The results presented below refer to the first part of the research which will eventually cover all three of the above-mentioned dimensions of sustainable development: ecological, economic and socio-cultural. This study analyzes the SBM-efficiency of the implementation of the sustainable development policy in the ecological dimension in 22 European Union countries in years 2005, 2010 and 2015 (5-year intervals were chosen because most of the variables adopted in the study did not change rapidly from year to year). The Malmquist index was calculated for the following periods: t = 2005 and t + 1 = 2015.
Data gaps were the reason for not covering all EU countries. Where possible, missing values were estimated: interpolation was used when sufficiently long time series were available, and if data were available only for the year preceding or following the analyzed year, the available value was taken as the best approximation of the missing one. In other cases, the countries were not taken into account (sufficient data were not available for Croatia, Cyprus, France, Italy, Latvia and Malta).
Due to the relative nature of DEA results, the study was conducted separately for each year.
3.1. SBM-Efficiency of EU Countries in 2005, 2010 and 2015
According to the proposed methodology, the study was conducted separately for each of the studied periods (2005, 2010 and 2015). Table 2
shows the results of the efficiency analysis of 22 EU countries (called in the study a country, a unit or a DMU). Each country presented in Table 2
has a ranking position according to the efficiency score obtained separately in each of the studied periods. The result obtained by each country indicates to what extent a country is efficient. The efficiency score
that is equal to 1.0 means efficiency, lower than 1.0 means inefficiency and if
exceeds 1.0 it means super-efficiency of the DMU.
All three studies demonstrated a similar number of efficient countries (efficiency scores equal or greater than 1.0)—nine in 2005 and eight both in 2010 and 2015.
It should be noted, however, that the efficiency score of each DMU was obtained in relation to other countries in the same year (more precisely—in relation to the reference units, i.e., benchmarks, established for a given DMU). The evaluation of efficiency would be different with different units (benchmarks) on the basis of which the ranking was built. Therefore, the efficiency analysis should rather address the ranking position than the efficiency score itself.
When comparing the results, quite a broad convergence in the rankings can be observed for each country in 2005, 2010 and 2015. Yet, several objects significantly changed their ranking positions, e.g., Greece showed a growth and a transition from inefficient in 2005 and 2010 to efficient in 2015, the Netherlands—a decrease in efficiency and a loss of efficiency status in 2015 or Portugal—a considerable increase in the ranking position in 2010 and 2015.
The efficiency scores obtained by Sweden and the United Kingdom are also noteworthy since they indicate a significant advantage over other countries in the study. Both countries were found super-efficient in all three analyzed years. In the case of Sweden, its high efficiency is mainly due to the highest share of energy from renewable sources (the lowest value of the input ‘Share_nonrenewable_energy’ in each year) compared to the other countries. Sweden was also characterized by the highest value of the output ‘Clean_energy’ (which is the quotient of primary energy consumption and greenhouse gas emissions) and the lowest degree of air pollution with PM2.5 particles (the highest value of the output ‘PM2.5’) in 2005, 2010 and 2015. As for the United Kingdom, its super-efficiency is primarily the result of the input ‘Popul_unconnect_watertreatment’ (the percentage of the population that is not connected to advanced wastewater treatment systems) which had the lowest value compared to other countries in all three analyzed years.
Moreover, the results of the efficiency analysis show an interesting geographical distribution. Table 3
presents average efficiency scores for each year, taking into account the geographical location of the countries.
Highly developed countries from Northern and Western Europe are the most efficient countries. There is, however, one exception, Slovenia, which reached a high third place in the rankings. The average efficiency in both groups of countries exceeds 1.0 in each of the analyzed years. These are the countries in which great importance is attached to the protection of the environment. The inefficient countries are usually those of Central and Eastern Europe (the probable reason is the lower level of wealth of these countries), the exceptions being Belgium and Ireland whose outputs to inputs ratio turns out to be poorer compared to the efficient countries.
The results presented in Table 2
and Table 3
also seem to indicate a very desirable tendency of the efficiency increasing over time. However, the comparison of the scores over the analyzed years should be made with prudence because of the relativity of DEA-efficiency. A lower efficiency of a given DMU in 2015 compared to, e.g., 2005 may result from a real deterioration of its outputs to inputs ratio, but may also result from a shift in the efficiency frontier thus from improving the efficiency of the DMUs forming this frontier (i.e., benchmarks or reference set in DEA terminology).
To confirm this apparent efficiency improvement over time, the Malmquist index for the period between 2005 and 2015 was calculated for each country. The results are provided in Table 4
The Malmquist Index (MI) as a product of the Catch-up and Frontier-shift effects shows changes in the total productivity of a DMU between period t and t + 1. MI > 1 indicates a progress, while MI = 1 and MI < 1 indicate no change and a regress, respectively.
The Catch-up effect shows changes in the relative efficiency of a DMU between period t and t + 1. Catch-up > 1 means progress in relative SBM-efficiency, while Catch-up = 1 and Catch-up < 1 mean the status quo and a regress, respectively. The Frontier-shift effect in turn indicates changes in the frontier technology around this DMU between period t and t+1. Frontier-shift > 1 means a progress in the frontier technology (i.e., shifting up the frontier), while Frontier-shift = 1 and Frontier-shift < 1 mean no change and a regress, respectively.
