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Is Europe an optimum currency area? Symmetric versus asymmetric shocks in the EC.


Much of the debate on the desirability of a monetary union in Europe has focused on the question of whether Europe can be described as an optimum currency area (OCA). The European Commission in its report 'One money, one market' takes the view that this theoretical framework gives useful insights for the analysis of the economics of EMU and its potential costs and benefits, even though it is not decisive, but it has to be complemented by other approaches. Many studies have tried to provide an answer to the topical question of the optimality of introducing a single currency, adopting different research strategies. This note explains why a knowledge of the nature of the shocks is crucial to evaluating the potential costs of creating a monetary union, and applies a statistical technique known as principal components analysis to distinguish between common and country-specific shocks. After surveying the existing literature on OCAs, we present some new empirical results which confirm the relative importance of asymmetric shocks in the Community. A well-functioning monetary union could require some instruments for adjusting to shocks of this kind, for example fiscal transfers across the member countries.

Optimum currency areas

The adoption of a single currency will have both benefits and costs. The former will be mainly in the form of lower transaction costs and of the disappearance of currency risks. The latter will be due to the inability of national governments and central banks to pursue independent monetary policies to stabilise the economy. The extent to which the loss of this policy instrument will affect the adjustment to equilibrium will depend on the degree of flexibility of factor markets and the nature of the shocks hitting the economy: the more rigid factor markets and the more country-specific the shocks, the more important will be the loss of monetary autonomy. These issues are addressed by the theory of optimum currency areas (OCAs), whose implications are crucial to answering the question whether Europe should proceed to adopting a single currency. If factors of production are not sufficiently mobile, asymmetric shocks result in high costs of adjustment, in terms of higher unemployment and lower output, in the presence of fixed exchange rates.(1)

New Classical economists have long suggested that the transaction costs resulting from multiple currencies should be weighed against the benefits of each country being able to adopt its own optimal monetary policy. In their view, the problem of setting monetary policy in an optimal way is not dissimilar from that of choosing the optimal tax structure, as the process of money creation can be seen as being essentially a tax on private agents' money holdings. Consequently, if the macroeconomic environment is significantly different across countries, different tax structures and currencies are the optimal outcome.

The arguments for and against monetary integration are not as straightforward as those concerning economic integration more generally. As Paul Krugman (1989) says:

'The economics of international money, by contrast |to those of trade integration~, are not at all well understood; they hinge crucially not only on sophisticated and ambiguous issues like credibility and coordination, but on even deeper issues like transaction costs and bounded rationality'

In its study 'One Market, One Money' (1990), the European Commission relies heavily upon the theory of optimum currency areas to evaluate the economic impact of EMU. Much of the analysis is based on the framework developed by Robert Mundell, Ronald McKinnon and other economists in the 1960s, though it is stressed that other fields of economic research are relevant for the analysis of EMU. They include new contributions to the analysis of the following topics:

* the workings of markets in the presence of externalities, adjustment or information costs (see Baldwin, 1990);

* the choice of an optimal exchange-rate regime in a stochastic environment (see Argy, 1990, for a survey);

* macroeconomic games between the authorities and the private sector and policy coordination issues (see the seminal paper by Barro and Gordon, 1983, and the survey by Currie, Holtham and Hughes Hallett, 1989);

* the relative performance of alternative exchange-rate systems (see Baxter and Stockman, 1988);

* the economics of EMU (see Brociner and Levine, 1992).

Costs and benefits of EMU are evaluated in 'One market, one money' by running a set of simulations with two macroeconomic models: the Quest model developed by the Commission Services, and the IMF Multimod model. The Commission concludes that EMU ensures more microeconomic efficiency and macroeconomic stability. The improvement in the latter is put down especially to a reduction in the degree of exchange-rate instability, and to higher credibility of the monetary authorities. The Commission, however, recognises that the nature of macroeconomic shocks is crucial to assessing the net benefit of EMU. As they put it:

'..the only important disadvantage of EMU concerns macroeconomic stability in the presence of asymmetric shocks. This is indeed a well-known argument and has unambiguously to be considered a cost, but one that should be weighed against the clear advantages EMU yields in other fields' ('One Market, One Money', p. 56).

The Commission also points out that, while country-specific shocks are by definition asymmetric, common shocks may affect national economies either symmetrically or asymmetrically, and that the main factors determining whether or not their impact is symmetric are the degree of product market integration, and differences in economic behaviour and structures. They empirically examine the degree of asymmetry in sector-specific shocks and find that sectors producing homogeneous goods with few trade barriers mainly experience symmetric shocks. In the other sectors, there appears to be an inverse correlation between the existence of trade barriers and the degree of symmetry of the shocks, with the obvious implication that the completion of the common market should decrease sector-specific asymmetric shocks.

