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PRELIMINARY DRAFT

Michele Caputo and Francesco ForteLincei Academy and University of Roma La Sapienza

ON THE CONVERGENCE AMONG THE EU FIVE MAIN COUNTRIES AND THE CRISIS OF THE

EURO AREA

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I GOVERNMENTS AND UNION OF GOVERNMENTS AS CLUBS1.1Club approach in public goods theory and Governments as clubs1.2. Optimal monetary area and optimal monetary union as “club”1.3. Convergence in endogenous and exogenous growth models.II CONVERGENCE ,CLUB INHOMOGENEITY AND INSTABILITY 2.1. The convergence model with memory formalism for the

countries member in an Economic Union-Club2.2. 15 Parameters of CLUB homogeneity to assess convergence 2.3 The convergence of France, Germany, Italy, Spain, UK. in the EU

club by measuring their distances from 2003 to 20112. 4.The in homogeneity and instability of the EU club 2.5. Weight of the parameters .Growth , Inflation, unemployment2.6.Interrelation of the real and financial parameters Structural Policy and EU architecture suggestions

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I GOVERNMENTS AND UNIONS OF GOVERNMENTS AS CLUB1.1. The club approach in the public goods theory and the Governments as clubs.

Club goods, according to the now familiar definition of James Buchanan [Buchanan (1965 and 2001) and Buchanan and Goetz (1972), are an intermediate category of public goods that are common in their use, but in some way and degree, excludable for those who do not accept to enter in a “Club” that offers them, in competition with other “Clubs”. The institutions offering club goods may be public or private; in both cases, they must be non-profit-institution of common use of the given goods. J. Buchanan defines as “non-ownership” this requisite. One may say that they behave as Commons or Cooperatives

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The theory of club goods has had a broad theoretical development and diverse application [ see Pauly (1970a) and (Pauly 1970b), Berglas (1976), Sandler & Tishart (1980),Breannan & Flowers (1980), Casella & Frey (1992), Cornes & Sandler (1996), Sandler & Tishart (1997),(S.Scotchmer 2002)]

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Common use may imply positive and negative effects of the presence and use of the other members. In the case of multiple members, some of them may harm other members with their presence or behavior, thus the potential members must weigh these harms with the benefits of the presence and behavior of others. Clubs, in the pure model, do not have a territorial jurisdiction on their members. The members do not have a “residence” in the space occupied by the pure Club territory. The mobility from one to another pure club, thus, does not imply the loss of local rents, for those who leave it. Those who enter in the “club” have the choice of opting out, in a setting of perfect mobility and of no exploitation by the owner of the good. The non-territorial club is similar to a taxi .

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Governments as territorial clubs, first theorized by Buchanan and Goetz (1972), for the Local Governments, imply territorial rents for the members. For Buchanan and Goetz 1971 and Buchanan 1997, Governments are territorial clubs if observe the principle of non-ownership and allow migration to public good clubs, in a free choices setting. In case of too heterogeneous preference a club might adjust the rules smoothing the type and conducts of the members and goods supplied to distribute the welfare losses among all members to minimize them. In a big club with heterogeneous preferences, this minimization may be too difficult and costly. Therefore, rational behaving clubs do not try to be too big, even if this could allow economies of scale. Anyway, the Local Governments as clubs of public goods that one may observe have a relevant degree of homogeneity. Those who have in-homogeneous preferences do not enter in them or, once entered, leave them. See Fedeli and Forte (2002), with Comments

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Migration to a territory, ruled by another municipality implies the loss of the location rent and may additionally imply the loss of common ownership. The cost of opting may be reduced and the freedom of choices broadened if there is the choice among higher-level governments that assure the fruition of many not (entirely) decentralized public goods. As seen, the possibility of opting out is the only mean to assure the non-ownership principle. Therefore, even at the upper level of the territorial clubs is desirable to have a multiplicity of public entities. See Buchanan ad Goetz (1971) in Buchanan(2001),§ 5

“The reality of Fiscal Mobility”, p.61See Buchanan ad Goetz (1971) in Buchanan(2001),§

6.Conclusions

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1.2. Optimality conditions for a monetary area and for monetary union as “a club”

Money, as a common good in theory infinitely non-rival, is a bundle of joint goods being medium of exchange and store of values, for transactions in the same and in other money. Its main requisite “monetary stability”. It implies that the Central Bank cannot follow the Philips curve logic (in which the level of employment depends from the level of prices) to increases employment by inflation. The central bank cannot finance the deficits of the member countries nor monetize high public debts by an inflationary policy. This last rule symmetrically implies that the central bank buys public debt to avoid a deflation, that endangers monetary stability.

