Beyond traditional arguments justifying the introduction of fiscal rules, this paper analyses their potential contribution to an indirect budgetary coordination between the member countries of a monetary union. Indeed, thanks to appropriate fiscal penalties, the noncooperative and decentralized equilibrium could get closer to the optimal equilibrium where the budgetary authorities cooperate. Our macroeconomic model shows that whatever penalty on the structural budgetary deficit would be optimal in case of asymmetric shocks. A moderate penalty on the excessive indebtedness level would be optimal in “normal times,” or in case of asymmetric shocks if openness to trade and price flexibility are sufficiently high, whereas the share of public consumption in GDP, taxations rates, and indebtedness levels is sufficiently weak in the monetary union. Besides, in case of symmetric shocks, a fiscal penalty would be useful to decrease the excessive budgetary activism, even if it doesn’t allow reaching the optimal and first-best equilibrium. Furthermore, the fiscal penalty should always be an increasing function of the share of public consumption in GDP and of taxation rates but a decreasing function of the strength of automatic stabilizers, of openness to trade, and of price flexibility in the member countries of the monetary union.
Monetary unification creates new financial externalities, which seem to necessitate a stronger fiscal discipline in a monetary union in order to avoid that a member state had to suffer from the irresponsible fiscal behaviour of another member country. Indeed, in a monetary union, the fiscal laxity of a country can increase interest rates and endanger financial stability for all partner countries. It is precisely what is happening since 2010 in Europe in the framework of the sovereign debt crisis. As mentioned by Buti and Franco [
In the European Economic and Monetary Union (EMU), to limit these risks of moral hazard problems, the “no bail-out” clause in the Maastricht Treaty excludes the possibility of a member state assuming liability for the sovereign debt of other member states. Nevertheless, the Greek situation since 2010 has proven the weak credibility of such a clause. Indeed, Lane [
Therefore, in a monetary union, even if the last autonomous instrument in the hands of national governments, budgetary policies, must keep some independence in order to stabilize asymmetric cyclical variations, fiscal rules are necessary. A fiscal rule is a permanent constraint on fiscal policy through simple numerical limits on budgetary aggregates. So, since the creation of EMU, fiscal discipline has essentially consisted in such fiscal rules (Maastricht criteria, stability and growth pact, and fiscal compact) intended to limit budgetary deficits and public debts for the member countries. Fiscal rules aim at ensuring the long-term sustainability of public finances; they can concern the budgetary deficit or the public debt. They must also avoid the tendency to conduct excessively lax budgetary policies. However, beyond the arguments previously mentioned, fiscal rules can have another advantage. In the framework of largely decentralized and autonomous budgetary policies, as in the EMU, where budgetary policies are widely independent and decided at the national level, they can also contribute to a kind of budgetary coordination.
Indeed, the formal and explicit coordination between budgetary policies is quite minimal in Europe, in the framework of the European Council or of the Euro-group. So, the aim of the current paper is to justify the existence of fiscal rules and penalties by their contribution to an indirect coordination between the European budgetary authorities. We show that appropriate fiscal penalties can sometimes be a kind of substitute to a formal coordination of budgetary policies in a monetary union. Indeed, they can contribute to influence the noncooperative and decentralized budgetary equilibrium. Thanks to appropriate fiscal penalties, the decentralized equilibrium can then get closer to the optimal and first-best equilibrium where the budgetary authorities cooperate. Therefore, fiscal rules could compensate for the lack of willingness from the European governments to coordinate more formally and in a more binding way their budgetary and fiscal policies. Indeed, the optimal contract for a central bank has widely been studied, in the tradition of Walsh in particular. But the current paper analyses the optimal contract regarding the decentralized governments in a monetary union. It studies the usefulness of fiscal discipline and of fiscal rules associated with penalties in case of deviations from a given target. Can such fiscal penalties be a substitute to a formal coordination of budgetary policies in a monetary union and can they make the decentralized budgetary policies closer to the cooperative equilibrium?
The second section mentions the evolution of fiscal rules and penalties in the EMU, as well as some results in the economic literature on their usefulness and efficiency. The third section describes a simple macroeconomic model, where monetary policy is conducted by a common central bank, while decentralized budgetary policies are decided by the governments. The model also includes a penalty on the deviation of the budgetary deficit or the public debt from a given targeted value. In the following sections, the idea is to define the optimal fiscal penalties that could make the decentralized Nash equilibrium for the budgetary policies closer to an optimal and cooperative centralized budgetary equilibrium. The fourth section studies how to limit the structural budgetary deficit or how to make the public debt converge towards a targeted level. The fifth and sixth sections analyse, respectively, how to make the decentralized noncooperative budgetary policies answer in a more optimal way to the symmetric or to the asymmetric supply or demand shocks. The seventh section concludes the paper.
