An Approach for Identifying a Global Core Indicator Set for Post-2030 International Development Goals

Abstract

The global indicator framework for monitoring the progress of the United Nations Sustainable Development Goals (SDGs) faces challenges such as insufficient data availability and comparability. However, fundamental changes to the SDG indicator framework are unlikely to occur by the SDG target year of 2030. An opportunity for improvements lies in the development of post-2030 international development goals. To contribute to future discussions on the post-2030 indicator framework, this study investigates how to address data availability and comparability issues. A suggested improvement is to develop a relatively small set of indicators, named “core indicators,” which are intended to reduce the data compilation burden for countries while enabling the monitoring of the overall progress of goals. To examine the feasibility of identifying the core indicators, this study undertook an analysis of official SDG data from 2000 to 2023, and selected 47 disaggregated indicators (DIs) utilizing statistical correlations between DI pairs. The analysis revealed that the 47 core DIs could produce country SDG progress scores similar to those calculated with a much larger dataset of 1112 DIs. The results indicated the usefulness of the proposed approach in selecting the core indicators for the post-2030 international development goals.

1. Introduction

The General Assembly of the United Nations adopted the Sustainable Development Goals (SDGs) in 2015 [1], which consisted of 17 goals and 169 targets to be achieved by 2030. Following the adoption, the Inter-Agency and Expert Group on SDG Indicators (IAEG-SDGs) developed the global SDG indicator framework to monitor the progress of the targets. The indicator framework includes 231 indicators, (The number of unique indicators was expanded to 234 in March 2025 but the analysis in this study was undertaken based on the previous 231 unique indicators.) excluding overlapping indicators, as of January 2025.

The SDG indicator framework faces various challenges such as insufficient availability of indicator data [2,3], inadequate data comparability and consistency across countries [4], and the incompleteness of indicators to capture all principal aspects of targets [4,5]. One of the major factors behind data deficiency is the immense volume and complexity of data requirements. Although the number of unique SDG indicators is 231, many of them include sub-indicators classified by “series”. Well over several hundred data series are registered in the SDG Data Structure Definition managed by the IAEG-SDGs [6]. In addition, some data series require broken-down data disaggregated by various attributes, such as age, sex, area (urban/rural), education level, disability status, occupation, income level, product type, and activity type. The total cost estimated for low- and middle-income countries to compile SDG indicator data could reach USD 44–45 billion over the SDG implementation period [7].

In the face of perceived challenges, significant efforts have been made to improve the indicator framework. According to the resolution adopted by the UN General Assembly [8], the global SDG indicators need to be refined annually, with comprehensive reviews occurring in 2020 and 2025. These processes have led to significant improvements in the clarity and specificity of individual indicators. A notable example is the elimination of Tier 3 indicators (SDG indicators adopt a tier classification system. The Tier 1 indicator is “conceptually clear, has an internationally established methodology and standards are available, and data are regularly produced by countries for at least 50 percent of countries and of the population in every region where the indicator is relevant” [9]. The Tier 2 indicator is the same as the Tier 1 indicator except its data are not regularly produced by countries. The Tier 3 indicator lacks an internationally established methodology or standards.)—62 indicators that lacked internationally established methodology or standards as of May 2018 [10]. Tier 3 indicators were phased out following the 51st session of the United Nations Statistical Commission held in 2020 [9].

However, any fundamental reform of the global SDG indicator framework to address the perceived challenges mentioned above does not seem practically feasible. Rather, it is deemed more realistic to establish an improved indicator framework for international development goals after 2030, the target year of the SDGs, building on the experience of monitoring the SDGs. Discussions on international sustainable development after 2030 will officially start at the UN General Assembly in September 2027 [11]. To contribute to future discussions on the indicator framework for post-2030 development goals, this study investigates how to address data availability and comparability issues.

1.1. Literature Related to the SDG Indicator Framework

Apart from the deliberations by the UN bodies described in the previous paragraphs, there is a significant amount of literature related to the SDG indicator framework. The development of the post-2030 indicator framework should build on knowledge from such literature.

There are studies that attempt to better understand the trends and characteristics of the global, regional, national or sub-national progress of the SDGs through reductions in dimensions from many individual indicators to fewer composite metrics through principal component analysis (PCA) [12,13,14] or entropy-based indicator weighting methods [15,16]. Similarly, multiple correspondence analysis (MCA) can be used for clustering metrics on the basis of their categorical attributes. For example, Parchomenko et al. applied MCA to cluster circular economy metrics [17]. Multi-criteria decision analysis (MCDA) is also widely used in sustainability analysis and a systematic literature review by Sousa et al. [18] confirmed various applications of MCDA to decision analysis for achieving the SDGs. The use of composite indicators for measuring multiple dimensions of development dates back to long before the SDG era, with the most well-known example of the Human Development Index (HDI) created by the United Nations Development Programme (UNDP) [19]; detailed guidance materials for comparisons and the use of various composite indices/indicators are available [20,21].

In the face of the expanding use of indicators and indices for development policy making and evaluation in recent years, however, some scholars such as Rottenburg and Merry have posed questions about the legitimacy of indicator/index numbers produced through increasingly sophisticated techniques despite the claims that they are essential for objective, democratic, and evidence-based decision-making [22]. The concern about legitimacy can be explained by the nature of numerical indicators/indices, which simplify intrinsically complex realities, and underlying nuances and assumptions are easily lost or forgotten when they are communicated [23]. Moreover, when indicators and indices are used for evaluation and comparison, they implicitly carry certain ideals or values as to the directions of progress in the guise of objectivity [23]. The neutrality of indicator selection is also a matter of concern. Fukuda-Parr [24] reported how indicators to measure income and wealth inequality for SDG 10 (reduced inequalities) were excluded in the negotiation process of the SDG targets and indicators. Similarly, Gaspar et al. [25] described how indicators of sustainable consumption for SDG 12 (sustainable consumption and production) were weakened in the negotiation process influenced by business interests.

Another group of studies focuses on interlinkages, including synergies and trade-offs, between goals, targets, and indicators of SDGs. Some studies have investigated interlinkages on the basis of Spearman’s or Pearson’s correlation coefficients, using either official SDG data [26,27,28] or alternative datasets [29]. Others have used more complex methods such as a non-linear non-monotonic model [30], a mixed effect model [31], or machine learning [32]. There are also studies that use qualitative assessment of interlinkages on the basis of systems thinking [33,34,35]. Network analysis is another common approach for understanding interlinkages, identifying important indicators, or finding clusters [31,33,34,35]. While the knowledge from these studies is useful for facilitating progress toward the SDGs by leveraging synergies and managing trade-offs, they do not provide concrete proposals for improving the monitoring framework of the SDGs, addressing its observed challenges described in the beginning of this section.

1.2. Significance of the Study

Considering that the excessive data compilation burden is behind other observed challenges, including data deficiency as well as insufficient data comparability and timeliness, a reduction in the number of indicators would be a key factor for improving the monitoring framework [36,37]. The resulting reduction in data requirements would enable countries and their external assistance providers to concentrate their resources to develop the statistical capacity for data compilation and quality improvement that conforms to related international standards. In line with this direction of improvement, this study proposes identifying a relatively small set of indicators, named “core indicators,” which are intended to reduce the data compilation burden for countries while enabling the monitoring of the overall progress of goals. As explained in the Methods subsection, the core indicators proposed in this study are a relatively small set of disaggregated indicators that are selected from the current disaggregated global SDG indicators on the basis of the abundance of statistical correlations with other indicators. The remaining part of this section discusses possible approaches for identifying the core indicators, which are not limited to the approach taken in this study.

