The paper presents a model of optimum currency areas using a general equilibrium approach with regionally differentiated goods. The choice of a currency union depends upon the size of the underlying disturbances, the correlation between these disturbances, the costs of transactions across currencies, factor mobility across regions, and the interrelationships between demand for different goods. It is found that, while a currency union can raise the welfare of the regions within the union, it unambiguously lowers welfare for those outside the union. [JEL F33, F36]

Abstract

The paper presents a model of optimum currency areas using a general equilibrium approach with regionally differentiated goods. The choice of a currency union depends upon the size of the underlying disturbances, the correlation between these disturbances, the costs of transactions across currencies, factor mobility across regions, and the interrelationships between demand for different goods. It is found that, while a currency union can raise the welfare of the regions within the union, it unambiguously lowers welfare for those outside the union. [JEL F33, F36]

A Formal Model of Optimum Currency Areas

AFTER A LONG period of relative stability, the set of existing or prospective currency unions has changed significantly over a very short interval. Plans for European Monetary Union (EMU), the breakup of the monetary unions in the former Soviet Union, Yugoslavia, and Czechoslovakia, and the reintegration of the two halves of Germany into a single currency zone have all contributed to this change. One of the results has been a reignited interest in the characteristics of a beneficial, or optimum, currency area.

The literature on optimum currency areas was initiated by Mundell (1961), 1 Mundell argued that, while the “costs of valuation and money-changing” were lower within a currency union, fixing the rate of exchange across regions by forming a currency union was costly in the face of asymmetric disturbances and price rigidities. However, these costs could be alleviated if a high level of factor mobility existed between regions. Hence, he viewed factor mobility as the key criterion in the choice for or against a currency union. McKinnon (1963) argued that openness to external trade should be another important criterion. If an economy was very open, a flexible exchange rate would be relatively ineffective, since changes in the exchange rate would destabilize the internal price level and have few beneficial effects on real wages or the terms of trade. Hence, currency unions that were relatively closed with respect to the rest of the world were preferable. Finally, Kenen (1969) argued that regions with high product diversification would be better able to maintain a currency union than those with low diversification since the latter are subject to larger disturbances.2

These three papers represent the core theory of optimum currency areas and have been the basis for much of the recent empirical work.3 However, as might be expected from contributions dating back to the 1960s, they present verbal arguments rather than forma! models. The object of this paper is to augment the existing literature by presenting a formal model of optimum currency areas using a general equilibrium model with regionally differentiated goods. Deriving the theory of optimum currency areas from a general equilibrium model of trade allows the various criteria that have been suggested for assessing currency unions to be integrated and compared.

Clearly, other papers have been written on the theory of optimum currency areas since 1969.4 The model presented in this paper differs from the existing literature in its use of a general equilibrium approach and stronger microeconomic foundations. In addition to clarifying the analysis, these microeconomic foundations make it possible to analyze the incentives involved in forming a currency union in more detail than in earlier papers.

The rest of the paper is organized as follows. The next section outlines the structure of the model, while Section II analyzes the resulting equilibria. This is done by comparing the results from a fully floating exchange rate regime with the results from a currency union made up of two regions, and then with the results from a currency union made up of any number of regions. Particular emphasis is put on the welfare effects of the different regimes, for regions both within and outside the currency union. Section III looks at how the model relates to the various criteria for choosing currency unions outlined in the literature, while Section IV concludes.

I. The Model

This section develops a small genera! equilibrium model with regionally differentiated goods. It has four features that are worth noting at the outset, since they define the issues that the model does and does not address. First, the model assumes a nominal rigidity: wages can rise in periods of excess demand, but they cannot fall below a certain level in periods of low demand. White not uncontroversial, the existence of nominal rigidities is central to most considerations of currency unions. With fully flexible prices, the costs of joining a currency union become minor, making the analysis of the issue of optimum currency areas largely pointless. Second, the model has no explicit role for financial assets or government policy, so issues such as financial integration or the conduct of monetary or fiscal policy are not discussed. Third, each region is assumed to be fully specialized in the production of one particular good. Hence, no account is taken of differential shocks to industries within a region.5 Finally, in order to provide a closed-form solution to the model, simple functional forms such as logarithmic utility have been used. The advantage of this approach is that it allows the resulting model to be analyzed in more depth, but at the inevitable cost of generality.