In 1992, article 104c of the Maastricht Treaty and the annexed Protocol 5 included thresholds and constraints on the global budgetary deficit (which had to be below 3% of GDP) and on the public debt (which had to be below 60% of GDP). Afterwards, in 1996, the stability and growth pact (SGP) added that national budgetary policies should “create room for maneuver in adapting to exceptional and cyclical disturbances,” while avoiding excessive deficits. Hence, EMU member countries should have a medium-term budgetary objective “close to balance or in surplus”; they should maintain a balanced budget over the economic cycle. This structural budgetary equilibrium should make enough room for maneuvering for automatic stabilizers to play and for economic stabilization in the short run in case of macroeconomic shocks.
After the reform of the SGP in 2005, there was more flexibility in the medium-term deficit target but also a more restrictive definition of the fiscal objective: it was clearly stated that the medium-term target should apply to the cyclically adjusted budget balance. Indeed, the primary budgetary deficit has two components: a structural part and a cyclical or conjunctural part. The conjunctural deficit is a decreasing function of the output gap, of the excess output in comparison with its potential value. On the opposite side, the structural deficit is the public deficit cleared of cyclical effects and one-off measures as well as temporary measures. In this framework, the main advantage of a shift to a structural deficit rule would be the increased flexibility in dealing with cyclical stabilization. On the other hand, the main difficulty relies naturally on the possibility to evaluate a structural deficit. Indeed, the operational simplicity of such an indicator is widely put into question given the reference to controversial magnitudes of the variables used in calculation, such as the output gap and the NAIRU.
Regarding the potential penalties imposed on the deviation of the budgetary deficit from its targeted value, in the framework of the excessive deficit procedure, sanctions could be applied if a given country did not take effective action to consider the council notification regarding the speed of correction of its excessive budgetary deficit. Sanctions consisted of a non-interest-bearing deposit combining a fixed element (equal to 0.2% of GDP) and a variable element, equal to one-tenth of the excess over the reference value, with a ceiling for the overall deposit of 0.5% of GDP. As long as the excessive deficit was not corrected, further deposits equal to one-tenth of the excess over the reference value (up to the aforementioned ceiling) would be required. After two years, deposits would be converted into fines.
However, the problem of the stability and growth pact relied on its lack of enforcement rules. After 2003, the deficit and debt rules were frequently broken without associated sanctions for the member states. Besides, the sovereign debt crisis has further contributed to underline the drawbacks of the European governance and, in particular, the lack of enforcement of fiscal rules in order to provide a sane fiscal framework in the EMU. That is why fiscal rules have been recently modified in the EMU.
On 29 September 2010, the European Commission proposed a revision of the stability and growth pact, a set of six legislative proposals aiming at strengthening the European economic governance (see, e.g.: European Commission [ Countries will face sanctions if public spending increases more rapidly than GDP, unless this is compensated by a rise in taxation or if they run a budgetary surplus. “The budgetary position of the general government of a contracting party shall be balanced or in surplus,” that is “at its country-specific medium-term objective Countries running a higher than 60% of GDP public debt ratio will be under an excessive deficit procedure (EDP) if this debt ratio does not fall by 1/20th per year of the gap between the effective debt and the 60% reference value (on average over 3 years). Nevertheless, given that most countries are today in EDP in the European Union and have to comply with agreed fiscal consolidation paths, they are granted a three-year period following the correction of the excessive deficit for meeting the debt rule. Guilty countries (countries with too rapid rises in public spending, countries not cutting their structural deficit, or not complying with the measures associated with an EDP) will have to make a deposit of between 0.2% and 0.5% of GDP, which will possibly be converted into a fine if requested measures are not implemented. Countries are supposed to introduce European rules in their fiscal frameworks (the 3% and 60% limits, the medium-term target of budgetary positions in balance) and to implement a surveillance of these rules by an “independent budgetary institution.” The member states have to introduce in their legislation a “balanced budget rules” limiting the structural budgetary deficit to 0.5% of GDP, as well as automatic correction mechanisms “in the event of significant observed deviations from the medium-term objective or the adjustment path towards it” (article 3(1) (e)). The EU Court of Justice will verify that it complies with European rules. Countries will need a qualified majority at the European Council to oppose sanctions for countries breaching the 3% ceiling or not complying with instructions given by the Commission, this being expected to ensure the automaticity of sanctions (“reverse qualified majority voting”) (article 7).
