A comparative analysis of the European Union member states in terms of public spending on environmental protection in 2004-2017

The main purpose of the paper is to present the results of the comparative analysis of the member states of the European Union in terms of expenditure on environmental protection made by the public sector. An additional purpose of the paper is to verify whether there is convergence in public spending on environmental protection of the member states of the European Union. In the study, the convergence models and cluster analysis were used. The research results indicate, among others, that there was convergence in total public spending on environmental protection in the member states of the European Union in 2004-2017, and that the structure of the member states in terms of amounts of public spending on various aspects of environmental protection in 2004-2010 differed from the structure of the member states determined for the years 2011-2017.


Introduction
The origins of the European Union's environmental policy can be traced back to the meeting of the European Council in Paris in 1972. At this meeting, the heads of state or government pointed to the need to develop the Community environmental policy. Since 1973, the European Commission has been announcing multi-annual Environmental Action Programmes (EAP).
They define, among other things, future objectives of the EU environmental policy (European Parliament, Environment Policy: General Principles and Basic Framework).
In 2013, the EU Council and Parliament adopted the seventh EAP for the period up to 2020 entitled Living well, within the limits of our planet. The seventh EAP lists nine priority objectives and what the EU needs to do to achieve them by 2020. They are (European Commission, Living well, within the limits of our planet. 7th EAP -The new general Union Environment Action Programme to 2020): '1) to protect, conserve and enhance the Union's natural capital; 2) to turn the Union into a resource-efficient, green, and competitive low-carbon economy; 3) to safeguard the Union's citizens from environment-related pressures and risks to health and wellbeing; 4) to maximise the benefits of the Union's environment legislation by improving implementation; 5) to increase knowledge about the environment and widen the evidence base for policy; 6) to secure investment for environment and climate policy and account for the environmental costs of any societal activities; 7) to better integrate environmental concerns into other policy areas and ensure coherence when creating new policy; 8) to make the Union's cities more sustainable; 9) to help the Union address international environmental and climate challenges more effectively'.
The implementation of the priority objectives of the EAP is supported, among others, by a public expenditure of the European Union Member States. The information on public spending on environmental protection in the European Union member states is available, for example, on Eurostat, which publishes data according to the classification of the public sector spending as per the COFOG (the Classification of the Functions of the Government) functions, in which public sector means the general government.
Financial data grouped according to the COFOG may be the basis for comparative analyses of the general government expenditure in various countries. Unfortunately, problems arise in the case of attempts to classify certain types of expenditure at the levels of the classification lower than the division. As a result, data concerning more detailed levels of the COFOG are not always available to the full extent for all member states of the European Union.
In the literature, there are publications presenting studies on the impact of public spending on the level of the economic development of countries (Pitlik and Schratzenstaller, 2011;Ryu, 2015). They demonstrate the existence of a positive correlation between the GDP and productive expenditure, and a negative correlation between the GDP and unproductive expenditure. Pitlik and Schratzenstaller (2011), on the basis of the findings of macroeconomic studies on the impact of fiscal policies on the level of economic development, divided public spending according to the COFOG into productive and unproductive expenditure. Public expenditure on environmental protection was classified as productive expenditure, but with a comment that its impact on the level of economic development was being challenged.
Countries have also been compared in terms of public expenditure by 10 divisions according to the COFOG using cluster analysis methods for this purpose (Ferreiro et al., 2010(Ferreiro et al., , 2013, and the occurrence of convergence in total public spending has been studied (Apergis et al., 2013;Ferreiro et al., 2013).
The concepts of convergence as a phenomenon occurring in economic systems are quite varied. Among the processes that favour the convergence of economic systems, Giertz and Mehta (1996) list a state policy, understood as the use by the state of various solutions in the institutional, tax, infrastructure and social spheres. Ferreiro et al. (2013) presented the findings of the study on the occurrence of convergence in total public spending (as a percentage of GDP) and in public spending by divisions of the Economic Classification (as a percentage of total public expenditure) and the COFOG (as a percentage of total public expenditure) in the years 1990-1998 and 1999-2007. The study was carried out using the box plot. First of all, the variability of the distributions of total public expenditure and public expenditure by divisions in the two analysed periods was compared. In addition, the cluster analysis based on public expenditure by divisions of the Economic Classification and the COFOG separately was carried out. The PCA (Principal Component Analysis) was performed in the analysis. In the COFOG, the data matrix is formed by 20 countries and 11 variables: the shares of the 10 items (as a percentage of total spending) and the size of public expenditure (as a percentage of GDP). The EU member states were clustered based on the five factors indicated by the PCA with the application of Ward's criterion. Seven clusters were created for the 1990-1998 data. For the data from the period 1999-2007, there was a smaller number of clusters than in the previous period, i.e. five clusters. Based on the study findings, the authors concluded that convergence had occurred in public spending in the years 1990-2007.
