  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.
