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We study how the recent run-up in housing and rental prices affects the outlook for inflation in the USA. Housing held down the overall inflation in 2021. Despite record growth in private market-based measures of home prices and rents, the government-measured residential services inflation was only 4% for the 12 months ending in January 2022. After explaining the mechanical cause for this divergence, we estimate that, if past relationships hold, the residential inflation components of the Consumer Price Index (CPI) and Personal Consumption Expenditure (PCE) are likely to move close to 7% during 2022. These findings imply that housing will make a significant contribution to overall inflation in 2022, ranging from one percentage point for headline PCE, to 2.6 percentage points for core CPI. We expect residential inflation to remain elevated in 2023.