Optimum Currency Areas , Real and Nominal Convergence in the European Union

It is well known and widely accepted by economists that the characteristics of the European countries that become the Eurozone in 1999 did not match the requirements of an Optimum Currency Area (OCA). The only criteria for membership of the new area were nominal. A strict level of convergence in inflation and interest rates was imposed. In addition to the nominal convergence (monetary), a process of convergence of nominal incomes in the new monetary unit was expected to be generated with the monetary integration. After summarizing the criteria for a successful currency area in the context of the OCA theory, we study the real and nominal convergence process for an older group (11) of countries to establish whether or not these countries form an OCA. We apply the original conditions imposed on ADF tests, together with the Schmidt-Phillips tests, and we estimate fractional differential process to overcome the disadvantages of the traditional tests. We conclude that a process of real divergence and nominal convergence does exist. We think this is a source of genuine imbalance in the European integration process that can destroy the harmonious development of a European Monetary Union. JEL Classification: C01, E24, F31, J31.


Introduction
In 1961, Robert Mundell published in the American Economic Review, his famous paper "A Theory of Optimum Currency Areas" (Mundell, 1961), presenting his idea of an optimal monetary area.
Nearly four decades later, in 1999, the European Union (EU) created its monetary area with the common currency the Euro.At the beginning, the European single currency was used purely as bank money, but in 2002, the Euro was introduced as a banknote and since then it has been used as the means of payment in the EU.
However, for centuries before, the situation in Europe and indeed, worldwide, seemed to be that each country had its own currency (Baldwin and Wyplosz, 2009), and at the extreme, some cities of regions differentiated their currencies.Hence, national symbols were displayed on coins and banknotes, and in earlier times, feudal lords had their faces stamped on gold and silver coins.
Apart from indicating national and regional boundaries, a currency is also useful because it enables and stimulates commercial and financial transactions, and because it is immediately recognized.The more people accept a currency, the more useful it is as a currency.
In that sense, a continent of many countries and states, as for example, Europe, can be expected to benefit from having the same currency (Rose, 2000;Frankel and Rose, 2002;Baldwin and Wyplosz, 2009;Eicher and Henn, 2009), which is acceptable anywhere in the region and which allows for global trade without incurring costly transactions.This is one of the main reasons underpinning the Optimum Currency Area (OCA) theory, and it is this that we discuss in this paper, not only to analyze whether the European Union (Eurozone) is indeed an Optimum Currency Area, but also to investigate the existence of real and nominal convergence in that geographical zone in which a restricted group of countries has shared the same currency since 1 January, 1999.
In fact, from the beginning of the introduction of the Euro, there have been many discussions on the issue of whether the Eurozone could actually be classified as an OCA and whether the decision to unify various EU member countries under one common currency, has been right.More recently, in the current monetary crisis, the skepticism concerning this decision has intensified (Furrutter, 2012), and hence, it is appropriate to re-appraise the EU-OCA discussion and to examine the rationale for founding the common currency area and the criteria for inclusion.
Our contribution to the debate and literature stems from the fact that we attempt to assess the depth of European integration under the two perspectives of real and nominal convergence.For this purpose, we study the processes of real convergence and nominal convergence based on spectral analysis, Hurts indicator, Augmented Dickey-Fuller (ADF), and Schmidt-Phillips unit root tests, and fractionally-integrated processes.
The paper is structured in five sections.In section 2 we summarize Robert Mundell's theory concerning OCAs by briefly reviewing the often-cited economic and political criteria for a successful currency area.In section 3, from Mundell's OCA-theory we address the question of whether the European Union (Eurozone) really is an OCA.In section 4, we answer this question by assessing the integration process of the older EU 12 (-1) member countries.
Finally, in section 5, we present some concluding remarks based on empirical evidence.