Therefore, the corrective part of the SGP has been strongly reinforced. Countries must submit each year a stability and convergence program (SCP) and reduce their budgetary deficits according to a schedule proposed by the Commission. Sanctions can now be imposed in case of deviations of the budgetary deficit or the public debt from a targeted value. This legislative package, the so-called “six pack,” is the fiscal part of a new “treaty on stability, coordination, and governance (TSCG),” called the “fiscal compact,” which entered into force on January 1st 2013, after ratification by 12 Euro area countries.
According to the fiscal compact, supranational rules must be introduced in the national constitutional or quasiconstitutional law; the European Court of Justice (ECJ) has the power to verify the enactment and the compliance of national laws with the new “golden rule” introduced in the fiscal compact. Besides, Fabbrini [
The previous section has shown that fiscal rules associated with penalties in case of deviations from targeted values have been successively imposed on the European countries members of the EMU. Indeed, we have mentioned the explicit financial penalties that can be imposed on a given country in the framework of the fiscal compact. But there are also the costs that the markets may inflict as well as the loss of “political credibility” that could be involved. Indeed, sanctions can also consist in the loss of reputation and credibility due to excessive budgetary deficits. This loss of credibility itself can have a financial cost if the financial markets increase the interest rates on the public debt of a given country. Besides, a penalty on the excessive structural budgetary deficit (as mentioned in the fiscal compact) depends on two things. The first one is the possibility to precisely observe the level of the structural deficit and, therefore, to penalize the deviation in comparison with a very uncertain and subjective value. Output gaps are measured with delays and are subject to substantial revisions. The second one is the will of the legislator to effectively impose sanctions on countries which encounter difficulties, because such a decision will be in practice suboptimal, and so the enforceability of the rule can be questioned. In this context, the economic literature underlying the advantages or drawbacks of fiscal rules is very large. Therefore, we will only mention some useful results of this literature for the aim of our paper: analysing the contribution of fiscal rules to a kind of coordination between the budgetary authorities in the EMU.
Firstly, in the framework of the stability and growth pact, fiscal discipline was often blamed for being detrimental to economic stabilization by constraining budgetary policies of countries whose deficits where initially excessively high and by implying procyclical budgetary policies. That is why the stress was progressively put on reaching a structural balance in equilibrium in order to have enough flexibility to stabilize macroeconomic shocks. For example, Artis and Buti [
However, can a uniform and same fiscal rule be efficient for all member countries of a heterogeneous monetary union? As mentioned by Buti et al. [
Regarding monetary policy, Jensen [
Besides, long-term considerations, like the level of the public debt and the risks of population ageing, must also be taken into account. That is why Hughes Hallett [
Then, what should be the characteristics of the “best” and most appropriate fiscal rules, in the framework of a monetary union? Theoretically, complex and state-contingent rules would be the most optimal. Indeed, Beetsma and Jensen [
Indeed, Schuknecht [
Therefore, in the following section, our model aims at defining clear and simple rules that could be optimal in order to incite the decentralized budgetary policies to be closer to the optimal and cooperative budgetary policies. In our model, the fiscal rule would be quite simple, as the member countries of the monetary union would have to pay a fine proportional to the differential between the squared deviation of the structural budgetary deficit or the public debt from their targeted level. However, the optimal fiscal penalties found by our model remain complex, as they depend on the nature of the shocks (symmetric or asymmetric, demand or supply) hitting the member countries of the monetary union, as these penalties are therefore necessarily state-dependent.
