Complexity Measures for the Analysis of SDG Interlinkages:

A Methodological Approach

Gabriel Pereira

, Arturo González

and Gerardo Blanco

Grupo de Investigación en Sistemas Energéticos (GISE), Facultad Politécnica, Universidad Nacional de Asunción

(FP-UNA), Campus Universitario, San Lorenzo, Paraguay

Keywords: Sustainable Development Goals (SDGs), Economic Complexity, Product-Space Theory, Revealed

Comparative Advantage (RCA).

Abstract: The 2030 Agenda, with its 17 Sustainable Development Goals (SDGs), 169 targets and 232 indicators, has

set an ambitious “plan of action for people, planet and prosperity”1 that must be achieved within 15 years

(2015-2030). These first years of implementation of the SDGs by the 193 member states of the United Nations

(UN) have served the international community to realize the complexity of the network of interactions

(synergies and trade-off) between goals, targets and indicators, within a context where each country has set

its priorities of development and those are not always aligned with the main objective of the 2030 Agenda

(lack of policy coherence; policy vs politics). As a result of this situation, one of the main difficulties that the

countries will need to overcome is to comprehend the nature and complexity of the intricate network of

interlinkages between the SDGs, considering their universal and integrated nature. The purpose of this study

is to improve the understanding of the level of sustainability complexity of each member state of the UN in

the process of the implementation of the SDGs based on the Product-Space Theory and the Economic

Complexity. Thus, we present a SDG priority-setting tool applied to the challenging and ambitious task of

accomplishment of the 2030 Agenda, through the understanding of the SDG interlinkages network and its

complexity. Our findings are significant for the on-going debate of policy coherence and alignment of national

policies with the SDGs and the sustainability path countries should follow to progress towards an integral

achievement of the 2030 Agenda.

1 INTRODUCTION

The 2030 Agenda, with its 17 Sustainable

Development Goals (SDGs), 169 targets and 232

indicators, has set an ambitious “plan of action for

people, planet and prosperity” that must be achieved

within 15 years (2015-2030) (UN, 2015). These first

years of implementation of the SDGs by the 193

member states of the United Nations (UN) have

served the international community to realize the

complexity of the network of interactions (synergies

and trade-off) between goals, targets and indicators,

within a context where each country has set its

priorities of development and those are not always

aligned with the main objective of the 2030 Agenda

(lack of policy coherence; policy vs politics).

https://orcid.org/0000-0001-9966-6715

https://orcid.org/0000-0001-5672-3679

https://orcid.org/0000-0001-9773-8922

In this context, countries members have begun to

send their Voluntary National Reviews (VNRs) to the

High-Level Political Forum on Sustainable

Development of the United Nations with their

performances and experiences in the implementation

of the SDGs at the national level (UN, 2016).

In this process of sharing the first results,

experiences, and difficulties on the 2030 Agenda

implementation, it has been evidenced that key gaps

and doubts remain in the understanding on the SDGs

interactions and their individual impact (influence and

dependence) in the whole SDG system (UN, 2016).

The main difficulties that countries, will need to

overcome is to understand the nature and impact

(synergies and trade-offs) of the interlinkages

between the different targets at the national level,

considering the universal and integrated nature of the

Pereira, G., González, A. and Blanco, G.

Complexity Measures for the Analysis of SDG Interlinkages: A Methodological Approach.

DOI: 10.5220/0010374600130024

In Proceedings of the 6th International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2021), pages 13-24

ISBN: 978-989-758-505-0

SDGs and that the decisions made by the country in a

specific goal will necessarily have an effect (positive,

negative, or neutral) in the achievement of the other

SDGs and in the probability as a country to

accomplish the full 2030 Agenda.

As many experts have underlined, in this global

scenario and facing the complexity and universality

of the SDGs, a priority setting for the implementation

of the 2030 Agenda is recommended (Allen et al.,

2018; Allen et al., 2018a; Weitz et al., 2018; Zelinka

& Amadei, 2019; McGowan et al., 2018), in order to:

improve the qualitative and quantitative

understanding on SDGs interactions; identify direct

and indirect effects of SDGs interactions; detect

patterns on SDGs interactions; identify critical goals

and targets (central nodes) in the SDG network; and

secondary analyses to increase synergies and avoid

trade-off in the implementation of the 2030 Agenda

and its alignment with the national plans of

development (UN, 2014).

The aim of this study is to propose a new

methodological approach for the analysis of the SDG

interlinkages and the progress of the countries in the

implementation of the 2030 Agenda, based on their

accumulated sustainability capabilities measured

through the use of complexity measures and network

theory.

This paper is organized as follow: first, in Section

II a brief account of state-of-the-art literature on

Sustainable Development Goals (SDGs) and SDG

interlinkages analysis is made. Then, in Section III

the methodology, based on the economic complexity

and the product space theory to evaluate the SDG

interlinkages is explained. Third, in Section IV, we

show the results and discussion of our analyses,

including the interpretation of the findings.

Finally, in Section V, the conclusions are

presented.

2 LITERATURE REVIEW

The UN Sustainable Development Goals (SDGs)

were adopted in September 2015 by the 193 United

Nations (UN) member states, in a document called

“Transforming our world: the 2030 Agenda for

Sustainable Development”. The SDGs with its 17

goals, 169 targets and 244 indicators, try to leave

behind the siloed approach applied by the countries in

the past, to propose an “indivisible and integrated”

agenda, focusing on the 3 dimensions of the

sustainable development: social, economic, and

environmental (UN, 2015). Additionally, the 2030

Agenda also considers the 5P (people, planet,

prosperity, peace, partnerships) as key elements for

delivering the SDGs.

These goals are a result of a major multilateral and

intergovernmental cooperation through a

participatory process that included the work of (UN,

2014), with the purpose of filling the gaps from the

Millennium Development Goals (MDGs) that were

less ambitious and more focused on poverty and

water sanitation issues (Le Blanc, 2015; Vladimorova

& Le Blanc, 2016; Gusmao et al., 2018).