There are multiple approaches for selecting such core indicators. For example, they may be selected and agreed upon through consultation and negotiation among experts and stakeholders. The global SDG indicators were developed through this approach, with statistical experts representing member states of IAEG-SDGs—in consultation with international agencies specializing in the subject matter of the respective SDGs and a few civil society representatives—discussing and determining the global indicators [10]. Another common approach is based on a set of explicitly defined selection criteria (hereafter called “the criteria-based approach”), which may include both qualitative and quantitative factors. A well-known example of this type of approach is the methodology used to produce the Sustainable Development Goals Index, where indicators are selected based on five criteria: global relevance and applicability, statistical adequacy, timeliness, coverage, and measurability of distance to targets [38]. Similarly, a study by van Vuuren et al. [37] used seven criteria to identify 36 targets and corresponding indicators to measure progress toward the SDGs.

Although these are all legitimate approaches, they still run the risk of producing indicator redundancy if considerations of interlinkages between indicators are not adequately taken into account. To mitigate the issue of redundancy, there is an alternative approach to narrowing down indicators by eliminating overlaps by leveraging statistical analyses. While many studies have investigated interlinkages between goals, targets, and indicators of SDGs as explained in the previous subsection, only a few studies have used the interlinkages to select a set of SDG indicators. Among them, Kubiszewski et al. [39] reported that only eight SDG indicators can represent 84% of the variance in life satisfaction survey scores across countries. The eight indicators were identified through the least absolute shrinkage and selection operator (LASSO) algorithm. Using the statistical correlation between indicators, Shuai et al. [40] identified 147 indicators that can explain more than 90% of the annual variation in 351 World Bank SDG indicators although the number of selected indicators is not significantly smaller than that of the official SDG indicators. Zong et al. [41] identified priority indicators at the provincial level in China with network analysis and the technique for order preference by similarity to the ideal solution (TOPSIS). However, no studies thus far have proposed a statistical methodology for identifying a relatively small set of indicators that can roughly represent countries’ overall progress in SDGs using the official SDG indicator data.

Based on the understanding described thus far and to address the above-mentioned research gap, this study addresses a research question of whether and how core indicators can be identified through statistical analyses of a dataset primarily populated by countries. To address this research question, this study proposes and demonstrates a statistical approach to identifying the core indicators to be a part of the development process of the indicator framework for post-2030 international development goals. The novelty of the proposed approach is the inclusion of disaggregated indicators in the core indicators, which provides a more granular understanding of correlations between indicators, on the basis of the analysis of official SDG indicator data, which demonstrates the applicability of the approach to the real setting of datasets that contain data provided by UN member states. The proposed approach has practical utility for reducing the data compilation burden for countries and resource requirements for statistical capacity development, which are particularly relevant for countries with constrained capacities and resource availability. Moreover, it has the theoretical benefits of reducing indicator redundancy and breaking thematic silos in indicator development for interconnected development goals. However, it is imperative to clarify from the outset that a statistical approach cannot be used in isolation to determine the core indicators. Rather, it is envisaged for use in combination with other approaches, such as the criteria-based approach, examples of which are given earlier in this sub-section.

The remainder of this article is composed of the following sections. Section 2 describes the data and methods used in the analysis. Section 3 presents the analysis results and discusses the implications and limitations of this study. Section 4 concludes with a brief summary and policy recommendations for the indicator framework of post-2030 international development goals.

2. Materials and Methods

Although this study proposes and demonstrates an approach to identifying the core indicators for post-2030 international development goals, it uses the current SDG indicators and the official SDG indicator dataset. This is because it is not possible to prejudge the post-2030 development goals and their indicators. The use of current official SDG indicator data has merit for demonstration purposes, as it provides a realistic setting of data availability and characteristics.

2.1. Materials

This study uses official SDG indicator data downloaded from the SDG Indicators Database [42] on 18 September 2024. This study used data for the Tier 1 indicators based on the tier classification by IAEG-SDGs [9] as of 6 March 2024, which was the most recent classification available at the time of analysis. According to the tier classification, Tier 2 indicators differ from Tier 1 indicators in that data are not regularly produced by countries. This study excluded Tier 2 indicator data to improve the reliability of correlation analyses to be undertaken at a later stage by using indicators with reasonably good data availability. Thus, the Tier 1 indicator data for all countries and areas—where data were available—were extracted for the period from 2000 to 2023. Non-numerical data were eliminated. The exclusion of Tier 2 indicators (Tier 3 indicators no longer exist in the dataset used because the Tier 3 category was phased out in 2020.) is due to practical considerations that the core indicators should consist of indicators whose data coverage extends to the majority of member states and whose data are provided regularly so that the global trends and progress toward development goals can be grasped. It should be noted, however, that this comes at a trade-off with a broad and balanced representation of goals, because some goals have disproportionately high concentrations of Tier 2 indicators.

The official SDG indicator data have many attributes. All the data have attributes of country (The attribute, “country,” comprises country and sub-national area because some SDG indicators include data for both countries and sub-national administrative areas. Examples of the latter include Puerto Rico (the United States), French Polynesia (France), and Greenland (Denmark). For simplicity, however, the attribute is called “country” throughout this article.), year, SDG indicator number, and series code (uniquely assigned to each data series). Some data additionally have one or more disaggregation attributes (e.g., sex, age group, and income level) depending on the indicator. For ease of data management and analysis, a composite attribute was created, combining the SDG indicator number, series code, and all relevant disaggregation attribute(s). This composite attribute is hereafter called the “disaggregated indicator” (DI). For instance, “3.2.1_under five mortality rate/male”, “3.2.1_under five mortality rate/female”, and “3.2.1_under five mortality rate/both sexes” are treated as different DIs, and a unique DI code is assigned to each. An example of DI having multiple disaggregation attributes is “16.2.2_detected victims of human trafficking/male/under 18 years of age.” Disaggregation attributes include aggregated members. For example, gender-disaggregated indicators have one of three disaggregation attributes: male, female, or both sexes. Likewise, age-disaggregated indicators have a disaggregation attribute of “all ages” or other corresponding to a specific age group. Despite what its name suggests, DIs also include aggregated indicators. The analysis of this study handles both aggregated and disaggregated indicators (and their data) equally and simultaneously. This treatment is consistent across all indicators, but data availability limits the use of some DIs; for example, data may be available for a DI for all ages but not for specific age groups.

All the extracted data were then grouped into five different year periods corresponding to the years 2000–2004, 2005–2009, 2010–2014, 2015–2019, and 2020–2023. If two or more data points had the same combination of DI, country, and year period, their average value was used. Based on the data processing thus far, all data have three attributes, i.e., DI, country, and year period.