In this section, we consider a dynamic open macroeconomic New-Keynesian model, in order to evaluate the optimal weight that should be given to fiscal goals in terms of structural budgetary deficit or of public debt. To this end, we calculate the excess of average welfare loss without budgetary cooperation in comparison with the situation where the budgetary authorities cooperate, in order to estimate the penalties that should be associated with fiscal rules in order to make the decentralized budgetary equilibrium closer to the cooperative and optimal equilibrium. This section defines these optimal fiscal penalties in order to reach a given budgetary or public debt target, whereas the following sections will study the penalties appropriate to stabilize efficiently symmetric or asymmetric demand or supply shocks in a monetary union. All variables are expressed in deviations from their long run equilibrium values. For simplicity, there are only two countries:
We use a stylized dynamic New-Keynesian model, which is broadly consistent with this literature, even if we do not detail here its underlying microeconomic structure (see e.g., Lieb [
With, in period
Traditionally, in New-Keynesian models, aggregate demand is driven by the optimizing behavior of households, which maximizes an intertemporal utility function. Thus, output depends on expected future output, because rational agents can smooth their consumption intertemporally. Variation in demand is also an increasing function of the variation in public expenditure in a given country in comparison with what is expected for the following period
The primary budgetary deficit in the country
The structural primary budgetary deficit depends on structural public expenditure net of structural tax revenues that are realized when the economy is in equilibrium at potential output:
Therefore, by combining (
The linearized supply function for the country
Indeed, in New-Keynesian models, aggregate supply results from the behavior of firms that set prices for their products so as to maximize profits in a monopolistic competition setting. Inflation then depends on expectations about future prices, because of learning effects. Besides, the output gap expresses the demand-pull factor and tensions on the utilization of productive capacities. In this framework, the parameter
Let us suppose that the goal of the common central bank is to preserve price stability in the whole monetary union
Therefore, in the framework of our model, the game between the governments and the common central bank can be summarized by conflicting economic policies in the following way. The higher the average structural budgetary deficit in the monetary union, the higher the common interest rate and the more restrictive the common monetary policy. In the same way, the higher the common interest rate, the more expansionary are the budgetary policies in the member countries of the monetary union. Therefore, the monetary authority fully sterilizes the consequences of anticipated budgetary shocks in order to stabilize prices.
In this context, in the short run, according to (
Therefore, in a given country
Besides, symmetric positive supply shocks decrease prices in the whole monetary union without affecting economic activity levels. On the contrary, an asymmetric supply shock implies expansionary and deflationary (recessionary and inflationary) tensions in the country of the monetary union positively (negatively) affected by the shock.
Quadratic contracts prescribe transfer payments that are constantly related to squared deviations of target variables from respective constant target values. So, we suppose that budgetary policies are endogenous and are the result of the minimization of the following quadratic loss function for each government
If we suppose that the public debt increases with the primary budgetary deficit and with the interest rate charges on this public debt
We suppose that the instrument of the government
Let us suppose that the governments have a fiscal rule only in terms of structural budgetary deficit (
With a goal in terms of public debt (
Indeed, a smaller structural budgetary deficit is necessary in order to decrease the common interest rate on previous public debt levels and to decrease the indebtedness levels of the member countries of the monetary union. Without budgetary cooperation, the budgetary policy is also contractionary in a given country if its indebtedness level was formerly higher than the targeted level. Indeed, according to the values mentioned in Appendix
However, the budgetary policies can then be insufficiently contractionary. Indeed, each budgetary authority is not active enough in reducing its structural budgetary deficit, as it does not take into account the beneficial effect of the reduction in the common interest rate also on the indebtedness level of the foreign country.