Achieving this highly ambitious agenda will

require not only political commitment, but also

important global investments of approximately 5-7

trillion USD per year (2015-2030) according to

estimations of (UNCTAD, 2014).

At the moment of writing this paper, there are

already available, at the Sustainable Development

Knowledge Platform, 227 documents reporting the

national voluntary reviews of the implementation of

the SDGs. These reviews have revealed the

difficulties of countries to implement the 2030

Agenda and the need of a better understanding of the

interactions between goals, targets, and indicators in

order to take advantage of the synergies and to

improve policy coherence (UN, 2016; Allen et al.,

2018; Allen et al., 2018a; Weutz et al., 2018).

2.1 The “Indivisible and Integrated”

Nature of SDGs

In the last years it can be observed an increase of the

literature related to assessment, analysis and

evaluations of the interlinkages between the SDGs,

covering different approaches and using a diversity of

methodological tools for SDG interactions.

As mentioned by (McGowan et al., 2018), “… the

indivisible nature of the SDGs is widely advanced as

axiomatic and underpins assessments of policy

coherence”. Therefore, the analysis of SDG

interlinkages offers fundamental information for

policymakers, guiding (through validated data) the

decision-making and the policy-design, aligned with

the sustainable development pillars.

Since the beginning of the implementation of the

2030 Agenda, the main part of the literature focused

on the study of the impact of one specific goal and its

interaction with the other goals or development

priorities (Vladimorova & Le Blanc, 2016, Alcamo,

2019; Nerini et al., 2017).

In the following years, the analysis of interactions

between goal sub-groups and the rest of the SDGs

have gained more relevance in the literature, in an

approach that is known as the “nexus approach”.

Under this approach it can be found a wide range of

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

studies, analyzing different combination of goals

(nexus combinations), for example: water-energy-

food nexus, energy-poverty-climate nexus, etc. (Liu

et al, 2018; Bleischwitz et al, 2018; Dargin et al.,

2019; Karnib, 2017).

Alternatively, with the purpose of improving the

comprehension of the interactions (synergies and

trade-off) between goals and targets, a new approach

appeared, based in more quantitative and data

visualization methods for the different analysis,

known as: network analysis (Allen et al, 2018; Allen

et al, 2018a; Weitz et al., 2018; Zelinka & Amadei,

2019; McGowan et al, 2018; Le Blanc, 2015;

Pedrosa-Garcia, 2018; Lusseau & Mancini, 2018).

Nevertheless, despite the existence of several

approaches, methods and studies about the SDG

interlinkages, there are still many questions as: which

is the real impact of the potential synergies and trade-

off at the different SDG levels (goals, targets and

indicators)?; which mechanisms intervene in those

interactions?; what is the impact of neutral

interactions?; how can be quantified the potential

impact of synergies and trade-off?; etc. (Nerini et al.,

2017; Nilsson et al., 2016; Nilsson et al., 2018; Maes

et al., 2019 : McCollum et al., 2018; Moyer & Bohl,

2019; Scherer et al., 2018; Singh et al., 2018).

2.2 SDGs Network System Analysis

Considering the universality, the diversity of sectors

and stakeholders involved in the implementation of

the 2030 Agenda, it becomes necessary for countries

the identification of priorities within the SDGs (Allen

et al, 2018; Weitz et al., 2018; McGowan et al., 2018;

Alcamo, 2019; Nilsson et al., 2016; Scherer et al.,

2018; Singh et al., 2018). As stated by (McGowan et

al., 2018), the selection of priorities reflects the

strategy and policy criteria of each country (expressed

by its policymakers) to evaluate the level of urgency

in each sector.

The pioneer study in this field related to the SDGs

was the one from (Le Blanc, 2015) that, even if it was

criticized for the superficiality of the wording

reference methodology implemented to analyze the

interactions between SDG and mapping its

interlinkages network. Then, (Vladimorova & Le

Blanc, 2016) have presented and analysis of 37

official reports from the United Nations to evaluate

the interactions between education and SDGs, based

again on the wording reference methodology. In this

case, the results have shown low levels of interactions

between education and the SDGs related to energy,

health and responsible consumption and production.

Applying the network approach and reinforcing

the results presented by (Le Blanc, 2015) about the

asymmetry of the interlinkages between the SDGs,

(McGowan et al., 2018) highlight that those

interlinkages are uneven, observing the lack of

connections between critical SDGs as those related to

gender equality, peace and governance. These authors

have based their analysis on the report from the

(Griggs et al., 2017) and based on the interactions

identified on it from a science-based perspective

(ICSU, ISSC, 2015), they constructed a SDG network

of interactions considering 4 main elements: degree

(number of links per node), strength (total number of

links from a node), closeness (distance with other

nodes in the network and centrality of a node in the

network), betweenness (flow of information through

the network).

Similarly, (Allen et al., 2018) and (Allen et al.,

2018a) have implemented a network approach for the

analysis of SDG targets interlinkages for 22 Arab

countries, based on the methodology of (Nilsson et

al., 2016) for the evaluation of the intensity of the

interactions (from -3 to +3), through a cross-impact

matrix to identify synergies, trade-off, and neutral

interactions. The SDG network obtained as a result of

the implementation of this methodology considers to

2 network metrics: outdegree and closeness

centrality. Then, these results have been used as input

for the evaluation of policy gaps and a multi-criteria

analysis, to set priorities for the Arab region analyzed.

Similarly, based in the same methodology (Weitz

et al., 2018) have evaluated the interactions between

34 SDG targets, obtaining results that reinforce the

hypothesis that there are more synergies than trade-

off in the SDG network, but in which the trade-off

represents a serious threat for the accomplishment of

the 2030 Agenda worldwide. Moreover, the SDG

network obtained has a deeper level of analysis

compared to the study from (Allen et al., 2018),

showing the directionality of the interactions between

SDG targets, type of interactions, intensity of the

influence of targets in the SDG network, the clusters

of SDG targets in the network, etc.

