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

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.