Models of supranational policymaking and the reform of the EMU*

Luciano Andreozzia, Roberto Tamborinib

Abstract

Under what conditions do sovereign governments agree to create a common policy institution? And what model of supranational policymaking may be preferable? To answer these questions, we introduce a policy game of two interdependent countries with reciprocal negative externalities created by shocks to a socially relevant variable. Depending on national peferences over policy options and their outcomes, both countries incur welfare losses if governments pursue non-cooperative policy choices. Then we examine what kind of supranational policy regimes (SRs) may be endorsed by both governments according to the Pareto criterion. Two SRs are "technocratic" (they do not take national preferences into account), two are "political" (they do). One political regime that we call "union" aggregates the national preferences additively. The thrust of our analysis is that the technocratic regimes are dominated by non-cooperation, so that the single alternative is between the union and non-cooperation. Yet an important point is that the union is the Pareto-dominant regime only within a limited range of asymmetry between countries' preferences. This result has notable implications for the debate on the reform of the European Economic and Monetary Union (EMU) facing the challenge of further integration of member countries.

Keywords: Policy games, design of supranational institutions, European Economic and Monetary UnionJEL Codes: P15, F55, D78

aDepartment of Economics and Management, University of Trento, Via Inama 5, 38100 Trento (Italy), luciano.andreozzi@unitn.it.b Corresponding author. Department of Economics and Management, University of Trento, Via Inama 5, 38100 Trento (Italy), roberto.tamborini@unitn.it.

* We gratefully thank for useful discussions and comments Carlo Bastasin, Federico Boffa, Marcello Messori, Sergio Fabbrini, Klaudijo Klaser, Lorenzo Sacconi, Gianni Toniolo, Crina Vinju. R. Tamborini also acknowledges support from the School of European Political Economy of the LUISS 'Guido Carli' University of Rome.

1. Introduction

It is a well-established principle that interdependent countries may enjoy various benefits from the creation of common policy institutions. Benefits accrue first and foremost in terms of "internalisation of externalities", provision of public goods, economies of scale (e.g. Alesina et al. 1995, 2005, 2017, Alesina and Spolaore 1997, Spolaore 2015). Yet countries also face costs represented by some limitations imposed on the pursuit of national preferences (in the broad sense of interests, cultural traits and national identity) concerning policy choices and their outcomes. These costs increase when preferences are heterogeneous across the countries. This may explain why creating supranational policy institutions is more praised than practised. Under what conditions do sovereign governments agree to create a common policy institution? And what model of supranational policymaking may be preferable?

These are the questions that we wish to address in this paper. Beside their own intrinsic interest for the design of policy institutions on international scale, today these question are also central in the life of one of the most important supranational realisations exitsing in the world, the European Economic and Monetary Union (EMU), a historical unicum for many aspects. EMU members, in addition to the various forms and levels of institutions of the EU, also share a more advanced layer of supranational policymaking, namely monetary policy entrusted to the European Central Bank (ECB), combined with a set of rules that limit fiscal sovereignty.

As a result of the dramatic "Europeanisation" of the global crisis exploded in 2008, the consensus view has emerged according to which the EMU needs deep reform of its architecture aimed at fostering further integration, which means enlarging the existing layer of supranational policymaking (e.g. Baldwin and Giavazzi (eds.) 2015, 2016. A direct institution-design approach has also been advocated (Campos and Sturm 2018). These claims have been endorsed by the top European institutions.* Granted that the direction and extent of reforms (if any) will eventually be

* See the so-called "Five Presidents Report" (Juncker et al. 2015), the White Paper about the future of the EU (2016) and the Reflection Paper on the Deepening of the Economic and Monetary Union (2017) both under the authorship of the European Commission, and speeches of the President of the European Central Bank (e.g. Draghi 2014a, 2014b, 2015).

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a political decision reflecting some balance of interests and power across governments, the results of our study may provide a normative guide to reform, i.e. to shed further light on what kind of supranational policymaking architecture may possibly be endorsed by democratic governments on behalf of their citizens.†

After discussing the relevant strands of literature in section 2, in section 3 we introduce a two-country policy-game in the tradition of Hamada (1976), largely employed in the international political economy as well as in the EMU literature (see e.g., respectively, the surveys by Ghosh and Ostry 2013, and Beetsma and Giuliodori 2010). In line with the first principles mentioned above, the focus is on interdependence, negative (non-pecuniary) externalities, and heterogeneous preferences across countries as determinants of governments' choices.‡

Our model is highly stylised in order to encompass possibly different policy fields (not necessarily economic ones) and models of supranational policymaking. Each of the two countries (i = 1, 2) is characterised by a socially relevant variable and a policy instrument. The former can be hit by shocks ui that displace it from the bliss point by the amount yi. Interdependence consists of each country's yi depending on the other's. Activation of the policy instrument xi can offset these shocks – this we call "good policy".§ This policy may be "whatever works"; we do not discuss policies per se: we just assume that one exists with no more efficient alternative. A particular value of it (xi*) can yield full protection against shocks, i.e. y(ui, xi*) = 0. Suppose for example yi measures changes in employment, and ui < 0: then xi > 0 can counteract the fall in employment, let it be a labour market reform that increases wage flexibility as well as more public investment. If the shock is say to labour force, xi may be some immigrant share, etc.

† "Which institutions and agencies are needed? In our view, not even asking the question, 'Which institutions should be redesigned or even created from scratch to carry our reform in Europe?' goes a long way towards explaining why reforms have not been implemented" (Campos and Sturm 2018, p. 1)‡ A well-known caveat is that not all externalities (e.g. pecuniary ones in Walrasian markets) necessarily imply the existence of Pareto superior allocations nor are externalities sufficiently important or certain in all possible fields so as to justify policy coordination or cooperation (see Korinek 2016 for a recent treatment).§ Interdependence can also be modelled by means of direct spillover effects of the policy instrument. This choice may be appropriate in further specific cases; it modifies the algebra but not the essence of the problem under examination.

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The key assumption is that any amount xi also bears a collateral welfare loss according to national preferences, let it be a "degree of policy aversion".** Therefore, each government seeks its own optimal trade-off between a limited use of xi and the consequent loss yi by minimising a standard quadratic loss function defined over yi and xi.

We first establish the welfare losses associated with independent, non-cooperative (NC) policy choices, which are characterised by less than full shock protection in both countries, and hence reciprocal negative externalities. These arise not because of interdependence per se but because of the cost of the "good policy". In general, Pareto improvements over the NC regime are possible by means of devices that coordinate the two governments on a larger use of xi and smaller change yi.

In section 4 we examine what kind of supranational policy regime (SR) may be endorsed by both governments according to the Pareto criterion vis-à-vis the NC regime. This criterion is particularly relevant in contexts, such as the EMU, where institutional arrangements, or their modifications, should be voted by member countries: only Pareto-improving solutions can obtain unanimity. This may help clarify the direction where EMU reforms should be, or should not be, headed to.