Optimum Currency Area Theory
The notion of an Optimum Currency Area was pioneered by the economist Robert Mundell (Mundell, 1961).Credit often goes to this author as the architect of the idea, but others (for example, Scitovsky, 1984) point to earlier studies conducted on the same subject, namely by Abba Lerner (Lerner, 1944(Lerner, , 1947).
An Optimum Currency Area (OCA) is a geographical region which, if sharing a single currency, would be able to maximize economic efficiency in that area.The theory attached to the OCA describes the optimal characteristics for the merger of currencies or the creation of a new currency.In that sense, the theory is a systematic way of trying to decide whether or not a group of countries would benefit from abandoning their national currencies and adopting a single currency.In its turn, a single currency is associated with monetary union, which itself is one of the final stages of economic integration.For this reason, this theory is often mentioned when discussing the European integration process, and the creation and functioning of the Eurozone.
The basic question which OCA theory attempts to answer is what conditions must be fulfilled for two or more countries to use the same currency instead of separate ones?At the same time, it is also pertinent to ask in the case of the Eurozone, is it advantageous for the current 18 member countries to use the Euro as their common currency rather than having their own currencies?
To answer these questions, the theory of OCA develops a set of economic and political criteria which recognize that the real economic cost of relinquishing the exchange rate instrument and accepting a single currency, arises in the presence of asymmetric shocks, which in themselves do not affect all monetary union member countries.
The main tenets of OCA theory are that for a currency area to operate properly, member countries must demonstrate similar economic and political conditions, and have sufficiently flexible labor, capital, and product market to permit adjustment in the face of asymmetric shocks.
There are four classic, and often-cited economic criteria for a successful currency area, these being: i) labor mobility across the region; ii) openness with capital mobility and price and wage flexibility across the region; iii) production diversification; and iv) similar business cycles for participant countries.In addition, three more political criteria can be identified, these being: v) fiscal transfer mechanism to redistribute income to areas/sectors which have been adversely affected by labor mobility and openness; vi) similar (homogeneous) preferences/ideologies; and vii) solidarity ('commonality of destiny') 1 .
The first criterion was suggested by Robert Mundell in 1961 when he developed the concept of an OCA (Mundell, 1961).His main underlying belief was that the costs involved in sharing a common currency would be eliminated if the factors of production, labor and capital, were fully mobile across borders.As it is usually supposed that capital is perfectly mobile, the real barriers then come from the absence of labor mobility.This criterion implies that countries with good opportunities should attract labor from those with few employment opportunities.In other words, if there is unemployment in one country, people must move to another country.So, according to the Mundell criterion, an OCA is one in which people can move easily.Such ease of movement requires not only the absence of visas, and the presence of workers' rights, but also the removal of any cultural and institutional barriers to free movement, such as different languages and different pension schemes throughout the region.Thus, the labor mobility criterion advocates that if member countries in a currency area are hit by asymmetric shocks, they should have a high degree of labor mobility so as not to create gross disparities between the member countries. 1The labor mobility criterion is related to the way of minimizing the costs of an asymmetric shock within a currency area.The three other economic criteria look at a different problem.They aim at identifying which regions are unlikely to be hit by external shocks infrequent or moderate enough to be of limited concern.The last three criteria deal with more political issues.They ask whether different countries are likely to help each other when faced with asymmetric shocks.In the explanation of the OCA criteria we follow very closely the presentation by Frankel and Rose (1998) and Baldwin and Wyplosz (2009).
The basic idea behind the second criterion, openness with capital mobility and price and wage flexibility across the region, was formulated by Ronald McKinnon, according to whom, countries which are very open to trade, and trade intensely with each other, form an optimum currency area (McKinnon, 1963).So, if trade is flowing freely, the market forces of demand and supply automatically distribute money and goods to where they are necessary.
Consequently, their prices will be the same at home and abroad.Changing the exchange rate will thus not affect the relative prices of such domestic and foreign goods.In other words, exchange rate changes leave the country's competitiveness unchanged.The more open the region, the more important is this observation.
However, in practice this does not work perfectly as there is no true wage flexibility.
For example, in the case of the Eurozone, member countries trade significantly with each other.
Intra-European trade is greater than international trade.As suggested by the most recent empirical analysis of the Euro effect, the use of the European single currency has increased trade by 5-15% in the Eurozone when compared to the trade between non-Euro countries (Micco, Stein and Ordonez, 2003;Rose, 2004;Baldwin, 2006;Berger and Nitsch, 2008;Bergin and Ching-Yi, 2012).
