This paper analyzes the pass-through from import prices to CPI inflation in real time. Our strategy follows an event-study approach, which compares inflation forecasts before and after import price releases. Inflation forecasts are modelled using a dynamic factor procedure that relies on daily panels of Swiss data. We find strong evidence that monthly import price releases provide important information for CPI inflation forecasts and that the behavior of updated forecasts is consistent with a time-varying pass-through. The robustness of this latter result is underpinned in two ways: an alternative CPI measure that excludes price components subject to administered pricing and panels capturing different levels of information breadth. Besides implying a time-varying pass-through, our empirical findings cast doubt on a prominent role of sticky prices for the low pass-through findings.