Sovereign ESG and the Hydrological Constraint: Rethinking the Determinants of Water Stress

Technical Summary: Sovereign ESG and the Hydrological Constraint

Problem Statement
The paper addresses a conceptual and methodological fragmentation in the literature on water stress. While hydrology treats water stress (the ratio of freshwater withdrawals to available renewable resources) as a physical outcome determined by climate and land systems, political science and development studies treat it as an institutional outcome driven by governance and allocation rules. These two perspectives have rarely been tested jointly on the same sample of countries using a unified framework. Furthermore, existing cross-country studies often fail to distinguish between within-country temporal movements and between-country structural differences, and they frequently neglect non-linearities and machine learning validation. The authors apply the World Bank's Sovereign ESG (Environmental, Social, and Governance) framework to water stress for the first time, testing whether these three pillars explain the hydrological constraint and identifying the specific determinants within each.

Methodology
The study analyzes up to 170 economies observed between 2002 and 2022 (with variations in sample size due to data availability for specific indicators). The dependent variable is the natural logarithm of the freshwater withdrawal-to-availability ratio. The authors estimate three distinct equations, each sharing the same dependent variable but differing only in the block of regressors supplied by the ESG pillars:

1. Environmental Equation: 170 economies, 3,501 observations (2000–2021).
2. Social Equation: 99 economies, 2,113 observations (2001–2022).
3. Governance Equation: 170 economies, 3,421 observations (2002–2022).

Each equation is analyzed along three parallel tracks to ensure robustness and methodological triangulation:

• Track 1: Panel Econometrics: Utilizing seven estimators including Pooled OLS, Fixed Effects (FE), Random Effects (RE), Between, Weighted Least Squares (WLS), and two-step Difference and System GMM. Diagnostics include tests for cross-sectional dependence (Pesaran), autocorrelation (Wooldridge), and collinearity. Crucially, the governance block addresses the high collinearity (0.81–0.95) among Worldwide Governance Indicators (WGI) by employing Principal Component Analysis (PCA) to create orthogonalized variables (Institutional Quality and Institutional Balance) rather than entering correlated dimensions side-by-side.
• Track 2: Unsupervised Clustering: Six algorithms (DBSCAN, Fuzzy C-Means, Hierarchical, K-Means, Model-Based GMM, Random Forest proximity) compete to classify countries based on their ESG-water profiles. Selection is based on eleven internal validity indices (e.g., Silhouette, Calinski-Harabasz, HHI) and an admissibility rule requiring all economies to be assigned to a group.
• Track 3: Supervised Validation: Six learners (Linear Regression, Regression Tree, KNN, Linear SVM, Boosting, Random Forest) are evaluated to validate the functional form of the econometric specifications rather than to forecast. A critical design choice involves two validation schemes: a random 70/30 hold-out and a grouped five-fold cross-validation where entire countries are held out to prevent data leakage (memorization of country identity).

Key Results

• Structural Nature of Water Stress: The most fundamental finding is that 99.1% of the log variance in water stress lies between countries, while only 0.9% lies within them over the 20-year period. This indicates water stress is a structural attribute of national territory, not a variable that fluctuates significantly year-to-year in response to policy or climate shocks.
• Environmental Pillar:
  • Determinants: Forest cover and population density are the dominant predictors. Forest cover shows a strong negative cross-sectional relationship, while population density is the only variable that remains significant in the Fixed Effects (within-country) model, suggesting urbanization drives dynamic pressure.
  • Non-linearity: Machine learning reveals a U-shaped partial dependence for agricultural land (stress falls then rises). The drought index (SPEI), while carrying the largest cross-sectional coefficient in the block, collapses to near-irrelevance under grouped validation (dropout loss of 0.71%), indicating it discriminates between countries but explains nothing within them.
  • Validation: Under grouped cross-validation, Random Forest outperforms linear models slightly (R² 0.41 vs. 0.31), but the linear specification captures the majority of the structure.
• Social Pillar:
  • Sign Reversal: There is a systematic sign reversal between Between and Fixed Effects estimators for variables like sanitation and clean cooking fuel. Cross-sectional coefficients reflect geographical confounding (arid, high-income economies have high service coverage and high stress), not causal social mechanisms.
  • Within-Country Drivers: Only fertility rate and undernourishment survive the within transformation, moving together as part of a shared development trajectory.
  • Clustering: The social block is largely one-dimensional (development gradient). However, a distinct "High-stress low-participation" cluster emerges, characterized by intermediate development levels but constrained labor force participation and high water stress.
  • Validation: Flexible learners perform worse than linear models when countries are held out (R² drops to near zero or negative), indicating social indicators are weak predictors of cross-country variation once country identity is removed.
• Governance Pillar:
  • The Null on Institutional Quality: The level of institutional quality (the first principal component of four WGI indicators, absorbing 91.9% of their variance) is unrelated to water stress in every estimator.
  • The Signal in Composition: The second principal component, representing "accountability relative to state capacity," carries a strong negative coefficient (−1.10) in cross-sectional models. Economies with high administrative capacity but low accountability (e.g., Gulf rentier states) exhibit the highest water stress.
  • Dominant Predictor: The female-to-male labor force participation ratio is the single most significant predictor across all three pillars. Its partial dependence reveals a sharp discontinuity (a step function) concentrated in a five-point interval (55–59%), a feature invisible to linear specifications.
  • Validation: In the governance block, Linear Regression outperforms all flexible learners under grouped cross-validation (R² 0.27 vs. 0.08), confirming that the relationship is effectively linear and that no non-linear structure is being missed by the econometric model.

Significance and Claims
The paper claims to resolve three gaps in the literature:

1. Conceptual: It is the first study to apply the sovereign ESG decomposition to water stress as a dependent variable, comparing the explanatory power of the three pillars on a common sample.
2. Estimation: By separating within-country movement from between-country structure, it demonstrates that case studies and cross-country literature have been answering different questions. The finding that 99.1% of variance is structural challenges the assumption that water stress is a policy variable responsive to annual adjustments.
3. Methodological: It treats the collinearity of governance indicators as a substantive measurement problem (requiring orthogonalization) rather than an estimation nuisance. It also uses machine learning not for prediction, but to validate the adequacy of linear functional forms and to detect specific non-linearities (U-shaped agricultural land, step-function labor participation).

The authors conclude that water stress is a constraint states inherit rather than a performance they deliver. Consequently, the "level" of institutional quality is uninformative for sovereign water assessment; instead, the composition of institutions (specifically the balance between capacity and accountability) and structural factors like labor force participation are the critical determinants. The paper argues that the sovereign ESG framework should incorporate water stress not as a rated performance metric, but as a structural risk factor, given its slow-moving, endowment-driven nature.