Production

Consider a world with a number of different regions, each of which has the same underlying economic structure but produces a different good. Each region has a fixed amount of labor that can be used to produce its particular good (the assumption that labor cannot move between regions will be relaxed later). The production function for region i is

Yi=Xiαeϵi(1)

where Yi is the output of the good of region i; Xi is the input of labor in the region; α is a parameter that is less than 1; and ∈i is a disturbance that is normally distributed with a mean of zero and is independent of the exchange rate regime.6 Letting lowercase letters represent logarithms, this can be rewritten

yi=αxi+i.(2)

The maximum amount of labor available in a region is 1, so Xi ≤ 1. Region 1 is different from the other regions in that the productivity disturbance ∈i, is always equal to 0, and hence the full employment level of output y1 is 1 (y1 = 0). The price of output in region 1 (P1) is the numeraire, so P1 = 1.7

Labor Market

Labor is supplied in a competitive market, with the wage (WiEi) (where Wi is the wage in local currency and Ei is the bilateral exchange rate with region 1) equal to the marginal product of labor:

wi+ei=log(α)+ϵi(1α)xi+pi.(3)

Nominal wages are assumed to be sticky in the following sense. The response of the wage in terms of the price of local goods, Wi, depends upon the state of excess demand in the labor market when the wage is at a “normal” level, ω = αPi, defined as the wage in local prices that ensures full employment when there is no productivity shock (∈i = 0) and the exchange rate Ei is normalized to 1. If there is excess demand for labor at this point, the nominal wage is raised to the level that is consistent with full employment (Xi = 1). On the other hand, if labor demand is below the full employment level when Wi = ω, the wage is assumed to remain at this high level, and some labor is unemployed.8 Hence, there is an asymmetry between the labor market response to excess demand and that to excess supply.

This labor market assumption has an important interaction with the exchange rate regime. If the region has a nominal exchange rate that is free to adjust in response to underlying disturbances, the wage is always set at the normal level, and movements in the exchange rate ensure that full employment is attained. By contrast, when the nominal exchange rate is not free to adjust fully because the region is part of a larger currency union, the rigidity in the labor market implies some loss in output through unemployment.

Exchange Rates

Each region has to choose its exchange rate regime with respect to the other regions. If region i chooses a separate currency from region J, the ratio Ei/EJ is allowed to vary. However, this flexibility results in a transactions cost between the two currencies.9 This is modeled using the “iceberg” model of trade, in which the goods that emanate from region J shrink by a factor (1 − TJ) on arrival in region i. For simplicity, the cost T is assumed to be the same for all external transactions. If regions i and J choose to form a currency union, the ratio Ei/Ej is fixed at unity. Because there is no longer any need to transfer currencies, the transactions cost is now zero (for simplicity, transportation costs between regions are ignored).

The iceberg model of trade was chosen for its analytic and expositional simplicity. An alternative formulation would be to assume that international transactions use labor, for example by assuming that transactions costs increase the amount of labor required to produce output for regions outside the currency union by a factor of 1/(1 − TJ). These two formulations wilt generally give different results, since the initial gains from lower transactions costs accrue to the recipient of the goods in the iceberg model, but to domestic output capacity in the alternative approach. However, given the assumptions of the rest of the model (in particular, the assumptions about demand discussed below), these two formulations produce identical results in this instance.

For a currency union involving several regions, the exchange rate for the region as a whole is assumed to equal the geometric average of the exchange rates for the individual regions if their exchange rates were freely floating (i.e., the exchange rates implied by full employment with wages equal to the normal level of ω). This assumption appears reasonable and provides a simple closed-form solution; however, it has no concrete microeconomic foundations. Since there is a nominal rigidity in the model, the assumption about the determination of the exchange rate affects the results. The formulation adopted ensures that in each period approximately half the regions in a currency union experience excess demand for labor, while the other half experience excess supply of labor.