Furthermore, several data screening procedures were applied. DIs with binary data entry and zero variance across all countries within the same year period were removed (DIs with binary data entry are typically those that count the number of countries that meet set criteria (1 = meeting criteria, 0 = not meeting criteria). An example of DIs with zero variance across all country/area within the same year period is 10.6.1 Proportion of voting rights of developing countries in the UN General Assembly (or other institutions where all member states have the voting right with an equal weight)). Indicator 13.2.2 regarding greenhouse gas emissions has two data series, i.e., one for Annex-I countries and the other for non-Annex-I countries of the UN Framework Convention on Climate Change. These two data series were collapsed into one new data series that included all countries. To improve the reliability of correlation analyses undertaken at the later stage, DIs with data from fewer than 100 countries, regardless of the year period, were removed. For the overlapping indicators, only the DIs related to the indicator with the smallest goal number were retained, whereas the others were removed. For example, Indicator 7.b.1 overlaps with 12.a.1; thus, DIs related to 12.a.1 were removed to avoid duplication in the dataset to be used for analyses.

Some indicators have two types of data series for the same metric of interest, i.e., one for a simple value, and the other for a relativized value. For example, indicator 1.5.1, the number of people affected by disasters, has two data series, one for the number of affected people and the other for the number of affected people per 100,000 population. When there were two such data series, the DIs for simple values were removed. For indicators that had no data series of a relativized value but a relativized value was deemed preferable for correlation analyses in the later stage, the data for the DIs related to such indicators were relativized by population, current or constant gross domestic product (GDP) (current or constant 2015 United States dollar (USD)), or territory land area. The data for population and GDP were retrieved from the World Development Indicators [43]. The choice between the use of current or constant GDP was made depending on the unit of measurement for the value to be relativized. For instance, the data for 1.5.2, direct economic loss attributed to disasters, are provided in the current USD. Thus, the values of DIs related to this data series were relativized by the current USD. A five-year average of population and GDP (current and constant) were calculated for the respective country and year period to be applied to the relativization. Data for the territory land area are included in the official SDG dataset as a data series of indicator 15.1.1. The data for the closest year of the year period for each country were used. The list of data series whose related DI data were relativized is provided in Table S1 in the Supplementary Materials.

As a result of these screening processes, the remaining dataset had 1033 DIs excluding overlapping DIs, which belonged to 148 indicators and 335 data series.

2.2. Methods

In this study, the core indicators were selected on the basis of the number of positive correlations with other indicators. In principle, indicators with more positive correlations with others are preferred in the selection over those with fewer correlations. The reason for this selection criterion is that the data for the core indicators can be used to estimate the data of other indicators that are correlated with the core indicators using statistical models of the observed correlations. The core indicators are intended for enabling rough assessments of countries’ progress toward development goals and targets but not for developing effective policies and measures to advance toward them. For the latter purpose, more detailed indicators and an understanding of the causal relationships between them are necessary, which is beyond the scope of this study. Trade-off correlations were not counted when selecting the core indicators because efforts should be made to change the trade-off relationships; therefore, they cannot be assumed to be left unchanged.

The correlation analysis for selecting the core indicators was undertaken at the DI level rather than at the indicator level or data series level because it was anticipated that, for some data series, DIs with disaggregated attributes could have more positive correlations than the corresponding aggregated DIs. For example, a DI with the attribute of female might have more positive correlations than the corresponding DI for both sexes. More concrete examples are given in Results and Discussions section. Therefore, the core indicators were selected at the DI level. Henceforth, they are called the “core DIs”.

Before undertaking the correlation analysis, DIs were classified into two groups; the first group included the more-is-better type of DIs (e.g., the proportion of the population using basic drinking water services), and the second included less-is-better DIs (e.g., the proportion of population below the international poverty line). The data values of the latter groups were multiplied by −1. By this procedure, if the sign of a correlation coefficient of a pair of DIs is plus (+), the DI pair is considered to have a positive linkage. If the sign is minus (−), the correlation represents a trade-off relationship. In some cases, it was not clear whether a DI fits in the more-is-better or less-is-better group. In such cases, the judgment was made according to the intention of the SDG target to which the DI belonged. For instance, it is not objectively clear whether a large agricultural value-added share of GDP is good, as it will depend on each country’s development strategy. However, because it belongs to Target 2.a, which is intended to enhance agricultural productive capacity in developing countries, a large agricultural share of GDP is regarded as better. This dataset, for which less-is-better DIs were multiplied by −1, was used for the subsequent analysis unless otherwise stated.

The correlation analysis was performed in four stages (Figure 1).

In the first stage, rough screening was implemented to detect correlations between all possible pairs of DIs through Spearman’s rank correlation analysis [44] because it can capture both linear and non-linear monotonic correlations [26]. For each pair of all possible combinations of DIs, a data value of one DI was matched with the data value of the other DI for the same country and year period. The number of matches made varied widely among the respective DI pairs due to the differences in data availability. Spearman’s rank correlation coefficient was calculated only when a DI pair had 50 or more data matches, in consideration of the reliability of the calculated coefficients. Furthermore, the analysis was not undertaken for any pairs of DIs that belonged to the same SDG indicator. This exclusion was necessary to avoid selection bias in the later stage of core DI selection toward DIs that belonged to indicators that had many disaggregation attributes. This is because such DIs naturally have many correlations with other DIs under the same indicator. Thus, only cross-indicator interlinkages were analyzed. A DI pair was considered to have a positive correlation when the calculated Spearman’s rank correlation coefficient (also known as “Spearman’s ρ”) was greater than 0.8 and a trade-off when it was less than −0.8. While there are different threshold values for the interpretation of Spearman’s ρ, this study uses the midpoint of the “Strong correlation” range suggested by Schober et al. [45] to make relatively conservative judgments of the existence of correlations.

In the second stage, the preliminary selection of DIs in each SDG was undertaken. For each SDG, the top five DIs were selected based on the number of positive correlations they have with other DIs and trade-off correlations were disregarded. Readers are reminded that correlations between DIs belonging to the same SDG indicators were not analyzed and, therefore, not counted in this process. When the top DI was selected, it was removed from the pool of DIs, and all records of correlations involved in the top DI were deleted from the linkage dataset before selecting the second DI to avoid double counting. The same procedure was repeated until the fifth DI was selected or there was no longer any correlation linkage left in the dataset that involved the remaining DIs under the SDG in question. If multiple DIs had the same number of positive correlations, the DI with the data values covering the largest number of countries was selected. The DIs selected from 17 SDGs form a group of candidate DIs.

In the third stage, simple linear ordinary least squares regression analysis was applied to all positive linkages that each candidate DI (selected in the second stage) had. This analysis used a dataset in which less-is-better DIs were not multiplied by −1. Three functional forms, i.e., (a) linear, (b) exponential, and (c) logarithmic, were used to model the relationship of each pair, as described in the following equations:

$${{\mathrm{x}}_{it}}^{\ast }=\left\{\begin{array}{c} x_{it}, if { x}_{min}>0\\ x_{it}+1-x_{min}, if { x}_{min}\le 0\end{array}\right. ,$$

(1)

$${{\mathrm{y}}_{it}}^{\ast }=\left\{\begin{array}{c} y_{it}, if { y}_{min}>0\\ y_{it}+1-y_{min}, if { y}_{min}\le 0\end{array}\right. ,$$

(2)

$$\left(a\right) linear: {{\mathrm{y}}_{it}}^{\ast }=\alpha {{\mathrm{x}}_{it}}^{\ast }+\mathrm{\beta }+{ϵ}_{it} ,$$

(3)

$$\left(b\right) exponential: ln {{\mathrm{y}}_{it}}^{\ast }=\alpha {{\mathrm{x}}_{it}}^{\ast }+\mathrm{\beta }+{ϵ}_{it} , and$$