So, what are then the optimal penalties on public debt levels in order to lead the governments to conduct the optimal budgetary policies and to imply automatically without cooperation the appropriate reduction in the structural budgetary deficits? According to the differential in welfare loss functions given in Appendix
Therefore, the optimal penalty on the excessive public debt level (
On the contrary, higher taxation rates
Finally, the simple modeling of the current paper only considers the interaction between two member countries of a monetary union. However, we can mention that if the number of countries increases in the monetary union, each country has a weaker influence on the average structural budgetary deficit and on the common interest rate in (
An asymmetric supply shock implies deflationary and expansionary (inflationary and recessionary) tensions in the country positively (negatively) affected by the shock. So, the budgetary policy can only be moderately contractionary (expansionary) in the positively (negatively) affected country in order to stabilize economic activity levels without excessively destabilizing prices and public expenditures. Anyway, if the member countries of the monetary union have a goal in terms of structural budgetary deficit (
The situation is a little bit more complex if the budgetary authorities have a goal in terms of public debt (
Therefore, noncooperative budgetary policies tend to be expansionary on average if the country
In this framework, as the average structural budgetary deficit should be zero in case of asymmetric supply shocks in a cooperative framework, in order to avoid an inefficient budgetary activism, what is the optimal fiscal penalty to impose on excessive public debt levels? According to the values in Appendix
So, as the economic activity target has usually the highest weight for the governments
Furthermore, our results are ambiguous regarding the consequences of a variation in these parameters. Indeed, the optimal penalty on the public debt level is not the same for both member countries of the monetary union. Therefore, the first and smallest root of (
An asymmetric demand shock implies inflationary and expansionary (deflationary and recessionary) tensions in the country positively (negatively) affected by the shock. Therefore, the country positively affected by the shock must conduct a more contractionary budgetary policy, whereas the country negatively affected by the shock must conduct a more expansionary budgetary policy. If the member countries of the monetary union have a goal in terms of structural budgetary deficit (
The situation is a little bit more complex if the budgetary authorities have a goal in terms of public debt (
Therefore, noncooperative budgetary policies tend to be expansionary on average if the country
In this framework, as the average structural budgetary balance should be zero in case of asymmetric demand shocks in a cooperative framework, in order to avoid an inefficient budgetary activism, what is the optimal fiscal penalty to impose on the excessive public debt level? According to the values in Appendix
So, either the public debt levels are identical in the member countries of the monetary union
Furthermore, our results are ambiguous regarding the consequences of a variation in these parameters. Indeed, the optimal penalty on the public debt level is not the same for both member countries of the monetary union. Therefore, the first and smaller root of (
Positive symmetric supply shocks decrease prices without affecting economic activity levels in the monetary union, according to (
However, with a fiscal rule in terms of structural budgetary deficit (
Indeed, specific national economic activity levels do not depend on symmetric supply shocks. Nevertheless, the preference for price stability can lead to conduct expansionary budgetary policies in order to limit the national deflationary tensions due to a positive supply shock, hoping that the foreign country will not act the same way. However, this excessive budgetary activism in a noncooperative framework can be reduced thanks to a penalty on the excessive structural budgetary deficit. Indeed, according to the values given in Appendix
With a goal in terms of public debt (
Nevertheless, in case of symmetric supply shocks, a fiscal penalty on the public debt level (
According to (
However, symmetric demand shocks imply expansionary and inflationary tensions in the member countries of the monetary union. Therefore, the countries can be tempted to conduct active and contractionary budgetary policies in order to compensate for the consequences of the shock. Indeed, according to the value mentioned in Appendix
However, the excessive budgetary activism in a noncooperative framework can be reduced thanks to a penalty on the excessive structural budgetary deficit. Indeed, according to the values given in Appendix
Therefore, the fiscal penalty on the excessive structural budgetary deficit should be as high as possible in order to constrain the excessively contractionary noncooperative budgetary policies and to make them closer to the inactive optimal budgetary policies. Besides, this penalty should increase with the share of public expenditure in GDP (
The situation is a little bit more complex if the member countries of the monetary union have a fiscal rule in terms of public debt (
So, in this framework, noncooperative budgetary policies are not only excessively active but also counterproductive. Indeed, expansionary budgetary policies accentuate the increase in the indebtedness level in case of a negative demand shock, whereas contractionary budgetary policies accentuate the decrease in the indebtedness level in case of a positive symmetric demand shock. However, this excessive budgetary activism in a noncooperative framework can be reduced thanks to a penalty on the excessive public debt level. Indeed, according to the values given in Appendix
According to the precise values of these parameters given in Appendix
Nevertheless, in case of a symmetric demand shock, a fiscal penalty on the public debt level
Monetary unification creates new fiscal externalities, which can justify the introduction of fiscal rules and the attention paid to the respect for budgetary discipline, in the member countries of a monetary union. Besides, beyond traditional arguments mentioned for the introduction of such fiscal rules and penalties in a monetary union, the aim of the current paper is to play a part in the analysis on their potential contribution to a kind of indirect budgetary coordination. Indeed, as formal and explicit coordination between budgetary policies is quite minimal in Europe in the context of the EMU, appropriate fiscal penalties could be a kind of substitute to a formal coordination of budgetary policies, in such a monetary union. Thanks to appropriate fiscal penalties, the noncooperative and decentralized equilibrium could get closer to the optimal and first-best equilibrium where the budgetary authorities cooperate.
