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Coalition formation in international monetary policy games
Journal of International Economics 56 (2002) 371–385 www.elsevier.com / locate / econbase
Coalition formation in international monetary policy games Marion Kohler* Bank of England, Threadneedle Street, London EC2 R 8 AH, UK Received 18 April 1996; received in revised form 10 September 2000; accepted 2 January 2001
Abstract This paper analyses coalition formation in monetary policy coordination games between n countries. We show that some but not all countries may join if the decision to be a member of the coalition is incentive-compatible for the individual country. Positive spillovers of the coalition formation process and the resulting free-rider problem limit the stable coalition size: since the coalition members are bound by the union’s discipline, an outsider can successfully export inflation without fearing that the insiders will try to do the same. These ‘gains from staying out’ arise even in the case of symmetric shocks. 2002 Elsevier Science B.V. All rights reserved. Keywords: Currency unions; International policy coordination; Free-riding; Coalition formation JEL classification: F33; F42
The economic debate on which countries should join a monetary union has often focused on ‘who should be let in’ rather than ‘who wants to join’. However, three members of the European Union — Denmark, the UK and Sweden — decided not to join the European Monetary Union from the beginning: the gains from joining the union may not outweigh the costs. This paper focuses on one type of gain from joining a union only, the gain that arises from coordination of monetary policies after a common shock. We draw attention to some reasons for why a country may
*Tel.: 144-20-7601-4182; fax: 144-20-7601-5018. E-mail address: [email protected] (M. Kohler). 0022-1996 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0022-1996( 01 )00128-3
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want to stay out, despite the existence of inefficiencies from non-coordinated policies. In the model by Canzoneri and Henderson (1991) after a negative supply shock countries try to export inflation via an appreciation of the exchange rate. Without cooperation, because all countries are doing so, none of them succeed but they all have contracted their money supply too much. This provides the ‘classical’ argument for the benefits from coordination in Hamada’s (1976) seminal article: all countries could do better by agreeing not to try to export inflation. However, the situation changes when there are some countries that join a union while others remain outside. Since the union members are now bound by the coalition’s discipline, an outsider can successfully export inflation without fearing that the insiders try to do the same. These additional ‘gains from staying out’ are the reason why the largest stable coalition comprises some but not all countries, even in the case of symmetric shocks. We find over a large range of parameter values that in our model only three countries want to join such a union. The paper here focuses on one type of cost only: the possibility of free-riding on the coalition’s discipline when remaining outside. This complements existing research in a number of ways and provides important insights into the feasibility of coalition formations and therefore the European Monetary Union. Asymmetries are often seen as the driving force for coalition formation — reflecting optimum currency area considerations whereby idiosyncratic shocks are the main reason for a country not wanting to join a monetary union. This is reflected in existing papers on international policy coordination involving both a union and outsiders such as Buiter et al. (1995), Canzoneri (1982) and Canzoneri and Henderson (1991). Their distinction of insiders and outsiders stems explicitly or implicitly from asymmetries in the underlying economies. Martin (1995) is closest to our analysis of free-riding incentives that restrict the coalition size. In a model with three countries he shows that economic convergence of a high-inflation country to a low-inflation union may lead to the build-up of these free-riding incentives. Since he restricts himself to a Phillips curve as representation of an individual economy and combines the issue of free-riding with convergence it is difficult to disentangle the relative contribution of these features. Indeed in a symmetric set-up in his model all countries would join the union. In contrast, we show that not all countries automatically join the coalition even in the symmetric case. We argue that it is not asymmetries but the type of externalities (i.e., strategic complements rather than substitutes) which is the reason for the existence of free-riding incentives. Another strand of literature has linked the economic gains from joining EMU to the purchase of reputation from the (German) central bank (see, for example, Alesina and Grilli, 1993, and Martin, 1995). However, reducing the EMU discussion to reputational considerations has one problem: if the ‘toughest’ country is to be a member of the coalition, another incentive apart from reputation is
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needed. We have omitted reputational considerations in our paper entirely and therefore the results in Alesina and Grilli are complementary to ours. In their model the constraint on the coalition size arises from restricted ‘entry to the club’, whereas in our model the restriction of coalition size arises from a lack of new members who want to join. The next section presents the basic shock stabilization game. The model underlying this is Canzoneri and Henderson (1991), extended to n countries. Readers who are familiar with their model may want to skip that section. Section 2 analyzes the stability of a coalition using a two-stage game. Section 3 concludes.
1. The underlying economy Since coalition formation is at the core of this paper we use a model with n countries where the individual country’s economy is based on Canzoneri and Henderson (1991). All variables represent deviations of actual values from zero-disturbance equilibrium values, and, except for the interest rate, are expressed in terms of logarithms. The domestic country’s variables are indexed by i; j 5 1 . . . n, j ± i denote the foreign countries. We focus our attention on a completely symmetric structure, restricting ourselves to examining the case of a productivity shock x that affects all countries in the same way. Each country specializes in the production of one good. Output y i increases in employment l i (where 1 2 a is the elasticity of output with respect to labor) and decreases with some (world) productivity disturbance x (independently distributed with mean 0): y i 5 (1 2 a )l i 2 x
0,a ,1
(1)
Profit-maximizing firms demand labor up to the point at which real wages (nominal wages w i minus the output price of the home good pi ) are equal to the marginal product of labor: w i 2 pi 5 2 a l i 2 x
(2)
In equilibrium, the money supply m i satisfies a simple Cambridge equation: m i 5 pi 1 y i
(3)
Monetary policy is effective because the monetary authorities have an information advantage arising from the timing of the game. They set the money supply when they know about the shock. Wage-setters fix nominal wages at the beginning of the period before they can observe the realization of the shock. They set w i so as to
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minimize the expected deviation of actual employment from full employment ] (l i 5 0): w i 5 m ie
(4)
with m ie the expected money supply deviation and w i the deviation from the full-employment wage-level. Actual labor demand might differ due to unexpected disturbances, but wage-setters guarantee that labor demanded is always supplied. The real exchange rate z is defined as the price of the foreign good in terms of the domestic good: z ij 5 (e ij 1 pj 2 pi )
(5)
e ij is the nominal exchange rate, i.e., the price of the currency of country j in terms of the domestic currency. The demand for the good produced in the home country is: n
O
O
O
j ±i
j ±i
j ±i
n n 1 1 ]] ]] yi 5 d z ij 1 (1 2 b )e y i 1 be y j 2 (1 2 b )n ri 2 bn rj n 2 1 j51 n 2 1 j 51 j 51
(6) Consumers consume the fraction e of their income y j . They spend the share b of their expenses on foreign goods and the rest (1 2 b ) on the domestic good. Demand for the domestic good rises with y j , j 5 1, . . . ,n. A rise in the relative price of a foreign good shifts world demand from the foreign good to the home good by d. The demand for all goods decreases with expected real interest rates r i . The residents in each country spend the amount n less for each percentage point increase in the expected real interest rate. The consumer price index qi is an average of the home good’s and the foreign goods’ price levels weighted analogous to the structure of the goods demanded. Price increases abroad raise the domestic consumer price level through the share of imported goods.