Finally, one of the most recent study in the SDGs

network system approach is the proposed by (Lusseau

& Mancini, 2018), which analyzed how the main

interactions of synergy and trade-off at the goal and

target levels vary according to the level of income of

countries, showing the existence of unstable networks

composed by antagonistic subgroups, where the

identification of development of priorities in each

country is needed.

Complexity Measures for the Analysis of SDG Interlinkages: A Methodological Approach

2.3 Evolution in the Understanding of

SDG Interlinkages

In this context, several authors have begun to focus

the analysis in the progress of countries in the

accomplishment of the SDGs, through rankings (by

goals, targets or indicators), qualitative

methodologies, traffic light approaches, and many

others (Griggs et al., 2017; ICSU, ISSC, 2015; Sachs

et al., 2018; Schmidt-Traub et al., 2017; Salvia et al.,

2019), in order to identify critical goals and targets

for the sustainable development of the countries.

The measurement made by (Sachs et al., 2018),

published annually since 2016 with Bertelsmann

Stiftung and the Sustainable Development Solutions

Network (SDSN), are the reference at the moment of

evaluating the progress in the accomplishment of the

SDGs worldwide.

The analysis and evaluation of the SDGs is a very

complex task, as it has been already underlined in

several studies (Dargin et al., 2019; Karnib, 2017;

McCollum, et al., 2018). Therefore, it has been

developed new methodologies to facilitate the

visualization, identification and understanding of the

existing synergies and trade-off between goals,

targets, and indicators, in order to broader our vision

of the complexity of the SDG network.

One of the most implemented methodology has

been the individual analysis of the impact of a goal

(directionality, intensity, effect, etc.) over another

goal or group of goals, having even some cases of

analysis at the target level (Alcamo, 2019; Nerini et

al., 2017; Maes et al., 2019).

Studies covering the analysis and evaluation of

SDG interlinkages at the indicator level are

practically inexistent, because of the complexity of

analysis of its interactions, the difficulty to access to

reliable, regular, and official SDG indicators data in

each country, added to the fact of the low level of

understanding that still exist about the impact of the

SDG indicators interactions (Taylor et al., 2017).

The results of these studies are relevant for

policymakers and stakeholders to comprehend the

nature of the SDG interlinkages and to improve the

SDG priority setting at the national level (Alcamo,

2019). Nevertheless, even if we still have low

understanding of the SDG interactions, the existent

literature in this topic have demonstrated that there

are more positive interactions (synergies) than trade-

off in the SDG network (Weitz et al., 2018; Nerini et

al., 2017; Maes et al., 2019).

Additionally, considering the need of including in

the analysis the indivisible and integrated nature of

the SDGs, studies have incorporated the nexus

approach. As mentioned by (Liu et al., 2018), the

nexus approach facilitates the identification of

synergies between goals, the improvement of policy

design and the implementation of policies. Moreover,

the nexus approach reduces the “silo-thinking” to

focus on the synergies of critical resources and the

promotion of wellbeing (Liu et al., 2018; Bleischwitz

et al., 2018; Dargin et al., 2019; Karnib, 2017).

Then, authors using the nexus approach underline

that the simple analysis of the type of interaction

(synergy or trade-off) is not enough, and it must be

complemented with the understanding of the impact

of the direct and indirect interactions of the SDGs

(Karnib, 2017).

Even with its limitations, the analysis of

interactions between SDGs (at the goal, target or

indicator level) are fundamentally important for

politics and policymakers, considering that allows

the identification of development priorities for the

countries, the validation of strategic policies through

the alignment with the priority goals and targets

identified (policy coherence and policy gaps) and the

evaluation of strategies for development at the

national level (Allen et al., 2018a), (Le Blanc, 2015;

Nerini et al., 2017; Karnib, 2017; Maes et al., 2019;

Griggs et al., 2017).

The challenge of understanding the intricate and

complex SDG network of interactions have been

clearly explained by (Weitz et al., 2018), which have

expressed: “Understanding interactions between

targets requires quite detailed information, but it also

requires the ability to maintain a holistic view of the

system as a whole, since it is possible that one policy

change can change the dynamics of the whole

system”.

2.4 Product-Space

The Product-Space (PS) has been applied in the

several studies focused on the analysis of growth

opportunities and the level of sophistication of a

country´s exports, in order to identify productive

capabilities, based on the revealed comparative

advantages (RCA) of the products made in each

country. Some examples include the case study of

Peru, Colombia, Uruguay, Paraguay, Panama,

Kazakhstan, China, United States, Sub-Saharan

Africa, among others (Hausmann & Klinger, 2008;

Hausmann & Klinger, 2008a; González et al., 2019;

Ourens, 2012; Vaillant & Ferreira-Coimbra, 2009;

Felipe & Hidalgo, 2015; Hausmann et al., 2016;

Abdon & Felipe, 2011).

Recently, a new approach proposed by (El-

Maghrabi et al., 2018) emerged, applying the PS and

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

the notions of Economic Complexity to prioritize the

SDGs and to evaluate the probability of countries of

becoming an over-achiever in a particular SDG

indicator. The hypothesis proposed by the authors

suggest that the probability of achieving a particular

SDG target can be estimated conditionally on the

observed progress on all the other targets. At the

moment, this is the only study implementing this

approach in the field of SDGs and the 2030 Agenda.

The PS, based on world export data, is a tool that

allows the identification of the probability to produce a

product A with RCA, given that it is produced a

product B with RCA. Then, the PS network shows the

relationship between the capabilities needed to produce

each pair of products (Hausmann et al., 2011).

In resume, this theory suggest that countries

should take advantage of their current productive

capabilities, diversifying their exports basket and

increasing its complexity by the development of new

products and industries that use capabilities similar to

those they already have, facilitating the development

of new capabilities and the production of more

complex and higher added value goods (González et

al., 2019; Abdon & Felipe, 2011; Hidalgo &

Hausmann, 2009).