According to the third criterion, initially identified by Peter Kenen, countries whose production and exports are widely diversified and of similar structure, form an OCA (Kenen, 1969).Therefore, a country that has a wide range of products will have a slower decrease in its production if external demand falls.On the contrary, a country with a low degree of diversification would then need to use its monetary policy to reduce shocks, whereas a highly diversified economy may find it valuable to form a currency union.In that case, good-specific shocks are likely to be of little aggregate consequence and to affect all member countries in a similar way, thus lessening the need for any exchange rate adjustment (Baldwin and Wyplosz, 2009).
Under these circumstances, member countries in a currency area should be well diversified and produce similar goods.In this way, there will be fewer macroeconomic shocks and they will be more symmetric.Countries that are well diversified will not often face changes in demand for their exports products, and that product diversification decreases the likelihood of asymmetric shocks.
The next relevant criterion of an OCA also implies that member countries of the currency area should not be subject to asymmetric shocks.Participant countries must have similar business cycles, which means that they should experience economic ups and downs at the same time, so that counter-cyclical measures adopted by the area's central bank will have positive effects on all countries (Long and Plosses, 1983;Artis and Zhang, 1995;Caporale, Pittis and Prodromidis, 1999).In fact, when one country experiences a boom or recession, other countries in the currency union are likely to follow.This allows the area's central bank to stimulate economic growth in downturns and to restrain inflation in booms.So, this criterion requires that member countries of the currency area should not be significantly different in terms of economic development and growth.
The fifth criteria, already of political order, states that for a currency area to operate optimally, there should be a risk-sharing system in the context of a harmonized fiscal policy, such as an automatic fiscal transfer mechanism to redistribute income to regions which have been harmfully affected by labor mobility and openness (Sala-i-Martin and Sachs, 1992;Baldwin and Wyplosz, 2009;Crespo-Cuaresma et al., 2011).Usually, this instrument takes the form of taxation redistribution to less developed countries.Thus, if a country in the area suffers an asymmetric shock, a central fiscal authority would transfer tax revenue collected from the countries that are not adversely affected to that one, or those, which are negatively affected.
Put differently, crisis areas pay less tax and receive more welfare benefits.Hence, this criterion implies that countries that do agree to compensate each other for adverse shocks, form an OCA.
However, this fiscal transfer mechanism, though theoretically accepted, is politically difficult to implement as the wealthy countries rarely give up their revenue easily2 .In fact, such transfers are often implicit, operating in most of the cases of the redistributive mechanism in the currency area like a common insurance against asymmetric shocks.
But political conditions also matter even for symmetric shocks, as is embodied in the sixth criterion of homogeneous preferences where the currency area member countries must reach a consensus on the way to deal with shocks (van Marrewijk, Ottens and Schuller, 2006).
In other words, this criterion requires that all countries agree on how to deal with each and every possible shock.However, in practice, there rarely exists one single way to combat bad shocks as the objectives to be achieved may change over time and from one country to another.For example, should a country be more concerned about unemployment, inflation, or about welfare payments?Should a country favor the consumers' agents, who wish to have a strong currency to increase their purchasing power, or the exporters, who prefer to have a weak currency to reinforce their competitiveness?This criterion also assumes that if the currency area member countries do not share the same preferences over such trade-offs, each of them will want the common central bank to pursue different policies.Therefore, there may exist strong political conflicts and at worst, the currency union may not survive.Under these circumstances, in an OCA, countries must agree on the way to conduct policy response, which frequently depends on institutions and ideologies.
The final criterion, solidarity ('commonality of destiny'), is also related with political considerations but much more so.As we have seen with the previous criteria, even when shocks are symmetric, these can generate political disagreements.Such divergences are usually accepted by member countries of the currency union as the costs incurred by living together (Baldwin and Wyplosz, 2009).The consequence is ultimately seen as acceptable because the economic agents of a country readily agree to extend their sense of solidarity to the whole area.
In this way, this criterion implies that when the common monetary policy gives rise to conflicts of national interest, the countries that form a currency area need to accept the costs in the name of a common destiny.This should be the strategy to better accept temporary conflicts of interest, especially if the shocks are asymmetric or produce asymmetric effects.

