ECONOMIC WELFARE IN CENTRAL AND SOUTHEASTEUROPEAN UNION COUNTRIES – AN ECONOMETRIC APPROACH

: The importance of economic aggregates per capita: final consumption expenditure and Gross Domestic Product, for the well-being of the entire population of a country determined the analysis of the economic convergence in the countries of the Central and South-Eastern European Union (CSE). The econometric approach of convergence as a steady state of these variables was performed on panel data models with an error correction term. Establishing the long-run and short-run equations describes the convergence of welfare in the CSE region and the choice of the best model.


Introduction
The indicators of economic development of each EU country are converging towards their national equilibrium.In the same way also the EU regions' economic development has different economic movements towards its own equilibrium.The Central and South-Eastern (CSE) part of the European Union includes the countries: Czech Republic, Hungary, Poland, Slovakia and Slovenia -in the centre of the EU, and Bulgaria, Croatia and Romania -in the south-eastern part.
Final consumption expenditure is an indicator of the economic well-being of each nation.Household final consumption expenditure represents the largest proportion of final consumption expenditure; shows the welfare of the population.
Fig. 1 shows the upward evolution of final consumption expenditure per capita of households in euro 2010 and their proportions in final consumption expenditure per capita in euro 2010, each year from 2000 to 2022, for each EU country from the central and south-eastern part.The 2008 financial crisis and the 2020 COVID-19 pandemic are the shocks perceived differently in intensity by these countries.
In Table 1 we observe in the descriptive statistics of the weights of final consumption expenditure of households that Romania had the highest values.Countries with lower proportions of final consumption expenditure of households allocated more to government consumption expenditure; the goal is the welfare of the entire population.
The evolution of household consumption proportions is very different for EU CSE countries and also during the two economic shocks of 2008 and 2020.
Economic growth provides the source of final consumption expenditures, and GDP per capita (euro 2010) is an important indicator to analyse.Final consumption expenditure and GDP per capita follow an upward trend towards long-term equilibrium, in Fig. 2. The importance of final consumption expenditure (FCONS) for the well-being of the population and GDP (GDPC) as an economic source led to the choice of these variables for the study.They are expressed in real terms per capita, in euros at constant 2010 prices.
The econometric approach of panel data allows the analysis of the convergence of GDP influence on final consumption expenditure, as a barometer of the economic development of the CSE EU countries.

Objectives and Methodology
The objective of this study is to analyse the equilibrium relationship of the CSE countries and their common economic equilibrium.To reach this purpose the econometric approach in Eviews is appropriate.
The cointegration of the variables final consumption expenditure per capita and GDP per capita must be proven as a condition of the existence of the long-term relationship.
If the variables are nonstationary, that is, I(1) integrated, and if they are cointegrated, then the variables have a long-run relationship.Both short-term and long-term dynamics can be examined with the panel VECM (Vector Error Correction Model).
The error correction model (ECM) is the short-run model for adjustments to the steady state.For each EU CSE country, the long-run and short-run model will show the evolution of final consumption expenditure per capita depending on GDP per capita.
The average levels of the two models for the panel data define this relation to the equilibrium as an economic convergence of the EU CSE countries.

Results and Discussion
To demonstrate the cointegration of the two variables FCONS and GDPC, they should first be non-stationary.Then their combination, which are the residuals, must be stationary.Transforming the two variables (LFCONS, LGDPC) into their logarithmic values allows a better interpretation of the models' coefficients as percentages.Fig. 3 provides a picture of the similar evolution of the variables at the panel data level.The Q statistic of global tests of stationarity in correlograms reject the null hypothesis and both variables FCONS and FGDPC are non-stationary.
The panel unit root tests in levels and then in their 1-st differences show that both variables FCONS and FGDPC have unit root and they are integrated of the same order, they are I(1).
There are two approaches of the Error Correction Model: one based on the VECM which automatically establish the model and the coefficients and another, based on the residuals of long-run model and then building the short-run model.

Panel Data Cointegration and VECM
The Panel Data Cointegration test of Pedroni with individual intercept and individual trend, and automatic selection of lag length gives 11 test statistics, of which in 5 cases, the probability is less than 5%; almost half of them indicate the rejection of the null hypothesis of no cointegration.
Running the Fisher Johansen test of panel cointegration, which is system based, one cointegration equation is significant.The individual cross section results indicate the rejection of null hypothesis and the variables are cointegrated at the level of each CES EU country.
The residual tests for cointegration conclude that the variables LFCONS and LGDPC are cointegrated.Having decided that the variables are cointegrated at the panel data level, the VECM is to be followed.
The representation of only the dependent variable LFCONS from the system, with 1 and 2 lags, the substituted coefficients is: The coefficient -0.1097 of the error correction term is negative and significant, and this proves the existence of the long run relation.This coefficient represents the speed of adjustment toward equilibrium.The whole system is getting back to long-run equilibrium at the speed of 10.97% annually.
The long-run relation is described by: LFCONS= 0.7637*LGDPC + 1.9127.Applying the Wald test to the C(4) and C(5) coefficients of the lagged values of LGDPC, we find that together they are not significantly different from 0, which means that there is no short-run relationship from LGDPC to FCONS.
If testing the system with 1 and 1 lags as in the representation of the dependent variable LFCONS, the substituted coefficients are: The coefficient of the error correction term is negative and significant, proving the existence of the long run relation between LFCONS and LGDPC with the speed of adjustment of 9.43% during each year towards the equilibrium, but on short term the relation running from LGDPC to LFCONS is not significant, because the coefficient C( 3) is not significant.

The Error Correction Model of Panel Data
The estimation cointegrating equation COINTREG LFCONS LGDPC allows to establish the residuals, called ECT -Error Correction Term.When establishing the short-run model, the regression table is in Table 2: The residuals of the short-run model are normally distributed, no autocorrelation and the cross-section independence is ensured.
The speed of adjustment towards the equilibrium at CES EU countries level during one year is of 11.42%.The coefficient of ECT is significant and negative.
The chart of LFCONS and both long-run and short-run models is in Fig. 4. The ECM model define the long-run equilibrium.Average values smooth the upward trend and are not relevant, but still useful when looking to the maximum and minimum values.

Conclusions
The best model is that selected by a procedure of looking into the models Autoregressive and with Distributed Lag (ARDL) until minimizing an informational criterion, here Akaike info criterion (AIC).The selected model was ARDL(4,1), meaning lag 4 for LFCONS and 1 for LGDPC.The estimation equation is describing the long-run, with the substituted coefficients: LFCONS = 1.0896*LGDPC.The regression model is presented in Table 4: The coefficients of cointegration term represent the speeds of adjustment.Romania had the highest speed of 55.7%, followed by Bulgaria with 45.9%, in Table 5.The two countries have lower values of final consumption expenditure per capita (2010 euro) than all other CSE countries, starting in 2000 and reaching their maximum value in 2022.It is understandable why they need to have higher speed of adjustment towards the long-run equilibrium of CSE region (Table 5).The coefficients of cointegration term of Slovakia is positive and insignificant, as indicates the probability in the last column of Table 5.For Slovakia there is no long-run relation between FCONS and GDP per capita.In Figure 5 we can see the very close theoretical values of LFCONS with the ECM short-run model and with ARDL(4,1) at the CES region level.

Table 5
Comparing the theoretical values of FCONS with ECM and ARDL(4,1) models at CSE region level