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•A Monetary Union among different countries may cause the enlargement of the market. However, to be successfully, unique market is not enough, the preferences for the monetary policy must be homogenous. Countries with higher nominal deficits and public debts ratios to GDP may prefer a higher price level than countries with low deficits and low -debt/GDP ratios. Less competitive countries may prefer a lower rate of exchange than countries with a high rate of exchange.

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The “monetarist” theory of the optimal currency area (Mundell 1961 and 1963) sets necessary but not sufficient conditions for a monetary union. No barriers should exist to the mobility of the factors and final goods. The differences in productivity in the various areas, under the given rate of exchange may create surpluses in the balance of payment in some countries and deficits in others. But the mobility of the factors (and firms) reduces them However labor may be more sticky. Countries with productivity gaps caused by too high nominal wages cannot devalue by an inflationary policy, to increase exports and decrease imports . Deflation may appear. But the constraint of the fixed rate of exchange shall obliged the unions to bloc wages increases (Mundell 1973) and shall induce the unions to accept wage flexibility (Mc Kinnon ,1999). However, why labor union would adopt this line instead of asking the government to take care of the unemployed and increase their deficits to fight against deflation ?

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The non-ownership principle that implies that decision making rules are informed to the proportionality principle is adopted for the decisions of the ECB and EU. However, as for the requisite of freedom of exit, a paradox arises. The conventional money must be a territorial good , because is a credit note with legal course on a given territory under a Central Bank with monetary jurisdiction on that territory and control on its financial intermediaries. To assure the credibility of the money of the Union one must assure the financial credibility of the member states and that the weakest do not leave the Union exit particularly if they are the important ones .Wolgemuth (2011) theorizes the exit of the strongest to solve the paradox of the in-homogeneity .

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1.3 Convergence in endogenous and exogenous growth models.

In Solow and Barro & Sala Y Martin (1994) MODEL with only one good representing GDP and a given rate of saving and investment in capital K , GDP growth is determined by kxlp. With diminishing return and exogenous technological progress, high GDP countries H have a slower rate of growth than emerging countries E, that started recently. For Barro and Sala y Martin (1991,1994) and Sala Y Martin (1996), the diffusion of H technology gives to E sustained growth .Labor productivity increases, under flexible labor supply . The price of labor in E is lower due to lower wages and service prices. Firms of H decentralize in E, where productivity is lower, but not much with their technologies. Therefore a monetary Union should enhance growth.

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• II CONVERGENCE ,CLUB INHOMOGENEITY AND INSTABILITY 2.1. 15 Parameters of CLUB homogeneity to assess its convergence and viability hypothesis • 1 growth GDP• 2 GDP per capita• 3 inflation rate• 4 unemployed/GDP• 5 Labour product per person• 6 labour product per hour• 7 investments/GDP• 8 Gross savings/GDP• 9 VA agriculture/GDP• 10 VA industry/GDP • 11 public expenditure/GDP• 12 general government deficit/GDP• 13 balance payments• 14 balance payments current• 15 bond yeld

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•2.2. The convergence model with memory formalism for the members of the club of countries in an Economic Union • In a previous paper was considered a club formed by n members yi(t) and assumed that the members are related to each other by the equations of a fractional derivativeIn practice, the derivative of fractional order of f(t) is constructed by taking a weighted mean of the first order derivative [df(t)/dt]z in the time interval [0,t], so as to induce a sort of feedback system. That is the values of [df(t)/dt]z at time z far apart from t are given smaller weight than those at times z closer to t. Given that the weights are increasingly smaller with increasing time separation from time t, the effect of the past fades away as time goes by.

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•2.4. The convergence of France,Germany, Italy, Spain and UK in the EU club by measuring their distances The spread (standard deviation) of the distances is obtained normalising each parameter pj to the yearly maximum value of its norm, acquiring a new set of normalised parameters Our work is based on the following hypotheses•a) Larger spread of distance between the members of a clubs, measured by the distance of their parameters means large inhomogenities. •b)Large spreads between two or more members is a sign of instability of the club. •c)The inhomogeneity is measured with a single parameter U

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• 2. 5.The measure of the stability of the EU club, formed by France, Germany, Italy, Spain, UK. , from 2003 to 2011

To study the homogeneity and stability of the club we consider the values of the 15 parameters of Table 1 in the 8 years 2003, 2005, 2006, 2007,2008, 2009, 2010, 2011. We start in 2003 to avoid the possible trauma caused by the transition from the local currency to the Euro, occurred in the period 2000-2002.

