +++ gαg βγ βδ γδ αβγ αβδ αγδ βγδ 44 444 , i(6) =+++ tαγδg αβγ αβδ αγδ βγδ 4 444 , i(7) =+++ b γβαg αβγ αβδ αγδ βγδ 4 444 , i(8) =+++ mδαβg αβγ αβδ αγδ βγδ444 . i(9) Remark 1. When more government spending is needed ()g ¯, for example, because of the COVID-19 pandemic, the first best implies that this additional expenditure will be financed by a combination of taxes and debt, and part of his debt has to be bought by the central bank. Equation (9)shows the optimal level of monetary financing. It has to be emphasized that the literature on central bank independence has not highlighted very often the fact that part of the government expenditure should be financed via debt monetization. This means of financing public expenditure, instead, has been treated rather as a taboo. However, that equation does not imply that, as a result of this monetary financing, it is optimal that the money supply spirals out of control. On the contrary, it should not increase beyond the level characterized by that equation (9). In the present context of the pandemic and the recession it has caused, there is a widespread consensus that the central bank’s purchases of sovereign bonds should be carried out to a greater extent than in other downturns. There are two reasons for this occurrence. On the one hand, to boost the economy, monetary policy has lost its traditional ammunition, namely, interest rates are so low that there is (almost)no room to reduce them further. Therefore, fiscal authorities have been assigned a fundamental role in this crisis, namely, government spending has increased dramatically but without being financed by raising taxes. Having said that, fiscal policy cannot afford to work in isolation from the monetary policy because, to avoid the increase in interest rates stemming from that extraordinary fiscal expansion, central banks are required to carry out unprecedented purchases of sovereign bonds. Notice that equation (9)shows that, in the presence of a shock, as the COVID-19 pandemic, the level of debt monetization should increase if joint social welfare of the union is to be maximized, and this level depends, among other things, on the size of the negative side effects of the central bank’s debt purchases, which is captured by the parameter γ in equation (2). In this scenario, this increase in monetary financing should be greater as the link between inflation and the volume of bond purchases by the central bank becomes weaker (lower γ ), which has been a recent trend starting from the Great Recession. 4 A Government Dependent Central Bank As stated in Section 1, we assume throughout the article that each government is benevolent, in the sense that it Debt Spillovers in a Monetary Union: A Novel Rationale for Central Bank Independence 127 does not pursue electoral nor partisan interests but those of the citizens in its own country. On the other hand, it has to be made clear that each government, when taking its policy actions, only pays attention to the welfare of its own country, but not to that of the other member country. This gives rise to an externality that is a key element in our analysis. As for the common central bank, when we refer to it as being benevolent, we mean that it maximizes not just the welfare of one single country but the joint welfare of all the states in the union. We begin by assuming that the central bank has this type of social preferences. The interactions among the central bank and the governments are modeled by making use of a two-stage game. In the first stage, governments simultaneously choose their expenditure, taxes, and public debt (taking the other country’sfiscal variables as given),and bearing in mind that the central bank, in the second stage, will carry out the unconventional monetary policy consisting in buying a portion of these sovereign debts. Therefore, we assume that the fiscal authorities movebeforethecentral bank. This timing is in line with the usual assumption that, in practice, monetary policy decisions to buy bonds can be changed more easily than fiscal policy. The reason is that, while the volume of government debt purchases carried out by the central bank can be adjusted almost instantaneously, fiscalvariablestakemoretimetobeimplemented:theyhave to be proposed, voted in parliament, and then put into practice. That is why the fiscal authorities are modeled in this literature as first-movers against central banks (see Beetsma & Giuliodori, 2010). We look for a subgame perfect equilibrium of the twostage game by applying backward induction. Therefore, we begin by solving the second stage, where the sovereign bond purchases by the central bank take place, once it has observed the values of the public expenditures and taxes decided by the member countries’governments. Thus, the problem that the central bank solves is (from equation (4)): (( ) ( ) ()) { } ∑=−++−− ++ ≠ Lαggβtδgtm γm m Min . mm ij iiiii ij , CB 2 22 2 2 12 (10) The first-order condition yields the central bank’s reaction functions: () () =+−−++ + mgγ δ γg tγ δ γt γδ 2222 4 . iij ij (11) From an inspection of equation (11), we conclude that when one country, say country i, increases its government spending (or lowers its taxes)the central bank will purchase more of its public debt increasing the common risk in the union. That is, there is a negative spillover, which is a key element of this article, and can be stated as follows: Remark 2. In a monetary union with a benevolent central bank, negative fiscal externalities arise, namely, when a country increases its government spending or lower its taxes, the other member country is made worse offbecause the common risk rises. In the case where there is no monetary union, the central bank would also buy sovereign bonds. Nonetheless, in this context, that spillover effect is absent, because the country that carries out this type of fiscal policy bears all the costs of its actions. By contrast, in a currency union, if no commitment technology exists that limits government deficits, that negative externality implies that national governments will be more prone to incur fiscal deficits than in thecasewherethereisnosinglecurrency. Remark 3. In a monetary union that is not a fiscal union and where governments and the central bank are benevolent, welfare is not maximized because a deficit bias will arise, causing central bank purchases of sovereign bonds to be suboptimally high. We prove this result by solving the problem that country i’s government faces in the first stage (from equations (4)and (11)): () ( ) () () () {} =−++−− ++ =+−−++ + Lαgg βtδgtm γm m mgγ δ γg tγ δ γt γδ Min s.t. 2222 4. gt iSiiiii ij iij ij , 222 2 ii (12) Solving the first-order conditions one finds: () =++ +++ ggα βγ βδ γδ αβγ αβδ αγδ βγδ 42 422 , i (13) =+++ tgαγδ αβγ αβδ αγδ βγδ 2 422 . i (14) Now, substituting into equation (11), equations (13) and (14)(and taking into account expression (1)) yields: =+++ mgαβδ αβγ αβδ αγδ βγδ422 , i(15) =+++ b γβαg αβγ αβδ αγδ βγδ 4 422 . i (16) Comparing equations (6)–(9)with equations (13)–(16), it can be checked that (see the Appendix)in a monetary 128 Juan Cristóbal Campoy and Juan Carlos Negrete union, that is not a fiscal union and governments are benevolent: (i)government spending, purchases of bonds by the central banks, and the resulting common risk are suboptimally high; and (ii)taxes are suboptimally low. Therefore, the first best is not achieved and the reason is the existence of the fiscal negative externalities claimed in Remark 2. 5 A Fiscal Union One possible way to solve this fiscal externality problem is to create a fiscal union. This can be done by collectively choosing the taxes and government expenditure levels or by setting penalties on fiscal deficits. We follow the latter route, which is the one followed by the European Monetary Union (EMU). We model this fiscal institution by adding a new (fifth)term to the governments’objective functions in equation (4). This additional component will be modeled by assuming that there is a fine ( ) fon budget deficits, so that each government does not overlook the effect that its fiscal policy has on the other member country’s welfare. That is, the augmented loss function of country i’s government ()L iG is expressed as follows: () ( ) ()() =−++−− +++− L αg g βt δg t m γm m fg t. iGiiiii ij ii 222 2(17) On the other hand, we depart from the previous game by adding a new stage, where the choice of the fiscal penalty, f , takes place. This design stage will be located at the beginning of the game, because altering the design of a fiscal union is more complex and difficult than changing government expenditures, taxes, or the level of bond purchases by the central bank. Therefore, the timing is now: (1)Fiscal union design stage: Governments cooperatively select the fine on deficits ( ) f. (2)Fiscal policy stage: National fiscal authorities decide their expenditure levels and taxes in a noncooperative way ( ) gt, ii . (3)Monetary policy stage: The benevolent central bank buys sovereign bonds ()mi. We apply backward induction. Therefore, by solving the last stage, we get the central bank’s reaction functions, which have been obtained in equation (11), because the central bank was also assumed to be benevolent in the previous section. Taking into account equation (11), in the second stage, the problem faced by the government in country iis: () ( ) ()() () () {} =−++−− +++− =+−−++ + Lαgg βtδgtm γm m fg t mgγ δ γg tγ δ γt γδ Min s.t. 2222 4. gt iGiiiii ij ii iij ij , 222 2 ii (18) The first-order conditions yield the values of the fiscal variables in this scenario (the superscript FU stands for Fiscal Union): () =++++ +++++++ gf gαβγ gαfγ gαβδ gαfδ gαγδ αβγ αfγ αβδ αfδ βfγ αγδ βfδ βγδ 44 2 44 42 2 , iFU (19) () =++ +++++++ tf gαfγ gαfδ gαγδ αβγ αfγ αβδ αfδ βfγ αγδ βfδ βγδ 42 44 42 2 . iFU (20) Now, substituting these equations into equation (11) yields: () =+++++++ mf δαβg αβγ αfγ αβδ αfδ βfγ αγδ βfδ βγδ44 42 2 . iFU (21) Finally, in the first stage, the penalty ( ) fon deficits is selected to maximize joint social welfare. Formally, it is obtained by solving: (( ) ( ) ()) ⎧ ⎨ ⎪⎪⎪⎪⎪⎪ ⎩ ⎪⎪⎪⎪⎪⎪ () () () {} ∑ += −++−− ++ ==++++ +++++++ ==++ +++++++ ==+++++++ ≠ LL αgg βtδgtm γm m ggf gαβγ gαfγ gαβδ gαfδ gαγδ αβγ αfγ αβδ αfδ βfγ αγδ βfδ βγδ ttf gαfγ gαfδ gαγδ αβγ αfγ αβδ αfδ βfγ αγδ βfδ βγδ mmf δαβg αβγ αfγ αβδ αfδ βfγ αγδ βfδ βγδ Min s.t. 44 2 44 42 2 , 42 44 42 2 , 44 42 2 , f SS ij iiiii ij ii ii ii 12 2222 2 FU FU FU (22) where the six constraints (three for each country)appear in equations (19)–(21): The solution to the problem is expressed as follows: =+> ∗ f γδ γδ 2 40 . (23) Proposition 1. In a monetary union, the first best is achieved when a fiscal union is created and the optimal fine on government deficits is imposed on countries. Debt Spillovers in a Monetary Union: A Novel Rationale for Central Bank Independence 129 Proof. Substituting equation (23)into equations (19)–(21) and checking that these values are the ones that achieve the first best (appearing in equations (6)–(9)). The intuition behind this proposition is as follows. In a monetary union, if no government takes into account the negative effects that its fiscal policy has on the welfare of the citizens in the rest of the union (stated in Remark 2), a prisoner’s dilemma situation arises. This spillover can be dealt with by penalizing fiscal deficits. This kind of “pigouvian tax”can be designed in such a way that each government internalizes not just the “private”cost of its fiscal actions but the “social cost”of the whole union. In the case of the EMU, even though fiscal institutions such as the Stability Pact in 1997 and the Fiscal Compact in 2013 have been designed to deal with the deficit bias, they have not given rise to a full-fledged fiscal union. In practice, the countries that have not followed the rules have not been fined. In 2003, France and Germany breached the 3 per cent deficit limit established in the Stability Pact but avoided sanctions, and in 2016, Spain and Portugal were also given € 0fines after failing to comply with deficit targets. Since these precedents do not favor the credibility of the EMU fiscal institutions, we look for another solution to the problem in the following section, namely, the design of an independent central bank. □ 6 An Independent Central Bank We now analyze another commitment technology that deals with the fiscal externalities that arise in a monetary union, that is not a fiscal union. We assume that each government is only interested in its country’s welfare and that there is no penalty on budget deficits or, if it exists, it cannot be enforced. This new institution consists in delegating monetary policy to an independent central bank whose preferences will be cooperatively chosen by the member countries of the union. Those preferences cannot be the ones of a benevolent central bank because, as shown in Section 4, the resulting scenario would not achieve the first best, since the negative externality of fiscal policies would not be internalized. We model this monetary regime by introducing two changes in the scenario in Section 4: (i)The central bank’s weight on its purchases of sovereign debt is collectively set by the governments so that it ceases to be γ and becomes +γ ϕ , where ϕ is the choice parameter. That is, if ()><ϕϕ00 ,it implies that the common central bank resulting from the optimal design should be more (less)concerned than countries about the pooled risk that stems from its purchases of sovereign debts. Then, the monetary authorities loss function is now: (( ) ( ) ()( )) ∑ =−++−− ++ + ≠ L αg g βt δg t m γϕmm. ij iiiii ij CB 2 22 2 2 (24) (ii)We add a new stage where the choice of that new parameter, ϕ , takes place. This design stage will be at the beginning of the game (before the other two stages), because altering the design of an institution such as the central bank is more difficult than changing fiscal and monetary variables. Therefore, the timing is now: (1)Central bank design stage: Governments cooperatively choose the preference parameter of the common central bank ()ϕ. (2)Fiscal stage: Governments decide their levels of expenditure and taxes in a noncooperative way ( ) gt, ii . (3)Monetary policy stage: The central bank buys sovereign bonds ()mi. Again, solving the last stage gives the central bank’s reaction functions: ()()()() =++−++−+++ ++ mgγδϕtγδϕgγϕtγϕ γδ ϕ 22222222 42 . i1122 (25) In the second stage, the fiscal authorities in country i, face the following problem (from equations (4)and (25)): () ( )( ) ()()()() {} =−++−−++ =++−++−+++ ++ L α g g βt δ g t m γ m m mgγδϕtγδϕgγϕtγϕ γδ ϕ Min s.t. 22222222 42 . gt iSiiiii ij i , 2222 1122 ii (26) The first-order conditions yield the government spending and taxes (the superscript ICB stands for Independent Central Bank): () ()()() =+++++ + ++ gϕ ϕαgβγ βδ βϕ γδ δϕ αgγδ βγ βδ γδ K 4824 42 4 4 2 , iICB 0 (27) () ()() =++ + tϕ ϕδαg γ ϕ δγαg γ δ K 44224, iICB 0(28) where ( ) =++++++ K ϕ αβγ αβδ αβϕ αγδ αδϕ βγδ βδϕ48 2 4 4 2 4 2 0+ (+γδ4)( ) +++αβγ αβδ αγδ βγδ422 .Now, substituting these equations into equation (25)yields: 130 Juan Cristóbal Campoy and Juan Carlos Negrete