Macro variables frequently display time-varying distributions, driven by the dynamic and evolving characteristics of economic, social, and environmental factors that consistently reshape the fundamental patterns and relationships governing these variables. To better understand the distributional dynamics beyond the central tendency, this paper introduces a novel semi-parametric approach for constructing time-varying conditional distributions, relying on the recent advances in distributional regression. We present an efficient precision-based Markov Chain Monte Carlo algorithm that simultaneously estimates all model parameters while explicitly enforcing the monotonicity condition on the conditional distribution function. Our model is applied to construct the forecasting distribution of inflation for the U.S., conditional on a set of macroeconomic and financial indicators. The risks of future inflation deviating excessively high or low from the desired range are carefully evaluated. Moreover, we provide a thorough discussion about the interplay between inflation and unemployment rates during the Global Financial Crisis, COVID, and the third quarter of 2023.

翻译：宏观经济变量常呈现时变分布特征，这源于经济、社会及环境因素持续演变的动态属性不断重塑着支配这些变量的基本模式与关联。为超越中心趋势更深入地理解分布动态，本文基于分布回归领域的最新进展，提出一种构建时变条件分布的新型半参数方法。我们提出一种高效的基于精度的马尔可夫链蒙特卡洛算法，可同步估计所有模型参数，同时显式强制条件分布函数满足单调性约束。应用该模型，我们以一组宏观经济与金融指标为条件，构建了美国通胀的预测分布。研究系统评估了未来通胀过度偏离目标区间（过高或过低）的风险。此外，我们深入探讨了全球金融危机、新冠疫情及2023年第三季度期间通胀率与失业率之间的相互作用机制。