In practice, the PS provides, as mentioned by

(Hausmann et al., 2011), the easier and less risky paths

through which productive knowledge is accumulated

for each country under study. In other words, this

approach helps countries to identify products that

require similar capabilities to those that a country

already have and therefore, have higher probabilities to

be produced and co-exported (if the country decides to

do it) (Hausmann et al., 2011; Hidalgo & Hausmann,

2009; Hausmann & Klinger, 2007; Hausmann et al.,

2014; Hidalgo & Klinger, 2007; Hausmann et al.,

2007; Hausmann & Hidalgo, 2011).

The representation of the resulted network of

products exported worldwide by countries is called

“Product Space”, translating global trade data in a

network of nodes and edges (Hausmann et al., 2011;

Hidalgo & Hausmann, 2009). In its original model,

the nodes represent the different products traded

worldwide, the sizes of the nodes are proportional to

the volume of participation of each product in world

trade, while the classification of the products are

expressed through the colors of the nodes (Hausmann

et al., 2011).

The distance between nodes (links) are

determined by the proximity. The proximity (ϕ)

represents the conditional probability that a country

that exports product p also exports product p´.

There are 2 main elements to be considered in the

implementation of this methodology. First, the RCA

in a product p, that according to (Balassa, 1965) is

achieved if the country exports the product p with a

share that is equal to the share of total world trade that

the product represents (Hausmann et al., 2011;

Balassa, 1965).

𝑅𝐶𝐴



𝐴























(1)

Where X

represents exports of good i of country

A, X

is the total exports of country A, X

the world

exports of good i, and X

total. If RCA (A

) ≥ 1, then

the product i of country A has revealed comparative

advantage otherwise it has not.

Higher levels of RCA are understood as higher

level of competitiveness in the international market.

Second, the Proximity, that according to the

literature, represents the idea that 2 products that need

similar capabilities or productive knowledge have

higher probabilities to be co-exported or produced in

tandem, while products that need more different

capabilities have lower probabilities to be produced

together or to be co-exported. Then, it should be easier

for countries to improve their productive structure by

making shorts steps towards near products in the

product-space network (Hausmann et al., 2011;

Hidalgo & Hausmann, 2009; Hidalgo et al., 2007).

Mathematically, the proximity between 2

products, “i” and “j”, can be calculated as the

minimum distance between the probability that

countries can export a product “i” with RCA, since

they export the good “j” with RCA and the probability

of countries exporting a “j” good with RCA, since

they export product “i” with RCA:

 minPVCR

 1| VCR

1,

PVCR

 1| VCR

1



(2)

The proximity matrix is constructed using the

results from the RCA analysis as inputs, showing a

matrix of countries and products, where a value of 1

is given if product p for a given country c has RCA≥1

or 0 (zero) otherwise. Then, the “Mcp” matrix can be

expressed as follows (Hausmann et al., 2011):

𝑀





1 𝑖𝑓 𝑅𝐶𝐴



1

0 𝑖𝑓 𝑅𝐶𝐴



1

(3)

Finally, the proximity measure, understood as the

conditional probability that a country that exports a

product p, will also export a product p', is calculated

based on the previously mentioned M

matrix.

Formally, the proximity of a pair of products “pp´”

can be expressed as follows (Hausmann et al., 2011):

Complexity Measures for the Analysis of SDG Interlinkages: A Methodological Approach

𝜙

´













´



,

,

´,



(4)

2.5 Complexity Measures

The economic complexity it is related with the

ubiquity and diversity of the accumulated knowledge

in a determined economy. Then, in a specific country,

as more people from different sectors interact,

combining their knowledge to produce a diversity of

products, a more complex economy could be

expected. Therefore, the economic complexity can be

expressed as the share of productive knowledge

accumulated by a country, as a result of using and

combine that knowledge (Hausmann et al., 2011).

The knowledge can be only accumulated,

transferred and preserved if it is incrusted in a people´s

network or in organizations that apply that knowledge

for productive purposes. If producing a product

requires a specific type or combination of knowledge,

then the countries that produce that product reveal that

they have the capabilities and required knowledge to

produce it (Hausmann et al., 2011).

The economic complexity of a country is reflected

in the amount of productive knowledge of its

economy, measured by the use of 2 main indicators,

the diversity and the ubiquity.

The diversity it refers to the amount of products

produced in a specific country, while the ubiquity

refers to the amount of countries that produce a

specific product.

𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦𝐾𝑐,0

∑

𝑀𝑐𝑝



(5)

𝑈𝑏𝑖𝑞𝑢𝑖𝑡𝑦𝐾𝑝,0

∑

𝑀𝑐𝑝



(6)

In order to generate a more accurate measure of

the number of available capabilities of a country, or

the required capabilities for a product, it is necessary

to correct the information that the diversity and

ubiquity hold, through the use of each of them to

correct the other, and vice versa. As proposed by

(Hausmann et al., 2011), this can be expressed as the

following equations:

𝐾𝑐,𝑁



,

∑

𝑀𝑐𝑝  𝐾𝑝,𝑁 1



(7)

𝐾𝑝,𝑁



,

∑

𝑀𝑐𝑝  𝐾𝑐,𝑁 1



(8)

𝐾𝑐,𝑁



,

∑

𝑀𝑐𝑝



,

∑

𝑀𝑐´𝑝  𝐾𝑐´,𝑁  2

´

(9)

𝐾𝑐,𝑁

∑

𝑘𝑐´,𝑁 2

∑

´

, ,

´

(10)

This can be rewritten as follows:

𝐾

,



∑

𝑀



´

𝐾

´,´

(11)

Finally, it can be obtained the following

expression:

𝑀



´



∑







´



,



,



(12)

Note that Eq. 12 it is fulfilled when K

c;N

= k

c;N-2

= 1. This it is the eigenvector of M

cc´

that is associated

with the highest eigenvalue. The eigenvector is a

vector of 1, so it is not informative. It is expected

instead, that the eigenvector associated to the second

largest eigenvalue, to capture the highest amount of

variance of the system. Therefore, the Economic

Complexity Index (ICE) is defined as follows

(Hausmann et al., 2011):

𝐸𝐶𝐼





⃗





⃗







⃗



(13)

Where, 𝐾



⃗

> is an average, stdev() represents the

standard deviation and 𝐾



⃗

is the eigenvector of 𝑀



´

associated with the second largest eigenvalue.