O
n 1 qi 5 (1 2 b )pi 1 b ]] (e 1 pj ) n 2 1 j 51 ij
(7)
j ±i
The expected real interest rate is: r i 5 i i 2 q ei 1 qi
(8) e
where i i is the nominal interest rate and q i is the expected value of the consumer price index tomorrow based on the information available today.
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International capital mobility and perfect substitutability of bonds give the condition of uncovered interest rate parity, ensuring that private agents are indifferent between holding either of the bonds: i i 5 i j 1 e ije 2 e ij .
(9)
1.1. Policymaker’ s objectives The policymaker has access to a single policy instrument m i , which we identify with money growth. He evaluates the effects of monetary policy according to a loss function over the deviation of employment and inflation from the zerodisturbance equilibrium. The parameter s denotes the relative weight of the objective ‘full-employment’: 1 Li 5 ] (s l 2i 1 q 2i ) 2
(10)
1.2. Reduced form of the economy’ s behavior We can reduce Eqs. (1)–(9) in the symmetric case to two equations for each country.1 They determine the constraints for the policymaker’s optimization problem. The money supply m i is free as an instrument for optimizing the loss function. The reduced forms for l i and qi are: li 5 mi qi 5 lm i 2 m
(11)
O m 1x j
(12)
j 51 j ±i
with l 5 a 1 [ b (1 2 a )(1 2 e (1 2 (n /(n 2 1))b )) /(d n 1 n (1 2 (n /(n 2 1))b )2 )] and m 5 ( l 2 a ) /(n 2 1); note that l and m are always positive. First consider the effect of a reduction in domestic money supply. Each country’s employment l i falls one-for-one with the domestic money supply (Eq. (11)), and output falls. Since real wages have to rise (2), the price of the domestic good falls. The exchange rate appreciates in order to equilibrate goods markets ((5), (6)), thus lowering the price of imports. Consequently, the consumer price level, which is a
1
The reduced form of the economy can be derived in two steps. The reduced form for l i can be derived by substituting Eqs. (4), (2) and (1) into (3), and using that m ei 5 0. Deriving the reduced form for qi involves substituting Eqs. (1)–(5) into (7), summation of Eqs. (6) and (8) over all countries, and substituting the terms in Eq. (7) (using also Eq. (9)).
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weighted sum of the domestic good price and the prices of the imported goods, falls. This explains why l in (12) is positive. Abroad, the price of imports is increased, thus causing inflation. Thus monetary policy creates an externality, which is reflected in the negative coefficient ( m . 0) of foreign monetary policy in (12). Consider now a symmetric, negative world productivity shock (x . 0), which gives rise to a stabilization game. Without policy intervention, the shock would have no effect on employment because nominal output is unaffected. Real output falls and the output price rises by the same amount, since employment only remains constant if the real wage falls ((1), (2)). There is no change in the real exchange rate since real output falls in all countries by the same amount. Consequently, the consumer price index rises. In short, a negative productivity shock will leave employment unchanged and increase CPI inflation. Each policymaker now has an incentive to contract the money supply a little bit in order to lower inflation. He accepts the small loss from reducing employment below the full-employment level in favor of the significant gain from lowering inflation. But he also causes at the same time inflation abroad. If all policymakers perform anti-inflationary policies, they enter into a competitive appreciation. The exchange rate in the end remains unchanged but all policymakers have contracted too much with respect to their optimal money supply. This could be avoided if all countries coordinated on a less contractionary monetary policy.2
2. A noncooperative game with coalition formation In the previous section we have outlined how policymakers will react to a negative productivity shock if they do not cooperate at all. Since they impose negative externalities on each other, the literature on monetary policy coordination has argued that coordination may be beneficial for all parties involved. In this section we will analyze whether countries may prefer forming a coalition to full coordination. While other models, for instance that of Alesina and Grilli (1993), focus on the question of whether entry will be limited by the insiders, we focus on the question of whether outsiders will refuse to enter. A coalition is defined as a subset of countries that optimize a common loss function. This common loss function is a weighted average of the member
2 Hamada (1976) pioneered the studies that uncoordinated policymaking across countries may be inefficient. The idea of shock stabilization after a negative productivity shock was formalized by Canzoneri and Gray (1985).
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countries’ loss functions. As all members have the same economic structure and the same loss function, we assume that the weights are equal.3
O ajLj 5O ]1k L k
k
j 51
j 51
+5
j
Following Yi (1997), we can formulate coalition formation as a two-stage game. In stage 1 countries irrevocably decide whether to join a coalition or not. In stage 2 countries engage in a shock stabilization game (given the coalition). The game is solved recursively. First, equating the reaction functions of the countries outside the coalition and of the coalition itself yields the outcome of stage 2: the equilibrium for a given insider-outsider structure. This outcome is dependent on the number of coalition members k. This is extended to an analysis of the individually optimal choices in stage 1: the ‘stability’ of the coalition, using an algorithm drawn from the industrial organization literature.
2.1. Stage 2: The optimal strategies and the equilibrium We assume that the first k out of the n countries are members of the coalition C; countries k 1 1, . . . ,n are outside the coalition.
2.1.1. The countries outside the coalition In order to solve the policymaker’s optimization problem when he is outside the coalition, we calculate the Nash strategy. The loss function (using Eqs. (11) and (12)) is minimized with respect to m i , subject to given strategies of the other countries, ] m j,nc for all outsiders and ] m j,c for all coalition members. Since we have a symmetric structure, we assume that all countries outside the coalition have the * . We can then derive the money supply of a same optimal money supply m nc nonmember as a function of the coalition’s money supplies:
O ]m k
* 5u m nc
j,c
2 qx
(13)
j 51
with u 5 [ lm /(s 1 l 2 2 lm (n 2 k 2 1))] and q 5 (u /m ); note that u and q are always positive.
3 Differences in weights may change the results of the model entirely. For example, Casella (1992) shows that — when countries are asymmetric in their size — smaller countries will receive more than proportional weights in order to be induced to participate in a cooperative agreement. Similarly, in our model, offering outsiders higher weights may induce them to join. Thus the stable coalition size could be enlarged.
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Eq. (13) shows that the optimal policy outside the coalition depends positively on the coalition policy, i.e., the money supplies of a nonmember and a coalition member are strategic complements. This means that a less contractionary monetary policy of the coalition members triggers a less contractionary response from the nonmembers. The reasoning is as follows: the coalition creates less competitive appreciation for the nonmembers by contracting less. Hence, the countries outside the coalition also need to contract less, because they face less ‘imported’ inflation.
