This analysis is based on the estimated ??- and on Markov chains. The study deals with the economic convergence of the European countries and especially the convergence of the EU countries, including Romania. In this paper we present applications of indicators and patterns of convergence on the example of European Union member countries and some current economic impact assessments on European convergence processreal convergence, e-convergence, Markov chains

Liviu-Stelian BEGU

English

Research Papers in Economics

Review of General Management                       Volume 14, Issue 2, Year 2011          91
COHESION IN THE EUROPEAN UNION – USED 
MARKOV CHAINS METHOD 
Liviu-Stelian BEGU
* 
 
 
 
Abstract: This  analysis  is  based  on  the  estimated  ı-  and  on  Markov 
chains. The  study  deals  with  the  economic  convergence  of  the  European 
countries  and  especially  the  convergence  of  the  EU  countries,  including 
Romania. In this paper we present applications of indicators and patterns of 
convergence on the example of European Union member countries and some 
current economic impact assessments on European convergence process.
Keywords: real convergence, ı-convergence, Markov chains.
JEL Classification: F15, C13, C15. 
1. Introduction
“Sigma” convergence measures the dispersion of real GDP per capita 
(in  constant  prices)  between  regions  or  countries  based  on  standard 
deviation  of  the  cross-section  series  (Barro,  R.J.,  1992,  p.  169).  In 
probability theory and statistics, the variance/dispersion is used as a measure 
of how far a set of numbers are spread out from each other. It is one of 
several  descriptors  of  a  probability  distribution,  describing  how  far  the 
numbers lie from the mean. When the standard deviation is falling (rising) 
over time, the differences of GDP per capita between regions or countries in 
absolute terms gradually decrease (increase) and convergence (divergence) 
is approached. If standard deviation does not show any clear tendency but 
instead,  increases  or  decreases  successively,  then  a  mixed  process  of 
convergence and divergence is realized. A different way of measuring the 
‘sigma’ convergence is to use the coefficient of variation which results by 
dividing the standard deviation with the mean of the sample. The coefficient 
of variation is a measure of relative variability and is expressed usually, as 
                                                           
* The Academy of Economic Studies, Romania, liviubegu@yahoo.co.ukp.  Volume 14, Issue 2, Year 2011                     Review of General Management  92 
percentage  and  not  via  the  units  of  data  in  which  is  referred.  If  the 
coefficient of variation decreases over time we have convergence otherwise 
we have divergence. 
In mathematics, a Markov process or a Markov chain is a stochastic 
process which has the property that, given its present state, future states are 
independent  of  the  past.  The  current  status  of  such  a  process  holds  all 
information about the whole evolution process.  
A Markov chain is a multistage experiment consisting of a sequence of 
trials in which the state, or outcome, of each trial depends on the state of the 
trial that immediately precedes it. The goal in a typical problem involving 
Markov chain is to compute the probability that the system will be in a 
particular state at a specified time.  
For a Markov chain with m states, the transition matrix P is the m x n 
matrix in which the entry pij is the probability of going from state i to state j 
in one step. 
2. Convergence sigma
A commonly used indicator for measuring convergence is the variation 
coefficient on the level of GDP/capita, denoted by ı. This indicator is used 
to  measure  Sigma  convergence.  It  can  be  used  to  evaluate  the  real 
convergence level by measuring the dispersion of GDP/capita over a one 
year period, using for this purpose cross series (countries and regions). In 
this  case,  the  relevance  of  the  convergence  indicator  appears  only  when 
making comparisons.  
In our study, we have used this indicator to measure and predict the 
real convergence level for some EU countries, specifically the group of EU 
12. Data series refers to the 1998-2007 period. They will be symbolized 
with UE12 and are: Bulgaria, Cyprus, Czech Republic, Estonia, Hungary, 
Latvia, Lithuania, Malta, Poland, Romania, Slovakia, and Slovenia.  
Sigma convergence values for this period are: 0,6656; 0,6774; 0,6427; 
0,6098; 0,5817; 0,5692; 0,5398; 0,4918; 0,4512; 0,3841.  
The  considered  indicator  concerning  the  GDP/capita  variation 
coefficient of the EU countries shows an increase during 1998-1999. This 
increasing process reveals a divergent growth of the economies inside this 
group  of  countries,  with  the  real  possibility  that  every  less  developed 
country will strive for higher levels of development. During 2000-2007 the 
evolution of the variation coefficient of GDP/capita is a decreasing one, Review of General Management                       Volume 14, Issue 2, Year 2011          93
which indicates the tendency of increasing convergence of the economies of 
the mentioned countries. 
The Theil index is a particular case of the Generalised Entropy Index 
with coefficient 1. The following figure displays the Theil index for 1998-
2008 periods. 
 