Analogously, it is defined the Product Complexity

Index (PCI). Due to the symmetry of the problem, it

can be done simply by exchanging the index of

country (c) with the products (p) in the before

mentioned equations. Then, the PCI can be expressed

as follows (Hausmann et al., 2011):

𝐼𝐶𝑃





⃗





⃗











⃗



(14)

Where, 𝑄



⃗

is the eigenvector of 𝑀



´

associated to

the second largest eigenvalue.

3 METHODOLOGY AND MODEL

ESPECIFICATION

This research develops an analysis of the

interlinkages among the Sustainable Development

Goals, through the use of the economic complexity

and product space theory, offering a new approach to

the study of SDG interlinkages.

Additionally, the methodology applied serves as a

tool for policymakers to improve decision-making,

facilitating the setting of priorities in the 2030

Agenda at the national level through the analysis of

the interlinkages, synergies and trade-off existing in

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

the structure of the SDGs and their impact in policy

design and its implementation.

The implementation of the methodology is

structured in 2 phases:

• Revealed Comparative Advantage: to identify the

SDGs with RCA for each country under study. This

information will serve as input for the complexity

measures.

• Product-Space Analysis: to evaluate the SDG

network and the interlinkages between goals. Then, to

calculate and evaluate the Sustainability Complexity

Index (SCI) and the Goal Complexity Index (GCI),

and its implications in the prioritization of the SDGs.

3.1 Measure the RCA

In the first stage, through the use of the concepts of

the RCA, it has been identified for each of the

countries under study, the SDGs that present a

“revealed comparative advantage” considering their

performances in the accomplishment of the 17 SDGs

for the year 2018, according to (Sachs et al., 2018).

As a result of this first stage we have obtained a

new matrix of country and goals, known as Mcg

matrix, identifying for each country the SDGs with

RCA according to their respective level of

accomplishment. The Mcg (country-goal) matrix is

obtained using the same theoretical framework

explained previously, but with the only difference is

that we analyze SDGs instead of products.

𝑅𝐶𝐴





















(15)

Where,

𝑋



: the normalized value of the accomplishment

of the SDG “g” in the country “C”

𝑋





∑

𝑋







: Sum of all the normalized values of

the accomplishment of all the SDGs in the country “C”

𝑋





∑

𝑋







: Sum of all the normalized values

of the SDG “g” in all the countries under study “W”.

𝑋





∑

𝑋





∑

𝑋







: Sum of the normalized

values of the SDG “g” for all the countries under

study “W”

Then, using the M

matrix as input, we were able

to calculate the proximity for each pair of SDGs,

which is an important information for the further

analysis of complexity measures.

The database used have been extracted from

(Sachs et al., 2018) for the 156 countries that provides

reliable data for the 17 SDGs of the 2030 Agenda.

This database is available at the SDSN website.

3.2 SDG Complexity Analysis

In this stage, based on the complexity measures, the

Sustainability Complexity Index (SCI) and the Goal

Complexity Index (GCI), it has been analyzed the

situation from a different perspective.

First, we identify the level of complexity of

countries in the accomplishment of the SDGs through

the SCI. In this evaluation, the are 2 elements that

must be considered: the ubiquity and the diversity.

Considering RCA, it can be express the Mcg matrix

(countries vs goals).

𝑀





1 𝑖𝑓 𝑅𝐶𝐴



1

0 𝑖𝑓 𝑅𝐶𝐴



1

(16)

Mathematically, and based on the complexity

measures from (Hausmann et al., 2011), the SCI is

defined as follows:

𝑆𝐶𝐼

𝑅



⃗

𝑅



⃗



𝑠𝑡𝑑𝑒𝑣 𝑅



⃗

(17)

Where 𝑅



⃗

 represents an average, stdev is the

standard deviation and 𝑅



⃗

is the eigenvector of 𝑀



´

associated with the second largest eigenvalue.

Second, it has been evaluated the SCI as a tool to

predict wellbeing and development of countries,

comparing the SCI against different index

Third, based on the results of the GCI, it has been

analyzed the complexity of the SDGs, in order the

comprehend the nature of each goal and to identify

the goals that require more or less sustainability

capabilities to be fully accomplished. Formally, and

based on the theoretical framework from (Hausmann

et al., 2011), the GCI is expressed as:

𝐺𝐶𝐼





⃗





⃗



 



⃗

(18)

Where 𝑆



⃗

 is the eigenvector of 𝑀



´

associated with the second largest eigenvalue.

4 RESULTS

The Sustainability Complexity Index (SCI) proposed

in this study could be an interesting tool to improve

the implementation of the 2030 Agenda, considering

that it allows to measure the sustainability capabilities

that each country has for the accomplishment of the

SDGs.

Additionally, we observe that the SCI it is not only

related to economic growth, but it is also strongly

Complexity Measures for the Analysis of SDG Interlinkages: A Methodological Approach

related to a wide and ambitious variety of critical

indicators for the development of the countries,

aligned with the integrated and indivisible nature of

the SDGs.

In Fig.1, we can observe a strong correlation

between GDP per capita and SCI. It must be

underlined, that from the first quadrant, the trend line

clearly fits an exponential behavior, with highest level

of GPD per capita explaining highest levels of SCI.

Figure 1: Relationship between SCI and GDP per capita.

Figure 2: (A) Relationship between GPD per capita and SCI

in countries where natural resources exports are lower than

10% of GDP. (B) Relationship between GPD per capita and

SCI in countries where natural resources exports are higher

than 10% of GDP.

Then, in Fig.2 it has been disaggregated the

analysis between exporters and non-exporters of

natural resources, based on the groups of countries

proposed in (Hausmann et al., 2011).