European Union: An Optimum Currency Area?
Based on the Krugman and Obstfeld (2009) case study on Europe as an OCA, this section summarizes the rich and unending debate around the question of whether Europe (the Eurozone) really fulfils the criteria of an OCA.
Theoretically, the OCA criteria should tell us whether it makes sense to create a currency union in Europe.However, several controversies exist in making this decision (see, e.g., Bofinger, 1994;Karras, 1996;Bayoumi and Eichengreen, 1997;Kim and Chow, 2003;Mongelli, 2008 andFurrutter, 2012).Indeed, the benefits of the establishment of a currency union in Europe are hard to quantify, and it may only be possible to fulfil some of the seven OCA criteria.That said, it should be noted that the criteria established for EU member countries to join the Eurozone are not the same as those established by Mundell (1961) for an OCA in a general sense.
The so called Maastricht criteria3 require that a country intending to join the Eurozone must converge with the rest of the countries on the basis of: i) inflation, that for a given member country must not exceed by more than 1.5 percentage points that of the three best-performing member countries in terms of price stability during the year preceding the examination of the situation in that member country; ii) long-term interest rates, that must not exceed by more than 2 percentage points that of, at most, the three best-performing member countries in terms of price stability; iii) deficits, where the ratio of the annual public deficit to Gross Domestic Product (GDP) must not exceed 3% at the end of the preceding financial year; and iv) debt, were the ratio of gross public debt to GDP must not exceed 60% at the end of the preceding financial year; and must also have v) exchange rate stability, according to which countries need to respect the normal fluctuation margins provided for by the Exchange Rate Mechanism of the European Monetary System, for at least two years, without devaluing against the currency of any other member country.
As already noted, these criteria are not the same as those required by OCA theory, and there is nowadays considerable debate as to whether the Eurozone is optimal in terms of a common currency.This section aims to contribute to enrich this debate.So, based on the Krugman and Obstfeld (2009) case study, where the authors examine Europe's suitability for being an OCA discussing the extent of intra-European trade, mobility of Europe's labor force, similarity of economic structure, and the amount of fiscal federalism within the EU, we try to answer the question as to whether the Eurozone is an OCA, and we do this by analyzing the seven criteria one by one.
So, in what concerns labor mobility, as we have seen before, the OCA theory suggests that this can go a long way toward alleviating the costs of an asymmetric shock when the exchange rate cannot be adjusted (Mundell, 1961;Baldwin and Wyplosz, 2009).However, Europeans do not seem to take much advantage of the Single Market which allows them to work and 'become calm' anywhere in the EU.In fact, Europeans do not even move much across regions within their own countries.People in Europe move less than half as much as US citizens.In Europe, while 21% moved to another region in the same member country, only 4.4% moved to another member country (Baldwin and Wyplosz, 2009).This situation of low labor mobility within the Eurozone is due to various barriers.Indeed, although travel within European countries is relatively easy, requiring no visas, especially within the Schengen area, there are various obstacles relating to work permits, different languages, different customs and traditions, various welfare and pensions schemes, different cultures, national attachment, and others.Even worse is the fact that European citizens move mainly for personal reasons, with professional reasons accounting for only 5%.So, it is not surprising that when asymmetric shocks occur, migration plays a smaller role in Europe4 .This implies that there is a risk of high unemployment rates in the case of product market disturbances, since there is no way of balancing economic shocks via labor migration within the currency union.Under these circumstances, we can say that Europe (Eurozone) is far from fulfilling the labor mobility criterion.
In what concerns openness, this criterion matters in OCA theory because, in a small open economy, most of the goods produced and consumed are traded on international markets5 .Therefore, their prices on the domestic market are largely independent of local conditions and any change in the value of the currency tends to be promptly passed into domestic prices.For this reason, most European countries are very open to international trade, usually the more so the smaller they are6 .As far as the McKinnon criterion is concerned, this explains why the smaller countries have traditionally the most enthusiastic supporters of the currency union.On the other hand, the Kenen criterion is built on the idea that asymmetric shocks are less likely among countries that share similar production patterns and whose trade is diversified.
Based on the study of Baldwin and Wyplosz (2009) who made the decomposition of trade into three types of goods (agriculture, minerals, and manufacturing) and took Germany as a benchmark to determine the level of difference between each country's trade structure, we can conclude that diversification and similarity in Europe (Eurozone) is quite high.Dissimilarity with Germany is highest for Norway, an oil exporting country, with Greece, where agriculture plays a major role, and with the Netherlands, quite dependent on natural gas, and yet an enthusiastic, and so far happy European Monetary Union (EMU) member country.This case well illustrates that the Kenen criterion of production diversification is not absolute, that it focuses on the costs of EMU membership, ignoring the economic and political benefits.
According to the OCA criteria, a key element required to minimize the disturbances caused by the presence of idiosyncratic business cycles is the existence of similarities in economic structure, and here especially, similarities in the types of produced goods.Regarding this criterion, and based on the study of Caporale, Pittis and Prodromidis (1999), and also on the work of Furrutter (2012), we can say that member countries of the EU (Eurozone) are not entirely distinct in their industrial and manufacturing structure.In fact, they have a high volume of intra-industry trade, which is trade with the same product variants.However, although the countries are all European, and share common cultural traits, they are also very diverse in their business cycles and trade partners.By way of example, Ireland is likely to be more synchronized with the UK than with Eastern and Central European countries.Also the level of GDP per capita and the growth patterns of the member countries of the EMU vary considerably as well as their economic structure.
Looking at the labor force qualification and capital stock there are considerable differences between northern and southern Europe.While the north is in general, highly equipped with skilled labor, capital, and a high-quality production structure, the south disposes from a less innovative and specialized manufacturing structure, from less capitalization, as well as from a smaller volume of qualified labor.In this context, we can conclude that there is little reasoning for the formation of the Eurozone in the geographical extent we are experiencing nowadays.The high intra-industry trade is a pro-argument of course, but it seems to be outweighed by the number of contra-arguments providing dissimilarities in the economic structure/business cycle.
According to the OCA theory, countries or regions hit by a temporary negative shock could also receive transfers from better-off countries as a compensation for having lost the exchange rate instrument after joining the currency union.Within most countries perceived as currency areas, this redistributive mechanism is automatic, and the transfers are typically the outcome of the combined effect of the tax system and welfare payments (unemployment benefits, subsidies to poor people, etc.).However, in the case of Europe (Eurozone) there is no such system at work 7 .Fiscal harmonization is only now being seriously considered in Europe as a requisite for the success of the Euro.Unlike the US, the EU is made up of national governments, all carefully guarding their sovereignty8 .
The EU budget is small, less than 2% of GDP, and almost entirely spent on Common Agricultural Policies and Structural Funds which support the poorer regions independently of whether they are hit by adverse shocks (Baldwin and Wyplosz, 2009).Any transfer system would need a significant increase in the EU budget, which is not likely any time soon.Under these circumstances, on this criterion, again Europe (Eurozone) is definitely not an OCA.
In respect of the homogeneous preference criterion, as already noted, OCA theory assumes that all countries must share similar views about the use of monetary policy.However, based, for example, on inflation rates, this does not seem to be the case.In fact, low-inflation Germany and formerly high-inflation Italy or Greece have very little in common.Similarly, looking at public debts, there seems to be a gulf separating European countries (Baldwin and Wyplosz, 2009).
In this context, in what concerns the homogeneity of ideologies, we can conclude that there is mixed behavior.So, it may be too early to determine whether Europe (Eurozone) is definitely characterized by homogeneous preferences.
Finally, regarding solidarity ('commonality of destiny'), we can say that Europe is far from fulfilling the seven OCA criteria, as there is also mixed behavior within the continent.
We can identify some common histories, but also wars and conflicts.Important national differences reveal much heterogeneity in people's sentiments toward politics in general, and the Eurozone in particular.Nevertheless, while national sentiment dominates, the first years of the Eurozone have not provoked the kind of reaction that differing economic situations could have motivated.Therefore, again, Europe (Eurozone) may not be scoring high on this criterion, but nor is it completely failing, it seems.So, in summary, we can say that Europe (Eurozone) is far from fulfilling the seven OCA criteria.According to some authors (e.g.Ricci, 2008), this situation is in part responsible for the actual Eurozone economic difficulties.In fact, while the Eurozone performs well on some of the criteria characterizing an OCA, for example, most European countries do well on openness and production diversification, they do nonetheless, report lower labor mobility and cannot rely on fiscal federalism (fiscal transfers) to smooth out regional and sectorial economic disturbances.