 
Figure no. 1 - Theil Index in EU-12 
 
The value of the index shows a reduction of disparities among EU-12 
countries which is in line with the results obtained above with other measures. 
However, it clearly appears that this reduction is due to the fact that dispa-
rities among Members States are strongly decreasing. The most simple and 
frequently used non-parametric density estimator is the histogram (see, for 
instance, Boldrin and Canova, 2001). However, this instrument suffers from 
two severe limitations. First, histograms are not smooth, and second, they 
depend on end points of the sub-intervals selected to cover the data values. 
 
 
Figure no. 2 - Histogram for EU-12 
 
The evolution of the distributions between 1998 and 2008 indicates a 
convergence process at work for the EU-12. Frequencies around the mean 
significantly increase, while they tend to decrease for values below 80% and 
above 120% of the EU-12 average.   Volume 14, Issue 2, Year 2011                     Review of General Management  94 
Total  crossing  matrix  between  1998  and  2007  is  presented  in  the 
following  table.  We  used  eight  stages  for  indicator  GDP/inhabitants.  All 
data are expressed in Euros.  
Table 1 
Total matrix of GDP/inhabitants stages 
 
Based on this matrix we calculated the matrix of probability. 
 
 Review of General Management                       Volume 14, Issue 2, Year 2011          95
Probability vector is: 
 
 
The forecast based on probability vector for the next three years is as 
follows:  
 
  
 
We can say there are increases the probability for higher stages, for 
example  the  last  stage  [17150-19400)  increase  from  4.86%  in  2008  to 
7.67% in 2010 and on the other hand the first stage [1400-3650) decreases 
from 13.93% in 2008 to 8.73% in 2010.  
3. Conclusions
This  paper  has  reviewed  a  number  of  methods  and  instruments 
developed for the analysis of economic and/or social inequalities and that 
can be used for examining disparities among EU12 countries. 
One objective of the paper was to produce an update analysis of the 
convergence  process  among  EU  countries.  Another  was  to  show  that 
instruments vary significantly in terms of their specificities and qualities and 
that it is therefore important to be aware of their limits when measuring the 
extent and evolution of countries disparities within the EU. These results 
also underline that the analysis of convergence is in fact complex. 
Finally,  even  if  the  analysis  of  countries  disparities  is  conducted 
thoroughly,  it  says  little  about  the  effectiveness  of  EU  Cohesion  Policy. 
Keeping  track  of  countries  disparities  and  monitoring  their  evolution  is 
definitely of key importance for the design and management of Cohesion 
Policy. However, it must be kept in mind that the analysis of disparities, 
whether  pointing  to  the  presence  or  absence  of  convergence,  generally  Volume 14, Issue 2, Year 2011                     Review of General Management  96 
cannot be used to infer firm conclusions concerning the success or failure of 
the policy. For this, it is necessary to proceed to further analysis, notably by 
controlling  other  variables  likely  to  affect  the  convergence  process,  as  a 
proper econometric analysis would do. 
 
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Convergence, in:

Convergence, Topic 2, Dynamics and Convergence, JPE Puplishing House,

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Regional Cohesion: Evidence and Theories of Regional Growth and Convergence, in:

Twin Peaks: Growth and Convergence in Models of Distribution Dynamics, in:

COHESION IN THE EUROPEAN UNION – USED MARKOV CHAINS METHOD

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COHESION IN THE EUROPEAN UNION – USED MARKOV CHAINS METHOD

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