From Fig. 2A we can infer that GDP per capita it

is an optimal proxy of SCI in countries that are not

highly dependent on natural resources exports (i.e.

oil, natural gas, etc.). In the other hand, the correlation

of GPD per capita and SCI it is low to moderate, for

countries highly dependents on natural resources

exports. This situation could be a secondary effect of

what in economics it is known as the dutch disease,

potentially also affecting the accomplishment of the

SDGs.

Furthermore, from other perspective, in Fig. 3 we

can observe the relationship between the SCI and the

GDP per capita in terms of purchasing power parity

(PPP), showing the same exponential behavior,

especially for GDP pc (PPP) from 6.000 US$.

Figure 3: Relationship between SCI and GDP per capita in

terms of purchasing power parity (PPP).

Moreover, in Fig. 4 we can distinguish the

different levels of correlation between the SCI and a

diversity of development index as the SPI, GCI

(World Economic Forum), HDI (United Nations) and

the WHI (United Nations).

From Figure 4, we observe that SCI shows a good

fit, especially with development index that consider

different variables and sectors in the analysis, as the

SPI, the GCI and the HDI, reinforcing the fact of the

universality of the challenges behind the SDGs. In the

other hand, the WHI does not seem to be a good

explicative variable of the accomplishment of the

SDGs.

Additionally, we have also found that the SCI

shows a low correlation with the Gini Index (R

0,14), a moderated level of correlation with the

average years of education (0,56) and low to

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

Figure 4: (A) Relationship between the SCI and the Social Progress Index (SPI). (B) Relationship between the SCI and the

Global Competitiveness Index (GCI). (C) Relationship between the SCI and the Human Development Index (HDI). (D)

Relationship between the SCI and the World Happiness Index (WHI).

Figure 5: SCI heat map (World) – warmer colors reflects lower levels of sustainability complexity.

moderate levels of correlation with the indicators of

the Worldwide

Governance Index Components (i.e. control of

corruption, government effectiveness, political

stability, regulatory quality, rule of law and voice and

accountability).

Finally, in Fig. 5 we can observe the first attempt

of implementation of the methodological approach

proposed in this study, showing the results of the SCI

for the 156 countries with available data in (Sachs et

al., 2018).

Complexity Measures for the Analysis of SDG Interlinkages: A Methodological Approach

From Fig. 5, it is clear that the biggest challenges

for the accomplishment of the SDGs mainly remain

in Africa and South East Asia. In South America,

Bolivia and Venezuela present the lowest level of

SCI.

Additionally, the Goal Complexity Index (GCI)

has been measured, obtaining the results shown in

Fig. 6. (darker colors reflects higher levels of GCI).

Figure 6: GCI Index.

From the GCI, we conclude that the top 3, of more

complex goals in the 2030 Agenda, are the SDG12

(Responsible Production & Consumption), SDG13

(Climate Action) and SDG17 (Peace, Governance &

Partnerships). In the other hand, the least complex

goals are SDG9 (Industry, Innovation and

Infrastructure), SDG3 (Health & Wellbeing) and

SDG7 (Energy).

In this context, an optimal strategy for countries

could be following the sustainability complexity path,

in order to fully achieve the 2030 Agenda, advancing

from the accomplishment of less complex goals to

more complex goals.

Finally, following studies should be oriented to

analyze and to identify, through the use of network

theory and product-space theory, how the

accomplishment of a specific SDGs could lead to the

accomplishment (or not) of another SDG.

5 CONCLUSIONS

The methodological approach proposed in this study

shows strong evidence of its usefulness for the

purposes of measuring the accomplishment of the

SDGs, aligned with the 2030 Agenda. This

complexity measures shows strong correlation with

several development index that could explain the

accomplishment of the SDGs in the different

countries.

At the moment, the analysis of the SCI is limited

to the availability of reliable data from the countries

about their progress in the accomplishment of the

different SDGs. It must be underlined, that the input

data use in this methodology is based on SDG Report,

published annually by the Sustainable Development

Solution Network (SDSN) and the Bertelsmann

Stiftung Foundation, that provides data that due to

methodological limitations are not comparable year-

by-year.

Nevertheless, we believe that the main

contribution of this study is the innovative and

interesting methodological approach to evaluate the

progress in the accomplishment of the SDGs and the

2030 Agenda, offering a new tool to policy-makers

and decision-makers to set development priorities and

to identify opportunities or synergies to accelerate the

accomplishment of the SDGs, based on complexity

measures. Additionally, this index may provide a

more synthetic summary to help predicting better

adjustment policies.

Finally, considering that the methodology

proposed in this study it is relatively new and the

literature background of its implementation it is still

relatively low, we suggest further studies in order to

improve the experimentation and validation of the

SCI and GCI for the analysis of the SDGs worldwide.

ACKNOWLEDGEMENTS

The authors are very grateful to the Paraguayan

National Council of Science and Technology

(CONACyT) for financial support through the project

PINV15-531 and PRONII Program.

REFERENCES

Abdon, A., Felipe, J., 2011. The Product Space: What Does

It Say About the Opportunities for Growth and

Structural Transformation of Sub-Saharan Africa?.

Working Paper No. 670, Levy Economic Institute of

Bard College.

Alcamo, J., 2019. Water quality and its interlinkages with

the Sustainable Development Goals. Current Opinion in

Environmental Sustainability, 36, pp. 126–140.

SDG GCI

SDG12 1,65700123

SDG13 1,57927816

SDG17 1,22489455

SDG15 0,98658457

SDG6 0,56162096

SDG16 0,21317229

SDG11 0,1373906

SDG5 ‐0,0195058

SDG10 ‐0,07001025

SDG1 ‐0,07214902

SDG14 ‐0,19094156

SDG8 ‐0,28877772

SDG2 ‐0,6670405

SDG4 ‐0,7780202

SDG7 ‐0,9705432

SDG3 ‐1,24560092

SDG9 ‐2,05735319

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

Allen, C., Metternich, G., Wiedmann, T., 2018. Prioritising

SDG targets: assessing baselines, gaps and

interlinkages. Sustainability Science.

https://doi.org/10.1007/s11625-018-0596-8

Allen, C., Metternich, G., Wiedmann, T., 2018a. Initial

progress in implementing the Sustainable Development

Goals (SDGs): a review of evidence from countries.