The seminal paper on optimum currency areas (OCAs) is due to Mundell (1961). In his definition, an optimum currency area is an economic unit where factors of production are mobile and whose regions are affected symmetrically by shocks. Mundell stressed that the degree of labour mobility should be the main criterion for the choice of such an area. In a famous example, he considered the case of two countries A and B producing good a and b respectively. If there is a permanent preference shift from a to b, equilibrium can be restored by a change either in quantities or in the relative price. Migration of the labour force across the two countries will achieve the first. As for the second, given the fact that the nominal exchange rate can not be changed if there is a common currency, the remaining possibility is a fall in the price level in A relative to B. In the presence of rigidities, there will be a sluggish adjustment and A will incur unemployment costs. Hence the adoption of a single currency is optimal only if factors are highly mobile. However, even high labour mobility does not necessarily imply that the adoption of a single currency should be optimal, as

'It is simply doubtful that the movement of working masses can be relied on as a substitute for payments adjustment when it can be assumed that they are reluctant to move even within the same country' (Ishiyama, 1975)

A further criticism often levelled against Mundell's type of analysis is that it ignores the fact that floating exchange rates can result in non-cooperative or sub-optimal policies.

The permanent preference shock discussed above is an example of an asymmetric shock, in which case the constraints of a monetary union are binding if labour is not sufficiently mobile. The recessionary effects are transmitted across countries because the exchange rates are fixed, and they can not be used to offset disturbances. Under these circumstances, it would be optimal to adjust the exchange rates, i.e. the countries are not an OCAs. Clearly, a common policy response would be optimal only if the disturbance affected all the countries in the same direction and to the same extent. Hence some knowledge of the incidence of the two different types of shocks, i.e. Community-wide and country-specific disturbances, is necessary to give a realistic assessment of the prospects for EMU.

Mundell's criterion of a high factor mobility (capital as well as labour) is not the only one proposed in the theoretical literature on currency unions to determine the desirability of such a union (see Masson and Taylor, 1992, for a similar discussion). We mentioned above the reduction in transaction costs which derives from the creation of a currency union. This clearly implies that, the higher the degree of interdependence between the prospective members of the union in terms of trade flows, the greater will be the benefits from a monetary union. A related result is due to McKinnon (1963), who showed that in more open countries the exchange rate is less effective as a policy instrument, and hence its loss represents a lower cost. Krugman (1989) argues that the costs of fixing the exchange rates are outweighed by the benefits if there is intensive trade within the currency area.

A further criterion is based on the degree of diversification of the economy (see Kenen, 1969). The more specialised countries are in the production of different goods, the more likely it is that shocks will be asymmetric, the more costly it is to forego exchange-rate flexibility. Finally, an issue not considered in the original literature is the flexibility of wages and prices. There is plenty of evidence that real wages are quite rigid in Europe, which implies that the real exchange rate is also quite rigid (see Eichengreen, 1991). Consequently fluctuations in the nominal exchange rate do not have large real effects in the labour market, and its irrevocable fixing (or, equivalently, the adoption of a single currency) would not be particularly costly in terms of unemployment.(2)

In the empirical literature, some studies have looked at the variability of real exchange rates as an indication of the asymmetry of the shocks, as this should be related to demand or supply shifts across countries. Poloz (1990) found that real exchange rates between Canadian provinces are more volatile than those between the major four European countries, and hence a monetary union is feasible. Conversely, they seem to be more variable in Europe than between US regions (see Eichengreen, 1990b, who uses consumer price indices for four geographical regions), and less variable within European countries than between them (see De Grauwe and Vanhaverbeke, 1991, whose analysis is based on unit labour costs). Similarly, real share prices, which should reflect the present value of present plus expected future profits, are found to diverge more in Europe than in Canada, with the implication that shocks are less symmetric across Europe (see Eichengreen, 1990a).

Other papers examine the behaviour of output with the aim of establishing the nature of the shocks. Cohen and Wyplosz (1989), who associate asymmetric with transitory shocks and symmetric with permanent shocks, find that symmetric shocks to France and Germany dominate the asymmetric ones. However, the opposite is true when France and Germany taken together ('Europe') are compared to the US, suggesting that a monetary union between France and Germany would be more well-functioning than one between 'Europe' and the US. A similar approach is taken by Weber (1990). He finds that, in the original members of the ERM, real wages and the unemployment rate during the EMS period are dominated by asymmetric shocks, whereas inflation is mainly affected by symmetric shocks.

