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Multidimensional Economic Complexity and Inclusive Green Growth

Viktor Stojkoski, Philipp Koch, César A. Hidalgo

arXiv:2209.08382v2econ.GNcond-mat.stat-mechcs.CYq-fin.EC

TL;DR

Trade-based complexity metrics can miss innovative activities relevant to inclusive green growth. This paper combines trade, patent, and research data and finds that complexity across these dimensions helps explain growth, inequality, and emissions.

  • Problem

    Trade-based complexity metrics can miss information about innovative activities relevant to inclusive green growth, while these dimensions are rarely combined to explain its geography.

    Source: Introduction · p. 1, Discussion · p. 17

  • Method

    The paper combines geographic data on exports by product, patents by technology, and scientific publications by research field to explain growth, inequality, and greenhouse emissions.

    Source: Introduction · p. 3

  • Results

    Technology complexity adds explanatory power to trade complexity for growth and income inequality, while all three complexity dimensions complement each other for greenhouse gas emissions.

    Source: Discussion · pp. 17–18

  • Takeaways & Limitations

    Multidimensional complexity improves on trade-based measures when explaining international differences in growth, income inequality, and greenhouse gas emissions.

    Source: Discussion · p. 20

    Patent and research datasets may favor English-speaking countries or those with high English proficiency, and patent applications could be gamed with spurious submissions.

    Source: Discussion · p. 19

Abstract

from arXiv · show

To achieve inclusive green growth, countries need to consider a multiplicity of economic, social, and environmental factors. These are often captured by metrics of economic complexity derived from the geography of trade, thus missing key information on innovative activities. To bridge this gap, we combine trade data with data on patent applications and research publications to build models that significantly and robustly improve the ability of economic complexity metrics to explain international variations in inclusive green growth. We show that measures of complexity built on trade and patent data combine to explain future economic growth and income inequality and that countries that score high in all three metrics tend to exhibit lower emission intensities. These findings illustrate how the geography of trade, technology, and research combine to explain inclusive green growth.

Introduction

The paper examines how combining trade, patent, and research-publication data to measure economic complexity can explain cross-country variation in inclusive green growth. It considers growth, inequality, and emission intensity, including how complexity dimensions interact across these outcomes.

Introduction

  • The paper addresses the difficulty of comparing sustainable development’s economic, social, and environmental factors by combining geographic data on exports, patents, and scientific publications into three complexity measures.It uses these measures to explain international variation in economic growth, income inequality, and greenhouse-gas emissions.Source: Introduction · pp. 1, 3
  • Combining trade, patent, and research complexity significantly and robustly improves explanations of inclusive green growth; trade and technology complexity explain growth and inequality, while high scores across all three metrics tend to accompany lower emission intensity.Trade and technology complexity have a negative interaction for growth, but not inequality; for emissions, interaction terms dominate. Robustness checks include additional controls and an instrumental-variable approach using structurally similar non-neighbors.Source: Introduction · pp. 3–4

International differences in Multidimensional Economic Complexity

  • The three complexity measures are correlated but yield distinct country profiles: trade rankings tend to understate complexity in Australia and New Zealand and overstate it in Mexico and Czechia.Mexico and Czechia rank higher in trade than in technology and research complexity, while Australia and New Zealand show the reverse pattern; the figures compare rankings and values using 2014 data.Source: International differences in… · p. 5, Figure 1 · p. 6
  • A 7-percentage-point gain over the trade-complexity regression yields adjusted R² = 0.41 for the growth model combining trade and technology complexity; their interaction is negative and significant.Research complexity is not significantly related to future growth, and the final model also includes GDP per capita, human capital, and natural-resource exports per capita.Source: International differences in… · p. 9, Table 1 · p. 10
  • The trade-and-technology model best explains inequality (adjusted R² = 0.56), with no significant interaction between the two complexity measures; research complexity adds little explanatory power.The final model includes population and human capital alongside multidimensional complexity and the Kuznets term.Source: International differences in… · p. 11, Table 2 · p. 12
  • For emission intensity, the best multidimensional model includes the three-way interaction of trade, technology, and research complexity (adjusted R² = 0.40); countries scoring high across all three tend to have the lowest emission intensities.The relationship extends beyond variation accounted for by natural-resource export intensity, but complexity is not robustly related to embodied emission intensity, a consumption indicator.Source: International differences in… · p. 13, Table 3 · p. 14
  • The weighted multidimensional ECI correlates with increased economic growth and decreased income inequality and emission intensity.The index weights each ECI coefficient by the size of its regression coefficient in the final model.Source: International differences in… · pp. 15–16, Figure 3 · p. 16
  • Complexity interactions suggest mild substitution for growth, additive effects for inequality, and lower emission intensities where countries score high across all three metrics.The growth interaction is negative; the inequality interaction is not significant, while all emission-intensity interaction terms are significant.Source: International differences in… · p. 15
  • More than 50% of cross-country variation in economic growth and income inequality, and almost 40% in emission intensity, is explained by final models adding technology and research complexity to trade metrics.Technology complexity adds explanatory ability for growth and inequality, while trade, technology, and research complexity complement one another for emissions.Source: International differences in… · p. 15, Figure 3 · p. 16