(4)

$$\left(c\right) logarithmic: {{\mathrm{y}}_{it}}^{\ast }=\alpha ln {{\mathrm{x}}_{it}}^{\ast }+\mathrm{\beta }+{ϵ}_{it} ,$$

(5)

where ${\mathrm{x}}_{it}$ denotes a data value for a candidate DI (i.e., x) in country i in year period t; ${\mathrm{y}}_{it}$ represents a data value for a DI (i.e., y) with a positive linkage with $x$ in country i in year period t; $x_{min}$ and ${ y}_{min}$ are the minimum values of x and y, respectively; $\alpha$ and $\mathrm{\beta }$ are regression coefficients to be estimated; and ${ϵ}_{it}$ denotes the error term. ${{\mathrm{x}}_{it}}^{\ast }$ and ${{\mathrm{y}}_{it}}^{\ast }$ are adjusted values of x_it and y_it if their minimum values are zero or negative so that the logarithms of ${{\mathrm{x}}_{it}}^{\ast }$ and ${{\mathrm{y}}_{it}}^{\ast }$ exist for all the data values of x and y. Theoretically, the monotonic positive correlations detected by Spearman’s rank correlation analysis could be better represented by other functional forms except the above three. However, only these three models were applied for simplicity. After the regression models for a pair of DIs were estimated with the three functional forms, the best model with the largest coefficient of determination (typically denoted as R²) among the three was selected. If the largest coefficient of determination was less than 0.64, no model was adopted, and it was determined that there was no positive linkage for the pair.

In the fourth stage, the core DIs were selected from the candidate DIs on the basis of the number of positive linkages that each candidate DI had, as determined in the third stage. First, the DI that had linkages with the largest number of indicators was selected. These indicators included the one to which the selected DI directly belonged, as well as others that were connected through the confirmed positive linkages with DIs under them. Then, the first DI was removed from the group of candidate DIs, and all positive linkages involving the first DI were deleted from the linkage records to avoid double counting. Next, the second DI was selected based on its linkages with the largest number of new indicators, excluding those already connected to the first DI. After the selection, the second DI was removed from the group of candidate DIs, and all positive linkages involving the second DI were deleted to prevent double counting. This process was repeated until no more linkages with a new indicator could be formed by selecting any one of the remaining DI candidates. If multiple DIs had linkages with the same number of additional indicators, the DI with the data values that covered the largest number of countries was selected. The selection process continued by selecting the DI that had the largest number of inter-indicator linkages formed by positive correlations among the remaining candidates, and the linkage records were deleted. Inter-DI linkages under the same indicator pair are only counted once. In other words, a DI’s linkages with two or more DIs under one indicator constitute one linkage. If multiple DIs had the same number of new inter-indicator linkages, the DI with data values covering the largest number of countries was selected. This process was repeated as long as the inclusion of the additional DI formed six or more new inter-indicator linkages. This termination threshold was arbitrary and allowed consideration of two competing objectives: the first was to increase the number of linkages that the selected core DIs collectively have with other indicators, and the second was to reduce the number of core DIs; this process resulted in a set of DIs that formed the core DIs.

After the core DIs were selected, their ability to represent the characteristics of all DIs under each SDG was assessed. This assessment was conducted by comparing two scores for each country for each SDG—that is, the one calculated with the core DIs (hereafter called the “estimated score”) and the other calculated with all DIs that remained after the screening process described in Section 2.1 above (hereafter called the “reference score”). The country score was calculated with the following equation:

$$S_G^a={\displaystyle \frac{1}{n^G}}\sum _{j=1}^{n^G}\left\{{\displaystyle \frac{1}{m^j}}\sum _{k=1}^{m^j}\left({\displaystyle \frac{x_a^{jk}-x_{min}^{jk}}{x_{max}^{jk}-x_{min}^{jk}}}\right)\right\} ,$$

(6)

where $S_G^a$ denotes the score for country a for goal G, $n^G$ denotes the number of indicators under goal G, $m^j$ denotes the number of DIs under the j-th indicator of goal G, $x_a^{jk}$ denotes the data value for country a of the k-th DI under the j-th indicator, and $x_{max}^{jk}$ and $x_{min}^{jk}$ denote the maximum and minimum data values, respectively, among all countries’ values of the k-th DI under the j-th indicator. This method of calculating the SDG score uses the min–max normalization of data, gives an equal weight to all indicators under the same goal, and takes a simple average of the indicator scores. There are other normalization methods such as Z score normalization and clipping of outliers. Similarly, it is possible to assign different weights to indicators or assume non-linear functional forms between the SDG score and individual indicators to compute the SDG score as a more complex composite index. It is also possible to reduce indicator numbers through principal component analysis (PCA) before the SDG score is calculated. The method taken in this study was selected by prioritizing the methodological simplicity, because it is a valuable attribute for gaining understanding and buy-in by stakeholders as diverse as those of international development goals.

With Equation (6), reference scores were calculated using all available DI data values, whereas estimated scores were calculated using the DI data values of the core DIs and the estimated data values of DIs that had positive correlations with the core DIs. DIs with data for fewer than 50 countries were not used for the calculation of the reference scores. The estimations of the data values of the correlated DIs were conducted using the regression models established in the third stage. If a DI had correlations with multiple core DIs, the average of the values estimated from the relevant core DIs was used for the data value of the DI. This treatment may introduce biases to the estimated values. For instance, if the dataset of core DIs contains inexplicable outliers, the estimated values from them can also be outliers which are then averaged with other estimates, resulting in biased estimates. Ideally, the reliability of multiple estimates should be evaluated, and those below a certain reliability threshold should be removed or weights assigned according to the reliability evaluation results before averaging. In the absence of a feasible reliability evaluation method, however, this issue was not addressed. This is a limitation of this study.

3. Results and Discussions

As a result of Spearman’s rank correlation analysis (the first stage of the analysis), correlations were found for a total of 674 pairs of data series, among which 96% showed positive linkages and 4% were trade-offs. No pair of data series had both positive and trade-off correlations. Likewise, correlations were found for 383 pairs of indicators, among which 95% showed positive linkages only, and 4% were trade-offs only. Two pairs of indicators (indicator pairs 7.1.2–8.4.2 and 8.3.1–8.4.2) had both positive and trade-off correlations among the different pairs of data series under them. Overall, positive linkages outweigh trade-off linkages, which corroborates the results of existing studies [27,29].

The fourth stage of the analysis described above resulted in a group of 29 DIs selected as the core DIs (

Table 1. List of core DIs.