Bayoumi and Eichengreen (1992) point out that movements in relative prices and output contain only limited information regarding the nature of the shocks, as they could be due to either asymmetric shocks or different speeds of adjustment. Their approach to identifying the disturbances is, following Blanchard and Quah (1989), to decompose a bivariate VAR including the first difference of the logarithm of output and prices. They assume that demand and supply shocks are uncorrelated and that only the latter have permanent effects on output. Their main findings are that supply shocks are larger in magnitude and less correlated across regions in Europe than in the US, and that there is a core of EC members (Germany, France, Belgium, Luxembourg, the Netherlands and Denmark) whose supply shocks are relatively small and highly correlated and another group of states, the 'EC periphery', with bigger and more country-specific shocks.

Principal components analysis

In this section we report some estimates of correlation matrices for output innovations in EC countries. These correlation matrices will have large positive off-diagonal elements if output fluctuations are mainly due to aggregate shocks. We then employ a statistical technique known as principal components analysis to determine to what extent the system is driven by symmetric as opposed to asymmetric disturbances. Such procedure is, however, subject to an important caveat. The assumption made is that all comovements of the variables in the system can be attributed to common factors, that are by definition unobservable and that are identified as Community-wide shocks in our case. Since comovements can also be generated by unique factors (in our case, country-specific shocks) which are, however, correlated with each other, only an upper limit for the explanatory power of the aggregate shocks can be determined.

The percentage of the normalised total variance of each variable which can be explained by the individual principal components equals the squares of the factor loadings (also known as connection coefficients), which show the weight applied to each component in expressing each series as a function of the components. The sums of the squares of the factor loadings, known as communality estimates, can therefore be interpreted as the percentages of the total variance of each variable explained by all principal components included in the model.

We have to generate estimates of the shocks or innovations to the set of economies of interest. One way of doing this is to estimate the following vector autoregression (VAR):

|Delta~|y.sub.t~ = a + B|Delta~|y.sub.t - 1~ + C|Delta~|y.sub.t -2~ + D|Delta~|y.sub.t - 3~ + E|Delta~|y.sub.t - 4~ + |u.sub.t~ (1)

where |y.sub.t~ stands for the logarithm of nominal GDP, a is a vector of constants, B, C, D and E are coefficient matrices, and |u.sub.t~ is a vector of disturbance terms. The estimation period is 1970: 1 1991:4.(3)

Table 1 reports the correlation matrix of the shocks, and suggests that EC-wide disturbances do not play a very important role in driving GDP fluctuations. Although all the off-diagonal elements but one are different from zero, indicating that shocks are correlated across countries, most of them are not significant at the 5 per cent level.(4) The size of the correlation coefficients varies across countries, with Germany exhibiting some of the biggest coefficients. In most cases the correlation is positive, but the shocks to Belgium appear to be negatively correlated to fluctuations in the Southern countries, and, surprisingly, to shocks to the German economy. It is also to be noted that the shocks to Italy move in the opposite direction of these to France, and are not significantly correlated to shocks to the German or UK economy. Conversely, the shocks affecting the UK and French economies are highly correlated to the German ones. Disturbances in the Netherlands do not appear to mirror closely the shocks to the German economy, perhaps reflecting the role of energy in Dutch output. On the whole, fluctuations in the remaining countries, especially the Mediterranean ones, are less closely related to those in the three 'core' countries, although the correlations between Germany and Denmark, France and Spain, and the UK and Belgium are quite high.
Table 1. Nominal GDP: correlation matrix of shocks

 Denmark Spain Portugal Greece

Denmark 1.00
Spain 0.09 1.00
Portugal 0.39 0.02 1.00
Greece 0.18 0.24 0.26 1.00
Germany 0.34 0.03 0.47 0.07
France 0.17 0.26 0.10 0.12
Belgium -0.28 -0.02 -0.16 -0.21
Netherlands -0.15 0.36 0.00 0.04
Italy 0.08 -0.01 0.09 0.31
Ireland 0.17 0.17 0.15 0.08
UK 0.04 -0.21 0.01 -0.22

 Germany France Belgium Netherlands

Germany 1.00
France 0.20 1.00
Belgium -0.31 0.01 1.00
Netherlands 0.01 0.16 0.40 1.00
Italy -0.11 -0.24 0.21 -0.03
Ireland 0.09 0.10 0.21 0.18
UK 0.25 0.25 0.22 0.10

 Italy Ireland UK

Italy 1.00
Ireland 0.29 1.00
UK 0.01 0.16 1.00

Number of observations: 79.