2.1.2. The optimal strategy of the coalition and the equilibrium The coalition as a whole plays a Nash game against the outsiders, which means that it solves its optimization problem subject to a given money supply of the nonmembers. Using the symmetry assumption m *j,c 5 m c* for all j 5 1, . . . ,k we can derive a coalition member’s reaction function. By equating the reaction functions we obtain the equilibrium of the Nash game with a coalition as: m *c 5 2 r x
(14)
m *nc 5 2 v x
(15)
with r 5 [(s 1 l 2 1 ml)( l 2 m (k 2 1)) /((s 1 l 2 )(s 1 l 2 1 m 2 (k 2 1)2 2 ml(n 1 k 2 3)) 1 lm 3 (k 2 1)(n 2 1) 1 l 2 m 2 (k(n 2 k) 2 2(n 2 1))]) and v 5 [ l(1 1 m kr ) / (s 1 l 2 1 lm (n 2 k 2 1))]; with some rearrangement it can be shown that r and v are always positive. The losses in equilibrium are given by: Lc 5 s m c* 2 1 ( lm *c 2 m (k 2 1)m *c 2 m (n 2 k)m *nc 1 x)2
(16)
* 2 m km c* 2 m (n 2 k 2 1)m nc * 1 x)2 Lnc 5 s m *nc 2 1 ( lm nc
(17)
The equilibrium policies both are linear functions of the shock x. If the shock is zero, the optimal policies are zero as well, since there is no need for a stabilization game. If the shock is negative, i.e., x . 0, the optimal policy for all countries is a contractionary monetary policy. The coalition eliminates the negative externalities that the member countries impose on each other. Therefore the coalition members conduct a less contractionary, and thus less deflationary, policy and so lower their losses. But if the coalition countries contract less, the inflation in the nonmember countries is lower as well, since the currency of a coalition member appreciates less against all currencies. It means that the coalition formation process produces positive spillovers for nonmembers, since also their losses are lowered. In the following, we will analyze
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whether there is a stable coalition size where the spillovers from the coalition formation process are high enough that a country prefers to stay outside.
2.2. Stage 1: The stability of coalitions in equilibrium We will determine which coalition size is stable — if any — using a stability concept from the cartel literature by D’Aspremont et al. (1983). The loss function of a nonmember is denoted by Lnc (k). If it joins the coalition (and no other country changes from one group to another), it will have the loss Lc (k 1 1). If Lnc (k) , Lc (k 1 1), the country has no incentive to join the coalition — the coalition is called ‘externally stable’. A similar condition holds for the coalition members. If Lc (k) , Lnc (k 2 1), the country has no incentive to leave the coalition. The coalition is called ‘internally stable’. If both conditions are fulfilled the coalition is stable with size k. Our stability conditions do not allow the coalition to block a further extension of the coalition. However, the coalition in our game would never want to limit entry since the coalition members’ losses decrease when new countries enter the coalition (see Fig. 2). Hence we do not need a condition which ensures that ‘free entry’ is possible.4 Lemma 1. A coalition of two countries is internally stable, i.e., Lnc (1) . Lc (2) for all n. Proof. We evaluate Eqs. (17) and (16) for k 5 1 and k 5 2, respectively. Some algebraic manipulation, using that m 5 [( l 2 a ) /(n 2 1), shows that
sx2 s 1 l 2 s x 2 (s 1 l 2 1 ml)2 (s 1 ( l 2 m )2 ) Lnc (1) 2 Lc (2) 5 ] ]]]2 2 ] ]]]]]]]]]] . 2 (s 1 la ) 2 ((s 1 la )(s 1 l 2 ) 1 (s 2 la )m 2 )2 After forming a common denominator, this expression has a positive denominator. Expanding and judiciously factorizing some terms (details available on request from the author), we see that also the numerator is always positive. h Lemma 2. A coalition of all countries is internally unstable [ (and hence a coalition with n 2 1 members is externally stable) for sufficiently large n: Lnc (n 2 1) . Lc (n). 4 In contrast to our model, coalition formation which is based on reputational considerations, as in Alesina and Grilli (1993), faces this problem. It is not in the interests of the coalition to admit a ‘weaker’ member, which would deteriorate the ‘stronger’ members’ positions.
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Proof. We evaluate Eqs. (17) and (16) for k 5 n 2 1 and k 5 n, respectively. Some algebraic manipulation, using that m 5 ( l 2 a ) /(n 2 1), shows that
S
sx2 1 ] ]]] Lnc (n 2 1) 2 Lc (n) 5 2 2 (s 1 l 2 ) 2 (s 1 a 2 )
S
s 1 (a 1 m )( l 1 m ) 3 ]]]]]]]]]]]]] 2 (s 1 l )(s 1 (a 1 m )2 ) 2 ml( l 2 a )(a 1 m )
DD 2
After forming a common denominator, this expression has a positive denominator. Expanding and judiciously factorizing some terms (details available on request from the author), we see that the numerator is always negative for sufficiently large n. h Proposition. If the number of countries n is large enough there exists a stable coalition size k* which does not comprise all countries. Proof. Let $ (k) 5 Lc (k) 2 Lnc (k 2 1) for a given n. A coalition k* is stable if $ (k*) # 0 and $ (k* 1 1) $ 0. By Lemma 1 $ (2) . 0 and therefore k* $ 2. By Lemma 2, for n sufficiently large $ (n) . 0 and therefore k* , n. Thus, by the intermediate value theorem on $, there exists a k* meeting the desired condition. h
2.2.1. The stability of the coalition We have seen in the previous paragraph that the stable coalition does not comprise all countries for sufficiently large n. In light of the number of parameters, the nonlinearities in the model, and the mixture of discrete and continuous variables, we have performed numerical simulations to establish the stable coalition for specific parameter values (the base scenario chosen was: a 5 b 5 0.5, e 5 0.8, n 5 0.05, s 5 1, d 5 0.3 and n 5 22). Fig. 1 illustrates the stability conditions. The coalition is internally stable only for k 5 2 and k 5 3. When the coalition size exceeds three, each coalition member individually could gain by leaving the coalition. The coalition is externally stable for all constellations where three or more countries are in the coalition. When the coalition size is one or two, a country outside could reduce its losses by joining the coalition. Hence the stable coalition size, where no country wishes to change its status quo, is k* 5 3. Table 1 gives the results of a robustness analysis of this result over different values of the model parameters (if not noted otherwise, the parameter
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Fig. 1. External and internal stability. Negative ‘gains from changing the group’ imply that changing does not pay and, hence, the group is stable. The convex graph shows the internal stability of the coalition where only coalition sizes of three or less are stable (negative gains from leaving). The concave graph shows the external stability where only coalition sizes of three or more are stable (negative gains from joining). Therefore, only a coalition of three countries fulfils both stability criteria. The graph shows the stability conditions for n 5 22, a 5 b 5 0.5, e 5 0.8, n 5 0.05, s 5 1 and d 5 0.3.