In this period the EU countries have undergone the international financial boom and burst of the 2006-2009 period which has generated a deep fluctuation in their GDP rate of growth from 1.3 in 2002, to 1.5 in 2003,to 2.0 in 2005, to 3.0 in 2006, to 2,9 in 2007, to 0.0 in 2008, to -4.3 in 2009 ,to1.8 in 2010, to 1.3 in 2011.

 

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The sum Ui of the distances of each member of the club from the other of

the club members as function of time.

sum dist. each econ. from others in club A

3

4

5

6

7

8

9

2003 2005 2007 2009 2011year

dis

t

ITFRGERSPUK

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Concerning the stability we note in te Figure the large rapid oscillations of Ui(t), which imply significant instability of the club. We note also the

significant sharp increase of Ui(t) before 2008 just one year before the down

turn of the economic cycle and subsequent crisis.We also note that the distances of UK were among the highest until 2005 and

went down dramatically in the burst. Clearly, inside the EU club, there has

been a lack of coordination between the two monetary areas of the euro and

the pound. The other country whose divergence has been particularly affected

by the boom and the next depression is Germany with two peaks. Spain and

France recorded their maximum divergence (inhomogeneity) and instability in

the same year as UK while Italy and Germany recorder the maximum in the

subsequent year 2008. Generally, the process of convergence, which was

taking place before the cycle, was interrupted by the boom and by the

following crisis. The in-homogeneity after the boom was much larger than

before, with France and Italy with the highest distance from Germany.

192002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

0.4

0.45

0.5

0.55

0.6

0.65 Time variation of the divergence (inhomogeneity) U(t) of the 5 coun-tries as a whole in the EU club.

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The inhomogeneity of the club in the period/d 2007-2010 obviously mimics that shown in the figure 1a. The trend to the convergence does not seems to be stabilizing again in 2011and, as there is an increase of divergence. However it seems small relative to the amplitude of the previous oscillations Concerning this aspect of the analysis of the evolution of the club, among other, we must remember that the convergence could be reached also in stagnation.

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Average values of Ui (squares) and of spread of Ui (diamonds)

In the period of the boom the standard deviations i.e. the spreads between the behaviors of the five countries did inflate with a peak in 2007, the year of the peak of the boom. After 2007 there has been a downward trend of the spread and a new peak of it in 2010 . intervention by the EU s to constrain the five countries to undertake a similar adjustment process. However while the in-homogeneity increases the spread between 2010 and 2011 decreases , signaling a common behaviors inside the two groups of well performing and bad performing diverging countries.

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

2003 2004 2005 2006 2007 2008 2009 2010 2011

st.dev.

U

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Correlation of the values of Ui(t) in the 8 years for

the couples of members of the club A large correlation would imply that the 2 economies considered are having the same evolution: for instance the Italian, Spanish and German economies; as well as UK, France and Spain. On the contrary, a small value would imply different evolutions as the economies of France and Germany as well as Italy and UK and Germany and UK. While for the last two couples of countries the explanation of the lack of correlation may be easily found in the fact that they belong to different monetary clubs, the significant correlation between France and Span and UK perhaps may be found in the fact that all three are on the Atlantic sea and geographically close. Note that each value of the standard deviation is normalised to the value of U of the club in that year.

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Correlations between Standard deviation of the values of the yearly Ui(t) of the club and the standard deviations of all the parameters of Table 1.

Considering the correlations between the standard deviation of the yearly values of U(t) of the club and the spreading (standard deviations) of the parameters (all in the range [ -0.60, 0.39]) the obvious conclusion is that the 2 entities considered are not correlated -

The lack of correlation between the spread of the parameters and the measure of the spread of Ui(t)should not be surprising since the effect of each parameter on the economy is delayed by the memory mechanism which, probably, has different characteristics for each parameter which will cause different delays for the different parameters (Caputo 2014 ). Excluding the existence of an instantaneous effect of the spread of the single or all normalized parameters on the normalized spread of U i(t), the direct use of the values of the parameters and of their spread is not viable for the estimate of the evolution of the convergence or spreading of the members of a club. The present approach is more reasonable and acceptable

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Time variations of the inhomogeneity of the club (diamonds)and spread of the sum of the effects of the parameters on U (squares). The values of U(t) are related to the sum of the distances of the club members, which measures its lack of convergence while the spread is related to the

differences of the contribution of the set of parameters on the measure of U(t).  

. . 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 20120.4

0.45

0.5

0.55

0.6

0.65

U dia; st.dev. sum effects all param.squ

U

st.dev.

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Instability increased during the boom period. Decreased during the subsequent recessionary period, while going down to a minimum level in 2010 , an year of recovery but increased again in the subsequent year in which the recovery started to fade and the inhomogeneity increased again.