Principal components analysis was then carried out on the estimated residuals |u.sub.t~. For the EC as a whole, we find that a large percentage of the fluctuations of GDP is driven by three principal components. Table 2 contains the eigenvalues and cumulative |R.sup.2~ for each component. The characteristic roots equal the sum of the squared loading factors, and the cumulative |R.sup.2~, which is the fraction of the total variance of the original variables explained by all the components up to and including the third, is equal to the corresponding eigenvalue divided by the number of variables. It appears that 50 per cent of the total variance is accounted for by the three principal components, which can be interpreted as EC-wide shocks.

It is of interest to consider whether similar patterns can be observed across the EC member states. Factor loadings by country are reported in Table 3. They show the direction in which the corresponding variable moves with regard to the other variables, positive loadings indicating that there is comovement. The first principal component has positive loadings for all countries, with the exception of Belgium and the Netherlands, which seem to move in the opposite direction to their European partners. The factor loadings for the second principal component would indicate that Germany and the rest of the Community, with the exception of Denmark and Portugal, do not have synchronised cycles. Concerning the factor loadings for the third component, it appears that Germany, France, the UK, Belgium and the Netherlands have similar economic cycles, whilst the other countries, which have factor loadings of the opposite sign, experience different economic fluctuations.
Table 2. Nominal GDP

Component Eigenvalue Cumulative |R.sup.2~

1 2.24 0.20
2 1.85 0.37
3 1.44 0.50
Table 3. Nominal GDP: factor loadings

 PC1 PC2 PC3

Denmark 0.71 0.12 0.02
Spain 0.29 -0.43 0.20
Portugal 0.72 0.02 0.03
Greece 0.48 -0.07 0.56
Germany 0.70 0.08 -0.37
France 0.39 -0.33 -0.43
Belgium -0.44 -0.69 -0.03
Netherlands -0.02 -0.74 -0.08
Italy 0.07 -0.27 0.63
Ireland 0.28 -0.57 0.14
UK 0.07 -0.31 -0.59

Finally, Table 4 gives in turn the percentage of the variance of the shocks affecting each country explained by each of the three principal components, by the first two components, and by all three of them. As can be seen, the percentage explained by the first two components ranges from a minimum of 8 per cent in Italy to a maximum of 67 per cent in Belgium. When a third component is added, the range is from 30 per cent (Spain) to 67 per cent (Belgium). The third component adds significantly to the explanatory power of the principal component model in many EC countries, especially Italy, where it seems to be the only symmetric shock of substantial importance.

We have carried out the same analysis for real GDP. A system of fixed exchange rates requires nominal convergence but not necessarily real convergence, where real TABULAR DATA OMITTED convergence is taken to mean narrowing the dispersion of real variables, e.g. output per head or unemployment rates(5). The latter might not even be desirable during the transition period, although it is a long-term goal of European integration. Therefore it is important to distinguish between static and dynamic convergence. In steady state, given free factor mobility, factor price equalisation (FPE) and purchasing power parity (PPP) for tradeable goods will hold in EMU (see Mundell, 1961). However, the dynamic adjustment towards the steady state might require the persistence of some differentials to bring about convergence in the long run, which means that further real convergence prior to the establishment of EMU might not be called for.

The shocks are again generated by estimating a VAR and a principal components model is then estimated. The correlation matrix (see Table 5) now contains even less significant coefficients. The correlation patterns, though, are rather similar, with the shocks to Belgium and the Netherlands being negatively correlated to those to Denmark, Portugal, Greece and France. The correlation coefficients between Ireland and the UK, and the Southern countries are also negative. Furthermore, it appears that the correlation between real shocks to the Dutch economy and shocks to Germany and France is, if anything, negative. The percentage of the total variance explained by the model is slightly lower in the case of real shocks, equalling 49 per cent (see Table 6). The factor loadings on the first two components (see Table 7) show, respectively, that the cycles in the Netherlands and Ireland are not synchronised with the rest of the Community, and that only fluctuations in Denmark and Portugal follow those in Germany. As for the third component, it suggests that Germany, Denmark, Ireland and the UK move in the same direction in response to real shocks to their economies. The first two components (see Table 8) account for a maximum of 64 per cent of the total variance (France) and for a minimum of 13 per cent (UK). When a third component is added, the maximum becomes 68 per cent (France), and the minimum 23 per cent (Ireland).
Table 5. Real GDP: correlation matrix of shocks