Order of Selection	Indicator Number	Data Series	Direction of Progress	Disaggregation Attributes	Additional Indicators Covered	Additional Inter-Indicator Linkages
1	3.2.1	Under-five mortality rate, by sex (deaths per 1000 live births)	↓	Both sexes	25	24
2	3.8.1	Universal health coverage (UHC) service coverage index	↑		6	22
3	8.a.1	Total official flows (disbursement) for Aid for Trade, by recipient countries (millions of constant 2022 United States dollars (USD)): transformed relative to millions of constant 2015 USD	↑		4	3
4	8.3.1	Proportion of informal employment, by sector and sex—13th International Conference of Labour Statisticians (ICLS) (%)	↓	Female, 15 years+, All activities	3	21
5	15.1.2	Average proportion of Terrestrial Key Biodiversity Areas (KBAs) covered by protected areas (%)	↑		3	2
6	17.11.1	Developing countries’ and least developed countries’ share of global merchandise imports (%)	↑		3	2
7	5.5.1	Proportion of seats held by women in national parliaments (% of the total number of seats)	↑		2	1
8	1.a.1	Official development assistance grants for poverty reduction, by recipient countries (percentage of Gross National Income)	↑		2	1
9	10.5.1	Regulatory capital to assets (%)	↑		2	1
10	3.1.1	Maternal mortality ratio	↓		1	17
11	1.4.1	Proportion of population using basic sanitation services, by location (%)	↑	Both urban and rural	1	15
12	9.5.2	Researchers (in full-time equivalent) per million inhabitants (per 1,000,000 population)	↑		1	9
13	8.6.1	Proportion of youth not in education, employment or training, by sex and age—19th ICLS (%)	↓	Female	1	8
14	17.9.1	Total official development assistance (gross disbursement) for technical cooperation (millions of 2022 USD): transformed relative to millions of 2015 constant USD	↑		1	1
15	6.3.1	Proportion of safely treated domestic wastewater flows (%)	↑		1	1
16	1.a.2	Proportion of total government spending on essential services (%)	↑		1	1
17	5.3.1	Proportion of women aged 20–24 years who were married or in a union before age 18 (%)	↓		1	1
18	3.2.2	Neonatal mortality rate (deaths per 1000 live births)	↓	Both sexes	0	16
19	6.1.1	Proportion of population using safely managed drinking water services, by urban/rural (%)	↑	Both urban and rural	0	15
20	3.9.1	Age-standardized mortality rate attributed to household air pollution (deaths per 100,000 population)	↓		0	13
21	4.1.2	Completion rate, by sex, location, wealth quintile and education level (%)	↑	Male, primary education, Both urban and rural, all income levels	0	12
22	4.5.1	Adjusted location parity index for completion rate, by sex, wealth quintile, and education level	↑	Both sexes, lower secondary education, all income levels	0	12
23	7.1.1	Proportion of population with access to electricity, by urban/rural (%)	↑	Both urban and rural	0	11
24	7.1.2	Proportion of population with primary reliance on clean fuels and technology (%)	↑	Rural	0	11
25	4.a.1	Proportion of schools with access to electricity, by education level (%)	↑	Primary education	0	11
26	17.6.1	Fixed broadband subscriptions per 100 inhabitants, by speed (per 100 inhabitants)	↑	All speed	0	9
27	1.1.1	Proportion of the population below the international poverty line (%)	↓	Both sexes, both urban and rural, all ages	0	7
28	4.1.1	Proportion of children and young people achieving a minimum proficiency level in reading and mathematics (%)	↑	Both sexes, primary education, reading	0	7
29	17.8.1	Proportion of individuals using the internet (%)	↑	Both sexes	0	6

“Direction of progress” shows ↑ for more-is-better indicators and ↓ for less-is-better indicators. “Additional indicators covered” means the number of indicators newly added to the network of linkages (either by direct belonging to or positive correlations) with the core disaggregated indicators (DIs) by adding the DI concerned, on top of the indicators already added to the network by the DIs listed above the DI concerned. “Additional inter-indicator linkages” refers to the number of new pairs of inter-indicator linkages added to the network, in addition to the linkages already added to the network by the DIs listed above the DI concerned.

). Collectively, they had 188 confirmed positive linkages with other DIs, not including linkages between the core DIs, based on the regression analysis in the third stage. The regression models that best fit the 188 linkages consisted of 72 linear, 62 exponential, and 54 logarithmic models. The list of the 188 linkages is provided in Table S2 and their summary statistics are provided in Table S3 of the Supplementary Materials. The core DIs under indicators 5.5.1, 17.11.1, and 6.3.1 present relatively high average values of R² although these core DIs have only a few linkages. Core DIs with many linkages (e.g., core DIs under indicators 3.2.1, 8.3.1, and 1.4.1) have modest average R² values (Table S3). The ratio of the mean absolute error (MAE) to the root mean square error (RSME) is theoretically close to 1.253 when the distribution of errors follows the normal distribution [46], which is an assumption of linear regression models. Some core DIs such as those under indicators 10.5.1, 17.11.1, and 5.5.1 have high MAE to RSME ratios, which indicate that these estimations may be affected by outliers (Table S2). It should be noted that the core DIs are selected by statistical analysis; therefore, their inclusion in Table 1 does not necessarily mean that the indicators’ intrinsic values represent the goals to which they belong.

The list of core DIs in Table 1 indicates that some DIs have more linkages with other indicators than do the corresponding DIs with a lesser degree of disaggregation. For example, DIs for females of “8.3.1 Proportion of informal employment (≥15 years, all activities),” and “8.6.1 Proportion of youth not in education, employment or training” were selected rather than the corresponding DIs for both sexes. Similarly, “4.1.2 Completion rate of primary education (both urban and rural, all income levels)” for males was selected instead of the same for both sexes, and “7.1.2 Proportion of population with primary reliance on clean fuels and technology” for rural areas was selected instead of the same for both urban and rural areas. These examples suggest that, despite requiring greater efforts for data compilation, disaggregation pays off, at least for some indicators, when analyzing positive linkages between indicators.

With respect to the distribution of the 29 selected DIs across 17 SDGs, SDG3 (Good health and well-being) has the largest share (five DIs), followed by SDG1 (No poverty), SDG4 (Quality education), and SDG17 (Partnerships for the goals) (four DIs each). In contrast, SGD2 (Zero hunger), SDG11 (Sustainable cities and communities), SDG12 (Sustainable consumption and production), SDG13 (Climate action), SDG14 (Life below water), and SDG16 (Peace, justice and strong institutions) have no DIs selected. In the second stage of the analysis, only up to five DIs were selected from each SDG. If this ceiling of five DIs was not set, the share of DIs under SDG3 increased.

Table 2. Core DIs with numerous linkages with other indicators (network hub DIs).

Indicator No.	Data Series/Disaggregation Attributes	Goals
		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
3.2.1	Under-five mortality rate/both sexes	3	3	7	4		2	1	4
3.8.1	Universal health coverage (UHC) service coverage index	2	3	5	2	1	1	2	2	2								2
8.3.1	Proportion of informal employment—13th International Conference of Labour Statisticians (ICLS)/female, 15 years+, all activities	2	1	8	3		1	1	3	1		1						1
3.1.1	Maternal mortality ratio	2	1	6	3		2	2	1			1
1.4.1	Proportion of population using basic sanitation services/both urban and rural	1	1	8	3		2	2
3.2.2	Neonatal mortality rate/both sexes	2	2	4	3		1	1	4			1
6.1.1	Proportion of population using safely managed drinking water services/both urban and rural	1	2	6	3		1	2	2	1
7.1.2	Proportion of population with primary reliance on clean fuels and technology/rural	2	1	5	3		2	1	1	1

The core DIs that have 16 or more linkages with other indicators are shown in this table. The numbers represent the counts of linkages with other indicators in each SDG. A thick frame shows the number of linkages with indicators within the same goal that a core DI belongs to. Note that the sum of the number of linkages for each core DI is not necessarily equal to the corresponding number of “Additional inter-indicator linkages” column of Table 1 above because this table allows double-counting of linkages between indicators formed by two core DIs, whereas double-counting is not allowed in Table 1.

shows the number of linkages that core DIs have with indicators for each goal. Only core DIs that have 16 or more linkages (named here “network hub DIs”) are included in the table. In this table, the double-counting of the linkages between indicators formed by two core DIs is allowed to show the total linkages that each DI has, whereas double-counting is not allowed in Table 1. Network hub DIs have many linkages with a similar set of goals, that is, SDGs 1–4 and SDGs 6–8, which suggests that the indicators under these SDGs form clusters. In contrast, they collectively have only a few or no linkages with SDG 5, 10–17. The core DIs under SDG 3 tend to have many linkages with indicators under the same goal. Notably, all the network hub DIs have the largest number of linkages with indicators under SDG 3. This may be partly because SDG 3 has the largest number of indicators among all SDGs but also because SDG 3 has many indicators that are highly correlated with those under other goals.