The Malmquist index values presented in Table 4
indicate an increase in efficiency in 20 out of 22 countries that could be observed in the period between t
= 2005 and t
+ 1 = 2015. Only Germany and Spain showed deteriorated total productivity during this period (MI
< 1), although it should be noted that Germany remained an efficient country. Moreover, significant progress in the frontier technology (Frontier-shift effect > 1) was observed in all 22 countries. These results are promising and mean that almost all analyzed countries implement, to a higher or lesser degree, a sustainable development policy recommended by the United Nations and the European Commission.
A Catch-up effect of less than 1.0 observed only for 8 countries means a regress in the relative SBM-efficiency of these units. It may indicate a deterioration of the outputs to inputs ratio of these countries or a situation in which this ratio has not changed but other DMUs in the group, and particularly the benchmarks that form the efficiency frontier have improved their efficiency. The latter case means moving the efficiency frontier up (i.e., a frontier shift) and the Frontier-shift effect values > 1 (see Table 4
) seem to confirm this finding. An in-depth analysis of the raw data describing these eight countries reveals that both inputs and outputs did not deteriorate significantly between 2005 and 2015. Only in the case of Spain the outputs to inputs ratio deteriorated considerably. The level of non-afforestation in Spain significantly increased between 2005 and 2015 (input ‘Non_forest
’ increased from 44.2% in 2005 to 60.8% in 2015) which seems to be the main reason for the decrease in its efficiency score.
The Malmquist index MI = 3.65 for the United Kingdom is also noteworthy. The values for both the Catch-up and Frontier-shift effects are exceptionally high (2.07 and 1.76, respectively) and indicate a considerable improvement in its efficiency. As previously mentioned, the United Kingdom is the country with the lowest level of the population that is not connected to advanced wastewater treatment systems (input x2). Furthermore, between 2005 and 2015 it reduced the level of input ‘Share_nonrenewable_energy’ by almost 20 percentage points (from 95.9% to 77.7%). This gave it the prevailing position in all three rankings. The question arises whether the United Kingdom will maintain such an extraordinary progress after the announced exit from the European Union.
3.2. Analysis of the Sources of Super-Efficiency and Inefficiency
For countries with an efficiency score exceeding 1.0, a super-efficiency analysis can be performed. A closer look at the efficiency of a given country may highlight those factors, the deterioration of which does not result in a loss of the efficiency status. For inefficient countries, in turn, it may identify areas in which improvement can lead to efficiency.
Such an analysis of the sources of super-efficiency and inefficiency provides detailed guidance on how to improve the efficiency of implementing the sustainable development policy and thus enables a faster way to achieve efficiency by inefficient objects. Because such analyses are generally quite similar for each DMU, a sample analysis for selected countries will be presented below. Each country belongs to a different geographical group and has different characteristics and efficiency scores. The analysis of the sources of super-efficiency and inefficiency is illustrated in detail for three selected countries: Poland, Portugal (inefficient countries) and the United Kingdom (a super-efficient country). The results of the entire analysis of the sources of super-efficiency and inefficiency are included in the Appendix B
, Figure 2
and Figure 3
(each for a different year analyzed) contain the suggested changes of the input and/or output values in order to achieve efficiency or, if the country is efficient, the figures show (for a given input or output) the surplus (the aforementioned ‘reserve’) over the value of the variable that is needed to obtain the status of an efficient object (e.g., a surplus in a given input means that even if a country has increased this input value, it will retain its status of an efficiency country). Each country is characterized by eight variables listed in Table 1
which are illustrated by four columns of inputs and four columns of outputs.
The columns illustrate the changes (expressed as a percentage) in the inputs and outputs. A positive value of the input column indicates a possible increase in the input without losing the status of an efficient unit (hence positive values of the input columns relate only to super-efficient countries). A negative value of the input column indicates the required reduction of the input in order to gain the status of an efficient object (hence the negative values of the input columns relate only to inefficient countries).
The interpretation is reversed for the output columns. A positive value indicates the required increase of the output by which a country achieves the efficiency status. For the efficient countries (because of the model’s input orientation), the output changes are always equal to zero.
It is important to note that an inefficient country needs to reduce all inputs for which the method implies a change in order to become efficient (assuming that all its outputs do not change). It is not enough to improve the value of only one input. On the other hand, it is enough for an efficient (or super-efficient) unit to exceed the range of changes in one area (relative to one input) to lose its status of being efficient.
illustrates the results of the analysis of the sources of super-efficiency and inefficiency in 2005 for the selected three countries.
The numbers in brackets that stand next to the name of each country in Figure 1
are the efficiency scores obtained by these countries in 2005 (see Table 2
In 2005, the United Kingdom was an efficient country. For this reason, as mentioned earlier, the suggested output changes equal zero. The high value of the ‘Popul_unconnect_watertreatment’ indicates that the country has a high “reserve” of this input which means that even if this input was 80.31% larger in 2005 the United Kingdom would still remain on the efficiency frontier (assuming that all other variables would not change).
