Soft-Noncrossing Bayesian Panel Quantile Regression for Measuring Climate Tail Risk

2026-08-05

AI Summary

This study addresses the challenge of modeling systemic tail risks to national economic growth arising from climate shocks by proposing a hierarchical Bayesian panel quantile regression framework. The approach integrates Gaussian process priors to smooth individual quantile trajectories, incorporates a common time effect to capture global shocks, and innovatively employs monotone Bernstein polynomials with individual perturbations to enforce soft non-crossing constraints across quantiles, accompanied by formal identification conditions and an upper bound on crossing probabilities. Application to a panel of 33 countries over 1979–2023 reveals that temperature shocks generate undiversifiable downside tail risks, with emerging markets exhibiting heightened vulnerability. Out-of-sample prediction losses are reduced by approximately one-third relative to country-specific independent models.

Abstract

We develop a hierarchical Bayesian panel quantile regression model in which unit-specific coefficient paths are smoothed across quantiles by Gaussian processes, while a common time effect absorbs aggregate shocks. Componentwise-monotone Bernstein polynomials, perturbed by unit-specific deviations, deliver soft noncrossing, and we provide identification conditions together with a bound on the crossing probability. Applying the model to 33 countries over 1979--2023, we find that global temperature shocks generate a systemic, non-diversifiable downside risk to output growth. This risk is concentrated in the lower tail and disproportionately affects emerging markets. Finally, we apply our framework to risk analysis and show that the model reduces out-of-sample tail-risk forecast loss by roughly one-third relative to country-specific quantile regressions.

Problem

• climate tail risk
• panel quantile regression
• noncrossing
• systemic risk
• economic growth

Innovation

• Bayesian panel quantile regression
• Gaussian processes
• soft noncrossing
• Bernstein polynomials
• tail risk forecasting