In this framework, our dynamic macroeconomic modeling shows that if the governments have a goal in terms of structural budgetary deficit, in “normal times” and without macroeconomic shocks, whatever positive penalty on the deviation of the effective structural budgetary deficit in comparison with its targeted level is optimal. But if the governments have a goal in terms of public debt, this goal cannot be reached automatically by the control variable (variation in the structural budgetary deficit) in a noncooperative framework if the public debt levels were initially distinct between the member countries of the monetary union. Indeed, noncooperative budgetary policies can then be insufficiently contractionary to decrease public debt levels which were initially excessively high. An optimal penalty on the excessive public debt level can then allow to reach the cooperative equilibrium, a penalty which must be an increasing function of the share of public consumption in GDP, of taxation rates and of the differential in indebtedness levels, but a decreasing function of the openness to trade, of price flexibility, and of the strength of automatic stabilizers in the member countries of the monetary union.
Furthermore, in case of symmetric supply shocks, budgetary policies should not react, as they have no consequences on average economic variables. However, a positive symmetric supply shock implies deflationary tensions in all member countries of the monetary union. So, a given country could be tempted to conduct a noncooperative expansionary budgetary policy in order to stabilize prices. In the same way, in case of a positive symmetric demand shock, budgetary policies should not react with a goal in terms of structural budgetary deficit, and they should even be expansionary in order to compensate for the automatic consequences of the shock with a goal in terms of public debt. However, noncooperative budgetary policies are then contractionary in order to compensate for the expansionary and inflationary consequences of the shock, even if such policies are useless if all member countries of the monetary union conduct the same policies. Therefore, in case of symmetric shocks, whatever the fiscal rule, the penalty on the excessive level of one fiscal variable in comparison with its targeted level should be as high as possible in order to constrain the excessively active noncooperative budgetary policies and to make them closer to the inactive optimal budgetary policies. Besides, a fiscal penalty on the public debt level seems more efficient to constrain the budgetary activism in case of symmetric supply shocks and if public debt levels were initially high, whereas a penalty on the structural budgetary deficit seems more efficient in case of symmetric demand shocks. In case of symmetric shocks, fiscal penalties should also always increase with the weight of the public sector in GDP and with taxation rates, whereas they should decrease with openness to trade and automatic stabilizers in the monetary union.
Finally, budgetary policies should be inactive on average and exactly the opposite in the member countries of a monetary union in case of asymmetric demand or supply shocks. This optimal solution is obtained without fiscal penalty with a goal in terms of structural budgetary deficit. However, budgetary activism tends to increase with the differential between the public indebtedness levels of the member countries of the monetary union. In this framework, in case of asymmetric shocks, the optimal equilibrium can be reached thanks to a moderate penalty on the excessive public debt level only if the share of the private sector in GDP, openness to trade, and price flexibility are sufficiently high, whereas on the contrary automatic stabilizers, taxation rates, and indebtedness levels are sufficiently weak in the member countries of the monetary union. In the opposite case, a fiscal penalty on the excessive public debt level could only decrease the budgetary activism, without reaching the optimal and cooperative equilibrium where the average structural budgetary deficit is zero.
So, fiscal penalties on the excessive structural budgetary deficit or on the excessive public debt level are beneficial. They can contribute to reduce an inefficient budgetary activism and to a kind of indirect coordination between the budgetary policies of the member countries of a monetary union. Indeed, budgetary policies are then less active and closer to the optimal cooperative equilibrium. With the values that we propose, there is no longer a problem of credibility and cooperation between the budgetary authorities, as optimal policies can be enforced thanks to fiscal penalties in the framework of decentralized and noncooperative budgetary policies. Nevertheless, optimal fiscal penalties seem quite difficult to define for the governments, as they depend on the nature of the macroeconomic shocks in the framework of our model. Therefore, another trade-off appears between the efficiency of the optimal fiscal rule and its degree of complexity. Perhaps fiscal rules which are less efficient but easier to implement and to enforce would be more beneficial. That is why the fiscal compact has defined a state-independent and simple fiscal contract for the European countries, which is quite easy to implement, even if it is not fully optimal from a theoretical point of view.
By combining (
Solving (
Then, by combining (
On average for the whole monetary union, we have
So, if expected demand and supply shocks equal zero, and if the monetary authority aims at stabilizing average prices in the monetary union
We can replace this value of
Without budgetary cooperation, using (
So, we obtain
Therefore, if we suppose that all shocks and targets are independent, the differential between the noncooperative and cooperative loss functions implies
Consider
The author declares that there is no conflict of interests regarding the publication of this paper.