values where those chosen for the basic simulation). For parameter sets with very low s ( # 0.1) and b ( $ 0.8) the stable coalition is 4 or 5. But in each case, for sufficiently large n, we found a unique stable coalition which does not comprise all countries. Given the nonlinear nature of our model, we cannot exclude the possibility of multiple equilibria. But this does not affect our conclusion that a stable coalition has a size smaller than n for sufficiently large n. When a country decides whether or not to join a coalition, two factors are involved. The country balances the gains from entering the coalition against the costs of giving up an optimal policy ‘against’ the coalition. The gains from entering arise from the elimination of competitive appreciations against the countries in the coalition. The gains from staying outside are given by the possibility of exporting inflation into the coalition. As the size of the coalition is increased, the amount of contraction within the coalition declines and therefore
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Table 1 Multivariate sensitivity analysis over s, a, b, and over e, n, d Parameter
Number of countries
s
a
b
3
4
5
6
7
8
9
10
11
12
13
14
15
0.1
0.1
0.1–0.5 0.6 0.7 0.8 0.9
3 3 3 3 3
3 4 4 4 4
3 4 4 4 4
3 4 4 5 5
3 4 4 5 5
3 4 4 4 5
3 3 4 4 5
3 3 4 4 5
3 3 4 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 3 4
0.1
0.2
0.1–0.5 0.6 0.7 0.8 0.9
3 3 3 3 3
3 4 4 4 4
3 4 4 4 4
3 4 4 4 5
3 4 4 4 5
3 3 4 4 5
3 3 4 4 4
3 3 4 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 3 4
3 3 3 3 4
0.1
0.3
0.1–0.5 0.6 0.7 0.8 0.9
3 3 3 3 3
3 3 4 4 4
3 4 4 4 4
3 3 4 4 4
3 3 4 4 4
3 3 4 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 3 4
3 3 3 3 4
3 3 3 3 3
3 3 3 3 3
0.1
0.4
0.1–0.6 0.7 0.8 0.9
3 3 3 3
3 3 4 4
3 4 4 4
3 3 4 4
3 3 4 4
3 3 4 4
3 3 3 4
3 3 3 4
3 3 3 3
3 3 3 3
3 3 3 3
3 3 3 3
3 3 3 3
0.1
0.5
0.1–0.7 0.8 0.9
3 3 3
3 3 4
3 4 4
3 3 4
3 3 4
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
0.1
0.6–0.9
0.1–0.9
3
3
3
3
3
3
3
3
3
3
3
3
3
0.6
0.1 0.2–0.9
0.1–0.8 0.9 0.1–0.9
3 3 3
3 3 3
3 4 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
1.1–3.1
0.1–0.9
0.1–0.9
3
3
3
3
3
3
3
3
3
3
3
3
3
e
n
d
3
4
5
6
7
8
9
10
11
12
13
14
15
0.1–0.9
0.1–0.9
0.1–0.9
3
3
3
3
3
3
3
3
3
3
3
3
3
also the degree of competitive appreciation against the outsiders. At the same time it increases the possibilities for outsiders to successfully export inflation as the insiders are bound by the coalition discipline. When the coalition has reached a certain size, countries prefer to stay outside, as they are no longer engaged in a competitive appreciation of any considerable extent, and they can successfully export inflation.
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Fig. 2. Loss functions of insiders Lc (k) and outsiders Lnc (k) (n 5 22).
2.2.2. Coalition formation process We will now have a more detailed look at the coalition formation process. For k 5 1, when there is no coalition, countries have an incentive to form a coalition of two. But there is a free-rider problem, since the countries outside the coalition have lower losses than the coalition members for any value of k (see Fig. 2, which shows the loss functions for n 5 22 and k from 1 to 22). Every country would like the others to enter the coalition rather than joining itself. This may create an obstacle to coalition formation at the very beginning, since every country would wait for the others to go ahead. However, for every country it would be better to form a coalition of two countries than to form no coalition. This may be incentive enough to get the coalition formation started. In our game the outsider has then been somehow ‘smarter’. Of course our model cannot tell which countries will be the ones to join the union. Asymmetries may provide the answer to this question. Such asymmetries include, amongst others, differences in country size or the relative weight of output in the loss function. Dealing with such asymmetries becomes intractable within an n country model. A detailed assessment of the impact of asymmetries is therefore an avenue for future research.
3. Conclusions This paper has shown that — in the framework of a standard international policy coordination model — the explicit possibility of coalition formation
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generates results which are different from the ones often assumed for coordination models with more than two countries. Since in our model monetary policies are strategic complements, the process of coalition formation creates positive spillovers for the outsiders allowing them to free-ride. These positive spillovers are the reason why not all countries may want to join the coalition. This result holds — unlike other models for coalitions in monetary policy — even in the symmetric case. The literature on optimum currency areas places considerable focus on asymmetries as the reason why countries may not want to join a monetary union. However, this paper shows that even within a symmetric model some countries may want to remain outside the union, merely because of the spillover effects of monetary policy. The existence of a union which does not comprise all countries has important policy implications for EMU. If asymmetries are the reason why not all countries join an agreement like EMU, policy-making should focus on whether countries have converged. But the reduction of structural differences alone may not be sufficient to ensure that all countries want to join the union. Indeed, we show that coalition formation may in fact involve only a subset of countries even in a symmetric model.
Acknowledgements This paper is a shortened version of Chapter 2 of my PhD thesis written at the European University Institute, Florence, Italy. I am indebted to my thesis supervisors Mike Artis and Mark Salmon. The comments of Matthew Canzoneri, Rebecca Driver, Paolo Guarda, Esther Hauk, Dale Henderson, Berthold Herrendorf, Jeroen Hinloopen, Enrique Ila Alberola, Mark Lauer, Stephen Martin, Alessandro Missale, Peter Neary, Bruno Versaevel and seminar participants at the European University Institute and at the Bank of England are gratefully acknowledged. The views expressed are those of the author, not necessarily those of the Bank of England.
References Alesina, A., Grilli, V., 1993. On the feasibility of a one- or multi-speed European Monetary Union, Discussion Paper Series 792, CEPR. Buiter, W.H., Corsetti, G., Pesenti, P.A., 1995. A centre-periphery model of monetary coordination and exchange rate crises, Discussion Paper Series 1201, CEPR. Canzoneri, M.B., 1982. Exchange intervention policy in a muliple country world. Journal of International Economics 13, 267–289. Canzoneri, M.B., Gray, J.A., 1985. Monetary policy games and the consequences of non-cooperative behavior. International Economic Review 26 (3), 547–564.
