Distributed Causality in the SDG Network: Evidence from Panel VAR and Conditional Independence Analysis

TL;DR

The study investigates whether SDG interdependencies form a hub-and-spoke structure or a distributed network using Panel VAR with fixed effects and PCMCI+ on $N=168$ countries over $T=24$ years (2000–2025), focusing on an $8$-SDG subset and supplementing with full-$17$-SDG PCMCI+ analysis. It finds a distributed causal architecture with $10$ significant Granger links among the $56$ possible edges and $11$ direct PCMCI+ links among all $17$ SDGs, with Education $\rightarrow$ Inequality emerging as the strongest direct path ($r=-0.599$, $p<0.05$) and substantial heterogeneity across income groups. A three-tier priority framework is proposed: Upstream Drivers (Education, Growth), Enablers (Institutions, Energy), and Downstream Outcomes (Poverty, Health), underscoring that effective SDG acceleration requires coordinated, multi-dimensional interventions rather than single-goal strategies. The paper also documents income-dependent dynamics (e.g., Education reduces inequality strongly in high-income countries but weakly in lower-middle-income ones) and discusses practical implications for policy design, climate justice, and donor coordination. Overall, the work provides a first-of-its-kind causal map of SDGs, with actionable guidelines for tailoring policies to country development levels and for aligning funding around a three-tier framework to accelerate sustainable development.

Abstract

The achievement of the 2030 Sustainable Development Goals (SDGs) is dependent upon strategic resource distribution. We propose a causal discovery framework using Panel Vector Autoregression, along with both country-specific fixed effects and PCMCI+ conditional independence testing on 168 countries (2000-2025) to develop the first complete causal architecture of SDG dependencies. Utilizing 8 strategically chosen SDGs, we identify a distributed causal network (i.e., no single 'hub' SDG), with 10 statistically significant Granger-causal relationships identified as 11 unique direct effects. Education to Inequality is identified as the most statistically significant direct relationship (r = -0.599; p < 0.05), while effect magnitude significantly varies depending on income levels (e.g., high-income: r = -0.65; lower-middle-income: r = -0.06; non-significant). We also reject the idea that there exists a single 'keystone' SDG. Additionally, we offer a proposed tiered priority framework for the SDGs namely, identifying upstream drivers (Education, Growth), enabling goals (Institutions, Energy), and downstream outcomes (Poverty, Health). Therefore, we conclude that effective SDG acceleration can be accomplished through coordinated multi-dimensional intervention(s), and that single-goal sequential strategies are insufficient.

Figures (8)

• Figure 1: Granger Causality Network (8-SDG Subset) Heatmap showing pairwise Granger causality tests. Rows = source SDGs, columns = target SDGs. Color intensity indicates significance level (darkest = $p<0.01$, medium = $p<0.05$, lightest = not significant). Network exhibits distributed structure with multiple nodes showing moderate connectivity; no single hub dominates.
• Figure 2: PCMCI+ Refined Causal Graph Directed acyclic graph showing statistically significant direct causal links among 17 SDGs identified by PCMCI+ algorithm. Edge thickness = effect magnitude (partial correlation coefficient). Edge color indicates lag: black=lag 0 (contemporaneous), gray scale=lags 1-3. Algorithm filters 70 Granger links to 11 direct effects, removing indirect and spurious associations.
• Figure 3: Impulse Response Functions with Bootstrap Confidence Intervals Orthogonalized IRFs showing dynamic effects of one-SD shocks. Panel A: Education $\rightarrow$ Inequality (strongest direct effect). Panel B: Growth $\rightarrow$ Climate (heterogeneous). Solid lines = point estimates, shaded regions = 95% bootstrap CI (200 iterations). Horizontal axis = years after shock, vertical axis = response magnitude.
• Figure 4: Heterogeneity in Causal Effects by Income Group Comparative IRFs across High-Income (blue), Upper-Middle Income (green), and Lower-Middle Income (red) countries. Panel A: Education $\rightarrow$ Inequality (effect strength decreases with lower income). Panel B: Growth $\rightarrow$ Climate (direction reverses: negative in HIC, positive in LMIC). Demonstrates that SDG causal structures are income-dependent.
• Figure 5: Figure S1. Granger Causality Test Results: 17x17 Matrix Full heatmap showing results of all pairwise tests. Diagonal elements excluded.