Figure 2 shows the distribution of indicators that include the 29 core DIs (red blocks) and DIs that have positive correlations with the core DIs (blue blocks) across 248 SDG indicators, including overlaps. Indicators represented by white blocks have neither core DIs nor DIs with positive correlations with the core DIs. However, they have at least one DI that remains in the dataset after the data screening process described in Section 2.1. Indicators represented by black blocks have no DI remaining after the data screening.

Figure 2 illustrates a skewed distribution of core DIs. Goals with two or more DIs are concentrated in SDGs 1 to 8, with the exception of SDG 2, and SDG 17. A disproportionate share of core DIs are found under the first indicator of the first target for SDGs 1, 3, 4, 6, and 7. Although there is no evidence indicating that the order of indicator numbers reflects their priorities, it would not be unreasonable to infer that the first indicator of the first target is a key indicator for each SDG. Despite the value-agnostic approach taken to select the core DIs in this analysis, many of the selected core DIs overlap with these seemingly key indicators of the respective SDGs.

SDGs 2, 11–14, and 16 are underrepresented in the selected core DI set with zero core DIs under these goals. Moreover, SDG 13 is entirely disconnected from the network of positive linkages with the core DIs. The underrepresentation of these goals is attributable to multiple reasons. Poor data availability of their indicators is the first possible reason. Black blocks in Figure 2, which represent indicators with poor data availability, are concentrated in SDGs 11 to 16. The proportion of black blocks in the total number of indicators exceeds 50% for SDG 5 and SDGs 11 to 16, except for SDG 15. These SDGs with low data availability roughly correspond to thematic areas such as gender, cities and settlements, environmental sustainability, and peace and justice. After excluding the black-block indicators, only three indicators remain for SDG 13, which is the lowest among all the SDGs, followed by SDG 14 (four indicators) and SDG 12 (five indicators). They require greater efforts to devise relevant indicators with reasonable data availability or additional investments in data compilation. The second reason is partly related to the first one and involves the selection method of the core DIs. There is an imbalance in the number of indicators across SDGs after excluding black-block indicators. SDG 3 has the largest number of indicators with 25 and also the largest share of core DIs. Because core DIs are selected on the basis of the number of positive linkages with DIs of other indicators both within and outside the goal to which they belong, the likelihood of being selected as a core DI would increase if it belongs to an SDG that includes many mutually correlated indicators. This may explain the strong representation of SDG 3 in the core DIs. Finally, the third reason is also related to the selection method and involves characteristics of the indicators. SDG 4 has a relatively small number of indicators after excluding black-block indicators and, nevertheless, has four core DIs, indicating that the underrepresented SDGs have distinctive indicators with little linkage with others, which implies a limitation of the selection method in its ability to identify distinctive yet important indicators.

3.1. Assessment of the Core DIs

Figure 3 shows the results of the assessment of the core DIs to represent the overall characteristics of all available DI data for each SDG as explained in the final part of Section 2.2. For this assessment, datasets for the periods 2015–2019 and 2020–2023 were used. The intention was to conduct the assessment with the most recent data. However, two core DIs had data for fewer than 50 countries in the period 2020–2023. Therefore, the average values of the periods 2015–2019 and 2020–2023 were used.

Data for 1112 DIs, belonging to 366 data series and 157 indicators, including overlaps, were used for the calculation of reference scores. To calculate the estimated scores, data for the 29 core DIs, belonging to 29 data series and 29 indicators—as well as estimated data for 64 DIs belonging to 42 data series and 32 indicators—were used. These numbers separately count overlapping data series and indicators. The number of data series used for the estimated scores was 19% ((29 + 42)/366) of that used for the reference scores. The equivalent percentage for the indicator number was 39% ((29 + 32)/157).

The graphs illustrate that the estimated scores have relatively good correlations with the reference scores for SDGs 1, 3, 4, 6, 8, 15, and 17. In contrast, the correlations are low for SDGs 2, 10, 11, 12, 14, and 16. Figure 2 shows that these SDGs with low correlations have low coverage of the core DIs (red blocks) and positively linked DIs (blue blocks). Furthermore, the graph for SDG 13 is not shown because its country scores are not calculable due to the absence of core DIs and DIs with positively linked core DIs under SDG 13.

An analysis was performed to investigate the possible reasons for the low correlation for some goals, and the results are reported in Table S4 of the Supplementary Materials. Generally, goals with low coverage rates (i.e., (red + blue blocks)/(red + blue + white blocks) in Figure 2) have low correlation coefficients between estimated and reference country scores. The Pearson’s correlation coefficient between the goal-specific correlation coefficients and the indicator coverage rate was 0.61. However, it does not explain the particularly low correlation coefficients for SDGs 2 and 10. This is likely due to high heterogeneity in the indicators of these goals. The average Pearson’s correlation coefficients for all combinations of the indicator-level reference country scores in Table S4 are low for SDGs 2 and 10 (0.013 and 0.037, respectively). This signifies that the distributions of country scores are dissimilar among the indicators under each of these two goals.

The result illustrates the limitation of selecting core DIs solely based on statistical linkages because it may lead to low indicator coverage in some SDGs. To improve the ability of the core DIs to represent the overall characteristics of the dataset, two DIs were added to the core DIs for SDGs 2, 10, 11, 12, 13, 14, and 16 because the supplementary analysis suggested that additional indicator coverage may improve the correlation by mitigating the effects of heterogeneity in the indicators. The two additional DIs were selected based on the number of countries covered for the whole dataset from 2000 to 2023. The DIs with the top two largest numbers of countries covered for each target SDG were chosen, excluding those under the indicators that are already covered by the core DIs or DIs with positive linkages to the core DI.

There may be other approaches to selecting additional DIs. Expert judgment is an obvious option but it was not attempted because this study intends to provide an alternative to the expert judgment approach to selecting indicators, which largely determined the current SDG global indicators. Selecting the first two available DIs is another option based on an assumption that indicators are numbered in the order of priority. This approach was attempted, but overall, it did not produce better outcomes than the one adopted in this study. An approach based on network centrality is another option, but it will not be effective because the goals with low representation by the 29 core DIs have indicators with limited interlinkages with other indicators.

After choosing the first additional DI, all other DIs of the same indicator were removed from the list to avoid selecting the top two additional DIs from one indicator. The list of additional DIs is presented in

Table 3. List of complementing DIs added to the core DI set.