Sustainability Science. https://doi.org/10.1007/s11625-

018-0572-3

Balassa, B., 1965. Trade liberalisation and “revealed”

comparative advantage. Manch Sch, 33(2), pp.99–123.

http://dx.doi.org/10.1111/j.1467-9957.1965.tb00050.x.

Bleischwitz, R., Spataru, C., VanDeveer, S.D., Obersteiner,

M., van der Voet, E., Johnson, C., Andrews-Speed, P.,

Boersma, T., Hoff, H., van Vuuren, D.P., 2018.

Resource nexus perspectives towards the United

Nations Sustainable Development Goals. Nature

Sustainability, Volume 1, pp. 737-743.

https://doi.org/10.1038/s41893-018-0173-2

Dargin, J., Daher, B., Mohtar, R.H., 2019. Complexity

versus simplicity in water energy food nexus (WEF)

assessment tools. Science of the Total Environment,

650, pp. 1566–1575. https://doi.org/10.1016/j.

scitotenv.2018.09.080

Dörgo, G., Sebestyén, V., Abonyi, J., 2018. Evaluating the

Interconnectedness of the Sustainable Development

Goals Based on the Causality Analysis of Sustainability

Indicators. Sustainability 2018, 10, 3766;

doi:10.3390/su10103766

El-Maghrabi, M. H., Gable, S., Osorio Rodarte, I., Verbeek,

J., 2018. Sustainable Development Goals Diagnostics:

An Application of Network Theory and Complexity

Measures to Set Country Priorities. World Bank Group

- Office of the Senior Vice President UN Relations and

Partnerships. Policy Research Working Paper 8481,

WPS8481.

Felipe J, Hidalgo CA. Economic diversification:

implications for Kazakhstan. Development and modern

industrial policy in practice. Issues and country

experiences. Cheltenham UK: Edward Elgar Pub; 2015.

Gusmao, R.G., Leal Filho, W., Gonçalves, O.L., de Mattos,

D.L., Veigas, L., 2018. A literature-based review on

potentials and constraints in the implementation of the

sustainable development goals. Journal of Cleaner

Production, 198, pp. 1276-1288.

https://doi.org/10.1016/j.jclepro.2018.07.102

Hausmann R, Hidalgo CA, Bustos S, Coscia M, Chung S,

Jimenez J., Simoes, A., Yildirim, M., 2011. The Atlas

of economic complexity: mapping paths to prosperity.

Cambridge, Mass: Center for International

Development, Harvard University; Harvard Kennedy

School; Macro Connections, Massachusetts Institute of

Technology

Hausmann, R., & Hidalgo, C. A. (2011). The network

structure of economic output. Journal of Economic

Growth, 16(4), 309–342. DOI:10.1007/s10887-011-

9071-4

Hausmann R, Klinger B. Growth diagnostic: Peru. Inter-

American Development Bank; 2008a. Tech. Rep.

Hausmann R, Klinger B. Achieving export-led growth in

Colombia Tech Rep. 2008. p. 2008.

Hausmann R, Hwang J, Rodrik D. What you export matters.

J Econ Growth 2007;12(1):1–25.

http://dx.doi.org/10.1007/s10887-006-9009-4.

Hausmann, R., Morales, J.R., Santos, M.A., 2016.

Economic Complexity in Panama: Assessing

Opportunities for Productive Diversification. HKS

Faculty Research Working Paper Series RWP16-046.

Hausmann, R., Hidalgo, C.A., Stock, D.P., Yildirim, M.A.,

2014. Implied Comparative Advantage. CID Working

Paper No. 276

Hidalgo CA, Hausmann R. The building blocks of

economic complexity. Proc Natl Acad Sci USA

2009;106(26):10570–5. http://dx.doi.org/10.1073/pnas.

Hidalgo CA, Klinger B, Barabási A-L, Hausmann R. The

product space conditions the development of nations.

Science (Wash D C) 2007;317(5837):482–7.

http://dx.doi.org/10.1126/science.1144581.

ICSU, ISSC, 2015.Review of the Sustainable Development

Goals: The Science Perspective. Paris: International

Council for Science (ICSU). ISBN: 978-0-930357-97-9

International Council for Science (ICSU), 2017. A Guide to

SDG Interactions: from Science to Implementation

[D.J. Griggs, M. Nilsson, A. Stevance, D. McCollum

(eds)]. International Council for Science, Paris. DOI:

10.24948/2017.01

Le Blanc, D., 2015. Towards Integration at Last? The

Sustainable Development Goals as a Network of

Targets. Sustainable Development, 23, pp. 176-187.

DOI: 10.1002/sd.1582

Liu, J., Hull, V., Godfray, H.C.J., Tilman, D., Gleick, P.,

Hoff, H., Pahl-Wostl, C., Xu, Z., Chung, M.G., Sun, J.,

Li, S., 2018Nexus approaches to global sustainable

development. Nature Sustainability, Volume 1, pp.

466-476. https://doi.org/10.1038/s41893-018-0135-8

Lusseau, D., Mancini, F., 2018. Income-based variation in

Sustainable Development Goal interaction networks.

Nature Sustainability. https://doi.org/10.1038/s41893-

019-0231-4

Karnib, A., 2017. Mapping the direct and indirect

interlinkages across the sustainable development goals:

A qualitative nexus approach. International Journal of

Development and Sustainability, Volume 6, No. 9, pp.

1150-1158.

Maes, M., Jones, K., Toledano, M. Milligan, B., 2019.

Mapping synergies and trade-offs between urban

ecosystems and the sustainable development goals.