Demand

The production technology is assumed to be owned locally; hence, the income for the region is equal to the nominal product, YiPi. Consumption in region j is based on a Cobb-Douglas utility function over all goods

Uj=i=1Nβjilog(Cji)ϕ(4)

where CJi is the consumption of good i in region j and ϕ is a constant term equal to the sum of βJilog(βJi).10

The βJi coefficients are assumed to satisfy two criteria, both of which are normalizations. First, the sum of βJi over (is equal to i for all J. Hence, the coefficient βJi represents the proportion of income in region J that is spent on good i. The second normalization is that the sum of βJi over J is equal to 1 for all i; this ensures that the aggregate demand for each product is symmetrical, and hence that all regions have the same level of income. From the form of the utility function, it follows that at the point of production,11 demand for the good i from region J is given by

Yji=βjiPjYj/Pi.(5)

These assumptions can be shown to imply that all regional incomes are equal to unity. To see this assume the result is correct. Since the sum of the βJi coefficients over j is 1 for all i, this implies that the demand for good i at the point of production is

Yi=jβji/Pi=1/Pi.(6)

Equation (6) does indeed imply that all regional incomes (PiYi) are equal to unity, confirming the initial assumption.

If the two regions are not in a currency union, then the volume of goods consumed in region j is less than the volume of goods demanded at the point of production i, due to the impact of transaction costs. From equation (5), consumption of good i in region J is

Cji=βji(1Tj)/Pi,(7)

where TJ is equal to T for regions outside the currency union and zero for regions within the currency union.12

The use of Cobb-Douglas preferences is clearly restrictive. The advantage of this approach is that it simplifies the analysis by eliminating the impact of income effects, thereby making it more tractable. The disadvantage is the loss of generality. In particular, since the productivity disturbance has no effect on regional income measured in terms of the numeraire (the change in output being exactly offset by the change in local prices), it is important for the model that nominal wages in a region be set with respect to local prices rather than with respect to the numeraire. This distinction would not be so important in a more general model with an intertemporal elasticity of substitution of less than one.

II. Equilibrium

This model can be used to analyze equilibrium with and without currency unions between the regions.

No Currency Unions

Consider first the situation in which all of the regions allow their currencies to float against each other. Since all of the exchange rates are fully flexible, nominal wages in local goods, Wi, are set at the “normal” level ω. Full employment implies that the logarithm of the exchange rate ei = ∈i and the logarithm of domestic output yi = ∈i. From the consumption function defined in equation (7) it follows that

cji=log(βji)+log(1Tj)+ϵi,(8)

and hence,

Uj=i=1Nβjiϵiijβjiτ,(9)

where τ = log(1 − T).

Since the exchange rate in each region is able to respond to the region-specific productivity disturbance, there is full employment and hence output at the point of production is maximized. However, the existence of separate currencies involves a cost in transferring goods not produced in the region from one currency to another. This cost rises with βJi, the proportion of good i in region J’s consumption bundle.

A Two-Region Currency Union

Consider now the equilibrium if two regions J and k choose to form a currency union. For simplicity it will be assumed that all other regions continue to float freely against each other.13 The exchange rate for the currency union is equal to the geometric average of the exchange rates of regions J and k in the free float analyzed above. Hence, eJk = (∈J + ∈K)/2.

The normal wage, ω, implies excess demand for labor in the region with the larger shock and too little demand for labor in the other region. Let j be the region with excess demand and k be the region with the shortfall. Output and wages in the two regions are then:

yj=ϵjt,wj=log(ω)+(ϵjtϵkt)/2(10)yk=ϵktα(ϵjtϵkt)/(2(1α)),wi=log(ω)

In region J, which has the excess demand for labor, the wage rises and labor remains fully employed. However, in region k the wage stays at the normal level of ω, and output falls below its full employment level. The equilibrium for the other regions remains unchanged.

The welfare effect of introducing the currency union can now be calculated from the difference between the utilities for the new equilibrium and those defined by equation (9). For regions J and k within the currency union and region m outside it,

ΔUj=βjkτβjkα(ϵjϵk)/[2(1α)]ΔUk=βkjτβkkα(ϵjϵk)/[2(1α)](11)ΔUm=βmkα(ϵjϵk)/[2(1α)].

The first two equations, which show the impact on regions within the currency union, have a very similar format. The first term shows the gain to welfare from eliminating the transactions costs with the other region.

This gain depends upon the size of these transactions costs (τ) and the importance in the home region’s consumption of the good produced by the other region (βJK or βKJ). The second term is the loss in welfare associated with the lower output in region k because of the lower flexibility of real wages caused by the currency union. This depends upon the importance of good k in regional consumption and upon the size of the difference between the two productivity shocks.