 Denmark Spain Portugal Greece

Denmark 1.00
Spain -0.08 1.00
Portugal 0.12 -0.10 1.00
Greece 0.09 0.10 0.21 1.00
Germany 0.32 0.04 0.32 0.20
France 0.29 0.48 0.04 0.27
Belgium -0.06 0.05 -0.12 -0.01
Netherlands -0.37 0.06 -0.19 -0.27
Italy 0.05 0.29 0.22 0.14
Ireland 0.09 0.08 -0.07 -0.09
UK 0.28 0.04 -0.14 0.02

 Germany France Belgium Netherlands

Germany 1.00
France 0.16 1.00
Belgium 0.18 -0.01 1.00
Netherlands -0.12 -0.39 0.16 1.00
Italy -0.02 0.31 0.12 0.23
Ireland -0.01 0.05 0.09 0.18
UK 0.13 0.15 0.23 -0.01

 Italy Ireland UK

Italy 1.00
Ireland 0.17 1.00
UK 0.05 0.05 1.00


In this note we have first briefly discussed the traditional criteria under which a currency union is deemed to be viable in the 'optimum currency area' literature. They are labour mobility, wage and price flexibility, diversification of the economies of the member countries, and interdependence as measured by the volume of trade between the potential members of the monetary union. We have then surveyed the other empirical studies carried out to date, which provide mixed evidence on whether or not the EC is an optimum currency area. The conclusion most often reached is that the forthcoming monetary union will be successful only if it will be restricted, at least initially, to those states with more economic homogeneity and who experience more similar disturbances (see e.g. the 'two-track' EMU proposal put forward by Dornbusch, 1990).
Table 6. Real GDP

Component Eigenvalue Cumulative |R.sup.2~

1 1426893-5312.28 E0-21
2 1.73 0.36
3 1.38 0.49

We have shown that asymmetric shocks account for a sizeable percentage of GDP fluctuations in the EC. Since principal components analysis only sets an upper limit to TABULAR DATA OMITTED the percentage of the total variance which can be explained by the common factors, they could be even more important than suggested by our results. This does not imply that EMU is not feasible, as real convergence is not required in the transition period before the establishment of a monetary union. However, it does indicate that the operation of a currency union could be rather difficult, although, unlike Bayoumi and Eichengreen (1992), we do not find conclusive evidence that there are in the EC a 'core' and a 'periphery'. Some instruments for adjusting to asymmetric disturbances, e.g. fiscal transfers, could therefore be necessary.
Table 7. Real GDP: factor loadings

 PC1 PC2 PC3

Denmark 0.62 0.22 0.39
Spain 0.32 -0.62 -0.37
Portugal 0.42 0.32 -0.19
Greece 0.54 0.09 -0.24
Germany 0.74 -0.30 -0.22
France 0.74 -0.30 -0.22
Belgium 0.01 -0.43 0.52
Netherlands -0.57 -0.53 0.07
Italy 0.31 -0.60 -0.27
Ireland -0.00 -0.44 0.19
UK 0.27 0.24 0.65


In principal component analysis the observations are normalised so that their expected value equals 0 and their variance equals 1, to yield:

| = ||| (t=1,2,...,T;g=2,...,N) (A1)

where |Mathematical Expression Omitted~ and || is the standard deviation of the variable. The matrix of simple correlation coefficients has then the following formula:

R = ZZ'/N (A2)

This normalisation, that expresses the deviations of the original observations from their arithmetic mean in their standard deviations, is done to make mutual comparison possible. The equation for a principal components model is:

| = ||f.sub.lg~ + |a.sub.i2~|f.sub.2g~ +...+ || + | (A3)


* | is the value at time t of the normalised observation on the gth variable (g=1,2,...N; t=1,2,...T);

* |a.sub.ig~ is the regression coefficient of the ith principal component for predicting the jth variable (i=1,2,...n; j=1,2,...m);

* |f.sub.ig~ is the value of the jth observation on the gth principal component;

* m is the number of principal components;

* | is the error term.