On the other hand, Apergis et al. (2013) studied the occurrence of convergence in public spending by 10 divisions of the COFOG based on data from 17 EU member states from the period 1990-2012. The methodology proposed by Phillips and Sul (2007) was applied. On the basis of the estimated regression model, the absence of convergence in total public expenditure and in public spending by divisions of the COFOG was confirmed. Next, the dip-test (Hartigan and Hartigan, 1985) was applied to verify the null hypothesis that the distribution was unimodal.
At the significance level of 0.10, the test outcomes resulted in the rejection of the null hypothesis for the majority of public spending as per the COFOG functions; spending on environment protection was the only exception. Hence, when applying two approaches to the convergence study, conflicting results were obtained for public expenditure on environmental protection.
Among publications on government spending on environmental protection, there are deliberations on selected aspects of the environmental protection. Public social expenditure is a popular area of study (e.g. (Halaskova, 2018;Leitner and Stehrer, 2016;Szarowska, 2011)). Halaskova (2018) clustered countries due to their public social expenditure. Convergence in the case of public social expenditure was also studied (De Simone et al., 2010). A much smaller number of publications refer to public expenditure on environmental protection only (Russu, 2017), also in break-down by groups (Ercolano and Romano, 2018). Russu (2017) analyzed public expenditure on environmental protection made in Romania as compared to other European Union member states in 1990, 1995, 2000, 2005and 2012. Ercolano and Romano (2018  This paper is part of the research trend represented by Apergis et al. (2013) at the level of total public expenditure on environmental protection, and Ercolano and Romano (2018)  The paper structure is as follows: Section 1 presents the objectives of the paper and the research questions; Section 2 presents the discussion of the research procedure; Section 3 presents the results of the empirical study with a discussion, and Section 4 is a summary of the considerations.

Data and methods
The comparative analysis of the European Union member states was carried out in accordance with the following research procedure: The box plot was applied to present selected distribution characteristics of empirical data concerning government expenditure on environmental protection. This graph is used to visualize some distribution characteristics of a variable. In this study, the box plot based on positional measures was used.
In the case of classical convergence, beta-convergence and sigma-convergence are distinguished. Beta-convergence occurs when countries with lower expenditure per capita increase it faster than the countries with higher expenditure per capita. In the case of betaconvergence, absolute convergence and conditional convergence are also distinguished. The former type of convergence is based on the assumption that amounts of expenditure per capita in individual countries converge to the same level called 'the steady state'. Conditional convergence is a situation in which each country has its individual level of the steady state.
Sigma-convergence occurs when the variability of the amounts of expenditure per capita in a particular group of countries measured with, for example, a standard deviation, decreases over time.
In the study of the occurrence of convergence, the occurrence of absolute beta-convergence and of sigma-convergence was verified: 1. Absolute beta-convergence (Barro and Sala-i-Martin, 1992): where: 0 , -the amount of public spending on environmental protection in the i-th country per inhabitant in the initial and final periods, T -the length of the analyzed period.
If the regression coefficient is statistically significant, and the assessment of this coefficient is a negative value, there is absolute beta-convergence in public spending on environmental protection in the EU member states.
The rate of convergence can be calculated using a regression coefficient assessment according to the following formula: The β coefficient shows the percent of the distance to the steady state that an economy covers in one period.
2. Sigma-convergence (Friedman, 1992;Quah, 1993): where: -standard deviation of logarithmic amounts of public spending on environmental protection in the member states per inhabitant, -time.
If the slope parameter in the linear trend is statistically significant, and the assessment of this parameter is negative, then there is sigma-convergence in government spending on environmental protection in the EU member states.
To eliminate the impact of short-term changes on the results of the comparative analysis of member states in terms of public spending on environmental protection, the annual data from the period of seven years were averaged. As a result, two periods were obtained covering the The Wilcoxon matched-pairs test (Wilcoxon, 1945) was used to check if public spending on environmental protection for the two periods differ.