Within the currency union each region has a 50 percent chance of facing excess demand for labor and a 50 percent chance of facing a shortage of demand for labor. The expected value of the change in welfare for a region in the currency union is, therefore,

E(ΔUj)=βjkτγβjjE(ϵjϵk|ϵj<ϵk)P(ϵj<ϵk)γβjkE(ϵkϵj|ϵj<ϵk)P(ϵj<ϵk)=βjkτγβjj2ϕ(0)σj22σjk+σk212γβjk2ϕ(0)σj22σjk+σkk212=βjkτγ(βjj+βjk)ϕ(0)σj22σjk+σk2(12)

where γ = α/2(1 − α); ϕ(.) is the density function for a standard normal variate with mean 0 and standard deviation 1; σj2 is the variance of the productivity disturbance in region J; and σ JK is the covariance between the productivity disturbances in regions J and k.14

Equation (12) illustrates the gains and losses involved in joining a currency union. The first term shows the gain in welfare from the lower transactions costs associated with trade with the other member of the union. This depends upon the degree to which home consumers desire the goods from the other region (βJK). The expected costs of joining a currency union depend upon the importance in consumption of all goods produced in the currency union (βJJ + βJK) and on the variance of the difference between the underlying disturbances. This variance in turn depends upon both the sizes of the underlying disturbances and the correlation between these disturbances, i.e., the expected size of asymmetric disturbances.

The analysis to this point has focused on the impact on the members of the currency union. However, equation (11) also shows that the impact of a currency union on other regions is unambiguously negative. In expected value terms the change in utility is

E(ΔUm)=γ(βmj+βmk)ϕ(0)σj22σ+σk2.(13)

The currency union reduces welfare for all regions outside of the union, with the largest reductions occurring in those regions whose consumption is most closely connected with the currency union. The intuition behind this result is straightforward. The gains from lower transactions costs are limited to regions within the currency union. However, the losses from a currency union, in the form of lower output caused by lower real wage flexibility, affect all regions through their trade patterns. Hence, while the welfare gains are limited to those regions within the currency union, the welfare losses affect all regions and depend, among other things, upon the suitability of the currency union itself in terms of the size and correlation of the underlying productivity disturbances.15

It should be recognized that the conclusion that a currency union automatically reduces welfare of regions outside the union depends upon the structure of the model. In particular, the combination of the iceberg model of trade and logarithmic utility implies that all gains from lower transactions costs accrue to the other regions in the union. In a more general formulation, these lower transactions costs might also provide benefits to regions outside the currency union. Nor is it difficult to think of other mechanisms by which a currency union could raise welfare outside of the union. For example, it could increase the level of potential output within the union through the operation of economies of scale, thereby raising world output and hence consumption. In addition, a currency union could reduce transactions costs outside of the union through lower costs of entrepôt trade and fewer units of account. To the extent that these factors are important, the gains from them should be set against the welfare losses highlighted above.

Currency Unions with More than Two Regions

Now consider a currency union made up of k regions, i = 1 to k. Compared to a situation when all regions have floating exchange rates with each other, the gain for region i comes from the lowering of transactions costs for products produced by other regions in the union. The losses come from expected output losses within the currency union caused by the rigidity in wages combined with the common exchange rate, which is equal to the mean of all of the productivity disturbances in the currency union, denoted ∈K. It is easy to show that region i has full employment when its productivity shock, ∈i, is above the average for the currency union as a whole, and output losses when its productivity disturbance is below this average. The expected loss in output for any region is therefore

E(Δyi)=γE(ϵiϵk|ϵi<ϵk)P(ϵi<ϵk)=γϕ(0)σi22σik+σk2,(14)

where subscript K refers to ∈K, the mean of the disturbances in the currency union. Since each region has this expected loss in output, the change in expected utility from forming a currency union made up of regions 1 to k to a region i within the currency union and region m outside it is

E(ΔUi)=kiβikτkγβikϕ(0)σk22σkk+σk2.E(ΔUm)=kγβmkϕ(0)σk22σkk+σk2.(15)

This is a multiregion version of equations (12) and (13). As in equation (12), the gains for regions within the currency union depend upon the importance of goods from other parts of the currency union in consumption, while the losses depend upon the importance of all currency union products in consumption and upon the expected size of the underlying asymmetric disturbances. As in equation (13), regions outside the currency union lose unambiguously.