In the case of Poland’s and Portugal’s inputs, the first four columns indicate the recommended reduction in inputs in order to achieve efficiency, e.g., the input ‘Share_nonrenewable_energy’ in the case of Poland should be 52.28% lower and in the case of Portugal 25.67% lower. Thus, these two countries should, among other things, increase the percentage of electricity generated by renewable sources in relation to the total use of electricity. Then Poland and Portugal could be assessed as efficient in this group of countries in 2005 (assuming that all their outputs do not change).
The suggested changes in the outputs are illustrated by the last four columns in Figure 2
. For Poland, high values for outputs ‘Clean_energy
’ and ‘PM2.5
’ are visible. This means that in these areas the country is very far from the efficiency frontier and requires a significant increase in the outputs. In order to become efficient, Poland should improve the relation between energy consumption and greenhouse gas emissions (output ‘Clean_energy
’) by 53% and increase the output ‘PM2.5
’ by 95% (which means a serious reduction of air pollutant PM2.5 from 26 to 17.5 µg/m3
As regards Portugal, an increase by more than 90% in outputs ‘Nutrient balance’ and ‘Clean_energy’ is recommended to improve efficiency. It is worth noting that the output ‘Nutrient balance’ for Portugal in 2005 was poor in comparison with other countries. Only the Netherlands and Lithuania recorded worse values of this factor.
The second study involved data from 2010. Figure 2
illustrates the results of the analysis for the same 3 out of 22 countries.
When comparing the ranking positions of all three countries in these two periods, an efficiency increase can be seen in the case of Portugal and The United Kingdom (see Table 2
). The United Kingdom has increased its super-efficiency by a further reduction in the level of population that was not connected to an advanced wastewater treatment system.
The areas in which Portugal should improve its activities are still: the input ‘Popul_unconnect_watertreatment’ (60% reduction indicated), the quality of energy (output ‘Clean_energy’ with a 97% improvement recommended) and the balance of nutrients in agricultural land (output ‘Nutrient_balance’ with only a 43% recommended improvement). When analyzing the raw data, it can be seen that Portugal actually improved the output ‘Nutrient_balance’ by 55% in 2010.
In the case of Poland, the main problem that its government has to solve can be clearly seen in the results of the analysis in 2010. In order to reach the efficiency frontier, Poland should increase the percentage of electricity generated by renewable sources in relation to the total use of electricity (input ‘Share_nonrenewable_energy’ should be 51% lower), increase the quality of energy (output ‘Clean_energy’ ought to be improved by 52%) and reduce the mean population exposure to air pollutant PM2.5 (123% improvement of output ‘PM2.5’ is recommended).
Generally speaking, recommendations regarding both inputs and outputs clearly show that Poland must address the issue of energy sources and air quality, which primarily means rethinking the coal-based economy.
The last part of the study involved the analysis of the sources of super-efficiency and inefficiency in 2015. Figure 3
illustrates the results of this study for the same three countries.
The United Kingdom increased its super-efficiency further—again due to the improvement of input ‘Popul_unconnect_watertreatment.’ In 2015, the percentage of population that was not connected to an advanced wastewater treatment system was close to zero while the average value of this input for other countries was almost 20%.
In the case of Poland, in 2015 there was an improvement in efficiency. The recommended changes for both inputs and outputs were lower. The improvement of output ‘PM2.5’ compared to 2010 is worth noting (from 27.1 µg/m3 in 2010 to 22.7 µg/m3 in 2015). However, it is still the worst value of this output compared to other countries—in each of these three years, Poland was regretfully the worst country among those analyzed in terms of the mean population exposure to air pollutant PM2.5. For comparison, in the Scandinavian countries (Finland and Sweden) this value in 2015 was below 6.5 µg/m3.
Turning to the results of Portugal, there is a visible improvement of the percentage of electricity generated by renewable sources in relation to the total use of electricity. The input ‘Share_nonrenewable_energy
’ in 2015 did not require any reduction (see Figure 3
). It should be emphasized that Portugal managed to reduce the share of non-renewable energy from 72% in 2005 (through 59% in 2010) to 47% in 2015.
It should be emphasized that the recommendations formulated above relate closely to the group of 22 European Union countries in a given year. Thus, on the basis of such comparisons one cannot determine whether the examined countries generally improved their performance over time unless the Malmquist index is calculated.
It should also be clearly stated that the above considerations refer to the results obtained from the use of DEA to assess the efficiency of EU countries. A specific set of variables (inputs and outputs) describing the countries were used and conclusions from the above study strictly refer to the results obtained under the DEA application. However, a full analysis of the efficiency of implementation of the sustainable development policy should also take into account a wide set of factors and conditions that particular countries have to face and which are not included in this study, e.g., the tyranny of geography, the involvement of citizens, the government policies, the degree of economic development, the availability of resources, the historical factors, the demographic weight, etc. The presented quantitative tool, as mentioned earlier, aims to support decision makers involved in implementing a sustainable development policy.