Variables were normalised with the application of the unitarisation method with fixed parameters over time: where: -the value of variable for the i-th object in period t, -the normalised value of variable for the i-th object in period t.
The member states were clustered using Ward's method. Ward's method minimises the total within-cluster variance. At each step, the pair of clusters with minimum cluster distance are merged. To implement this method, at each step one must find the pair of clusters that leads to a minimum increase in total within-cluster variance after merging. The calculations were made using the 'NbClust' function from the 'NbClust' package in R environment with 'ward.D2' option, which implements Ward's (1963) clustering criterion (Murtagh and Legendre 2014).
As a result of the application of hierarchical Ward's method, a set of partitions was obtained for each period, from a partition containing 27 single-element clusters to a partition containing only one 27-element cluster. Due to the sample size (27 member states), the assumed maximum number of clusters was 6. For partitions containing from 2 to 6 clusters, the values of selected cluster validity measures were calculated: Krzanowski-Lai (K-L) index (Krzanowski and Lai, 1988), Calinski-Harabasz (C-H) index (Calinski and Harabasz, 1974), Davies-Bouldin (D-B) index (Davies and Bouldin, 1979). On the basis of the values of the indices above, the optimum number of clusters was determined.
For each of the two partitions (for the periods: 2004-2010 and 2011-2017), the validity of country assignment to the clusters was assessed using the Silhouette (S) index (Rousseeuw, 1987). Finally, the two partitions were compared with the adjusted Rand index (Rand, 1971;Hubert and Arabie, 1985;Gates and Ahn, 2017).
The variables that were used in the clustering of objects are the basis for the description of clusters. Therefore, the average values calculated for public expenditure made by member states from a given cluster on particular aspects of environmental protection were used to describe the clusters.
In the end, an attempt at cluster profiling was made. Profiling is carried out on the basis of the variables that were not used in the clustering of objects. Its purpose is to indicate such attributes of objects that can explain the discovered structure of clusters. In this study, two qualitative attributes were taken into consideration, i.e.: 1. the period of a state's membership in the European Union: • 'old' -a state that joined the EU before 2004, • 'new' -a state that joined the EU in 2004 or later; 2. the level of economic development: • 'GDP_1' -a state with per capita GDP below the first quartile calculated for the EU member states in a particular period, • 'GDP_2' -a state with per capita GDP between the first quartile and the median, • 'GDP_3' -a state with per capita GDP between the median and the third quartile, • 'GDP_4' -a state with per capita GDP above the third quartile.
The selection of attributes for cluster profiling was related to an attempt at investigating whether the diversity of the European Union member states in terms of public spending on various aspects of environmental protection was related to the 'old-15' or 'new-13' status of the member states or to varying levels of their economic development.

Findings and discussion
Selected empirical distribution characteristics of the analysed variables were presented using the box plot. Figure 1 At the significance level of 0.05, the parameters of the model (13) are statistically significant (p-value is less than 0.01). Since the assessment of the regression coefficient ( 1 ) is a negative value, it can be concluded that there is absolute beta-convergence in public spending on environmental protection in the EU member states. This conclusion means that the member states with a lower expenditure of this type per capita increase their spending on environmental protection faster than those member states with higher per capita public expenditure on environmental protection.
In addition, the coefficient of the rate of convergence (2) was calculated: = 0.0388. The β coefficient indicates that the EU economy covers in one year ca. 3.9% of the distance to the steady state.
Next, the occurrence of sigma-convergence was verified. To this end, the linear trend function (3) was estimated: At the significance level of 0.05, the parameters of the model (14) are statistically significant (p-value is less than 0.01). Since the assessment of the slope value ( 1 ) in the linear trend is negative, it can be concluded that there is sigma-convergence in government spending on environmental protection in the EU member states.