Equation (15) shows the change in utility when a number of regions decide to move from independent currencies to a currency union in a bloc. The same approach can be used to see the marginal change in utility to a region if it joins an existing currency union. Letting J represent the entering region and k represent the regions already within the existing union, the expected change in utility for the entrant is

E(ΔUj)=kiβjkτγβjjϕ(0)σj22σjK+j+σK+12kβjkϕ(0)(σk22σkK+j+σK+j2σk2σiK+σK2),(16)

where subscript K+j represents the average of the disturbances including the new member and subscript K refers to the averages of the disturbances excluding the new member.

The first term in the equation, which shows the gain from lower transactions costs with the other members of the union, is the same as in equation (15). However, the losses from joining the union, represented by the second and third terms in the expression, are somewhat different from the earlier case. The second term shows the loss in expected welfare caused by asymmetric disturbances in the region joining the union. It has the same form as the second term in equation (15), but is limited to the joining region since the other regions are already within a currency union, and hence are already affected by the nominal rigidity. The third term represents the loss in utility caused by lower output in the regions that are already within the currency union. This loss results from the fact that a new member, with different underlying disturbances, has joined the union, thereby reducing the expected correlation between the individual disturbances experienced by specific regions and the aggregate disturbance in the entire union.16

Equations (15) and (16) indicate that the change in welfare from joining an already existing currency union is always greater than that from forming a new currency union made up of the same regions. This is because many of the output costs implied in forming a new currency union from scratch are already present for a region that is outside of an already existing currency union. Since these welfare losses are already present, as reflected in the reduction in utility for regions outside of the currency union shown in equations (13) and (15), they do not enter into the calculation of whether or not to join an existing union.

As a result, it is possible that a region which would ideally prefer that all regions have separate currencies may still have an incentive to join a currency union that other regions intend to form. This is because the region will still be negatively affected by the losses in output in other regions within the currency union caused by the common currency even if the region does not join the currency union itself. Since this part of the loss in welfare is out of the control of the region, it has no effect on its marginal decision to join a currency union that is being formed.

While the incentive to join an already existing union is always greater than the incentive to form a new currency union, the incentive to admit a new member to a union is not altered. The change in utility for a region i that is already within a currency union from region J joining the union is

E(ΔUi)=βijτγβijϕ(0)σj22σjK+j+σK+12kγβikϕ(0)(σk22σkK+j+σK+j2σk2σkK+σK2).(17)

The losses in utility in the second and third terms of the expression are very similar to the results for the entrant, shown in equation (16). The expected utility of regions within the existing union is reduced both by lower expected output in the entrant region and by the diminution of the correlation between individual regional disturbances with the mean disturbance within the currency union. Unlike equation (16), however, the gains from admitting the new region for existing members of the union are limited to lower transactions costs on trade with the new entrant. Hence, while the entrant benefits from reduced transactions costs with all of the existing regions in the union, the existing regions only receive lower transactions costs with the new entrant. In general, therefore, small outlying regions with close ties to an existing currency union will have a significant incentive to join that union, while existing members of the union will have no new incentives to let them in. This illustrates the importance of external openness in the benefits of a currency union, a point emphasized in McKinnon (1963) and Mélitz (1991, 1993).

A new entrant into an already existing currency union will also lower utility for regions outside the union. The loss in expected utility is not reported here since it is a simple variation on the losses in utility given in equations (16) and (17).

Labor Mobility

To this point the analysis has assumed that labor is not mobile between regions. In his original article on optimum currency areas, Mundell argued that labor mobility was a key criterion in the choice of a currency union. The reason for this can be clearly seen in the present analysis. The losses from forming a currency union are caused by the nominal rigidity in wages. However, if labor is mobile within the currency union then this will partially nullify the inefficiencies caused by the wage rigidity.

To analyze this issue, the implicit assumption that labor is immobile between regions within the currency union must be relaxed. Ideally, a fully specified process describing labor mobility between regions should be developed. Presumably the incentive for labor to move would be based on the difference between current and expected future income and the costs of moving. However, for the purposes at hand, a simpler mechanism will be outlined.

Assume that all labor that is offered employment within a region stays in that region. If labor is not employed, it can move to another region in the currency union. However, there are costs to this movement. As a result, the rise in effective labor in the region receiving the workers is only a proportion δ of labor that is not employed in the depressed region.17 Hence, if in the initial equilibrium with no labor mobility employment in region J is 1 and in region k is (1 − Z), the new equilibrium involves effective employment levels of (1 + δZ) and (1 − Z), respectively.