By SR we mean a system consisting of the two countries and a supranational entity variably entitled to enact a policy assignment (xi) for each country according to an objective defined in its entitlement. We compare four different models chosen among the main instances that can be found in the literature (see section 2). Two SRs are "technocratic" (they do not take national preferences into account, as represented in the governments' loss functions), and two are "political" (they do). Among the latter, one that we call "union" operates with the additive loss function of the two countries.

The thrust of our analysis is twofold. First, the governments' choice is sensitive to the model of SR that is proposed. Second, the technocratic SRs are systematically dominated by the NC regime and the union, while the union emerges as the single alternative to the NC regime. In line with the literature recalled above, however, the union dominates the NC regime only within a limited range of asymmetry between countries' national preferences (the degree of policy aversion).

** It would be naive to think that costless policies exist. Any policy choice has costly side effects that should be taken into account by the government.

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Section 5 summarises and concludes with some implications for the EMU reform. Our analysis lends support to the view that fostering supranational policymaking by means of technocratic, "non politicised", agencies may be unsuccessful. National preferences and their legitimate representatives cannot be muted in the policymaking process, though their being too dissonant may pose serious challenges to the design of the best supranational policy institution.

2. Reference to the relevant literature

The general background of our work is the political-economy literature on the creation of supranational institutions among sovereign states. This literature has established a few general principles in terms of cost and benefit analysis (e.g. Alesina et al. 1995, 2005, 2017, Alesina and Spolaore 1997, Spolaore 2015). Both costs and benefits are usually evaluated by national governments in consideration of national preferences (in the broad sense of interests, cultural traits and national identity) over policy choices and their outcomes. Agreements may lead to a full-fledged federation or be limited to the creation of some specific common policy institutions. The latter is the case of our interest.

This literature presents both positive and normative aims. On the one hand, the aim is to explain the birth, or death, of existing supranational institutions. On the other hand, the aim we also pursue here is to provide insights and guidelines for the creation of viable common policy institutions. Viable means, essentially, that benefits exceed costs for each and all partners. The typical analytical tool is Pareto-improving equilibria with respect to some alternative, let it be the status quo or an "outside" option.

A well-established principle is that interdependent countries may enjoy various benefits from creating common policy institutions, first and foremost in terms of "internalisation of externalities", provision of public goods, economies of scale. Yet they also face costs represented by some limitations imposed on the pursuit of national preferences. Generally, the crucial factors that affect the cost-benefit balance are three: the degree of interdependence across the member countries, the heterogeneity of their

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preferences, the extent and/or frequency of asymmetric shocks affecting their welfare.

For instance, the classic treatment of monetary unions provided by the "Optimum Currency Area" approach (Mundell 1961) focuses almost exclusively on the third factor. This is also the case with the bulk of the literature (positive and normative) on the creation of the EMU, when concern about its capacity to absorb asymmetric shocks was predominant and prompted constant empirical monitoring (e.g. Buti and Sapir 1989). In our study we concentrate on the other two factors mentioned above. One reason is that these factors have drawn less attention in the EMU literature, though, as our model will show, their interplay may generate welfare losses even with symmetric shocks. Another reason is that the importance of asymmetric shocks in the EMU largely remains an unsettled empirical issue (Franks et al. 2018). As a matter of fact, after almost ten years of overall stability, the European crisis was ignited by an EMU-wide shock.

Alesina et al. (2017) have provided up-to-date evidence of increased convergence and interdependence brought about by EMU membership. Interdependencies and policy spillovers in various fields (from fiscal to structural to sectoral policies) have emerged as a critical neglected factor: see e.g. in't Veld (2013), Berti et al. (2013), European Commission (2014), Alcidi et al. (2015). During the crisis, divergences (economic as well as political) in the EMU have also originated from countries' different attitudes towards policy options (Blyth 2013, Bastasin 2015, Brunnermeier et al. 2016). This is consistent with the idea that the costs of common policy institutions increase when social preferences are heterogeneous across the members of a union. As stressed by Alesina et al. (2017), this seems a major hurdle for further sharing of policy institutions in Europe despite ever increasing integration of member countries under various socio-economic dimensions.

For obvious reasons, the earlier EMU literature focused on a single model of supranational policy institution, namely a common central bank vis-à-vis national fiscal sovereigns. The main issues were two: the absorption of asymmetric shocks, and the best design of the system in order for the ECB to fulfil the single mandate of price stability. Here we have a different aim: how a supranational policy institution should be designed in order to achieve Pareto-improving policy choices with respect

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to the option of NC national policy choices. This is a more general problem, of which monetary policy is an instance.

The articulation of supranational policymaking in different models is stressed by Scharpf (2001). Our categorisation of "technocratic" vs. "political" models is similar to his, in that he also distinguishes between models where supranational actors exercise their functions without the participation of member-state governments and those where the latter exert their political prerogatives in the policymaking process. Clearly, the difference is the extent to which the policy outcomes may be closer to national interests and preferences.††

With our categorisation we also intersect the literature on the assignment of policymaking to politicians or independent agencies (e.g. Wilson 1989, Besley and Coate 2003, Alesina and Tabellini 2007). With this literature our model shares the point that the assignment is driven by welfare optimisation. Two are the main differences. The first is the supranational setup, such that the agency faces two independent sovereigns, with possibly different welfare objectives. The second is that the key issue is how the mandate of the agency fares with respect to the sovereigns' welfare objectives. In our model the government(s) and the agency execute their respective policy tasks perfectly, whereas the literature is more concerned with different ability, incentives, motivations of the politician and the agency in pursuing the same given task.

The distinction between "technocratic" and "political" models is also tangible in the debate on the EMU reform (e.g. Delatte et al. 2017). One view (also known as "Maastrich 2.0") moves from the premise that the EMU regulatory framework has proved to be too weak, unable to constrain elected policymakers properly. The typical symptoms are seen in the persistence of the deficit bias in fiscal policy, public debt growth, transmission of public finance distress. Therefore, reforms should deepen and strengthen the original rule-based conception of the EMU embedded in the Treaties. Further fiscal sovereignty devolution is preferably towards independent, non-political agencies as guardians of the rules. Another view (the so-called "US –or better, confederal− model") is critical of a number of flaws that are present in the original regulatory framework and have played a role in the mismanagement of the crisis. As a consequence, the concerns with the democratic deficit of Europe have widened in a crisis †† Notably, Scharpf sees all models at work under the same supranational structure of the European Union.

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of both "input" and "output" legitimacy. In this view, the confederal inspiration should be understood in a broad sense, meaning that the aim is the creation of bits of genuine supranational government (not just governance) with clear institutional legitimacy with respect to both the EU order and the national constitutional orders.