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Canzoneri, M.B., Henderson, D.W., 1991. Monetary Policy in Interdependent Economies: A Gametheoretic Approach. MIT Press, Cambridge, MA. Casella, A., 1992. Participation in a currency union. American Economic Review 82 (4), 847–863. D’Aspremont, C., Jacquemin, A., Gabszewica, J.J., Weymark, J.A., 1983. On the stability of collusive price leadership. Canadian Journal of Economics 16, 17–25. Hamada, K., 1976. A strategic analysis of monetary independence. Journal of Political Economy 84, 677–700. Martin, P., 1995. Free-riding, convergence and two-speed monetary unification in Europe. European Economic Review 39, 1345–1364. Yi, S.-S., 1997. Stable coalition structures with externalities. Games and Economic Behaviour 20, 201–237.
Coalition formation in international monetary policy games Marion Kohler* Bank of England, Threadneedle Street, London EC2 R 8 AH, UK Received 18 April 1996; received in revised form 10 September 2000; accepted 2 January 2001
Abstract This paper analyses coalition formation in monetary policy coordination games between n countries. We show that some but not all countries may join if the decision to be a member of the coalition is incentive-compatible for the individual country. Positive spillovers of the coalition formation process and the resulting free-rider problem limit the stable coalition size: since the coalition members are bound by the union’s discipline, an outsider can successfully export inflation without fearing that the insiders will try to do the same. These ‘gains from staying out’ arise even in the case of symmetric shocks. 2002 Elsevier Science B.V. All rights reserved. Keywords: Currency unions; International policy coordination; Free-riding; Coalition formation JEL classification: F33; F42
The economic debate on which countries should join a monetary union has often focused on ‘who should be let in’ rather than ‘who wants to join’. However, three members of the European Union — Denmark, the UK and Sweden — decided not to join the European Monetary Union from the beginning: the gains from joining the union may not outweigh the costs. This paper focuses on one type of gain from joining a union only, the gain that arises from coordination of monetary policies after a common shock. We draw attention to some reasons for why a country may
*Tel.: 144-20-7601-4182; fax: 144-20-7601-5018. E-mail address: [email protected] (M. Kohler). 0022-1996 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0022-1996( 01 )00128-3
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want to stay out, despite the existence of inefficiencies from non-coordinated policies. In the model by Canzoneri and Henderson (1991) after a negative supply shock countries try to export inflation via an appreciation of the exchange rate. Without cooperation, because all countries are doing so, none of them succeed but they all have contracted their money supply too much. This provides the ‘classical’ argument for the benefits from coordination in Hamada’s (1976) seminal article: all countries could do better by agreeing not to try to export inflation. However, the situation changes when there are some countries that join a union while others remain outside. Since the union members are now bound by the coalition’s discipline, an outsider can successfully export inflation without fearing that the insiders try to do the same. These additional ‘gains from staying out’ are the reason why the largest stable coalition comprises some but not all countries, even in the case of symmetric shocks. We find over a large range of parameter values that in our model only three countries want to join such a union. The paper here focuses on one type of cost only: the possibility of free-riding on the coalition’s discipline when remaining outside. This complements existing research in a number of ways and provides important insights into the feasibility of coalition formations and therefore the European Monetary Union. Asymmetries are often seen as the driving force for coalition formation — reflecting optimum currency area considerations whereby idiosyncratic shocks are the main reason for a country not wanting to join a monetary union. This is reflected in existing papers on international policy coordination involving both a union and outsiders such as Buiter et al. (1995), Canzoneri (1982) and Canzoneri and Henderson (1991). Their distinction of insiders and outsiders stems explicitly or implicitly from asymmetries in the underlying economies. Martin (1995) is closest to our analysis of free-riding incentives that restrict the coalition size. In a model with three countries he shows that economic convergence of a high-inflation country to a low-inflation union may lead to the build-up of these free-riding incentives. Since he restricts himself to a Phillips curve as representation of an individual economy and combines the issue of free-riding with convergence it is difficult to disentangle the relative contribution of these features. Indeed in a symmetric set-up in his model all countries would join the union. In contrast, we show that not all countries automatically join the coalition even in the symmetric case. We argue that it is not asymmetries but the type of externalities (i.e., strategic complements rather than substitutes) which is the reason for the existence of free-riding incentives. Another strand of literature has linked the economic gains from joining EMU to the purchase of reputation from the (German) central bank (see, for example, Alesina and Grilli, 1993, and Martin, 1995). However, reducing the EMU discussion to reputational considerations has one problem: if the ‘toughest’ country is to be a member of the coalition, another incentive apart from reputation is
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needed. We have omitted reputational considerations in our paper entirely and therefore the results in Alesina and Grilli are complementary to ours. In their model the constraint on the coalition size arises from restricted ‘entry to the club’, whereas in our model the restriction of coalition size arises from a lack of new members who want to join. The next section presents the basic shock stabilization game. The model underlying this is Canzoneri and Henderson (1991), extended to n countries. Readers who are familiar with their model may want to skip that section. Section 2 analyzes the stability of a coalition using a two-stage game. Section 3 concludes.
1. The underlying economy Since coalition formation is at the core of this paper we use a model with n countries where the individual country’s economy is based on Canzoneri and Henderson (1991). All variables represent deviations of actual values from zero-disturbance equilibrium values, and, except for the interest rate, are expressed in terms of logarithms. The domestic country’s variables are indexed by i; j 5 1 . . . n, j ± i denote the foreign countries. We focus our attention on a completely symmetric structure, restricting ourselves to examining the case of a productivity shock x that affects all countries in the same way. Each country specializes in the production of one good. Output y i increases in employment l i (where 1 2 a is the elasticity of output with respect to labor) and decreases with some (world) productivity disturbance x (independently distributed with mean 0): y i 5 (1 2 a )l i 2 x
0,a ,1
(1)
Profit-maximizing firms demand labor up to the point at which real wages (nominal wages w i minus the output price of the home good pi ) are equal to the marginal product of labor: w i 2 pi 5 2 a l i 2 x
(2)
In equilibrium, the money supply m i satisfies a simple Cambridge equation: m i 5 pi 1 y i
(3)
Monetary policy is effective because the monetary authorities have an information advantage arising from the timing of the game. They set the money supply when they know about the shock. Wage-setters fix nominal wages at the beginning of the period before they can observe the realization of the shock. They set w i so as to
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minimize the expected deviation of actual employment from full employment ] (l i 5 0): w i 5 m ie
(4)
with m ie the expected money supply deviation and w i the deviation from the full-employment wage-level. Actual labor demand might differ due to unexpected disturbances, but wage-setters guarantee that labor demanded is always supplied. The real exchange rate z is defined as the price of the foreign good in terms of the domestic good: z ij 5 (e ij 1 pj 2 pi )
(5)
e ij is the nominal exchange rate, i.e., the price of the currency of country j in terms of the domestic currency. The demand for the good produced in the home country is: n
O
O
O
j ±i
j ±i
j ±i
n n 1 1 ]] ]] yi 5 d z ij 1 (1 2 b )e y i 1 be y j 2 (1 2 b )n ri 2 bn rj n 2 1 j51 n 2 1 j 51 j 51
(6) Consumers consume the fraction e of their income y j . They spend the share b of their expenses on foreign goods and the rest (1 2 b ) on the domestic good. Demand for the domestic good rises with y j , j 5 1, . . . ,n. A rise in the relative price of a foreign good shifts world demand from the foreign good to the home good by d. The demand for all goods decreases with expected real interest rates r i . The residents in each country spend the amount n less for each percentage point increase in the expected real interest rate. The consumer price index qi is an average of the home good’s and the foreign goods’ price levels weighted analogous to the structure of the goods demanded. Price increases abroad raise the domestic consumer price level through the share of imported goods.