If Z is small, then log(l + Z) can be approximated by Z. For the two-region currency union the resulting equilibrium is

yj=ϵj+αδ(ϵjϵk)/2(2(1α)),wj=log(ω)+(1+δ)(ϵjϵk)/2,yk=ϵkα(ϵjϵk)/(2(1α)),wk=log(ω).(18)

The equilibrium for region k, where labor is not fully employed, is the same, since the level of employment is unchanged. However, output (and employment) in region J, the region with the excess demand for labor, is now higher since labor has moved to this region from the depressed region.18 This flow of labor reduces the fall in aggregate output for the monetary union, thus lowering the costs of monetary union for all.

This can be seen in welfare calculations. The expected changes in utility for a region J within the currency union and region m outside it become

E(ΔUj)=βjkτγ(βjj+βjk)(1δ)ϕ(0)σj22σjk+σk2E(ΔUm)=γ(βmj+βmk)(1δ)ϕ(0)σj22σjk+σk2.(19)

The gains from the monetary union remain unchanged. However, the losses in utility caused by lower output are reduced by a factor of (1 − δ). Hence, labor mobility lowers the costs associated with a currency union both inside and outside the union. Indeed, in the extreme case of perfect labor mobility (δ = 1), there are no output costs associated with forming a currency union.

These results easily generalize to the case of a currency union with any number of regions. If proportion δ of the labor in regions with low employment relocates to regions with excess demand for labor, the losses in output and welfare from the nominal rigidity also fall by proportion δ.

III. Reinterpreting the Criteria for Choosing a Currency Union

This model can be used to reinterpret the various criteria set out in the literature on optimum currency areas: the correlation of the underlying disturbances; the level of labor mobility; the openness of the economy; and the level of diversification of the economy. As will be seen, all these criteria are important.

As discussed earlier, the size and correlation of the underlying disturbances are clearly important for the choice of a currency union in this model. This can be clearly seen from the expected welfare calculations, and justifies the empirical literature that focuses on the nature and correlation of underlying disturbances within a region.19 Labor mobility has also been shown to be important, again supporting the empirical work on this form of adjustment.20

The level of openness of the economy to regions outside the currency union matters for both the gains and losses produced by a currency union. The gains from forming a currency union depend directly upon the level of demand for the products of other proposed regions. The losses depend upon the demand for the products of all regions in the union including the home region. Hence, assuming the same structure of underlying disturbances, a region will generally prefer to join in a currency union with another region whose products it uses more rather than less.21

Finally, industrial diversification is also relevant to the choice of a currency union. Consider a group of regions that have joined in a currency union. The regions are highly diversified if the underlying disturbances are not highly correlated. Since the common exchange rate is equal to the mean of these disturbances, it is clear that the more diversified the group of regions, the lower the variance of the external exchange rate. This, in turn, will generally lower the costs of expanding the currency union, since entrants will face fewer aggregate disturbances from the rest of the union.

IV. Conclusions

This paper sets out a formal model of optimum currency areas. The objective was to combine many of the insights from the earlier, less technical, literature in a well-specified model with a stronger basis in microeconomic theory. The result is a flexible framework, which incorporates such fundamental factors as the size of the underlying disturbances, the correlation between the disturbances in different regions, the costs of transactions between different currencies, the level of factor mobility across regions, and the interrelationship of demand between regions. As such, it embodies the criteria for optimum currency areas suggested in the original papers by Mundell, McKinnon, and Kenen.

The framework provides some valuable insights on the welfare effects of currency unions. One is that, while a currency union can raise the welfare of the regions within the union, it unambiguously lowers welfare for regions outside the union. This is because the gains from the union, in the form of lower costs of transacting business, are limited to the members of the union, while the losses from the union, in the form of lower output due to the interaction between the common exchange rate and the nominal rigidity, affect everybody. Hence, regions outside the union partake in the costs of the union but not in the benefits. This very strong result, that a currency union always lowers welfare for those outside the union, depends upon some of the underlying assumptions in the model. Clearly, one can think of circumstances outside the scope of the model in which a currency union could benefit those outside its boundaries—for example, if aggregate output rose within the union due to economies of scale or more efficient financial intermediation. However, the result is a useful reminder that the impact of a currency union need not be benign to those left out of its jurisdiction.

