Shelter (housing) costs constitute a large component of price indexes, including 42 percent of the widely followed core Consumer Price Index (CPI). The shelter prices measured in the CPI capture new and existing renters and tend to lag market rents. This lag explains how in recent months the shelter-price index (CPI shelter) has accelerated while market rents have pulled back. We construct an error-correction model using data at the metropolitan statistical area level to forecast how CPI shelter will evolve. We forecast that CPI shelter will grow 5.88 percent from September 2022 to September 2023 and 3.91 percent over the subsequent 12 months. We demonstrate that the most important factor supporting high future CPI-shelter growth is that a large part of past growth in market rents had not been captured in CPI shelter as of September 2022. We estimate that the headline CPI and core CPI will be 1.05 and 1.34 percentage points higher, respectively, from September 2022 to September 2023 as a result of above-average shelter inflation.