O
n 1 qi 5 (1 2 b )pi 1 b ]] (e 1 pj ) n 2 1 j 51 ij
(7)
j ±i
The expected real interest rate is: r i 5 i i 2 q ei 1 qi
(8) e
where i i is the nominal interest rate and q i is the expected value of the consumer price index tomorrow based on the information available today.
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International capital mobility and perfect substitutability of bonds give the condition of uncovered interest rate parity, ensuring that private agents are indifferent between holding either of the bonds: i i 5 i j 1 e ije 2 e ij .
(9)
1.1. Policymaker’ s objectives The policymaker has access to a single policy instrument m i , which we identify with money growth. He evaluates the effects of monetary policy according to a loss function over the deviation of employment and inflation from the zerodisturbance equilibrium. The parameter s denotes the relative weight of the objective ‘full-employment’: 1 Li 5 ] (s l 2i 1 q 2i ) 2
(10)
1.2. Reduced form of the economy’ s behavior We can reduce Eqs. (1)–(9) in the symmetric case to two equations for each country.1 They determine the constraints for the policymaker’s optimization problem. The money supply m i is free as an instrument for optimizing the loss function. The reduced forms for l i and qi are: li 5 mi qi 5 lm i 2 m
(11)
O m 1x j
(12)
j 51 j ±i
with l 5 a 1 [ b (1 2 a )(1 2 e (1 2 (n /(n 2 1))b )) /(d n 1 n (1 2 (n /(n 2 1))b )2 )] and m 5 ( l 2 a ) /(n 2 1); note that l and m are always positive. First consider the effect of a reduction in domestic money supply. Each country’s employment l i falls one-for-one with the domestic money supply (Eq. (11)), and output falls. Since real wages have to rise (2), the price of the domestic good falls. The exchange rate appreciates in order to equilibrate goods markets ((5), (6)), thus lowering the price of imports. Consequently, the consumer price level, which is a
1
The reduced form of the economy can be derived in two steps. The reduced form for l i can be derived by substituting Eqs. (4), (2) and (1) into (3), and using that m ei 5 0. Deriving the reduced form for qi involves substituting Eqs. (1)–(5) into (7), summation of Eqs. (6) and (8) over all countries, and substituting the terms in Eq. (7) (using also Eq. (9)).
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weighted sum of the domestic good price and the prices of the imported goods, falls. This explains why l in (12) is positive. Abroad, the price of imports is increased, thus causing inflation. Thus monetary policy creates an externality, which is reflected in the negative coefficient ( m . 0) of foreign monetary policy in (12). Consider now a symmetric, negative world productivity shock (x . 0), which gives rise to a stabilization game. Without policy intervention, the shock would have no effect on employment because nominal output is unaffected. Real output falls and the output price rises by the same amount, since employment only remains constant if the real wage falls ((1), (2)). There is no change in the real exchange rate since real output falls in all countries by the same amount. Consequently, the consumer price index rises. In short, a negative productivity shock will leave employment unchanged and increase CPI inflation. Each policymaker now has an incentive to contract the money supply a little bit in order to lower inflation. He accepts the small loss from reducing employment below the full-employment level in favor of the significant gain from lowering inflation. But he also causes at the same time inflation abroad. If all policymakers perform anti-inflationary policies, they enter into a competitive appreciation. The exchange rate in the end remains unchanged but all policymakers have contracted too much with respect to their optimal money supply. This could be avoided if all countries coordinated on a less contractionary monetary policy.2
2. A noncooperative game with coalition formation In the previous section we have outlined how policymakers will react to a negative productivity shock if they do not cooperate at all. Since they impose negative externalities on each other, the literature on monetary policy coordination has argued that coordination may be beneficial for all parties involved. In this section we will analyze whether countries may prefer forming a coalition to full coordination. While other models, for instance that of Alesina and Grilli (1993), focus on the question of whether entry will be limited by the insiders, we focus on the question of whether outsiders will refuse to enter. A coalition is defined as a subset of countries that optimize a common loss function. This common loss function is a weighted average of the member
2 Hamada (1976) pioneered the studies that uncoordinated policymaking across countries may be inefficient. The idea of shock stabilization after a negative productivity shock was formalized by Canzoneri and Gray (1985).
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countries’ loss functions. As all members have the same economic structure and the same loss function, we assume that the weights are equal.3
O ajLj 5O ]1k L k
k
j 51
j 51
+5
j
Following Yi (1997), we can formulate coalition formation as a two-stage game. In stage 1 countries irrevocably decide whether to join a coalition or not. In stage 2 countries engage in a shock stabilization game (given the coalition). The game is solved recursively. First, equating the reaction functions of the countries outside the coalition and of the coalition itself yields the outcome of stage 2: the equilibrium for a given insider-outsider structure. This outcome is dependent on the number of coalition members k. This is extended to an analysis of the individually optimal choices in stage 1: the ‘stability’ of the coalition, using an algorithm drawn from the industrial organization literature.
2.1. Stage 2: The optimal strategies and the equilibrium We assume that the first k out of the n countries are members of the coalition C; countries k 1 1, . . . ,n are outside the coalition.
2.1.1. The countries outside the coalition In order to solve the policymaker’s optimization problem when he is outside the coalition, we calculate the Nash strategy. The loss function (using Eqs. (11) and (12)) is minimized with respect to m i , subject to given strategies of the other countries, ] m j,nc for all outsiders and ] m j,c for all coalition members. Since we have a symmetric structure, we assume that all countries outside the coalition have the * . We can then derive the money supply of a same optimal money supply m nc nonmember as a function of the coalition’s money supplies:
O ]m k
* 5u m nc
j,c
2 qx
(13)
j 51
with u 5 [ lm /(s 1 l 2 2 lm (n 2 k 2 1))] and q 5 (u /m ); note that u and q are always positive.
