Price Gaps and Inflation Dynamics

The inflationary effect of a shock depends not only on its size, but also on the state of the economy when it hits. In menu cost models, this state is captured by the cross-sectional distribution of price gaps: the misalignment between firms’ actual and reset prices. However, this distribution is unobserved. We recast a random menu cost model in state-space form and develop Bayesian methods to recover latent reset prices from observed price paths. Applying the method to almost 35 million UK consumer price observations from 1996 to 2026, we construct a time-varying empirical distribution of price gaps and show that its shape varies substantially over time. Measuring this distribution lets us take the model’s state-dependence predictions directly to the data. We find substantial state dependence in shock transmission: at a two-year horizon, the response to the same monetary tightening ranges from almost fully dampened to amplified by 69 percent across pre-shock gap distributions, with similar patterns for oil-price shocks. The distribution also contains information about where inflation is headed. Gap moments predict future inflation beyond standard macroeconomic controls and improve out-of-sample forecasts relative to a random-walk benchmark up to 37 percent at two years.