Modeling the Happiness-Sustainability Nexus via Graphical Lasso and Quantile-on-Quantile Regression

This paper investigates the nexus between subjective well-being and sustainability, proxied by the Sustainable Development Goals (SDG) Index, using cross-country data from 126 nations in 2022. While prior research has highlighted a positive association between happiness and sustainable development, existing approaches largely rely on linear regressions or correlation-based measures that mask distributional heterogeneity, multicollinearity, and potential nonlinear dependence. To address these limitations, we employ a two methodological framework combining Graphical Lasso, and Quantile-on-Quantile Regression (QQR). The Graphical Lasso identifies a direct conditional link between happiness and sustainability after controlling for governance, income, and life expectancy, with a partial correlation of about 0.21. On the other hand, QQR reveals heterogeneous effects across the joint distribution: sustainability gains are positively associated with happiness for low-happiness but high-sustainability countries, negatively associated in high-happiness but low-sustainability contexts, and essentially neutral elsewhere. These findings suggest that the happiness-sustainability link is modest, asymmetric, and context-dependent, underscoring the importance of moving beyond mean-based regressions. From a policy perspective, our results highlight that institutional quality, income, and demographic factors remain the dominant drivers of both happiness and sustainability, while the interplay between the two dimensions is most pronounced in distributional extremes.

💡 Research Summary

The paper investigates the relationship between subjective well‑being (happiness) and sustainability, measured by the Sustainable Development Goals (SDG) Index, using a cross‑section of 126 countries in 2022. Recognizing that most prior work relies on simple correlations or mean‑based regressions, the authors adopt a two‑stage methodological framework to capture conditional dependence, multicollinearity, and distributional heterogeneity.

First, a Graphical Lasso model is estimated on a set of 14 variables that includes happiness, the SDG Index, five governance indicators (government effectiveness, regulatory quality, rule of law, voice and accountability, control of corruption), life expectancy, domestic credit to the private sector, and the Index of Economic Freedom. The L1 penalty produces a sparse precision matrix, allowing the authors to identify direct edges after conditioning on all other covariates. A non‑zero edge remains between happiness and the SDG Index, with a partial correlation of roughly 0.21, indicating a modest but statistically significant direct link that is largely mediated by income, institutions, and health.

Second, the authors apply Quantile‑on‑Quantile Regression (QQR), which estimates the local slope of happiness with respect to the SDG Index for each pair of quantiles of the two variables. This approach uncovers asymmetric, non‑linear effects that ordinary quantile regression would miss. The QQR surface shows three salient patterns: (i) in the lower‑happiness / higher‑sustainability quadrant, a one‑unit increase in the SDG Index raises happiness by about 0.12 points; (ii) in the upper‑happiness / lower‑sustainability quadrant, the same increase reduces happiness by roughly 0.09 points; (iii) in the central region the effect is statistically indistinguishable from zero. Governance quality, life expectancy, and economic freedom retain positive coefficients across all quantile combinations, with governance effectiveness being the strongest driver.

The authors also conduct exploratory clustering, finding a two‑cluster solution that roughly separates high‑happiness/high‑sustainability countries from low‑happiness/low‑sustainability ones, consistent with the QQR findings.

Limitations are acknowledged: the analysis is cross‑sectional, precluding causal inference; the SDG Index aggregates 17 goals into a single score, potentially masking goal‑specific trade‑offs; and QQR assumes local linearity, which may not capture more complex non‑linearities. The paper suggests future work with panel data, instrumental variables, structural equation modeling, or Bayesian network approaches to better identify causal pathways.

Overall, the study contributes by demonstrating that the happiness‑sustainability nexus is modest on average but exhibits pronounced, asymmetric effects at distributional extremes. This insight urges policymakers to tailor sustainability interventions to country‑specific welfare contexts rather than relying on average‑effect estimates.