The formalisation of governments' interplay in our model can be viewed as a "shortcut" consistent with the so-called "two level games" introduced by Putnam (1988) in the international relations literature. The first level of the game establishes the menu of choices of the government or of the negotiator vis-à-vis its domestic constituency. The second level of the game is played by each government vis-à-vis the other. The first-level game is examined by a vast specialised literature (see e.g. Boffa et al. 2016 for a recent contribution relevant to the choice between centralised vs. decentralized government). In our setup the result of the first-level game is embedded into the loss function of each government. Our focus on the heterogeneity of national preferences (the degree of aversion towards the "good policy" x) brings to the forefront as a structural factor that each country may be characterised by different majoritarian constituencies. The other assumption that the government faithfully acts according to loss minimisation also embeds, though implicitly, the notion that politicians may also pursue their own interest in being re-elected.

Our governments can always opt for NC policy choices, achieving Nash equilibria. This is generally seen as the status quo ante option. As to application to the EMU, it may be observed that the EMU members already accept some limitations to their policy sovereignty so that pure NC policies are not an option to them until they remain. Actually, one of the motivations for reform is that the EMU failed on this ground, so that members have proved able to pursue independent policies in many ways while remaining formally within the EMU.‡‡

3. The non-cooperative policy regime

To begin with, we deploy a simple policy-game model of two sovereign countries (i = 1, 2) tied by interdependence. For convenience, and without

‡‡ According to Scharpf (2001), NC policy choices, that he calls "mutual adjustment", are "the default mode of Europeanized policy responses to increasing interdependence" (p. 7). Feldstein (2013) draws a critical balance of the EMU in the same vein.

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loss of generality, let yi be the change in a socially relevant variable with respect to a desired level (which may well be zero), determined as follows(1) yi = aixi + bi yj + uiwhere the coefficient ai measures the effect of the policy instrument xi, bi the cross-country interdependence, and ui is an exogenous shock. The signs of ai and bi allow the model to be applied to a number of specific cases. Here we shall consider the case where (ai, bi) > 0, but different cases do not modify the essence of the model.

We introduce the notion of xi as "good policy" in that it can counteract any shock to yi. We do not discuss policies per se: we just assume that one exists with no more efficient (higher ai) alternative. Hence, to simplify the algebra, we assume that the most efficient policy in both countries has coefficient ai,j = 1. Though convenient for expository purposes, it is not necessary for xi to be the same for both governments.

After a shock, the effects on yi in each country are(2) yi = (ui + xi + bi(uj + xj))k k = (1

bibj)-1

with a crucial role played by interdependence. In fact, bi ≠ 0 implies that each country's yi also depends on the foreign shock and policy response, in addition to the domestic ones. Moreover, the common "multiplier" k, which measures the extent of the reciprocal spillovers, is larger the larger the coefficients bi,j. The standard condition bibj < 1 is assumed.

Note that there exists a pair (x1*, x2*) such that (y1, y2) = 0 for any (u1, u2). The solution, that we call "full protection", is(3) x1* = u1, x2* = u2with the following important features: each government activates xi only if, and to the extent that, its own country is hit by the shock if both governments choose their respective xi*, each is set independently of the other (no externality effect to be taken into account).

What is the problem then? We now introduce the assumption that the two governments faithfully reflect national preferences, which include protection of yi from shocks but also a cost in the use of policy xi.§§ This generates a trade-off between protecting yi and activating xi. Accordingly, governments, which faithfully reflect national preferences, decide their

§§ Since xi* is the policy choice that yields full protection against yi 0, but it has a cost, there is an analogy with the choice of insurance coverage.

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policy by minimising the following quadratic loss function (in absolute value):(4) Li = 0.5(y2

i + cix2i)

This posits that the country's welfare loss increases with yi 0, and xi 0, if ci > 0, where ci measures the loss due to xi 0 relative to the loss due to yi 0 (i.e. the latter is normalised to 1). Let us call ci the degree of policy aversion of the country.

Upon minimisation of its loss function, each government decides its optimal activation of xi, given by:(5) xi

c = (ui + bi(uj + xcj))i, i = (1 +

ci/k2)1where xi

c denotes the c-constrained choice of xi. Equation (5) is the reaction function of the government, which includes

the domestic shock, the foreign shock and the other government's choice of xj. The key factor in the reaction function is i, which depends on the degree of policy aversion ci and of interdependence k. Note that i decreases with ci (i.e. the more costly is xi, the less it is used), and it increases with k (i.e. the stronger the interdependence, the more the governments should use xi). This latter feature sheds light on one reason why governments dislike interdependence: it forces them to adopt costly policies more intensively. However, the problem is not interdependence per se, but the cost of policies: if ci,j = 0, then i,j = 1, the unconstrained solutions xi,j* would be feasible, and governments could safely ignore interdependence.

Another important result is that, with (ai, bi) > 0, xic in one country is

decreasing with respect to xjc in the other, i.e. they are substitutes. This is

indicative of where an "interdependence war" may originate (Bastasin 2015). In fact, the higher is ci (the lower xi

c) for one government, the more the other government should use its own xj. Conversely, each government would like a more intensive use of x by the other.

We can now move to the solutions to the policy game. We regard the resulting equilibrium as the reservation option for each government such that no other arrangement is feasible if inferior to this. For convenience we shall only report the reduced-form solutions; the full algebra is in an appendix available on request.

The simultaneous solution of the equations (5) of each government yields the NC (Nash) policy equilibrium, which we denote with (xN1, xN2):

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(6) x1N= −11u1 − 12u2 x2N = −21u1 − 22u2

where the parameters are combinations of (b1,2, c1,2), with positive sign. The NC policy regime entails the following effects on y in each country

(7) y1N = 11u1 + 12u2 y2N = 21u1 + 22u2

where the parameters are combinations of (b1,2, c1,2), with positive sign. Therefore, each country is less than protected from both domestic and foreign shocks. Note that all in each country increase with c1 and c2, i.e. the higher the cost of xi for both governments, the greater the exposure of each country's yi to domestic and foreign shocks.

If on the one hand the outcomes (7) for each country represent the optimal trade-off against the cost of using xi, the exposure of yi to foreign shocks may be another seed of interdependence war. For instance, after inspecting 12, government 1 might note that if c2 = 0, then 12 = 0, and hence claim that its country is being hurt by the unwillingness of the foreign government to make full use of the "good policy". Government 2 may claim likewise. The point is that each also depends on the domestic ci being nonzero. Hence an equally valid claim is that each government exposes its country to shocks because it is unwilling to make full use of the "good policy".

Finally, the welfare losses for the two countries are given by(8) L1N= 11u21 + 12u22 + 13u1u2

L2N = 21u21 + 22u22 + 23u1u2where the parameters are combinations of (b1,2, c1,2) with positive sign. Again, welfare losses are proportional to domestic as well as foreign shocks. Each country may claim that it would be betteroff if the other made full use of the "good policy", whereas both would be better-off if both made full use of it. The paradox is that interdependence becomes a matter of conflict because "good policies" are costly, not the other way round.