Let us now examine which parameters are the most important for the convergence and stability of the five main countries of the two clubs .

As thresholds for the separation between parameters with larger and smaller effect, considering that they are normalize to unity their average values would be 1 /15, as the threshold of the larger effect we selected (1/15) (1 + 10%) and as threshold for the smaller effect we selected (1/15) (1 - 30%)

7 Parameters with larger effect and 4 parameters with irrelevant effect

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Parameters with larger effect

• average of parameter effect/total effect

• 1 growth GDP, 0,115

• 3 inflation rate, 0.079

• 4 unemployed/GDP, 0.077

• 9 VA agriculture/GDP, 0.106

• 12 general government deficit/GDP, 0.121

• 13 balance payments, 0.085

• 14 balance payments current 0.111

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Parameters with irrelevant effect

• average of parameter effect/total effect

• 4 labour product per person 0.028

• 5 labour product per hour 0.023

• 11 public expenditure/GDP 0.031• 15 bond yield 0.03

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Parameters with an effect larger or equal to 0.075.

2003 2004 2005 2006 2007 2008 2009 2010 20110.04

0.06

0.08

0.1

0.12

0.14

0.16

par 1par 3par 4par 9par 12par 13par 14

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It is clear that the effects on U of the different parameters are not correlated in time. The memory operates on them differently .In 2008 the parameters are spreading in different ways. Par. 1 and 3 have opposite phase. In 2010 the effects of the parameters seem to stabilise .Par. 1, i.e. GDP growth rate is going downward to 1,1-0,9 were the parameters are clustering. Par. 3 i.e. inflation increases to approach that level, while par. 4 i.e. unemployment increases slowly remaining in that area. Par. 12, general government deficit/GDP does not converge. Goes upward to 0.12. Per capita GDP is not among the parameters that give the most relevant effect.Yet under nearly invariant population, GDP per capita it is strictly correlated with GDP growth rate.The explanation of the paradox lies in the variation of the population in the 5 countries, due to the fluctuation of new migration and of the young population in working age which moves to the better performing countries .The smaller impact of the memory on the mobility may be the explanation.

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While the dynamics of the 7 parameters responsible for the changes in U are not correlated because of the different role of the memory, an economic interpretation of their relevance shows that they are interconnected. Indeed GDP variation (par. 1) may likely be negatively interdependent with unemployment (par. 4), as shown from their opposite behavior in the above Figure, even if this interdependence presents itself in different ways with different time lags, in the various countries, in relation to different rigidities in the labor relations. A differential of inflation ( deriving from the rigidity of the domestic supply) as signaled by parameter 3, may increase the costs of the domestic production thus decreasing exports and increasing imports with a negative effect on the balance and current of payments (par. 13 and 14) and on GDP growth rate (par. 1) . A low or negative growth rate shall have a negative effect on Government revenues while may foster public expenditures growth because of the increased request of interventions by the public sector. Thus, the general government deficit (par. 12) may increase. On the other hand, the relevance of par. 9 tends to diminish in the initial convergence period, increases during the boom period. Then gradually tends to come back to the terminal level of the convergence period. One, therefore, may argue that the differences in the value added of agriculture are influenced by the long run GDP growth rate with a convergence trend when this rate is high.

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Trend of Inhomogeneity and Instability and of GDP average growth

rate of the five countries reduced to 1/15

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Trend of Inhomogeneity, Instability, GDP growth rate of the five countries on the same scale

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Concluding remarks A different EU and EMU policy is needed to have consolidation cum growth.To contrast the deflationary effects of the fiscal consolidation by individual states and the too high rate of exchange are required a timely expansionary fiscal policies by the EU and a timely policy of nonconventional measures consistent with monetary stability by EBC. Stable currency means stable low inflation rate without inflation or deflation. Presently in the EU there is a trade-off between reforms by the less well performing countries and expansionary policies. This trade off originates a chicken game between the EU and these countries which damages both consolidation and growth. To assure stability cum growth of the two clubs of EU and EMU a change of the existing fiscal and monetary policy rules is not needed. The fiscal and monetary policy instruments instrument are already institutionally available. Additional EU regulations, however are needed to complete the unique market, particularly as for the labor contracts and other liberalizations, to remove the the rigidities of the supply that cause inflation differentials and deflationary effects in the less well performing countries. Further integration would face the same issues, in a less free situation.

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BASIC RULE : RESPONSIBLE FREEDOM

• The golden rule of Beccaria, according to which individuals -with a social contract -renounce to the minimum possible of some freedom to increases all the others needs to hold also for the Clubs of Governments .