Instrumental Variable

  • Replacing each country’s complexity values with averages for its three most similar non-neighbors leaves the results virtually unchanged, reducing concern about omitted local factors.Similarity is based on specialization patterns in exports, technologies, and research areas; the method is intended to decouple local conditions from complexity estimates.Source: Instrumental Variable · p. 17

Discussion

Multidimensional complexity improves explanation of international differences in growth, inequality, and emissions, while the three dimensions interact differently across outcomes. The approach offers a broader basis for economic diversification, but its data and geographic scope constrain what it can capture.

Discussion

  • Trade and patent activity connect more directly to monetary outcomes, whereas research geography may affect them more indirectly; emissions correlate negatively with complexity in all three dimensions.The discussion links exports to revenues and patents to royalties, while suggesting research papers may affect monetary outcomes less directly.Source: Discussion · p. 18
  • The framework offers a broader diversification map across growth, inequality, and emissions and across products, patents, and research; greater sophistication may still benefit less advanced economies.The paper notes that not all economies may become equally sophisticated, while increases in sophistication may still enable more sustainable, inclusive, and prosperous economies in the developing world.Source: Discussion · pp. 18–20
  • The framework omits services, digital products, and cultural activities, while English-language data may favor some countries and patent applications may differ from granted patents or invite spurious filings.Internationally comparable fine-grained data for additional activities are unavailable; trade data also cover about 1,200 products versus about 300 research subject categories, a difference that may contribute to weak research-complexity effects and complicate combining datasets.Source: Discussion · p. 19
  • The results cannot be readily generalized to states and provinces, where complexity–inequality relationships may differ from international patterns.The discussion notes that the relationship between complexity and inequality reverses at the regional scale, limiting what this approach can say about regional effects.Source: Discussion · pp. 19–20
  • Potential multicollinearity, including between human capital and ECI, could enlarge standard errors, although the reported results remain robust despite this limitation.The authors state that this data limitation would play against finding significance.Source: Discussion · p. 20
  • Multidimensional complexity improves explanation of international differences in growth, inequality, and emissions; technology adds to trade for growth and inequality, while all three complement one another for emissions.Trade and technology are partly substitutes in the growth regression but not in the inequality model; the triple-interaction model has the highest predictive power for emission intensities, where lower intensities correlate with high scores on all three metrics.Source: Discussion · pp. 17, 18, 20

Methods

  • The standard ECI is estimated from specialization matrices through iterative complexity mapping, with normalization to make observation units comparable; results are robust to fitness and i-ECI alternatives.The authors use the standard definition for comparability with prior research and because it applies directly to all three datasets.Source: Methods · pp. 20–22

Author contribution statement

The supplementary statements record author contributions, competing interests, data and code availability, and the authors’ institutional affiliation.

Author contribution statement

  • V.S., P.K., and C.A.H. are credited with overlapping conceptual, methodological, analytical, and writing contributions, with V.S. also credited for software, data curation, validation, and investigation.Source: Author contribution statement · p. 29

Competing interests

Data availability statement

Green Growth

Supplementary Note 1. Data

The data section describes three country-level activity measures, their data sources and filtering rules, and a supplementary export-partner distribution used to contextualize value-chain integration.

Data

  • The analysis covers 150 countries over 24 years, measuring trade by export value, research by article counts, and technology by patent applications.Source: Supplementary Note 1. Data · p. 32

Product exports data

  • Country and product filters exclude small economies and low-volume categories; trade is classified at HS4, retaining products with at least $500,000 in world exports.Source: Supplementary Note 1. Data · p. 32

Supplementary Figure 1

  • The supplementary histogram describes each country’s 2010–2019 export share sent to its main partner, used to argue that Mexico and Czechia are integrated into neighboring value chains.Source: Supplementary Note 1. Data · p. 33

Patent applications data

  • Patent data use PCT applications assigned to inventor-residence countries and CPC technology classes, with low-activity classes excluded and 668 classes retained.Source: Supplementary Note 1. Data · pp. 33–34

Research publications data

  • Research publications come from Scopus statistics and are assigned to countries and research categories, with low-document, low-citation, and low-publication categories filtered out.Source: Supplementary Note 1. Data · p. 34

Supplementary Note 2. Regression analysis setup

The regression setup tests how trade, technology, and research complexity relate to growth, inequality, and emissions, both individually and through interactions.

