Who leads, who follows? A multiscale nonparametric quantile causality analysis of <scp>ESG</scp> uncertainty and implied volatility indices

Abstract This article investigates the causal dynamics between sustainability uncertainty (ESGUI) and implied volatility indices (stock, crude oil, gold, and exchange rate). In doing so, this study develops a multiscale nonparametric framework for testing causality across conditional quantiles and frequencies. Departing from conventional tests that focus on the linear conditional mean or a single quantile, this approach employs the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) to decompose each series into low‐, mid‐, and high‐frequency components, and then examines nonlinear directional dependence across the entire conditional distribution within each frequency band. The results show that ESGUI predicts implied volatility in euro exchange rates, oil, equities, and gold mainly through low‐frequency components, with stronger effects in the lower to middle quantiles, weaker influence at higher quantiles, and only sporadic transmission at high‐frequency components. In contrast, implied volatility indices exhibit broader predictive power for sustainability uncertainty, driven primarily by low‐frequency dynamics and supported by mid‐frequency effects, while variance‐based results indicate low‐frequency bidirectional dependence that weakens under extreme states. The study derives policy implications based on these findings.