## 5 Experimental Results
### Changes Analysis for DMUs Using MPI
#### 5.2.1 Efficiency Change  
Table 7 shows the year-on-year efficiency changes (or catch-up effect) for the 17 DMUs from 2013 to 2017. Figure 2 shows a diagram of the results. From 2013 to 2014, seven countries were found to have improved efficiency--the Netherlands, Belgium, Finland, France, Germany, Greece, and Italy (with a greater-than-1 efficiency change score). This implies that these seven countries improved the use of inputs to produce more desired output (GDP) and lesser undesired output (CO\({}_{2}\)). Among the seven countries, the Netherlands had the best improvement (+2.6%). However, the improvements made by these seven countries are minor. There are two countries (Hungary and Switzerland) with no change. The remaining eight countries recessed in their efficiency. They are Austria, the Czech Republic, Norway, Poland, Portugal, Spain, Sweden, and the United Kingdom, due to a less-than-1 efficiency change score. Among the eight countries, Norway recessed the most (\(-7.5\%\)), followed by Sweden (\(-7.3\%\)). From 2013 to 2014, the 17 countries as a whole improved 0.6%. From 2014 to 2015, 4 countries are found to have improved efficiency. They are Greece, Belgium, Germany, and the Netherlands (with a greater-than-1 efficiency change score). Among these four countries, Greece improved the most (+6.9%). Another three countries recessed. They were Finland, France, and Italy. Two countries (Poland and Switzerland) kept no change in their efficiency. There are 11 countries with deteriorated efficiency--Austria, the Czech Republic, Finland, France, Hungary, Italy, Norway, Portugal, Spain, Sweden, and the United Kingdom (with a less-than-1 efficiency change score). However, the number of recessing countries increases to 11 from 7. Among the 11 countries, Norway once again recessed the most (\(-6.9\%\)). From 2014 to 2015, the 17 countries as a whole recessed 0.8%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**DMU** & **2013–2014** & **2014–2015** & **2015–2016** & **2016–2017** & **Average** \\ \hline Austria & 0.995 & 0.977 & 0.987 & 0.992 & 0.988 \\ Belgium & 1.025 & 1.038 & 0.985 & 0.990 & 1.009 \\ Czech Republic & 0.992 & 0.990 & 1.015 & 1.007 & 1.001 \\ Finland & 1.014 & 0.970 & 0.985 & 1.002 & 0.993 \\ France & 1.004 & 0.962 & 0.999 & 1.002 & 0.992 \\ Germany & 1.025 & 1.015 & 0.993 & 0.996 & 1.007 \\ Greece & 1.015 & 1.061 & 1.010 & 0.943 & 1.008 \\ Hungary & 1.000 & 0.986 & 1.009 & 1.001 & 0.999 \\ Italy & 1.003 & 0.991 & 0.997 & 1.004 & 0.999 \\ Netherlands & 1.026 & 1.040 & 1.000 & 1.000 & 1.017 \\ Norway & 0.925 & 0.931 & 0.993 & 1.004 & 0.963 \\ Poland & 0.992 & 1.000 & 0.992 & 1.000 & 0.996 \\ Portugal & 0.980 & 0.975 & 0.994 & 1.001 & 0.988 \\ Spain & 0.979 & 0.998 & 0.992 & 1.011 & 0.995 \\ Sweden & 0.927 & 0.946 & 0.990 & 1.006 & 0.967 \\ Switzerland & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 \\ United Kingdom & 0.989 & 0.982 & 1.001 & 1.006 & 0.995 \\ _Average_ & 0.994 & 0.992 & 0.997 & 0.998 & 0.995 \\ _Max_ & 1.026 & 1.061 & 1.015 & 1.011 & 1.017 \\ _Min_ & 0.925 & 0.931 & 0.985 & 0.943 & 0.963 \\ SD & 0.029 & 0.033 & 0.009 & 0.015 & 0.014 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Year-on-year efficiency changes for the 17 DMUs from 2013 to 2017. From 2015 to 2016, four countries were found to have improved efficiency. They are the Czech Republic, Hungary, Greece, and the United Kingdom (with a greater-than-1 efficiency change score). Among them, the Czech Republic is the countries with the best improvement (+1.5%). Two other countries, the Netherlands and Hungary, had no change on their efficiency. The rest 11 countries had a regressive efficiency. They are Austria, Belgium, Finland, France, Germany, Italy, the Netherlands, Norway, Poland, Portugal, Spain, Sweden, and Switzerland (with a less-than-1 efficiency change score). Among the 11 countries, Belgium had the worst regression (-1.5%). However, the regressions and improvements of these countries are minor. From 2015 to 2016, the 17 countries as a whole recessed 0.3%.