Individual regressions setup

  • Period fixed-effects panel regressions estimate the relationship between each complexity dimension and growth, income inequality, or greenhouse gas emissions while controlling for other observed factors.Source: Supplementary Note 2. Regression… · pp. 34–35

Interactions regressions setup

  • The interaction analyses compare additive models, pairwise interactions, and a three-way interaction to examine how the complexity dimensions combine in explaining outcomes.Source: Supplementary Note 2. Regression… · pp. 35–36
  • A significant negative pairwise interaction indicates that two dimensions are substitutes, while a significant interaction with the same sign as both main effects indicates complementarity.Source: Supplementary Note 2. Regression… · p. 36

Model comparison

Supplementary Note 3. Robustness check setup

The robustness setup tests added controls, alternative economic-structure measures, and alternative complexity definitions, while noting the constraints of short panels.

Robustness checks

  • Robustness checks add controls, compare alternative model families, and include country fixed effects, although short panels limit the latter specification’s available variation.The growth panel has two periods and the income-inequality panel five; country fixed effects would consume too many degrees of freedom.Source: Supplementary Note 3. Robustness check… · p. 37

Additional explanatory variables

Comparison with alternate models

Production intensity

Concentration measures

Alternative complexity measures

  • Fitness is used in logarithmic form; i-ECI adjusts product-based complexity with patent data, but its patent assignment differs from the study’s inventor-residence approach because PCT applications seek protection across treaty countries.Source: Supplementary Note 3. Robustness check… · pp. 40–41

Supplementary Note 4. Economic growth regression analysis

The growth regressions use 10-year annualized GDP-per-capita growth and test whether multidimensional complexity results persist across added controls and alternative complexity measures. The final ECI specification performs better than the tested alternatives.

setup and robustness checks

  • The dependent variable is the 10-year annualized growth rate of GDP per capita in constant 2017 dollars adjusted for PPP, with initial GDP per capita included as the control variable.The analysis covers 1999–2009 and 2009–2019, the longest periods for which all data are available.Source: setup and robustness checks · p. 42

Economic growth multidimensional regression model additional explanatory variables

  • The final economic growth model includes human capital and natural-resource exports as additional explanatory variables and has adjusted R' = 0.513.The product ECI, technology ECI, and their interaction remain significant when additional explanatory variables are tested separately and together.Source: Economic growth multidimensional… · p. 46
  • The multidimensional Fitness growth model has adjusted R' = 0.380, but the ECI model’s coefficients remain highly significant while Fitness coefficients lose significance in the final comparison.The country-fixed-effects model does not adequately represent variation in the data.Source: Economic growth multidimensional… · p. 48
  • The multidimensional i-ECI growth model has adjusted R' = 0.334, while the ECI model’s coefficients remain highly significant and the i-ECI coefficients lose significance in the final comparison.The individual ECI trade, technology, and research regressions are reported in Supplementary Tables 1–3 and support robustness tests described in the main text.Source: setup and robustness checks · pp. 42–43, Economic growth multidimensional… · p. 48

Supplementary Note 5. Income inequality regression analysis

The income-inequality regressions use Gini coefficients and examine whether multidimensional ECI findings persist under added controls and alternative complexity measures. The final model includes human capital and population, and the ECI results remain significant in comparisons with several alternatives.

Supplementary Note 5. Income inequality regression analysis

  • Income inequality is measured with the Gini coefficient, and the regressions control for initial GDP per capita and its square under the Kuznets hypothesis.Because the Gini data are sparse and coefficients change slowly within countries, the analysis uses average values for five four-year panels from 1996–1999 through 2012–2015.Source: Supplementary Note 5. Income… · p. 62

Income inequality multidimensional regression model additional explanatory variables

  • The final income inequality model includes human capital and population as additional explanatory variables and has adjusted R' = 0.680.Product ECI and technology ECI remain significant when additional explanatory variables are tested separately and together.Source: Income inequality multidimensional… · p. 66

Income inequality multidimensional regression model production intensity robustness

  • The multidimensional ECI income inequality model remains robust against the production-intensity model, whose reported coefficients include trade, technology, and research intensities without interactions.In the comparison, ECI coefficients remain significant; the country-fixed-effects model does not adequately represent variation in the data.Source: Income inequality multidimensional… · pp. 66–67
  • In final specifications (Column 15), multidimensional ECI outperforms multidimensional HHI and production intensity: ECI coefficients remain highly significant while comparison coefficients lose significance.The HHI and Entropy variants include trade and technology, not their interaction (adjusted R' = 0.516 and 0.522, respectively); ECI technology regains significance in Column 15 after losing it in Column 13.Source: Income inequality multidimensional… · pp. 67–68
  • The multidimensional ECI income-inequality model remains robust against the multidimensional i-ECI model: its coefficients remain significant in direct comparison, a specification including all potential explanatory variables, and the final model specification.The i-ECI model includes only i-ECI (adjusted R' = 0.474).Source: Income inequality multidimensional… · pp. 68–69

Supplementary Note 6. Emission intensity regression analysis

The emission-intensity regressions use greenhouse-gas emissions relative to population and test multidimensional ECI findings with additional controls and alternative complexity measures. The ECI terms and interactions remain significant under the reported added-control checks.