Real and Nominal Convergence in the European Union
In this section we introduce the methodological principles of our empirical analysis and the data we have used to access the problem of convergence.The above criteria for an OCA will be confirmed in terms of empirical results concerning real technological and output convergence and also nominal convergence.

Empirical Methodology
In terms of β-convergence economies with a lower GDP tend to grow faster that thus with higher GDP per capita.This concept is related to mobility of different individual countries.
Another way to look to this concept in conditional terms is to admit that the growth rate of a country is positively related to the difference that separates it from its own steady state (Salai-Martin (1996)).These concepts are important for growth analysis.When we analyze the evolution of an area in terms of an optimum currency area we are not interested in a long run convergence process.We should look at the present to see if the economies are converging.
The concept of convergence is the so called σ-convergence: a group of economies is converging if the dispersion of the variables in question is decreasing over time.The two concepts are related, "a necessary condition for the existence of σ-convergence is the existence of βconvergence" (Sala-i-Martin (1996), p. 1021), but this last concept is not a sufficient condition.
So, in what follows our central concepts will be related to the σ-convergence, for real and nominal variables.
Our first analysis to establish the presence of convergence, real and nominal, is based on the evolution of the Gini coefficient.We want to see a picture of the convergence-divergence process by the evolution of this inequality indicator.Following Milanovic (2005Milanovic ( , 2012)), we calculate a non-weighted Gini coefficient and a weighted Gini coefficient.The first considers that a country is taken as an individual while the other explicitly considers that all individuals (countries) are different and so we must weight each one with its population.In this last situation, Europe is not an addition of countries but an addition of European citizens.
We also apply the usual tests of unit root to confirm the existence of a process of convergence, but we propose some changes to the usual interpretation derived from the growth literature.We investigate whether the differences in an economy with respect to the group average are stationary without constant, and stationary around a trend.In the first situation, if a country difference variable is stationary with a drift, this means a permanent difference between the two economies, and so the country is not converging.This is the reason why we restrict the constant to zero.But if the difference is stationary around a trend, the evolution of its values is fundamental.Suppose that the trend coefficient is positive and the variable has negative values, this means that the country is approaching the group values and so we conclude convergence.The inverse is also true -a negative trend coefficient and positive values.To test these behaviors we apply the ADF test without drift and with a trend.We know that ADF tests have a low power if the true data-generation process has an auto-regressive coefficient close to 1.The other important problem associated with ADF tests is related with deterministic regressors because they have a different interpretation under the null and alternative hypothesis.
So we also apply the Schmidt-Phillips Lagrange multiplier test (Schmidt and Phillips, 1992), S-P, under which the deterministic parameters have the same interpretation under the null or the alternative.This test allows the choice of the order of the polynomial trend which can be decided by the plotting of the variable under study.We use a second order polynomial for all tests.
In some way these tests continue the Hume tradition of a knife-edge decision: a series has or has not a unit root.Granger (1980) has justified and introduced the so-called fractionally integrated processes.We represent an autoregressive fractionally integrated moving average process as 1 − ∅ = .
The fractional difference parameter is 'd' and ∅ and are the autoregressive and the moving average polynomials.The usual hypotheses are made: the roots of and ∅ and are outside the unit circle and ε is a white noise process.
We supplement our analysis of unit root with the calculus of the order of a fractional process for each variable under study.A variable may be non-stationary and at the same time mean-reverting.So, a value of d<1 means that a variable may be a behavior like a random walk out of equilibrium for long periods but which finally returns to its equilibrium value.We will identify this situation as a convergence process.
The estimation of 'd' is made through two methods (Fraley et al., 2013), the first being the usual Geweke and Porter-Hudak (GPH) method (Geweke and Porter-Hudak, 1983).This estimator is based on a regression that uses the periodogram function as an estimate of the spectral density.The bandwidth used is bw = trunc(n k ), where 'n' is the number of observations and 'k' (0<k<1) is a parameter whose default value is 0.5 (Diebold and Rudebusch, 1989).The second method uses the Reisen estimator (Reisen, 1994).This method is based on a regression equation that uses the smoothed periodogram function as an estimate of the spectral density.It uses the same bandwidth of the first method and we take the value 'h', used in the lag Parzen window, equal to .9, bw2 = trunc(n h ).
The oldest test for testing long memory processes is the rescaled range statistic of Hurst (1951).A short-memory process has a value of H=.5 and values H>.5, far from .5, are taken as reflecting long memory.This test has a major problem, which is that it is sensitive to shortterm dependence and heteroscedasticity.And it is natural to have both problems in the variables we are using in the paper.
McLeod and Hipel (1978) define a process of long memory when the limit of the sum of the absolute value of the auto-correlation in not finite.This definition means that the spectral density of a long-memory variable is unbounded at low frequencies.We also use in our analysis of convergence, the representation of the spectral density of the variables under study 9 .The auto-correlations of a long memory process decline much more slowly than a stationary process and at the same time the spectral density is much higher when the frequency tends to zero, ω→0.