3.1 Full symmetryIt is worth emphasising that the key result of the NC regime, the welfare

losses generated by "good-policy" aversion, does not depend on asymmetries across countries. Identical countries undergoing symmetric shocks would simply generate the same (xN, yN) pair and equal results.

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A numerical example may be useful also for further uses. Let us assume the following common parameters (country indexes are dropped) b = 0.25, u = 1, c = 1.*** The two governments' reaction functions are:

x1c = 0.66 0.13x2c, x2c = 0.66 0.13x1c

These are the straight lines in Figure 1. The curves are the iso-loss levels traced by the two optimal policy responses to a given shock: two points on the same curve correspond to the same loss. The symmetric equilibrium values are therefore

xN = 0.59, yN = 0.55, LN = 0.323For each government, in the space (x, y) of Figure 2, xN lies at the

tangency between the target function (2) and the loss function (4).[Figure 1][Figure 2]

The degrees of interdependence and policy aversion play a critical role since it can be shown that, for both countries, LN/b > 0, LN/c > 0, i.e. the welfare loss increases with both b and c.

3.2 AsymmetriesDifferences among countries are however a major issue when

supranational policy institutions are to be created. As discussed in section 2, much of the EMU literature is concerned with asymmetric shocks; yet structural asymmetries, and in particular in national preferences, are more relevant in our context.

As to the role of the degree of interdependence, let one country be more dependent than the other, i.e. with a greater bi. Then it can be shown that, in the normal range bi,j [0, 1], Li

N/bi > LjN/bi > 0: welfare

*** This is a purely fictitious example for expository purposes. However, since we shall pay particular attention to the role of interdependence, we have chosen the value of parameter b with a view to the empirical literature on cross-border spillovers in the EMU. These studies are mostly macroeconomic in nature, but they may nonetheless be useful to indicate an order of magnitude of these phenomena. We have drawn the value of 0.25 from in't Veld (2013), who, by means of a simulated multi-country model of the EMU, quantifies the spillovers of a fiscal shock in one country on all the others. 0.25 is exactly the medium-run (three years) spillover effect of a fiscal shock in Germany onto the rest of the EMU, measured as the ratio of the change in the EMU's GDP relative to Germany's. The reverse effect is slightly lower (0.2). Smaller, but of the same order of magnitude, are also the spillovers across the largest members (Germany, France, Italy). The main sources of asymmetry are the dimension of the country and its degree of openness. Alcidi et al. (2015) provide a survey of the (controversial) evidence of fiscal spillovers in the EMU.

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losses increase in both countries, but more so in the more dependent country. Now let ci be larger in one country than in the other. Then, cet. par., Li

N/ci > LjN/ci > 0 welfare losses are increased in both countries, again

more so in the more policy averse one.Overall, asymmetries in interdependence or policy aversion exacerbate

negative externalities and worsens the policy trade-off for both countries, though more intensively so for the country with greater interdependence or policy aversion

4 Exploring supranational regimes

4.1 Preliminary considerationsThe next step in our analysis is to address this question: can

governments agree on a better choice of policies? "Better" here means the Pareto criterion according to which a different combination of xi and yi makes at least one country better-off and no one worse-off.

This notion can be formalised in the diagram à la Edgeworth in the (x1, x2) space of Figure 1 which portrays the numerical example of fully symmetric countries of section 3. The NC equilibrium N (x1N, x2N) is Pareto dominated by all combinations of x1 and x2 that belong to the north-east grey "lens". For all these combinations belong to iso-loss curves corresponding to smaller losses for both 1 and 2. The set of Pareto undominated combinations is the set of points in which the iso-loss curves are tangent. These are the points that belong to the hyperbolic curve, or contract curve. The part of the curve that passes through the grey area is the core of this system, that is, the set of Pareto efficient combinations that are also Pareto improvements over the NC equilibrium.

If the game is repeated, with no transaction costs or other "frictions", the folk-theorem ensures that all the points in the core can be achieved as subgame perfect equilibria (Mailath and Samuelson 2015). Note that in this area no government will ever choose xi* but both governments are willing to use xi more intensively so that they get closer to xi*. However, which policy combinations would result is not determined a priori.

As is well known, a solution can be provided by the Nash Bargaining mechanism, which minimises the joint loss function(9) LNB = (L1NB − L1N)(L2NB – L2N)where Li

NB = L(xiNB, yi

NB). In our full symmetric case, the result is

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xNB = 0.64, yNB = 0.48, LNB = 0.318For our purposes this result, i.e. the existence of the Pareto-optimal

bargaining solution, can be interpreted normatively as well as positively. Normatively, this solution is the benchmark against which any other

arrangement should be assessed. For instance, a supranational institution to which governments entrust policymaking, in order to be viable, should enact a policy assignment not inferior to the one resulting from (9).

Positively, one may wonder why supranational institutions exist, or resist, instead of direct bargaining between sovereign governments. The literature explaining the existence of supranational institutions focuses on the ability of these regimes to overcome a number of notorious obstacles that may prevent the success of direct bargaining.††† First, the operational implementation of the game repetition in the folk-theorem sense requires a set of conditions (from no transaction costs to "memory", from "patience" to consistency) that may easily be violated in international relations with changing governments over time. Second, once the agreement is reached, the problem of compliance arises, so that further specific conditions should be met in order for governments not to breach the agreement, and these may be part of the preroegative of the supranational insititution. We do not probe into these questions here, and directly move to the comparative analysis of different moldels of SRs vis-à-vis the option of the NC regime.

In our model, a SR is a system consisting of two countries and a supranational policy institution (variably) entitled to enact a policy assignment (x1, x2) for each country according to an objective defined in its entitlement. We will examine four SRs: two are "technocratic" (decentralised and centralised) where the policy institution does not take national preferences (as represented in the governments' loss functions) into account, and two are "political" (hegemonic, and union) where national preferences are taken into account. Regime ranking will be organised according to the Pareto criterion: in order to be endorsed by governments' voluntary and unanimous agreement, a regime R should satisfy LR

i < LRi', for all i and any other option R'.

4.2 Technocratic regimes. Decentralised

†††Romp 1997, chs. 8-10, provides a game-theoretic survey. Bayoumi (2014), and Ostry and Ghosh (2013) discuss these issues in historical perspective.

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To begin with, we examine technocratic regimes. In a technocratic regime (TR), each government is asked to confer upon a supranational technocratic agency (TA) the entitlement to enforce a policy assignment (x1, x2) for each country consistently with its mandate concerning the policy objective about the variables (y1, y2).

Such an agency is technocratic in two respects. First, it operates independently of governments and their preferences, though it has to comply with its own mandate.‡‡‡ Hence we formalise the TA by endowing it with its own objective function including all the variables (xi, yi), and with its mandate that defines the specific form of the objective function. Specifically, the TA is given the "single mandate" of minimising the deviations yi, which implies the choice of unconditional policy assignments. Consequently, since the structure of the economies is given and known, the difference between the TA and the governments as policymaker is that the TA operates as with zero policy aversion. This may appear a rather extreme version of independence; however, it helps emphasise the role of the TA as the supranational institution committed to overcoming the reciprocal negative externalities generated by policy aversion. We shall consider two types of TRs: the first is decentralised, the second is centralised.