Supplementary Note 6. Emission intensity regression analysis

  • The emission-intensity dependent variable is greenhouse-gas emissions in kilotons of CO2 relative to population, with larger values indicating higher intensity.The regressions control for GDP per capita, population, human capital, and natural resources, and use average values across six panels from 1996–1999 through 2016–19.Source: Supplementary Note 6. Emission… · p. 81

Emission intensity multidimensional regression model additional explanatory variables

  • The final multidimensional ECI emission-intensity model has adjusted R' = 0.397, with all variables statistically significant.The ECI terms and interactions remain significant when population, human capital, and natural-resource exports are tested as additional explanatory variables; the country-fixed-effects model has adjusted R' = 0.314.Source: Emission intensity multidimensional… · p. 85

Emission intensity multidimensional regression model production intensity robustness

  • The production-intensity emission model includes trade, technology, and research intensities, their pairwise interactions, and a three-way interaction, with adjusted R' = 0.448.The multidimensional ECI emission model’s coefficients remain statistically significant in specifications that include both models.Source: Emission intensity multidimensional… · pp. 85–86
  • The multidimensional ECI emission model remains robust against HHI, Entropy, and Fitness alternatives in comparisons that include both models.Those alternatives include only trade HHI, trade Entropy, or trade Fitness, respectively; their adjusted R' values are 0.334, 0.337, and 0.368.Source: Emission intensity multidimensional… · pp. 86–87
  • The multidimensional ECI emission model also remains robust against the i-ECI model, which includes i-ECI and research ECI and has adjusted R' = 0.328.ECI coefficients remain significant when both models are included.Source: Emission intensity multidimensional… · p. 87

Supplementary Note 7. Economic complexity and embodied

The paper tests an alternative dependent variable based on embodied emissions, which combine territorial and trade-related emissions. The embodied-emission ECI results are not robust to the reported alternative specifications.

emissions

  • Embodied emissions add territorial and imported emissions and subtract exported emissions; the analysis uses Global Carbon Project data.The model follows the emission-intensity formulation and uses GDP per capita, population, human capital, and natural resources as controls.Source: emissions · p. 100
  • The embodied-emission ECI model includes trade ECI, technology ECI, and their interaction, but the result is not robust to alternative specifications.The interaction suggests weak substitution, while the reported robustness checks indicate that the model is not robust against country-fixed-effects and production-intensity models.Source: emissions · p. 100

Supplementary Note 8. Instrumental variables robustness check

The IV checks address possible endogeneity using complexity from similarly specialized, non-neighboring economies as instruments. The multidimensional models are generally robust across outcomes, with qualifications for income inequality and emission intensity; service complexity is not a significant or robust explanatory variable.

Supplementary Note 8. Instrumental variables robustness check

  • The IV uses average complexity among a country’s three most similarly specialized non-neighboring economies; the authors exclude neighbors to reduce bias from geographically diffusing local conditions.The authors explain that neighboring countries could share local conditions that affect the target country’s outcome.Source: Supplementary Note 8. Instrumental… · pp. 107–108
  • The economic-growth model’s multidimensional ECI coefficients remain significant under IV and across additional-variable, production-intensity, HHI, and entropy specifications.The first-stage instrument F-statistics exceed 10 for the trade and technology ECI growth models.Source: Supplementary Note 8. Instrumental… · p. 112, Table 39 · p. 115
  • For income inequality, technology ECI loses significance without final-model controls under IV, but the multidimensional coefficients regain significance with added variables and alternative specifications.The first-stage instrument F-statistics exceed 10 for the trade and technology ECI inequality models.Source: Supplementary Note 8. Instrumental… · p. 116, Table 42 · p. 119
  • The emission-intensity model’s three-way term remains significant under IV, except when production-intensity variables are added; it regains significance with country fixed effects in that specification.The authors treat this more restrictive specification as evidence of robustness.Source: Supplementary Note 8. Instrumental… · p. 120, Table 46 · p. 124

Supplementary Note 9. What about services?

  • Across growth, income inequality, and emission-intensity regressions, service ECI is not a significant or robust explanatory variable.The authors conclude that current service data do not provide enough information for inclusion in their multidimensional complexity analysis.Source: Supplementary Note 9. What about… · p. 125, Table 49 · p. 128
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