Inflation volatility under rational inattention: A semi-parametric model and the directional volatility ratio

We propose a semi-parametric volatility model to estimate inflation volatility within a conceptual framework that incorporates rational inattention and price stickiness. The model is applied to inflation data for Germany, France, Spain, the Eurozone, the United States, the United Kingdom, Japan, and Canada over the period 2002–2024, and the United States during the Great Inflation and Moderation (1965–1990). Our estimator outperforms standard parametric and non-parametric alternatives in forecasting inflation volatility and exhibits a strong empirical relationship with survey-based measures of inflation uncertainty. We also introduce the Directional Volatility Ratio (DVR), a novel measure that captures time-varying asymmetries in the relationship between inflation levels and volatility. This measure is effective for tracking shifting inflation trends, identifying turning points, and characterizing inflation risk across different regimes.