Data Sources
As indicated earlier, we take 12 (minus Luxembourg) economies as a representative group in terms of economic integration in Europe: Germany, France, Belgium, Italy, Netherlands, United Kingdom, Denmark, Ireland, Greece, Portugal and Spain.We want to answer the question: have these rather older European countries evolved in a way that they could form a monetary union?Supposing that the answer is positive we can then put the problem of the entry in a subsample of these countries of other countries to form the union.But if the answer is negative, the enlargement of this group to include other countries can end in disaster because these core economies are not themselves in a condition where they can 9 We take m=1, and so L=3 for the Daniell kernel.
together form the union.We consider that the United Kingdom and Denmark have excluded themselves from the EMU because of political reasons and inappropriate economic conditions.
Almost all data is from AMECO (downloaded in October) from 1960 to 2012.The growth rate of TFP is also from this source.With data from the Unido Productivity Website (WPD, www.unido.org/data1/wpd/index.cfm) we have homogenized European TFP values in relation to USA values (2005=100 for this country).With these series of TFP we can compare relative differences between European countries and its average over the years.We have also used PWT, version 8, (Feenstra, 2013) variable PL_C to obtain a structure of prices for 2005 that was complemented with GDP deflators from AMECO.
For real convergence we have studied TFP and real GDP per capita and for nominal convergence, Consumer Prices, Nominal Wages, Consumers Price Inflation and Wage Prices Inflation.