We begin with the decentralised TR, where the TA exerts the powers defined above in the form of policy prescriptions, while policy implementation remains responsibility of each government. More specifically, the TA is endowed with the power to prescribe the policy response of each government conditional on the observed shock, to monitor its implementation, and eventually to sanction non compliance.§§§ We now examine how the decentralised TR fares with respect to the NC one, and we shall demonstrate that it is always dominated.

Under the above assumptions, the TA solves the policy assignment problem with target (y1 = y2 = 0) choosing (x1*, x2*). In order to assess this regime, it should first be noted that no government ever prefers (x1*,

‡‡‡ Natural reference here is the literature on independent central banking. For simplicity we also assume that our TA certainly pursues its mandate faithfully so that we ignore the problem of incentive schemes for the TA.§§§ The EMU provides an example with its fiscal regulatory framework and the role of the European Commission therein. An open issue in the debate about the reform is whether this model should be maintained, perhaps reinforced and extended to other fields, or whether it should be replaced (e.g. Delatte et al. 2017, Asatryan et al. 2018).

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x2*) to the NC equilibrium (xN1, xN2). In fact, consider the optimal response function (5) of government 1, and suppose it believes that government 2 will comply with the TA's prescription, i.e. x2* = −u2. Then, the optimal response of 2 is x1

c = u11 < x1* which makes x2* suboptimal. Knowing this, no government will ever comply. Any different ex ante commitment by governments has no value ex post.

The best the TA can do is to sanction non-compliance with xi*. A way to introduce this sanction is to extend the governments' loss function with the additional cost p(xi xi*)2, where p denotes the penalty rate applied to xi ≠ xi*. The penalty rate should be equal for all countries. Therefore,

(10) LiTD = 0.5(y2

i + cix2i + p(xi x*i)2)

Now the government perceives a loss when activating xi but also a loss to the extent that xi ≠ xi*. The new optimal choice of xi for each government is therefore

(11) xic = p'i xi* (ui + bi(uj + xc

j))"i 'i = (k2 + (c i + p))1 , "i (1+ (c i + p)/k2)1

It can be seen that the penalty p is a double-edge sword. On the one hand, it induces the government to get closer to xi*; on the other, it makes the "good policy" more costly and hence pushes in the opposite direction ('i and "i are both decreasing in p). The difference xi

c xi* proves to be decreasing in p. However, there is no finite value of p such that xi

c = xi*.

Regime rankingTo examine the regime ranking it is convenient to gauge the differential

loss with respect to the NC regime. In this case, LNi – Li

TD : government i prefers TD iff Li

N – LiTD > 0, where Li

N = L(yiN, xi

N) is given by (8) and LiTD=

L(yiTD, xi

TD) is the solution of (10). It can be shown that this regime is inferior to the NC one for any penalty rate p > 0.

Note first that LiTD depends on p. The overall effect with respect to Li

N

results from the composition of lower yi, higher xi and p(xi xi*). In general, Li

TD/p > 0. Since LiTD = LN

i for p = 0, it follows that increasing the penalty increases the differential loss monotonically, i.e. Li

TD > LiN for

any p > 0. Hence, this regime embeds a critical trade-off on the dimension of the

penalty. On the one hand, the TA may wish to set a large penalty in order to push the governments towards full compliance, but a large penalty generates large losses that jeopardise compliance. The other side of the

16

coin is that keeping the penalty sufficiently small of course does not generate a major improvement with respect to the NC equilibrium.

In conclusion, this regime is dominated by the NC one. Governments would prefer paying the penalty to full compliance, and sanctioning non compliance per se cannot be seen as the failsafe way to enforce the adoption of the "good policy" on a decentralised basis.****

4.3 Technocratic regimes. CentralisedIn the centralised TR, each government devolves its sovereignty to the

TA, which is now endowed with the power to enact policy directly on behalf of the entire entity represented by the countries together. By analogy with the decentralised TR, also the central TA has a single mandate and hence operates as with zero policy aversion.††††

This regime may at first glance appear superior to the previous one since the TA has the power to enact the unconditional policy assignment in each country. However, on closer inspection this is too hasty a conclusion.

In the first place, we already know for sure that that no government prefers the policy assignment (x*1, x*2) to the NC one (x1N, x2N). The argument that the central TA, having the power to implement (x*1, x*2), will overcome non-cooperative behaviour by national governments and will deliver full protection for both countries, does not take into account that this result may not be optimal vis-à-vis the (excessive) activation of policy xi according to the national preferences.

In the second place, the ability of the TA to implement the policy assignment on a differentiated basis may encounter non-trivial problems. One is that the TA may not have the right tools to do this task. It would need detailed information on the structure of each economy and their **** The self-defeating effect of penalties on compliance is a well-known paradox first reported by Gneezy and Rustichini (2000). This result may also explain why, according to some studies, the penalty-based EMU fiscal rules have been less binding than expected (Schuknecht et al. 2011, Wyplosz 2013). On the other hand, the model predicts that increasing the penalties is not the right response. Whether in practice governments' non-compliance with commitments, rules, etc. is as systematic as it should be theoretically is an open question. For the evidence about compliance and non-compliancei n the EU in general see e.g. Börzel T. A. (2001) and Beache D. (2006).†††† An instance here may be the ECB, with its single mandate for price stability (where y refers to inflation) or an interpretation of the "European Minister of Economy and Finance" envisaged by the Commission (EC 2017) as an independent non-political agency (see Asatryan et al. 2018 for a discussion).

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interactions. Moreover, this information ought to be common knowledge in order to avoid complaints about the fairness of the TA. It is quite likely that these obstacles would be hard to overcome. Therefore, we further characterise this regime as one where the TA operates with reference to the aggregate variables (X, Y), and its policy is enacted equally in all countries.‡‡‡‡

Accordingly, let X be the centralised policy variable, and Y y1 + y2 the aggregate target variable. The structural relationship between Y and X at the aggregate level results to be :

(12) Y = (AX+ U)kwhere A 2 + b1 + b2, U u1(1 + b2) +u2(1 + b1).§§§§

For any aggregate shock U, the unconditional policy response of the TA, such that Y = 0, is

(13) X* = U/A.Note that, as expected, X* internalises the externalities due to interdependence.

Regime rankingThe differential loss of this regime for each country is now LN

i – LiTC,

where LiTC = L(yi

TC, X*). We can show that by no means is this regime Pareto-improving with respect to the NC regime.

