New analytical model reveals two-speed progress toward the Sustainable Development Goals in the European Union
A study co-led by researchers from Spain, Poland, and the Netherlands introduces an Ensemble-DEA approach that enhances the accuracy of SDG assessments, overcoming dimensionality issues in large datasets of sustainability indicators
image: Map of EU countries’ performance toward the SDGs. The study co-led by UMH and UAM shows a clear pattern: Northern and Benelux countries are the most efficient, while Southern and especially Eastern Europe advance more slowly. Spain ranks 20th out of 27.
Credit: Aparicio et al. (Expert Systems with Applications, 2025).
European Union countries are progressing toward the United Nations Sustainable Development Goals (SDGs), but not at the same pace. A study co-led by Miguel Hernández University of Elche (UMH, Spain), Wrocław University of Economics and Business (Poland), and the Autonomous University of Madrid (UAM, Spain) reveals that Northern and Benelux countries are advancing the fastest. At the same time, Southern and Eastern Europe show slower progress. The findings are published in Expert Systems with Applications.
Researchers Juan Aparicio and Juan Francisco Monge, from the Operations Research Center (CIO) at UMH, co-led the development of a mathematical model designed to more accurately measure the efficiency with which EU member states are progressing toward the SDGs using their available resources.
“Our model offers a more realistic picture of Europe’s progress,” explains Aparicio, first author of the study. “It not only shows who is closer to achieving the SDGs but also incorporates each country’s initial resource endowment, providing clues about whether its strengths are being effectively used.”
The challenge of measuring progress using hundreds of variables
To avoid distortions when comparing countries with different characteristics, the research team relies on the Benefit of the Doubt (BoD) model, which lets the data determine the weights of each indicator rather than imposing external criteria.
Assessing SDG performance requires analyzing dozens of interconnected variables related to poverty, education, energy, gender equality, and other key areas. As the number of indicators grows, datasets become more dispersed, making it harder to identify stable patterns. This is known as the curse of dimensionality, a phenomenon that can reduce model accuracy or lead to misleading conclusions.
“The challenge is particularly evident in Europe,” explains Monge, “where the shared policy framework—such as the European Climate Law—allows us to compare countries with similar economic development, but using very large datasets. There are 17 SDGs evaluated with 102 indicators, 34 of which are used across multiple goals. And not all countries have complete data for all years.”
Given these constraints, the analysis focused on 2019, the most recent year with sufficiently complete information across EU countries.
Avoiding the curse of dimensionality with Ensemble-DEA
Applying the BoD approach to more than 100 variables introduces distortions. To address this, the researchers developed an enhanced version of Data Envelopment Analysis (DEA) and broke the problem into smaller, more manageable components.
The new method, called Ensemble-DEA, generates thousands of submodels, each using only eight indicators, and then aggregates their results. The process incorporates bootstrap resampling, in which some countries appear repeatedly in random subsamples to reinforce reliability.
“Simplifying it a lot, it is like measuring something many times with different rulers to make sure the final value is the right one,” says Monge. The authors demonstrate that this ensemble approach produces more stable, balanced, and fair evaluations, even when comparing countries with very different sizes, development levels, or data availability.
A two-speed Europe
The results confirm a clear territorial pattern:
- Scandinavia and the Benelux region—with Sweden, Finland, Denmark, the Netherlands, and Luxembourg at the top—are the most efficient performers in SDG progress.
- Several Eastern European countries occupy the lower end of the ranking, with uneven results in gender equality, innovation, and environmental sustainability.
- Spain ranks 20th out of 27, consistent with other socioeconomic indicators that place more developed welfare states toward the top and countries with weaker welfare structures toward the bottom.
The study also reveals two structural divides: a north–south gap and a west–east gap, both of which are clearly reflected in SDG performance.
In addition to Aparicio and Monge (UMH), the research team includes Magdalena Kapelko (Wrocław University of Economics and Business) and José L. Zofío, professor at UAM and Erasmus University Rotterdam (Netherlands).
Funding
The study was funded by the National Science Centre of Poland (project no. 2023/49/B/HS4/02991). Part of the computational work was conducted at the Wrocław Centre for Networking and Supercomputing.