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

TL;DR

The paper tackles the problem of inflation risk by modeling the full conditional distribution $F_{\pi_t|X_t}$ to capture state-dependent tail dynamics. It develops a time-varying parameter distributional regression (TVPDR) in which coefficients $\beta_{y,t}$ follow a random-walk, yielding $F_{Y_t|X_t}(y|X_t)=\Lambda(g(X_t)^\top\beta_{y,t})$, and imposes monotonicity to ensure a valid density. Empirical results for U.S. inflation (1982:Q1–2024:Q4) show deflation risk is primarily driven by demand weakness and inflation persistence, while excessive inflation risk is driven by supply-side shocks, especially energy and food prices; the unemployment-inflation link weakens in the tails. The paper also uses Shapley value decomposition and scenario analysis to identify time-varying, asymmetric transmission pathways and provides a policy-relevant framework for target-based inflation forecasting and risk management by delivering calibrated, full-density forecasts across the distribution.

Abstract

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.

Figures (6)

• Figure 1: Probabilities of Deflation and Excessive Inflation Risks ($\alpha=\gamma=0$)
• Figure 2: Expected Deflation and Excessive Inflation Risks ($\alpha=\gamma=1$)
• Figure 3: Contribution of risk factors to Inflation Risks
• Figure 4: Impact of Energy Price Inflation on Inflation Risk Probabilities
• Figure 5: Impact of Unemployment Rate on Inflation Risk Probabilities

Theorems & Definitions (1)

• Remark 1