In the first place, the centralised policy X* activated in each country achieves the target Y = 0, but it generally does not ensure that all yi = 0. In fact:

(14) yiTC = (ui uj)A1

The resulting yi in each country depends on the distribution of shocks, with the two countries displaying opposite effects that sum up to zero. It certainly happens that in one country the shock is under-adjusted and in ‡‡‡‡ The experience of the ECB is quite telling in this respect. By statute, the ECB is not allowed to pursue ad hoc policies on a national basis. Its Asset Purchase Programme launched in 2015, the socalled "quantitative easing", where the country distribution of purchases is crucial, has been carefully designed in order to overcome objections on this ground with the consequence of weakening its chances of success (Saraceno and Tamborini 2015). Indeed, according to other interpretations of the "European Minister of Economy and Finance", its role concerns control over the aggregate fiscal stance of the EMU consistently with the monetary policy stance (e.g. Draghi 2014a, Asatryan et al. 2018).§§§§ Assuming that the TA knows the correct aggregate equation of Y (e.g. by means of correct estimation of the aggregate variables) does not imply that it also possesses full information about the underlying structural parameters of each country.

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the other is over-adjusted. Therefore, full protection for each country (Y = yi

TC = 0) is possible only under symmetric shocks. This is nothing but the well-known "one-size-doesn't-fit-all" problem.

In general, this problem implies for the country with larger shock, say |ui| > |uj|, that|X*| > |xi*| and yi

TC 0.***** Hence this regime is certainly inferior to the NC one for this country. In fact, recall that L(yi

N, xiN) < L(0,

xi*) which certainly implies L(0, xi*) < L(yiTC, X*) because this country

faces both a larger policy effort than xi* and less than full protection. By transitivity, L(yi

N, xiN) < L(yi

TC, X*). Hence for at least one government the centralised TR is inferior to the NC one.

Let us consider the most favourable case with symmetric shock (u). Then X* = u, Y = yi

TC = 0, and the welfare loss for each government is:(15) Li

TC = 0.5ciu2

Note that X* = −u is now the same individual policy choice xi* that would yield yi = 0 with zero policy aversion. Yet this policy choice is still dominated by the NC one for both governments for any ci > 0.

It is also interesting to investigate the role of differences in policy aversion. Without loss of generality, we can set c2 = 1 as standard value, and let c1 vary as a dimensionless variable (c1 = 2 means that the policy aversion of country 1 is twice that of country 2 etc.).

For both governments the differential loss changes with the level of c1. From previous results we know that L1N/c1 > L2N/c1 > 0, L1TC/c1 > 0, L2TC/c1 = 0. Therefore, the regime ranking for government 1 depends on the different effect of its own higher policy aversion on the losses in each regime; the regime ranking for government 2 only depends on the negative externality exerted by the other country's policy aversion in the NC regime. Hence we may expect that the lower policy-aversion government prefers the centralised TR in order to bridle the other. However, this preference is not unconditional.

In the first place, the effect of increasing c1 on the differential losses of the two governments also depends on interdependence. In fact, we know that, in the NC regime, Li

N/bi > 0 (whilst LiTC/bi = 0). The implication

is that, cet. par., higher interdependence tilts the differential loss in favour of the centralised TR. Let us consider the case of equal b. The result for government 2 is, indeed, that in the domain c1 [1, ], b [0, 1], there exists a threshold level beyond which L2N − L2TC > 0. This threshold is ***** Compare (13) with (3), xi* = −ui

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lower, the higher is c1. Therefore, it is confirmed that the lower policy-aversion government prefers the centralised TR when the other government's policy aversion or the degree of interdependence are sufficiently high. The point is that no such a threshold exists for government 1: L1N – L1TC < 0 for any c1 [1, ], b [0, 1]. Hence no agreement is possible on the centralised TR.

This result is exemplified in Figure 3, which displays the relationship between the two differential losses and c1, for the "normal" value of b = 0.25 (panel (a)) and "very high" b = 0.5 (panel (b)). Note that the NC dominates even if the two countries are fully symmetric (c1 = 1).

[Figure 3]Therefore, our conclusion is that the centralised TR may be effective in

protecting the socially relevant variable at the aggregate level. It also shields each country against the (larger) welfare losses due to (greater) interdependence, but it is unlikely to be preferred to the NC regime by both countries even in the case of full protection at the country level.

4.4 Political Regimes. Hegemony

Having highlighted the limits that the pure TRs may encounter, we now move to "political" regimes, i.e. regimes where a supranational policy authority (PA) is created which in some way embeds national preferences. The rationale of these regimes is that they may offer the benefits of supranational policymaking, and also elicit legitimisation and ownership by reflecting national preferences.

As a first step, we still consider a centralised regime, where the PA's mandate is to choose the optimal aggregate policy X (and xi = X) by minimising a loss function isomorphic with that of governments, i.e. with nonzero policy aversion.

The determination of the policy aversion of the PA is problematic when the countries differ in this dimension. Here we consider the case in which the PA is "hegemonised" by one country. We do not examine how hegemonisation takes place. For instance, it may be the result of the negotiation process leading to the establishment of the PA.††††† For ††††† Hegemonic regimes have long been studied in international relations (e.g. Kindleberger 1981, Keohane 1980). The weight of German "preferences" in the (Franco-German) design of the ECB and of the fiscal regulations of the EMU is documented by several authors (e.g. Eichengreen and Frieden (eds.) 1994). The hegemonic drift of the EMU crisis management is carefully examined by Bastasin (2015, ch. 17) and Fabbrini (2015, ch.2).

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concreteness we assume that the hegemon is the country with the lowest policy aversion.‡‡‡‡‡ Therefore, let the two countries be different for policy aversion, with c1 > c2, and let country 2 be the hegemon, with c2 = 1.

In the hegemonic regime (HR), the PA chooses the optimal aggregate policy XH by minimising the loss function

(16) LH = 0.5(Y2 + X2)Given the target function (12), the optimal policy is

(17) XH = −UAk2/(1+A2k2), YH = Uk/(1+A2k2)

Regime ranking The differential loss for each country is now Li

N – LiH, where Li

H = L(yiH,

XH). We can show that also this regime fails to be Pareto-improving with respect to the NC one.

To begin with, we can immediately see from equation (17) that this regime, unlike that of the pure TR, in general does not deliver full protection at the aggregate level either, i.e. YH 0. Moreover, it suffers from the same "one-size-doesn't-fit-all" problem: in general yi

H YH 0, with a mirror opposite effect in the two countries, unless the two countries are fully symmetric. On the other hand, given nonzero policy aversion, XH

< X*, i.e. in this regime the PA also limits the use of X approaching governments' preferences. Thus this regime may entail a lower loss than the centralised TR by both countries.