Environmental Science and Policy, 93, pp. 181 -188.

https://doi.org/10.1016/j.envsci.2018.12.010

McGowan, P.J.K., Stewart, G.B., Long, G., Grainger, M.J.,

2018. An imperfect vision of indivisibility in the

Sustainable Development Goals. Nature Sustainability,

Brief Communication. https://doi.org/10.1038/s41893-

018-0190-1

McCollum, D.L., Gomez, L., Busch, S., Pachauri, S.,

Parkinson, S., Rogelj, J., Krey, V., Minx, J.C., Nilsson,

M., Stevance, A-S., Riahi, K., 2018. Connecting the

sustainable development goals by their energy inter-

Complexity Measures for the Analysis of SDG Interlinkages: A Methodological Approach

linkages. Environmental Research Letters 13.

https://doi.org/10.1088/1748-9326/aaafe3

Moyer, J., Bohl, D., 2019. Alternative pathways to human

development: Assessing trade-offs and synergies in

achieving the Sustainable Development Goals. Futures,

105, pp.199-210. https://doi.org/10.1016/j.futures.

2018.10.007

Nerini, F., Tomei, J., Seng To, L., Bisaga, I., Parikh, P.,

Black, M., Borrion, A., Spataru, C., Castán, V.,

Anandarajah, G., Milligan, B., Mulugetta, Y., 2017.

Mapping synergies and trade-offs between energy and

the Sustainable Development Goals. Nature Energy.

https://doi.org/10.1038/s41560-017-0036-5

Nilsson, M., Griggs, D., Visbeck, M., 2016. Map the

interactions between Sustainable Development Goals.

Nature, Volume 534, pp. 320-322.

Nilsson, M., Chisholm, E., Griggs, D., Howden-Chapman,

P., McCollum, D., Messerli, P., Neumann, B.,

Stevance, A-S, Visbeck, M., Stafford-Smith, M., 2018.

Mapping interactions between the sustainable

development goals: lessons learned and ways forward.

Sustainability Science, 13, pp. 1489-1503.

https://doi.org/10.1007/s11625-018-0604-z

Ourens, G., 2012. Uuruguay al espajo: Análisis de la

estructura productiva uruguaya a través del Métdo de

los Reflejos. Revista de Economía, Vol. 19, Nº 1, Mayo

2012. ISSN: 0797-5546.

Pedrosa-Garcia, J.A., 2018. Mapping Synergies and

Tradeoffs in the Sustainable Development Goals

Network: A Case Study from Jordan. Economic and

Social Commission for Western Asia (ESCWA).

E/ESCWA/SDD/2017/WP.2

Sachs, J., Schmidt-Traub, G., Kroll, C., Lafortune, G.,

Fuller, G., 2018. SDG Index and Dashboards Report

2018. New York: Bertelsmann Stiftung and Sustainable

Development Solutions Network(SDSN).

http://sdgindex.org/reports/2018/

Salvia, A., Leal Filho, W., Brandli, L., Griebeler, J., 2019.

Assessing research trends related to Sustainable

Development Goals: local and global issues. Journal of

Cleaner Production, 208, pp. 841-849.

https://doi.org/10.1016/j.jclepro.2018.09.242

Scherer, L., Behrens, P., de Koning, A., Heijungs, R.,

Sprecher, B., Tukker, A., 2018.Trade-offs between

social and environmental Sustainable Development

Goals. Environmental Science and Policy, 90, pp. 65-

72. https://doi.org/10.1016/j.envsci.2018.10.002

Schmidt-Traub, G., Kroll, C., Teksoz, K., Durand-Delacre,

D., Sachs, J., 2017. National baselines for the

Sustainable Development Goals assessed in the SDG

Index and Dashboards. Nature Geoscience, Vol.10, pp.

546-556. DOI: 10.1038/NGEO2985

Singh, G., Cisneros-Montemayor, A.M., Swartz, W.,

Cheung, W., Guy, J.A., Kenny, T-A., McOwen, C.J.,

Asch, R., Geffert, J.L., Wabnitz, C., Sumaila, R.,

Hanich, Q., Ota, Y., 2018. A rapid assessment of co-

benefits and trade-offs among Sustainable

Development Goals. Marine Policy, 93, pp. 223-231.

http://dx.doi.org/10.1016/j.marpol.2017.05.030

Taylor, P., Abdalla, K., Quadrelli, R., Vera, I., 2017. Better

energy indicators for sustainable development. Nature

Energy, 2, pp.1-4. DOI: 10.1038/nenergy.2017.117

United Nations, Synthesis of voluntary national reviews

2016. Department of Economic and Social Affairs,

New York, 2016.

United Nations, Report of the Open Working Group of the

General Assembly on Sustainable Development Goals,

A/68/970: New York, 2014

UNCTAD (United Nations Conference on Trade and

Development): World investment report. 2014

https://unctad.org/en/PublicationsLibrary/wir2014_en.

pdf

United Nations, General Assembly: Transforming our

world: the 2030 Agenda for Sustainable Development,

A/RES/70/1: New York, 2015.

Vaillant M, Ferreira-Coimbra N. Evolución del espacio de

productos exportados: ¿está Uruguay en el lugar

equivocado? Germany: University Library

ofMunich;2009. https://mpra.ub.unimuenchen.de/

47286/1/MPRA_paper_47286.pdf.

Vladimirova, K., Le Blanc, D., 2016. Exploring Links

Between Education and Sustainable Development

Goals Through the Lens of UN Flagship Reports.

Sustainable Development. DOI: 10.1002/sd.1626

Weitz, N, Carlsen, H., Nilsson, M., Skanberg, K., 2018.

Towards systemic and contextual priority setting for

implementing the 2030 Agenda. Sustainable Sciences,

13, pp. 531-548 https://doi.org/10.1007/s11625-017-

0470-0

Zelinka, D., & Amadei, B. (2019). Systems Approach for

Modeling Interactions Among the Sustainable

Development Goals Part 1. International Journal of

System Dynamics Applications, 8(1), 23–40.

doi:10.4018/ijsda.2019010102

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk