Inflation Target at Risk: A Time-varying Parameter Distributional Regression

Inflation exhibits state-dependent, skewed, and fat-tailed dynamics that make risk a central concern for monetary policy. Accordingly, inflation risks are distributional and cannot be fully captured by mean-based models. We propose a flexible time-varying parameter distributional regression model that estimates the full conditional distribution of inflation, allowing macroeconomic drivers to have nonlinear and asymmetric effects across the distribution. Applied to U.S. inflation, the model captures major shifts in tail-risk probabilities. Analysis of risk drivers shows that deflationary pressures arise primarily from demand-side weakness and inflation persistence, whereas upside risks are driven mainly by supply-side shocks, particularly energy price inflation. Examining the impact of key drivers further reveals that the unemployment-inflation relationship weakens in the distributional tails. Energy price shocks, by contrast, have little effect on deflation risk but exhibit strongly time-varying and asymmetric effects on high-inflation risk.