3 Differences in weights may change the results of the model entirely. For example, Casella (1992) shows that — when countries are asymmetric in their size — smaller countries will receive more than proportional weights in order to be induced to participate in a cooperative agreement. Similarly, in our model, offering outsiders higher weights may induce them to join. Thus the stable coalition size could be enlarged.
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Eq. (13) shows that the optimal policy outside the coalition depends positively on the coalition policy, i.e., the money supplies of a nonmember and a coalition member are strategic complements. This means that a less contractionary monetary policy of the coalition members triggers a less contractionary response from the nonmembers. The reasoning is as follows: the coalition creates less competitive appreciation for the nonmembers by contracting less. Hence, the countries outside the coalition also need to contract less, because they face less ‘imported’ inflation.
2.1.2. The optimal strategy of the coalition and the equilibrium The coalition as a whole plays a Nash game against the outsiders, which means that it solves its optimization problem subject to a given money supply of the nonmembers. Using the symmetry assumption m *j,c 5 m c* for all j 5 1, . . . ,k we can derive a coalition member’s reaction function. By equating the reaction functions we obtain the equilibrium of the Nash game with a coalition as: m *c 5 2 r x
(14)
m *nc 5 2 v x
(15)
with r 5 [(s 1 l 2 1 ml)( l 2 m (k 2 1)) /((s 1 l 2 )(s 1 l 2 1 m 2 (k 2 1)2 2 ml(n 1 k 2 3)) 1 lm 3 (k 2 1)(n 2 1) 1 l 2 m 2 (k(n 2 k) 2 2(n 2 1))]) and v 5 [ l(1 1 m kr ) / (s 1 l 2 1 lm (n 2 k 2 1))]; with some rearrangement it can be shown that r and v are always positive. The losses in equilibrium are given by: Lc 5 s m c* 2 1 ( lm *c 2 m (k 2 1)m *c 2 m (n 2 k)m *nc 1 x)2
(16)
* 2 m km c* 2 m (n 2 k 2 1)m nc * 1 x)2 Lnc 5 s m *nc 2 1 ( lm nc
(17)
The equilibrium policies both are linear functions of the shock x. If the shock is zero, the optimal policies are zero as well, since there is no need for a stabilization game. If the shock is negative, i.e., x . 0, the optimal policy for all countries is a contractionary monetary policy. The coalition eliminates the negative externalities that the member countries impose on each other. Therefore the coalition members conduct a less contractionary, and thus less deflationary, policy and so lower their losses. But if the coalition countries contract less, the inflation in the nonmember countries is lower as well, since the currency of a coalition member appreciates less against all currencies. It means that the coalition formation process produces positive spillovers for nonmembers, since also their losses are lowered. In the following, we will analyze
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whether there is a stable coalition size where the spillovers from the coalition formation process are high enough that a country prefers to stay outside.
2.2. Stage 1: The stability of coalitions in equilibrium We will determine which coalition size is stable — if any — using a stability concept from the cartel literature by D’Aspremont et al. (1983). The loss function of a nonmember is denoted by Lnc (k). If it joins the coalition (and no other country changes from one group to another), it will have the loss Lc (k 1 1). If Lnc (k) , Lc (k 1 1), the country has no incentive to join the coalition — the coalition is called ‘externally stable’. A similar condition holds for the coalition members. If Lc (k) , Lnc (k 2 1), the country has no incentive to leave the coalition. The coalition is called ‘internally stable’. If both conditions are fulfilled the coalition is stable with size k. Our stability conditions do not allow the coalition to block a further extension of the coalition. However, the coalition in our game would never want to limit entry since the coalition members’ losses decrease when new countries enter the coalition (see Fig. 2). Hence we do not need a condition which ensures that ‘free entry’ is possible.4 Lemma 1. A coalition of two countries is internally stable, i.e., Lnc (1) . Lc (2) for all n. Proof. We evaluate Eqs. (17) and (16) for k 5 1 and k 5 2, respectively. Some algebraic manipulation, using that m 5 [( l 2 a ) /(n 2 1), shows that
sx2 s 1 l 2 s x 2 (s 1 l 2 1 ml)2 (s 1 ( l 2 m )2 ) Lnc (1) 2 Lc (2) 5 ] ]]]2 2 ] ]]]]]]]]]] . 2 (s 1 la ) 2 ((s 1 la )(s 1 l 2 ) 1 (s 2 la )m 2 )2 After forming a common denominator, this expression has a positive denominator. Expanding and judiciously factorizing some terms (details available on request from the author), we see that also the numerator is always positive. h Lemma 2. A coalition of all countries is internally unstable [ (and hence a coalition with n 2 1 members is externally stable) for sufficiently large n: Lnc (n 2 1) . Lc (n). 4 In contrast to our model, coalition formation which is based on reputational considerations, as in Alesina and Grilli (1993), faces this problem. It is not in the interests of the coalition to admit a ‘weaker’ member, which would deteriorate the ‘stronger’ members’ positions.
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Proof. We evaluate Eqs. (17) and (16) for k 5 n 2 1 and k 5 n, respectively. Some algebraic manipulation, using that m 5 ( l 2 a ) /(n 2 1), shows that
S
sx2 1 ] ]]] Lnc (n 2 1) 2 Lc (n) 5 2 2 (s 1 l 2 ) 2 (s 1 a 2 )
S
s 1 (a 1 m )( l 1 m ) 3 ]]]]]]]]]]]]] 2 (s 1 l )(s 1 (a 1 m )2 ) 2 ml( l 2 a )(a 1 m )
DD 2
After forming a common denominator, this expression has a positive denominator. Expanding and judiciously factorizing some terms (details available on request from the author), we see that the numerator is always negative for sufficiently large n. h Proposition. If the number of countries n is large enough there exists a stable coalition size k* which does not comprise all countries. Proof. Let $ (k) 5 Lc (k) 2 Lnc (k 2 1) for a given n. A coalition k* is stable if $ (k*) # 0 and $ (k* 1 1) $ 0. By Lemma 1 $ (2) . 0 and therefore k* $ 2. By Lemma 2, for n sufficiently large $ (n) . 0 and therefore k* , n. Thus, by the intermediate value theorem on $, there exists a k* meeting the desired condition. h
2.2.1. The stability of the coalition We have seen in the previous paragraph that the stable coalition does not comprise all countries for sufficiently large n. In light of the number of parameters, the nonlinearities in the model, and the mixture of discrete and continuous variables, we have performed numerical simulations to establish the stable coalition for specific parameter values (the base scenario chosen was: a 5 b 5 0.5, e 5 0.8, n 5 0.05, s 5 1, d 5 0.3 and n 5 22). Fig. 1 illustrates the stability conditions. The coalition is internally stable only for k 5 2 and k 5 3. When the coalition size exceeds three, each coalition member individually could gain by leaving the coalition. The coalition is externally stable for all constellations where three or more countries are in the coalition. When the coalition size is one or two, a country outside could reduce its losses by joining the coalition. Hence the stable coalition size, where no country wishes to change its status quo, is k* 5 3. Table 1 gives the results of a robustness analysis of this result over different values of the model parameters (if not noted otherwise, the parameter
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Fig. 1. External and internal stability. Negative ‘gains from changing the group’ imply that changing does not pay and, hence, the group is stable. The convex graph shows the internal stability of the coalition where only coalition sizes of three or less are stable (negative gains from leaving). The concave graph shows the external stability where only coalition sizes of three or more are stable (negative gains from joining). Therefore, only a coalition of three countries fulfils both stability criteria. The graph shows the stability conditions for n 5 22, a 5 b 5 0.5, e 5 0.8, n 5 0.05, s 5 1 and d 5 0.3.
