The 17 Sustainable Development Goals (SDGs), adopted by all UN member states, aim for global peace and prosperity. Traditional sustainability perspectives, weak and strong sustainability, focus on balancing economic, social, and environmental pillars. However, this study adopts an integrated sustainability perspective, incorporating a fourth pillar: spillover effects from transboundary interactions. These interactions, transmitted through trade, natural flows (river flow, ocean currents, air flow), and other channels, can create synergies or trade-offs impacting SDG progress in various countries. Quantifying these transboundary interactions is challenging due to diverse transmission channels and varying outcomes. This study addresses this challenge by developing a framework to quantify transboundary SDG interactions, focusing on the impacts of both human-caused (e.g., international trade) and nature-caused flows on SDG indicators across 121 countries from 2010 to 2020. The study's importance lies in its ability to quantify the magnitude and direction of these spillover effects, a crucial element of integrated sustainability that has not been given adequate attention in previous studies.

Existing research acknowledges widespread interactions between SDGs across borders, including technological spillovers and trade profits. These transboundary synergies can aid receiving countries in achieving their SDGs. However, transboundary trade-offs also exist, such as wastewater flow into transboundary rivers, hindering SDG achievement in receiving countries. Previous studies highlighted the complexities involved in quantifying transboundary SDG interactions due to diverse transmission channels and varying outcomes. Several studies examined specific aspects of this problem, like the influence of international trade on environmental and socioeconomic impacts, the transport of air pollutants across borders impacting air quality and human health, and the effects of pollutants in waterways. However, a comprehensive quantification and analysis of the combined effects of these diverse channels, within an integrated sustainability framework, remains limited. This study aims to fill that gap, establishing a quantitative framework to analyze the intricate network of inter-country interactions shaping global progress toward the SDGs.

This study employed a four-step methodology to evaluate transboundary SDG interactions. **Step 1: Identifying SDG Indicator Pairs:** The study identified 768 pairs of SDG indicators with potential causal relationships from an interactive repository built through a systematic literature review. **Step 2: Constructing Spatial Weight Matrices:** Spatial weight matrices were constructed to represent different transboundary interaction channels: international trade (using Eora26 MRIO tables), river flow (HydroSHEDS database), ocean currents (based on maritime boundaries and coastal countries), and air flow (inverse distance-based). **Step 3: Row-Standardization:** The spatial weight matrices were row-standardized to ensure comparable weights across countries. **Step 4: Quantifying Transboundary Interactions:** Spatial econometric models, specifically a two-stage instrumental variable (2SIV) estimation method, were used to analyze transboundary spillover effects, addressing endogeneity issues. Higher-order spatial econometric models were utilized to account for multiple simultaneous transmission channels. A spatial interaction index (0-100) was developed to quantify the overall magnitude of transboundary interactions, decomposing it into synergistic and trade-off effects via human-caused and nature-caused flows. The study also analyzed interactions by income group (high, upper-middle, lower-middle, low income) using a modified spatial weight matrix. Interactions with neighboring and non-neighboring countries were compared using separate spatial weight matrices representing geographic proximity.

The study revealed that transboundary synergistic linkages were more prevalent than trade-off linkages across all channels (international trade and nature-caused flows). Specifically, 73.68% of trade-related linkages and 81.82% of nature-caused flow linkages were synergistic. Indicators related to target 7.1 (access to modern energy services) had the most international trade linkages, impacting various SDGs in other countries. Target 6.6 (protecting and restoring water-related ecosystems) exhibited the most linkages via nature-caused flows, with significant positive effects on multiple SDG indicators in other countries. A spatial interaction index showed that transboundary synergistic effects were 3.76 times stronger than trade-off effects globally. SDG 12 (responsible consumption and production) showed the strongest transboundary synergies. Target 6.6 showed the strongest net synergistic effect. High-income countries, despite their relatively small share of the global population (14.18%), significantly influenced total global transboundary SDG interactions (60.60%), displaying strong transboundary synergistic effects. Transboundary synergistic effects via international trade were 14.94% stronger with non-neighboring trade partners. Conversely, synergistic effects via nature-caused flows were 39.29% stronger with neighboring countries. High-income countries exhibited notably stronger synergistic effects with non-neighboring trade partners (18.14% increase).

The findings highlight the significant role of transboundary interactions in achieving the SDGs, underscoring the importance of international collaboration. The dominance of transboundary synergistic effects through international trade supports the positive impact of globalization and openness on global sustainability. The study's results, however, reveal that the direction and magnitude of transboundary interactions vary by interaction channel and geographic proximity, demonstrating the non-uniformity of transboundary interactions and the importance of both Tobler's first law of geography and metacoupling framework. The study advocates for a flow-based governance approach considering transboundary flows in international policy making, particularly emphasizing the need to internalize the costs and benefits of transboundary interactions, including the use of tradable pollution permits. While the study's focus is on trade, river flow, ocean currents, and air flow, future research should explore other transboundary flows (e.g., maritime transportation, technology transfer, migration, disease dissemination) to gain a more comprehensive understanding of global SDG interactions.

This study provides a comprehensive quantification of transboundary SDG interactions using an integrated sustainability framework. The findings highlight the significant role of both human-caused and nature-caused flows in shaping SDG outcomes across countries, emphasizing the need for global cooperation and effective transboundary governance mechanisms. Future research should incorporate additional transboundary flows and refine the methodologies for modeling complex flow dynamics to enhance our understanding of the interplay between national actions and global SDG achievement.

The study's limitations include data availability, which restricted the analysis to 121 countries and 55 SDG indicators for the period 2010-2020. The choice of spatial econometric models and the specific spatial weight matrices used might affect the results. The study also acknowledges that the definitions of neighboring and non-neighboring countries can be subjective and context-dependent, impacting the interpretation of results based on geographical proximity. Future research should explore diverse methodologies and address the limitations imposed by the availability of comprehensive data for all the SDGs and countries.