Empirical Estimations and Results
The spectral analysis gives a picture of a not long memory process for all variables, as does the Hurst indicator.In this case, the values for a more recent sub-period are lower than for the whole period, indicating a more intensive integration for this sub-period.However, we cannot forget that the dimension of our base is very small for the application of these tests 10 .
In what follows we begin with real convergence and after with nominal convergence.

Real convergence
The concept of convergence applied to an optimum monetary area is one of sigmaconvergence.We apply this concept to the most promising variable, TFP, for the study of real convergence and also to GDP per capita (Dowrick and Nguyen, 1989;Bernard and Jones, 1996).
From Figure 1 it is seen that during the 1960s we had a real convergence process, but between the beginning of the 1970s and the beginning of the 1980s, stagnation took hold, and thereafter, a substantial increase in real divergence is evident.
10 All results can be provided upon request.We obtain a similar result for GDP convergence (Figure 2).Since the beginning of the 1980s we see a process of real divergence that contrasts with the evolution witnessed before the 1980s when a genuine convergence process was in force.integration, 1973 and 1986 to 2007, respectively.We present only the results of the ADF tests, S-P tests and the estimation of the fractional integration, but can provide all results upon request.
In what concerns TFP convergence, and in terms of ADF and S-P tests (     With respect to real convergence we must conclude that not only, as a group, but also individually, the evidence is against convergence since the number of countries that converge is very small.A deeper analysis might draw a darker picture because the countries are diverging in opposite directions.

Nominal convergence
We apply the concept of nominal convergence to levels of prices and wages, and then to inflation of prices and wages.In Figures 3 and 4 we see a continuous process of convergence from 1960 until now.Initially, during the 1960s, the process was slow, but thereafter it began to accelerate until 2000.
We begin our individual analysis with ADF and S-P tests applied to nominal wages (Tables 5 and 6).For the whole period, 1960-2012, it is not possible to reject a convergence process for Germany, United Kingdom, Ireland, Greece, Portugal, and Spain.For the sub-    Concerning GDP prices (Tables 7 and 8), and for ADF and S-P tests, for the period 1960 to 2012, only France and Greece do not converge.For the sub-period 1980-2007, Germany, Netherlands, Greece, and Spain (even during the integration period) do not converge.
But the evolution of inflation is different, since for Germany inflation is lower than average while for Greece and Spain it is greater than the average.So, the reasons for non-convergence Let us now see the results for wages inflation (Tables 9 and 10).For the whole period, in terms of ADF and S-P tests, we can accept convergence for all the countries except for Greece.For the sub-period, 1980-2007, Germany, Ireland, Spain, Denmark, andPortugal (andalso for the integration period) are diverging.These results for the whole period, for differential differentiation, confirm the above unit root analysis: we can accept the convergence for all these countries because the value of 'd' is always less than 1.For the period 1980-2007, only one country always has a value of 'd' greater than 1, that being Ireland.But for the integration period the values for Ireland are also less than 1.Summing up, we conclude that there is evidence of a convergence process in the evolution of wage increases for all these countries, although some doubts exist for Germany, Ireland, Spain, Denmark, and Portugal.