The model can be written in matrix form as:

Z = AF + e (A4)

where Z is the matrix of normalised observations, A is the matrix whose elements |a.sub.ij~ are known as factor loadings or connection coefficients, F is the matrix of components, and e is the vector of errors. Substitution of (A4) into (A2) gives the relationship between R, the correlation matrix of the normalised observations, and A, the matrix of the connection coefficients:

R = ZZ'/N = AF(AF)'/N = AFF'A'/N = AA' (A5)

where the product FF' is 1 since by construction the components are uncorrelated with each other and have unit variance. It can be shown that the vectors |a.sub.j~ are orthogonal because they are proportional to the characteristic vectors |v.sub.j~ of the matrix R, being of the following form:

|Mathematical Expression Omitted~

where the ||Lambda~.sub.j~ are the characteristic roots of R. Thus the 'aspect' vectors |a.sub.j~ are nothing else than the scaled characteristic vectors of the symmetric, positive definite matrix R (the term 'aspect' is used to denote the column vector with elements |a.sub.ij~ or |Mathematical Expression Omitted~, i=1,2,...n, containing the pattern of motion produced by the general causal factor |f.sub.j~). Principal components analysis selects m characteristic vectors |f.sub.j~ out of the n characteristic vectors of the matrix R which can describe the variables in terms of equation (A4).


Quarterly GDP data are available only for the four major European economies (Germany, France, Italy, UK). For the other countries, the annual data have been interpolated to produce quarterly series. The seasonally adjusted quarterly path for nominal GDP has been determined using information from the industrial production and consumer prices series; real GDP has been made to grow in line with industrial production. The data sources are the following:

Nominal GDP:

* Germany: Statistische Beihefte zu den Monatsbereichten der Deutschen Bundesbank, Reihe 4; DM billion.

* France: OECD Quarterly National Accounts; FF billion.

* Italy: Istituto Centrale di Statistica (ISTAT); Lire billion.

* UK: Economic Trends, Quarterly Article on National Income, |pounds~ million.

* Other EC countries: OECD Economic Outlook diskettes (mnemonic: GDP).

Real GDP:

* Germany: Statistische Beihefte zu den Monatsbereichten der Deutschen Bundesbank, Reihe 4, Table 1, Brutto Inlandsprodukt, 1985 prices, DM billion.

* France: OECD Quarterly National Accounts, France section, Table 1B, GDP, 1980 prices, FF billion.

* Italy: Istituto Centrale di Statistica (ISTAT), 1985 prices, Lire billion.

* UK: Economic Trends, Quarterly Article on National Income, Table A1, GDP at 1985 market prices (CAOO), |pounds~ million.

* Other EC countries: OECD Economic Outlook diskettes (mnemonic: GDPV), 1986 prices, million.

Industrial production series:

OECD Main Economic Indicators, total industrial production, seasonally adjusted data.

Consumer prices series:

OECD Main Economic Indicators, not seasonally adjusted.


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(1) Note that it is argued by some that the theory of OCAs gives limited insight because does not take into consideration that policy is not a non-negligible source of disturbance to an economy. A change of regime may imply a change in the institutional structure of policymaking and the incentive structure of policymakers. In the case of the EMS, it may be argued, the operational requirements implied by the participation in its exchange-rate mechanisms have changed the policy of member governments and, therefore, the shocks that are caused by policy.

(2) Note that this result only holds for the evaluation of real shocks, and it assumes that changes in the nominal rate do not have permanent real effects. If some assets held abroad are fixed in nominal foreign currency then a change in the nominal rate appears to have real effects. Many shocks are nominal, and removing the nominal exchange rate removes a nominal shock absorber.

(3) For a more technical explanation of principal components analysis, see the Appendix. Standard references are Mulaik (1972), Gorsuch (1974), and Harman (1976).

(4) Under the null hypothesis |H.sub.o~:p=0, p being the population correlation coefficient, the variable Z=|z|Sigma~.sub.z~, where |Mathematical Expression Omitted~ is the sample size and r is the sample correlation coefficient, is distributed approximately N(0,1). The critical value at the 5 per cent level is 1.96, which, given a sample size of 79, implies that values of +/-0.22 are required for significance.

(5) This raises the issue of 'cohesion', and it is mainly a political judgement whether or not only market forces should be relied upon to achieve real convergence (see Britton and Mayes, 1992, or Barrell, ed., 1992). Note also that there is a third kind of convergence, which can be called structural convergence, i.e. the convergence of institutions and economic structures (see again Britton and Mayes, 1992).

I would like to thank Ray Barrell and Nicholas Oulton for helpful comments and suggestions.
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Author:Caporale, Guglielmo Maria
Publication:National Institute Economic Review
Date:May 1, 1993
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