Another insight is that the incentives for a region to join a currency union are different from the incentives to admit a region into a union. The entrant gains from lower transactions costs on trade with the entire existing union, while the incumbent regions only gain on their trade with the potential entrant. As a result, a small region will always have a greater incentive to join a union than the union will have an incentive to admit the new member. A corollary of this is that, even if a country would prefer a free float across all regions, it may still have an incentive to join a currency union with other regions if it is going to be formed. This is because most of the welfare losses from the nascent union will occur whether or not the region decides to join. This set of incentives may explain why some countries in the European Union that are not particularly convinced of the merits of EMU are also worried about being relegated to the second division of a two-speed EMU.

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*

Tamim Bayoumi is an Economist in the Research Department. He is a graduate of Cambridge and Stanford Universities. The author would like to thank Jacques Mélitz for suggesting the topic of the paper, and Jacques Méiitz, Paul Masson, and Erling Vardal for useful comments on an earlier draft.

1

This was largely a response of the wider debate on the value of fixed and flexible exchange rates (Friedman (1953)). Recent work on the choice of exchange rate regimes, such as Canzoneri (1982), have some features in common with the optimum currency literature. Flood and Marion (1992) provide a survey.

2

See Ishiyama (1975), Masson and Taylor (1993), and Tavlas (1993, 1994) for surveys of the optimal currency area literature.

3

Most of this work has been on EMU. Eichengreen (1992) and Bean (1992) provide surveys of this literature, which includes work on the nature of the underlying shocks, factor mobility, and other mechanisms to alleviate asymmetric shocks such as federal fiscal policy. There is much less work on other regions, although Bayoumi and Eichengreen (1994) and Ghosh and Wolf (1994) provide some wider-ranging results.

4

Tavlas (1993, 1994) surveys this literature. Many of the issues discussed by him are not dealt with in the relatively simple framework adopted here. These include the effectiveness of monetary policy; the roles of political preferences, time inconsistency, and fiscal policy in the choice of regime; the speed with which external adjustment affects the domestic economy; and the relationship between the regime and the speed of adjustment. Like this paper, Mélitz(1991, 1993) has tried to further integrate the theory of optimum currency areas with the theory of international trade. This paper differs from his in using a simpler framework with greater focus on microeconomic foundations. Casella (1990) presents a model of behavior in a currency union with more emphasis on microeconomic foundations, but focuses on the issue of relative weights of countries within a common central bank.

5

Clearly, exchange rate policy cannot respond to disturbances of this type. This is discussed further in Mélitz (1991).

6

The assumption of normality simplifies the analysis later, but is not necessary.

7

The assumption that region 1 has no productivity disturbance simplifies the definition of the numeraire, but has no other importance in the model.

8

This type of adjustment is similar to that assumed in the disequilibrium models originated by Clower (1967).

9

This represents all the costs of transferring from one currency to another, including those associated with transactions, different units of account, and legal and institutional differences between currency unions.

10

The ϕ term simplifies the analysis later.

11

Since the transactions costs arc modeled using the iceberg assumption, the demand for goods at the point of production need not be equal to consumption at the point of delivery.

12

The consumption price for good i in region J is Pi/(1 − TJ), Consumption prices for good i can differ across regions because of transactions costs; they are only equalized at the point of production.

13

The existence of other currency unions has no material implications for the analysis.

14

The expected value of a standard N(0,σ2) normal variate ∈ given that ∈ > X is σ ϕ(X)/Φ(X) where ϕ(.) and Φ(.) are the density function and the cumulative density function of a standard N(0,1) normal distribution.

15

This analysis has something in common with that of customs unions (Viner (1950)), where again the impact on those outside the union is often detrimental.

16

For the union as a whole, the expected output must fall since the addition of a new region increases the variance of total disturbances within the currency union. Individual regions within the union could, however, have a rise in expected output if their output disturbances are highly correlated with those of the region that is joining the union.

17

The initial model can be thought of as having δ = 0.

18

The approximation log(1 + Z) = Z slightly underestimates the rise in aggregate output since it fails to account for the fact that labor is moving from a low-productivity region to a high-productivity one.

20

Blanchard and Katz (1991) and Eichengreen (1992).

21

This mechanism, however, is rather different from the one proposed by McKinnon.