Conclusion
We have presented the conditions that a group of economies must obey to form an OCA.In almost all situations an OCA was the result of a political process that has motivated integrated regional economies to converge.This process was a real and nominal one.So, the European process, based as it was on a political decision, cannot be considered an unusual one.
What was different was the nature of this area in as much as there was no political unification, with countries continuing as sovereign entities.The decision was made to respect nominal criteria in order to guarantee monetary and financial stability and the creation of the single market to accomplish the remainder of an OCA.Active public intervention occurred to achieve some of the nominal criteria but almost no intervention occurred to achieve real convergence.
Consequently, the OCA has continued without free mobility of labor and with mitigated mobility of physical capital.
We have analyzed the integration process for an older group of European countries and we confirm the existence of price inflation convergence, and asking what is the consequence of the integration of goods markets.We also conclude that wage inflation convergence exists, but we think this is more the result of contagion and Union behavior than of European labor market integration.We also observe the existence of wage convergence but perhaps the most important result is the absence of real convergence.Summing up our results, wage convergence, without intensive capital mobility, (+) real divergence, we see that we have the worst of all possible results and we must say that this will be a source of real imbalance between countries in the process of European integration.

Figure 2 :
Figure 2: Gini Coefficient for real GDPpc The results obtained with GDPpc still reduce the number of countries converging to the average, for the whole period: Belgium, United Kingdom, Netherlands, and Denmark, and for the period of more intensive integration: France, Denmark, and Ireland.Concerning fractional differentiation an almost analogous situation to TFP was obtained.For the whole period, Netherlands, United Kingdom, and Denmark also converge in terms of GDPpc, and this group is now accompanied by Portugal and Spain.The results for the sub-period are quite impressive.Only Netherlands has experienced a convergence process between 1980 and 2007.If we consider the 1986-2007 period we have to add Spain to Netherlands.
period 1980-2007 the group consists of France, Belgium, Italy, and Denmark, and for their integration periods(1973/86-2007)  Ireland, Portugal, and Spain.In terms of fractional differentiation for the whole period, only United Kingdom and Denmark can be taken as converging.For the sub-period 1980-2007, Germany, Italy, Netherlands, Denmark, and Ireland can be taken as converging.

Figure 3 :
Figure 3: Gini Coefficient for GDP Prices are different.Concerning differential differentiation, for the whole period three countries always present a value of 'd' greater than one: France, Netherlands, and Greece.While Greece shows an opposite evolution.For the period 1980-2007 every country has at least one estimation value of 'd' less than one, which means convergence.In conclusion, for GDP prices, for 1980-2007 we have a global picture of inflation convergence.The big surprise comes from Portugal, with its values for the integration period, 1986-2007, reflecting a non-convergence process.

Table 1
period of 1980-2007 (and integration period for Ireland, Portugal, and Spain), the equivalent group is formed only by the Netherlands, United Kingdom and Denmark.So, in conclusion, in terms of fractional integration, the deepening of the European integration has not caused a real convergence process in terms of TFP.
converged, these being: Germany, France, Belgium, Denmark and Portugal.In terms of 'd' (Table2), for the whole period, Germany, Belgium, Netherlands, Denmark and Portugal experienced a technological catching-up all over the period between 1960-2012.For the sub-sample Note: ADF.1 and ADF.2 are the usual ADF tests without drift and with trend, respectively.SPT and SPR are theSchmidt-Phillips 'tau' and 'rho', respectively.

Table 2 : Fractional Integrated Analysis of TFP
Note: GPH corresponds to the application of the Geweke and Porter-Hudak method, and Raisen to the Raisen method.SE means standard error.

Table 3 : Unit Roots Tests of GDP
Note: See notes in Table1.

Table 4 : Fractional Integrated Analysis of GDP
Note: See notes in Table2.

Table 9 : Unit Root Tests of Wn Inflation
Note: See Table1.

Table 10 : Fractional Integrated Analysis of Wn Inflation
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