Indicator Number	Data Series	Direction of Progress	Disaggregation Attributes
2.5.1	Number of transboundary breeds (including extinct ones)	↑
2.a.1	Agriculture value-added share of GDP (%)	↑
10.a.1	Proportion of tariff lines applied to imports with zero-tariff (%)	↑	All products
10.7.4	Number of refugees per 100,000 population, by country of origin (per 100,000 population)	↓
11.6.2	Annual mean levels of fine particulate matter (population-weighted), by location (micrograms per cubic meter)	↓	All areas
11.5.1 (overlapping with 13.1.1 and 1.5.1)	Number of deaths and missing persons attributed to disasters per 100,000 population (number)	↓
12.a.1 (overlapping with 7.b.1)	Installed renewable electricity-generating capacity (watts per capita)	↑	All renewables
12.c.1	Fossil-fuel subsidies (consumption and production) per capita (nominal United States dollars)	↓
13.1.2 (overlapping with 11.b.1 and 1.5.3)	Score of adoption and implementation of national DRR strategies in line with the Sendai Framework	↑
14.b.1	Degree of application of a legal/regulatory/policy/institutional framework which recognizes and protects access rights for small-scale fisheries (level of implementation: 1 lowest to 5 highest)	↑
14.6.1	Progress by countries in the degree of implementation of international instruments aiming to combat illegal, unreported and unregulated fishing (level of implementation: 1 lowest to 5 highest)	↑
16.1.1	Number of victims of intentional homicide per 100,000 population, by sex (victims per 100,000 population)	↓	Both sexes
16.a.1	Countries with National Human Rights Institutions in compliance with the Paris Principles (0 = No status; 1 = Status B, partially compliant; 2 = Status A, fully compliant)	↑

“Direction of progress” shows ↑ for more-is-better indicators and ↓ for less-is-better indicators.

, which includes four overlapping DIs. SDGs 11 and 13 shared the same overlapping DI, which ranked within the top two in terms of coverage, and this DI was therefore selected to serve both SDGs. Therefore, there are 13 additional unique DIs or 18 additional DIs with overlaps. The new core DI set—including these additional DIs—is hereafter referred to as the “extended core DIs.” The extended core DIs have 42 unique DIs or 47 DIs, including overlaps.

Figure 4 shows the results of the assessment of the ability of the extended core DIs to represent the overall characteristics of all available data. The reference scores are the same as those in Figure 3. To calculate the estimated scores, data for the 47 extended core DIs (including five overlaps), belonging to 47 data series and 47 indicators—as well as estimated data for 64 DIs belonging to 42 data series and 32 indicators—were used. These numbers separately count overlapping data series and indicators. The number of data series used for the estimated scores was 24% ((47 + 42)/366) of that used for the reference scores. The equivalent percentage for the indicator number was 50% ((47 + 32)/157). The share of the number of data series and indicators of the extended core DIs in the whole dataset used was 13% (47/366) for data series and 30% (47/157) for indicators, respectively.

The correlations are improved or remain the same as those in Figure 3 for all the SDGs. Significant improvements in the correlation coefficients are observed for SDGs 10, 11, 12, 14, and 16 as a result of adding additional DIs for these goals (

Table 4. Comparison between the original and extended core DIs in terms of Pearson’s correlation coefficients.

Goals	(a) Pearson’s r with Original Core DIs	(b) Pearson’s r with Extended Core DIs	Difference (b) − (a)
1	0.81	0.86	0.05
2	0.14	0.24	0.10
3	0.87	0.87	0.00
4	0.83	0.83	0.00
5	0.65	0.65	0.00
6	0.71	0.71	0.00
7	0.62	0.81	0.19
8	0.78	0.78	0.00
9	0.65	0.65	0.00
10	0.01	0.67	0.66
11	0.59	0.87	0.28
12	0.17	0.70	0.52
13	–	0.86	–
14	0.56	0.79	0.22
15	0.82	0.82	0.00
16	0.25	0.74	0.49
17	0.73	0.73	0.00

Pearson’s r refers to Pearson’s correlation coefficient.

). The comparison is newly made for SDG 13, which shows a good correlation. The correlation for SDG 2 is improved but still very low. The correlations for SDGs 5, 9, and 10 are also low. An in-depth analysis of the selection of core DIs for SDG 2 is needed to improve the correlation. An experiment-based approach is an option to improve the performance, which experiments with all DIs and selects the best performers. However, this approach may result in inconsistent selection across different datasets. Despite the modest representation of some goals, the results of the analysis indicate that a relatively small set of extended core DIs can reasonably estimate country scores that are close to those calculated by all available datasets for most SDGs. This finding suggests that the approach demonstrated in this study could be useful for selecting the core indicators.

3.2. Sensitivity Analysis

A sensitivity analysis was conducted to check the influence of the threshold values of Spearman’s ρ (>0.8) in Stage 1 (see Figure 1) and the coefficient of determination (R² ≥ 0.64) in Stage 3 for the recognition of positive correlations on the selection of the core DIs. First, alternative threshold values of Spearman’s ρ (>0.9, >0.7, and >0.6) without changing the coefficient of determination (R² ≥ 0.64) were tested. Then, a combination of Spearman’s ρ (>0.7) and the coefficient of determination (R² ≥ 0.49) was also tested.

Table 5. Results of the sensitivity analysis.

Cases	Case Settings of Threshold	Results
		Number of Core DIs Selected	Commonality (%) with the Original DI Set
			DI Level	Data Series Level	Indicator Level
Original	Spearman’s ρ > 0.8; R2 ≥ 0.64	29
Case 1	Spearman’s ρ > 0.9; R2 ≥ 0.64	9	44.4	55.6	66.7
Case 2	Spearman’s ρ > 0.7; R2 ≥ 0.64	31	61.3	77.4	83.9
Case 3	Spearman’s ρ > 0.6; R2 ≥ 0.64	29	69.0	75.9	86.2
Case 4	Spearman’s ρ > 0.7; R2 ≥ 0.49	45	42.2	53.3	60.0

R² refers to the coefficient of determination. Commonality (%) is the percentage of common DIs between the original case and a test case relative to the total number of core DIs selected in the test case. A pair of DIs selected in the original case and the test case are determined to be common at the DI level if they are the same DIs. They are determined to be common at the data series level if they belong to the same data series. Likewise, they are determined to be common at the indicator level if they belong to the same indicator.

shows a summary of the results and more detailed results are included in Supplementary Table S5. The original case of core DIs referred to in this subsection is the original 29 DIs, not the extended 47 core DIs.

Case 1 (Spearman’s ρ > 0.9) results in only nine DIs being selected, indicating that this threshold is too restrictive. The numbers of selected core DIs are similar to those of the original case for Cases 2 and 3 with different Spearman’s ρ thresholds, which indicates that the selected number is controlled by the other threshold of R² ≥ 0.64. It is counter-intuitive that the number of core DIs for Case 3 is smaller than that for Case 2 despite the lower threshold value. However, this could occur depending on the composition and selection order of the core DIs. The commonality of the selected DIs between the original case and Cases 2 or 3 is relatively high, particularly at the data series level and the indicator level. Case 4 results in a greater number (45) of core DIs than the original case does, and the commonality with the original case is relatively high considering that the commonality percentage in Table 5 is relative to the number of DIs for Case 4. The commonality percentages relative to the number (29) of DIs for the original case are 65.5% (DI level), 82.8% (data series level), and 93.1% (indicator level), respectively.