values where those chosen for the basic simulation). For parameter sets with very low s ( # 0.1) and b ( $ 0.8) the stable coalition is 4 or 5. But in each case, for sufficiently large n, we found a unique stable coalition which does not comprise all countries. Given the nonlinear nature of our model, we cannot exclude the possibility of multiple equilibria. But this does not affect our conclusion that a stable coalition has a size smaller than n for sufficiently large n. When a country decides whether or not to join a coalition, two factors are involved. The country balances the gains from entering the coalition against the costs of giving up an optimal policy ‘against’ the coalition. The gains from entering arise from the elimination of competitive appreciations against the countries in the coalition. The gains from staying outside are given by the possibility of exporting inflation into the coalition. As the size of the coalition is increased, the amount of contraction within the coalition declines and therefore
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382
Table 1 Multivariate sensitivity analysis over s, a, b, and over e, n, d Parameter
Number of countries
s
a
b
3
4
5
6
7
8
9
10
11
12
13
14
15
0.1
0.1
0.1–0.5 0.6 0.7 0.8 0.9
3 3 3 3 3
3 4 4 4 4
3 4 4 4 4
3 4 4 5 5
3 4 4 5 5
3 4 4 4 5
3 3 4 4 5
3 3 4 4 5
3 3 4 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 3 4
0.1
0.2
0.1–0.5 0.6 0.7 0.8 0.9
3 3 3 3 3
3 4 4 4 4
3 4 4 4 4
3 4 4 4 5
3 4 4 4 5
3 3 4 4 5
3 3 4 4 4
3 3 4 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 3 4
3 3 3 3 4
0.1
0.3
0.1–0.5 0.6 0.7 0.8 0.9
3 3 3 3 3
3 3 4 4 4
3 4 4 4 4
3 3 4 4 4
3 3 4 4 4
3 3 4 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 4 4
3 3 3 3 4
3 3 3 3 4
3 3 3 3 3
3 3 3 3 3
0.1
0.4
0.1–0.6 0.7 0.8 0.9
3 3 3 3
3 3 4 4
3 4 4 4
3 3 4 4
3 3 4 4
3 3 4 4
3 3 3 4
3 3 3 4
3 3 3 3
3 3 3 3
3 3 3 3
3 3 3 3
3 3 3 3
0.1
0.5
0.1–0.7 0.8 0.9
3 3 3
3 3 4
3 4 4
3 3 4
3 3 4
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
0.1
0.6–0.9
0.1–0.9
3
3
3
3
3
3
3
3
3
3
3
3
3
0.6
0.1 0.2–0.9
0.1–0.8 0.9 0.1–0.9
3 3 3
3 3 3
3 4 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
1.1–3.1
0.1–0.9
0.1–0.9
3
3
3
3
3
3
3
3
3
3
3
3
3
e
n
d
3
4
5
6
7
8
9
10
11
12
13
14
15
0.1–0.9
0.1–0.9
0.1–0.9
3
3
3
3
3
3
3
3
3
3
3
3
3
also the degree of competitive appreciation against the outsiders. At the same time it increases the possibilities for outsiders to successfully export inflation as the insiders are bound by the coalition discipline. When the coalition has reached a certain size, countries prefer to stay outside, as they are no longer engaged in a competitive appreciation of any considerable extent, and they can successfully export inflation.
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Fig. 2. Loss functions of insiders Lc (k) and outsiders Lnc (k) (n 5 22).
2.2.2. Coalition formation process We will now have a more detailed look at the coalition formation process. For k 5 1, when there is no coalition, countries have an incentive to form a coalition of two. But there is a free-rider problem, since the countries outside the coalition have lower losses than the coalition members for any value of k (see Fig. 2, which shows the loss functions for n 5 22 and k from 1 to 22). Every country would like the others to enter the coalition rather than joining itself. This may create an obstacle to coalition formation at the very beginning, since every country would wait for the others to go ahead. However, for every country it would be better to form a coalition of two countries than to form no coalition. This may be incentive enough to get the coalition formation started. In our game the outsider has then been somehow ‘smarter’. Of course our model cannot tell which countries will be the ones to join the union. Asymmetries may provide the answer to this question. Such asymmetries include, amongst others, differences in country size or the relative weight of output in the loss function. Dealing with such asymmetries becomes intractable within an n country model. A detailed assessment of the impact of asymmetries is therefore an avenue for future research.
3. Conclusions This paper has shown that — in the framework of a standard international policy coordination model — the explicit possibility of coalition formation
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generates results which are different from the ones often assumed for coordination models with more than two countries. Since in our model monetary policies are strategic complements, the process of coalition formation creates positive spillovers for the outsiders allowing them to free-ride. These positive spillovers are the reason why not all countries may want to join the coalition. This result holds — unlike other models for coalitions in monetary policy — even in the symmetric case. The literature on optimum currency areas places considerable focus on asymmetries as the reason why countries may not want to join a monetary union. However, this paper shows that even within a symmetric model some countries may want to remain outside the union, merely because of the spillover effects of monetary policy. The existence of a union which does not comprise all countries has important policy implications for EMU. If asymmetries are the reason why not all countries join an agreement like EMU, policy-making should focus on whether countries have converged. But the reduction of structural differences alone may not be sufficient to ensure that all countries want to join the union. Indeed, we show that coalition formation may in fact involve only a subset of countries even in a symmetric model.
Acknowledgements This paper is a shortened version of Chapter 2 of my PhD thesis written at the European University Institute, Florence, Italy. I am indebted to my thesis supervisors Mike Artis and Mark Salmon. The comments of Matthew Canzoneri, Rebecca Driver, Paolo Guarda, Esther Hauk, Dale Henderson, Berthold Herrendorf, Jeroen Hinloopen, Enrique Ila Alberola, Mark Lauer, Stephen Martin, Alessandro Missale, Peter Neary, Bruno Versaevel and seminar participants at the European University Institute and at the Bank of England are gratefully acknowledged. The views expressed are those of the author, not necessarily those of the Bank of England.
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