As to the comparison with the NC regime, let us consider again the most favourable case of symmetric shock u. The two governments face the following losses

(18) L1H = (c1 + )u2, L2H = ( + )u2

where (, ) are parameters depending on (b1, b2). Governments' choice runs as in the centralised TR: account should be

taken of the effect of national policy aversion, of that of the other country, and of interdependence. We already know these effects in the NC regime. In the HR, L1H/c1 > 0, L2H/c1 = 0, i.e. a larger c1 implies that the loss increases for the high policy-aversion government, but not for the hegemon, which is in fact immunised by the PA. As to interdependence, it affects the losses (18) because the central PA delivers incomplete internalisation of spillovers owing to nonzero policy aversion. In the case of

‡‡‡‡‡ Hence, the centralised TR can be regarded as a special case of the HR where the hegemon has ci = 0.

21

equal b, the interdependence effect is L1H/b > L2H/b > 0, i.e. it is stronger for the higher policy-aversion government.

The regime ranking for the lower policy-aversion government 2 is analogous to that of the centralised TR. That is to say, in the domain c1 [1, ], b [0, 1], there exists a threshold level of b beyond which L2N − L2H > 0. This threshold is lower, the higher is c1, and it is lower than in the centralised TR. As may be expected, the HR expands the domain of the hegemon's switch to the SR. What is perhaps unexpected is that the HR is not systematically preferred to the NC regime by the hegemon itself: preference for the HR requires combinations of sufficiently large policy aversion of the other government or high interdependence. The reason is again that, although hegemonised, the PA operates on the aggregate variables of the two countries, which, cet. par., is suboptimal for country 2.§§§§§

On the other hand, the ranking of government 1, too, is analogous to that in the centralised TR, namely there is no combination of the parameters c1 [1, ], b [0, 1] such that L1N – L1H > 0.

Figure 4 replicates Figure 3 showing the differential losses of the two countries as a function of c1 in the case of b = 0.25 and with "very high" interdependence b = 0.5. Note that in both cases country 2 switches in favour of the HR for values of c1 sufficiently large; the switch occurs earlier when interdependence is stronger, and earlier than in the centralised TR. It should also be noted that both countries prefer the NC regime even when they are fully symmetric (c1 = 1).

[Figure 4]The conclusion is that, despite the larger domain of preference of the

hegemon government, also a centralised political, hegemonised, regime fails to represent a Pareto improvement with respect to the NC regime.

4.5 Political regimes. UnionWe now move to a fourth possible regime that we call "union". The

union does not have coercive power, but it is a means whereby the two players can be coordinated on a combination (xU1, xU2) which takes

§§§§§ Indeed, why should government 2 devolve its policy sovereignty to a mirror policymaker which, however, should also take into account the state variable of the other country? The classic answer is: sterilisation of spillovers. However, we have seen that it is only partially achieved by the central PA.

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national preferences into account.****** If say the union's policy assignments have to be voted, the Pareto criterion ensures unanimity. Normatively, we already know that the Pareto optimal solution is provided by the Nash Bargaining equation (9). Let us consider, like Alesina et al. (2005), that the union uses a Utilitarian loss function that minimises the sum of the two countries' losses††††††:

(19) LU = L1U + L2U

where LiU = L(xi

U, yiU)

Regime rankingGiven (19), the differential loss of the union regime (UR) relative to the

NC one is LiN – Li

U. We shall see that this regime may or may not be Pareto improving depending on the characteristics of each country.

It is known that the policy assignment given by (19) coincides with the Nash Bargaining solution if the countries are fully symmetric. The policy assignment is xU > xN; it coordinates the two governments on a larger use of x, and allows both countries to achieve yU < yN so that LN – LU > 0 is always strictly verified for both countries.

The picture is ambiguous when the countries are not symmetric in policy aversion, even in the case of symmetric shock u. The losses of the two countries result

(20) L1U = 1u2, L2U = 2u2 where (1, 2) are combinations of parameters (b1, b2, c1, c2). Let c2 =1 and c1 > 1 like above. Recalling that for c1 = 1, L1U = L2U < L1N = L2N, the question is whether this regime ranking holds for any c1 > 1, or a preference switch occurs for any country.

We already know that in the NC regime L1N/c1 > L2N/c1 > 0. This also occurs in this regime, L1U/c1 > L2U/c1 > 0. Therefore, in order to answer the above question, the point is, for each government, under which regime, beyond c1 = 1, the marginal loss is larger.

In this regard, consider that for c1 [1, ], L1N/c1 > L1U/c1 and L2N/c1 < L2U/c1. That is to say, the marginal loss in the UR is smaller

****** This is similar to Scharpf's (2001) "joint decions" model, which "combines aspects of intergovernmental negotiations and supranational centralization" (p.17).†††††† This is also a way to model international cooperation games (Romp 1997, ch. 10). Ferré (2008) follows the same method to analyse "broad fiscal coordination", as opposed to "narrow" (i.e. our NC regime) in a model of the EMU where the common central bank is also present.

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than in the NC regime for country 1, whereas the opposite holds for country 2. The reason is that the UR, by coordinating both governments on a higher level of x while "balancing" their respective national preferences, requires an additional policy effort which is lower for the more policy-averse government and higher for the less policy-averse one. Thus, the preference for the UR increases with c1 for government 1 and decreases for government 2. Both countries are better-off with the UR only up to a certain degree of asymmetry beyond which the less policy-averse country is worse-off with respect to the NC equilibrium.‡‡‡‡‡‡

Note, also, that interdependence plays a twofold role. On the one hand, as expected, it plays in favour of the UR since it generates welfare losses in the NC regime. On the other, it should also be taken into account that, for any given c1 [1, ], L2U/b > L1U/b > 0: higher interdependence generates larger losses also in the UR because the two governments agree on a greater policy effort, the more so the stronger is interdependence. But we have seen that the marginal welfare loss is larger for the lower policy-aversion government. Therefore, a combination of high asymmetry in policy aversion and/or strong interdependence may jeopardise the UR from the point of view of the lower policy-aversion government.

Figure 5 displays the differential loss for each country as a function of c1. The region of Pareto-improving agreement of the two countries is non-empty for any degree of interdependence b [0,1] but it shrinks when b is higher, as shown in the standard case of b = 0.25, and with "very high" interdependence, b = 0.5. In the former case, government's 2 tolerance for government's 1 policy aversion is c1 [1, 1.51], in the latter it is c1 [1, 1.34]

[Figure 5] 4.6 Overall regime ranking when countries' policy aversions differ

So far we have compared each SR with the NC one. To complete our analysis we now present the ranking of all regimes for each country allowing for asymmetric policy aversion. Although the main qualitative ‡‡‡‡‡‡ A paradox appears here. At first sight, one might think that it is country 1 (say Greece, or Britain) that suffers most from remaining in Europe owing to its higher policy aversion. However, at some level of asymmetry, it is country 2 (say Germany) with lower policy aversion that suffers more and opts out for non-cooperation. By implication, the exit threat of high policy-aversion countries is not credible (whereas it is for low policy-aversion countries) or is based on miscalculation of their welfare losses in the NC regime.