The representation of goals, i.e., the number of SDGs that have at least one core DI, is much smaller for Case 1 than for the original case. The goal representations of Cases 2 and 3 are the same as those of the original case. As previously stated, SDGs 11–14, and 16 had no core DIs in the original case and the same applies to Cases 2 and 3. However, Case 4 has DIs belonging to SDGs 11, 13 and 16, although SDGs 12 and 14 are still missing. This may suggest the merit of Case 4 over the original case but the number of core DIs and the efficiency of representation exhibit a trade-off relationship. The ratio of the number of goals directly represented by the core DI to the number of core DIs is 0.41 (12/29) for the original case and 0.33 (15/45) for Case 4. The ratio of the number of indicators covered by the core DIs (i.e., indicators that have at least a core DI or a non-core DI with a positive correlation with a core DI) to the number of core DIs is 2.00 (58/29) for the original case and 1.76 (79/45) for Case 4, excluding the overlaps of positively correlated indicators in both cases. These two ratios show better representation efficiency in the original case than in Case 4. The corresponding goal coverage and indicator coverage per core DI for the extended core DI set (excluding overlaps) are 0.40 (17/42) and 1.69 (71/42), respectively. Although the indicator coverage is slightly higher for Case 4 than the extended core DI set, Case 4 does not have representation for SGD 12 and 14, and some correlations of Case 4 may have lower ability to estimate correlated DIs because the threshold was lowered to R² ≥ 0.49, which are drawbacks of Case 4. Because the number of core DIs is related to the data compilation burden, a judgment must be made in consideration of the trade-off between the number of core DIs and their efficiency of the goal/indicator representation.

3.3. Limitations of This Study and Research Gaps

One of the principal limitations of this study is that the approach demonstrated for selecting the core indicators is solely based on the number of positive correlations with other indicators and the data availability. This resulted in the omission of indicators that have fewer correlations with other indicators. However, it by no means indicates that such indicators are not important. Likewise, this study may have omitted potentially important indicators due to the lack of data availability (including the lack of disaggregated data which undermines the merit of the proposed approach), and disregarded potentially important aspects of goals and targets owing to the lack of availability of adequate indicators. The approach demonstrated in this study should be applied in combination with other approaches based on the assessment of the relevance and importance of indicators. Further research is needed to demonstrate the effectiveness and feasibility of such combined approaches.

The choice of analysis methods in this study leans toward selecting conceptually simple methods. This is because simplicity provides a significant advantage in gaining understanding and buy-in from diverse stakeholders, not limited to academic communities, involved in the design and implementation of international development goals. However, it may have sacrificed the technical rigors of the analysis and its results. For example, the analysis only considers synergistic linkages between DIs and disregards trade-off relationships, which fails to provide guidance for adequate management of potential trade-offs. Moreover, the correlation analysis in this study may be vulnerable to ecological fallacy [47] by relying solely on country-level data although data disaggregated by urban and rural areas are used for some indicators. The correlations found in the country-level data may not be found at the individual level, or even at the municipal or community levels. Furthermore, this study used Spearman’s ρ for screening positive correlations between DIs because of its relatively simple concept and its ability to detect non-linear monotonic relationships between DIs. Spearman’s ρ is less sensitive to outliers and clustered data than the more widely used Pearson’s correlation coefficient but it is not capable of detecting non-monotonic relationships and the estimation may be inaccurate if the dataset includes many tied rank data. Potentially, alternative methods, such as Kendall’s tau, PCA, or mutual information, may have been a better option but these were not attempted in favor of the conceptual simplicity of Spearman’s ρ. Similarly, three regression models (i.e., linear, exponential, and logarithmic) were selected for simplicity and comparability with the common metric of R². However, model diagnostics, such as residual analysis or examination of heteroscedasticity, as well as comparisons with other potentially better models such as polynomial, spline or machine learning-based estimation methods were not performed, which constitutes a limitation of this study.

In calculating country scores for each SDG, this study took a simple average of normalized DI values. However, this method may be problematic in that it bundles together DIs with diverse nature and data distribution characteristics. There could be better methods of integrating the data values of DIs in consideration of their nature and statistical characteristics. Alternatively, there may be entirely different and more appropriate approaches for assessing a country’s progress in the SDGs without counting on a single score per goal for comparison. Some DI data were relativized by dividing them by population, GDP, or land area, but there could have been more appropriate choices for their respective denominators. The denominator selection process lacked examinations of alternatives. Further methodological exploration is required in future research.

The SDGs consist of 17 goals. However, considering the many positive correlations observed among indicator data across different goals, it may be possible to devise more effective groupings of issues for sustainable development, reflecting positive linkages. For example, issues with strong positive linkages may be grouped into the same goal even if they are typically separated under conventional thematic classifications. Exploration of such an alternative approach to goal and target setting, leveraging statistical analyses, may be useful for designing post-2030 international development goals for sustainable development.

4. Conclusions

Political discourse on international goals for sustainable development after 2030 will commence soon. It is imperative to start the conceptual and methodological exploration of the options to design post-2030 goals and their monitoring framework. To contribute to such discourse, this study proposed an approach to identifying a relatively small set of core indicators to monitor global progress toward sustainable development goals. The benefits of having such a small set of core indicators include reductions in the data compilation burden and associated costs as well as the relative ease of improving data quality, timeliness, and comparability by concentrating resources for data standardization and statistical capacity development on the core indicators. The significance of the approach proposed in this study lies in the use of statistical correlation analysis to identify potential indicator redundancy and thereby streamline the number of indicators, which is an aspect overlooked in the SDG indicator framework. Apart from its practical benefits, adopting a small set of global core indicators has the benefit of increasing the role of localized indicators at the regional, national, subnational or organizational levels. As Nilsson et al. [33] observed, local context matters in interpreting the SDGs, and localized indicators reflecting the local context have significant potential to improve the monitoring of progress toward development goals. The risks of such an approach limiting the global indicators and expanding the role of localized indicators include the selective implementation of actions toward some goals and targets and the avoidance of addressing issues that national or local authorities are reluctant to address [48]. To mitigate such risks, periodic open review processes, with the participation of a broad range of stakeholders, to check the validity of and progress against global and local indicators will be useful.

To demonstrate the feasibility of identifying the core indicators, this study conducted correlation analyses at the DI level to narrow down the list of indicators from the current SDG indicators while preserving specific characteristics of the global SDG indicator set. The results showed that 42 unique DIs, or 47 DIs including five overlapping DIs, could produce similar country scores for most SDGs as those calculated by 1112 DIs, which belong to 366 data series and 157 indicators. This suggests the usefulness of the methodology in identifying the core indicators for post-2030 development goals.

The results also revealed the limitations of the approach. Notably, indicator selection based on statistical correlation analysis failed to identify suitable indicators for some SDGs for which the indicators had relatively low correlations with others. Considering that there should be important but independent indicators (independent in that they have low correlations with others), the approach demonstrated in this study is not for use in isolation but needs to be applied in combination with other approaches that can address its weaknesses.

The findings of this study point to at least two future research subjects. One is the exploration of more options of indicators for SDGs 11–14 and 16 to find ones that are suitable for measuring the principal aspects of these goals and are also practically feasible to collect sufficient and timely data. The other involves identifying cross-thematic clusters of indicators that are correlated with each other so that multi-desciplinary groups of experts and stakeholders for each cluster can discuss a minimum essential set of core indicators, bearing the inter-indicator correlations and the avoidance of indicator redundancy in mind. The approach proposed in this study may be used for the clustering of indicators and the identification of correlations between indicators within each cluster.

The author expects that the demonstrated usefulness, practicality, and limitations of the proposed approach will stimulate discussions on the indicator framework for post-2030 development goals.