The measures applied to assess the cluster validity are based on various criteria. Thus, in research practice, the indications regarding the optimum number of clusters may vary depending on the adopted measure (Sokołowski et al., 2019). In this study, three popular measures were used to assess the cluster validity, i.e. the Krzanowski-Lai index, Calinski-Harabasz index and Davies-Bouldin index. Table 1 presents three indications for each of the analyzed measures in the order corresponding to the descending cluster validity level. Bold font was used to highlight the number of clusters selected for subsequent analysis.       Note: 'old' -a state that joined the EU before 2004, 'new' -a state that joined the EU in 2004 or later; 'GDP_1' -a state with per capita GDP below the first quartile calculated for the EU member states in a particular period, 'GDP_2' -a state with per capita GDP between the first quartile and the median, 'GDP_3' -a state with per capita GDP between the median and the third quartile, 'GDP_4' -a state with per capita GDP above the third quartile. Source: the author's calculations made using the 'NbClust' package in R environment (Charrad et al., 2014) and the 'factoextra' package in R environment (Kassambara and Mundt, 2017  To assess the similarity of two partitions, the adjusted Rand index was used (ARI = 0.179).
The adjusted Rand index suggests that the two partitions (for the periods: 2004-2010 and 2011-2017) are not very similar to each other.
In the next stage of the analysis, the clusters were described. For this purpose, average amounts of public expenditure on particular aspects of environmental protection as a percentage of the GDP were calculated, and the results are shown in Table 3. The highest average amounts of public expenditure on particular aspects of environmental protection are marked in green, while the lowest amounts are marked in red. The values in Table 3  In 2011-2017, Greece -forming the C_6 single-element cluster -dominated in the area of public spending on 'Waste management' (GF0501) and 'Pollution abatement' (GF0503). In turn, Croatia, forming the second single-element cluster C_5, made the highest public expenditure on 'Environmental protection n.e.c.' (GF0506). The lowest average expenditure on 'Waste water management' (GF0502) was recorded in the C_1 cluster, while the highest -in the C_4 cluster.
The C_2 cluster is characterised by the highest average expenditure on 'Protection of biodiversity and landscape' (GF0504). The highest average spending on 'R&D Environmental protection' (GF0505) was recorded for the C_3 cluster.
In order to profile the clusters, Table 2 presents information about the length of the membership of a given country in the European Union and the level of its economic development.
Based on the analysis of cluster compositions it cannot be unequivocally confirmed that, in the analyzed periods, there was a correlation between the division of the member states of the European Union due to the amounts of funds allocated to various aspects of environmental protection and the division of countries into 'old' and 'new' ones due to the dates of their accession to the European Union, or the division of the member states due to the level of their economic development measured with per capita GDP.
It should be noted, however, that for the years 2004-2010, the C_2 cluster included mainly the countries with an average level of economic development (per capita GDP between the first quartile and the third quartile), while the C_3 cluster was dominated by countries with the highest level of economic development (per capita GDP above the third quartile).
In the years 2011-2017, it was noticeable that the C_1 and C_3 clusters were dominated by the member states with an above-average level of economic development (per capita GDP above the median). The C_2 cluster comprised countries with an average level of economic development (per capita GDP between the first quartile and the third quartile). In contrast, the C_4 cluster was dominated by countries with the highest level of economic development (per capita GDP above the third quartile). The member states forming the C_5 and C_6 singleelement clusters were characterised by the level of economic development below the average level recorded for the European Union member states in 2011-2017 (per capita GDP below the median or the first quartile).

Conclusions
The findings of the empirical study made it possible to answer the research questions: Studies in this area should be continued.
When confronting the conclusions formulated on the basis of the findings of the empirical study with the present knowledge on the analyzed problem, it should be stated that they are: • consistent as regards the occurrence of convergence in total public spending on environmental protection with the results obtained using the dip-test by Apergis et al. (2013); • inconsistent as regards the occurrence of convergence in total public spending on environmental protection with the conclusions presented by Ercolano and Romano (2018).
The reasons for the consistency or inconsistency of the conclusions drawn on the basis of this study with the findings of other studies on the occurrence of convergence in total public spending on environmental protection may be seen e.g. in the length of the analyzed period - In further studies, the author intends to: • apply various research approaches to the same data set to check the stability of the analysis findings; • continue the study following the direction set in Ercolano and Romano (2018), i.e. study the relationship between public spending on environmental protection and some environmental outcomes.
The results of the conducted research enrich the knowledge on the occurrence of convergence in public spending on environmental protection in the European Union countries.
Additionally, the results of cluster analysis allow indicating the countries belonging to the European Union, which were similar in terms of the structure of public spending on environmental protection in the years 2004-2010 and 2011-2017. Extend the research to include the assessment of the relationship between public spending on environmental protection and some environmental outcomes should allow finding the optimal model of public spending on environmental protection in the European Union.