24

results expounded so far have general validity, for concreteness we still make use of the numerical model used so far. Country 2 is taken as benchmark for policy aversion (c2 = 1). The exercise consists in drawing and comparing the levels of welfare losses in each regime and each country as functions of the policy aversion of country 1. For any value of c1 the Pareto dominant regime is the one with the lowest loss for both countries. The result can be seen in Figure 6.

[Figure 6]First recall that when c1 = 1 we are in the full symmetric case, and as

already explained the UR is Pareto dominant. Any other SR is also dominated, for both countries and in the same order, by the NC regime. Let us recall why. The decentralised TR with penalty (not reported) is systematically dominated by the NC regime for any non-zero penalty. It may however dominate the others for a sufficiently small penalty. The centralised TR is dominated by all the others, because, although it grants full shock protection in each country, it ignores social preferences and it fails to deliver a better trade-off with the required effort in the use of the "good policy". With equal policy aversion, the regime with political central authority (coincident with HR) ranks in the middle.

Now let us examine the regime ranking for each country when their policy aversion differs (c1 > 1). In the first place, for both countries the centralised TR continue to be dominated by all the others. The next is the HR, and interestingly, as explained above, this is also true for the hegemonic country 2, unless country 1's policy aversion is sufficiently high. Therefore, the single alternative remains the UR vs. the NC regime. However, this exercise makes it clear that while the high policy-aversion country 1 always prefers the union to non-cooperation, the low policy-aversion country 2 agrees on the union only up to a threshold level of policy aversion of country 1 (c1 = 1.5) beyond which country 2 switches to non-cooperation. The union is the dominant regime only within a limited range of asymmetry in social preferences between countries.§§§§§§

§§§§§§ Another caveat, specific to the EMU fiscal policy, is that the common monetary authority is already in place with its own mandate, and the prevailing view in the earlier EMU literature was that un-coordinated (and constrained) fiscal policies of member states would safeguard "monetary dominance", i.e. the ECB's ability to pursue price stability (see the survey by Beetsma and Giulidori 2010). However Ferré (2008) has shown that a "broad type" of coordination (i.e. a joint loss minimisation similar as in our "union") is preferred by governments, and also produces superior outcomes for the EMU as a whole.

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5 Conclusions

Countries tied by interdependence that creates reciprocal negative externalities are bound to incur welfare losses if their governments pursue purely non-cooperative policy choices. Can Pareto improvements be obtained shifting policymaking at the supranational level? We have shown that the answer depends of what model of supranational policymaking is considered.

We have examined four SRs: two "technocratic", which do not take national preferences into account (as represented in governments' loss functions over policy outcomes), and two "political", which do. We have studied the Pareto ranking of the correspondent SRs relative to the option of the NC regime.

The main result of our analysis is that the TRs are dominated by the NC regime and by the UR, and that the true eventual alternative is between the latter and the NC regime. The UR is one where the supranational institution does not have coercive power, but it can coordinate the governments on a combination of policy assignments which minimises the sum of the two governments' loss functions.

We have also shown, however, that the agreement on the UR may not be unconditional. A critical factor is asymmetries across countries, notably in the degree of policy aversion. If this is too large, the lower policy-aversion government minimises its loss by opting for the NC regime, whereas the same option for the higher policy-aversion government may not be credible or based on miscalculation of the losses of non-cooperation.

Our results may shed light on the preferable direction of the EMU reform. The main implication of the UR being the dominant one is that the strategy of further integration by extending and strengthening the EMU regulatory framework based on rules enforced by technocratic, "non politicised", agencies may not be successful. In a viable SR national preferences over policy options cannot be muted: they can find their way with no need to exit from the SR formally. A symptom can be read in the drift towards disguised de facto "politicisation" of the EMU governance by way of the disorderly enlargement of the so-called intergovernmental

26

method.******* As a matter of fact, full-fledged federal systems do not operate by enacting "good policies" at the level of each federal unit independently of their preferences, but by aggregating preferences of federal units through the electoral system, and then allocating different competences and powers across the various levels of government.

However, we have also shown that sharp differences across countries may jeopardise their agreement for the UR. Hence there are two main political-economic implications to be investigated further. The first is the progressive reduction of asymmetries. The so-called "structural reforms" in a variety of fields, that play a central role in the EMU governance strategy, can be read in light of this aim. However, the actual efficacy and viability of this long-standing, restless, strategy is open to question, the more so the closer the reforms are to entrenched national preferences. More fundamentally, should supranational institutions be conceived as means to reduce national differences or as a means to cope with them?

The second implication is that, as taught by the theory and practice of international agreements, compensations may be necessary.††††††† In our model, the recipient of compensation should be the less policy-averse country. Compensation may be pecuniary or non-pecuniary, such as benefits in other fields open to negotiation. One major form of compensation to be further analysed in our setup is the change in the weights of countries in the policy decision making process represented by the joint loss function of the two countries. It can be expected that, in order to prevent the less policy-averse country from leaving, the weight granted to its preferences should be increased vis-à-vis the policy aversion of the other country, though not beyond the point where it is the latter that leaves.

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******* Penetrating, detailed analyses of this process are provided by Bastasin (2105) and Fabbrini (2103, 2015). In light of our model, our own criticism of the intergovernmental method is that it has been disguised and disorderly, whereas it should be harnessed within openly political institutions. ††††††† Bordo and James (2016) make use of this argument in drawing their road map towards the EMU Fiscal Union. See also Mongelli (2010).

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Figure 1. NC equilibrium (N) and the "core" of the game. Fully symmetric country after unit negative shock (u = −1)

Figure 2. NC equilibrium for each single country

x2

x1

N

gov.

gov.B

31

Figure 3. Differential loss LNi – LT

i with increasing policy aversion of country 1 (a) u = 1, c2 = 1, b = 0.25

(b) u = 1, c2 = 1, b = 0.5

Note: negative values of the differential loss indicate preference for the NC regime

32

Figure 4. Differential loss LNi – LH

i with increasing policy aversion of country 1 (a) c2 = 1, b = 0.25

(b) c2 = 1, b = 0.5

Note: negative values of the differential loss indicate preference for the NC regime

33

Figure 5. Differential loss LNi – LU

i with increasing policy aversion of country 1 (a) u = 1, c2 = 1, b = 0.25

(b) u = 1, c2 = 1, b = 0.5

Note: negative values of the differential loss indicate preference for the NC regime

34

Figure 6Regime ranking for country 1 with increasing policy aversion relative to country 2 (u = 1,

b = 0.25, c2=1)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

-0.1

-8.32667268468867E-17

0.0999999999999999

0.2

0.3

0.4

0.5

0.6

Non-coop.Centr. TR

Union

Hegemonic

C1

L1

Regime ranking for country 2 with increasing policy aversion of country 1 (u = 1, b = 0.25, c2=1)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

0.1

0.2

0.3

0.4

0.5

0.6

c1

Centr. TR

Hegemonic

Non-coop.

Union

L2