The NYT had a piece discussing the views of members of the Federal Reserve Board's Open Market Committee (FOMC), which sets monetary policy, on the course of interest rates over the next year. The piece notes that inflation has consistently been below both the Fed's 2.0 percent target and the FOMC members projections, as they have consistently over-predicted the impact of tighter labor markets on the inflation rate.
It is worth noting that even the modest inflation we are seeing is largely due to rising rents. A measure of core inflation that excludes rent has risen just 0.6 percent over the last year.
Consumer Price Index, Excluding Food, Energy, and Shelter
Source: Bureau of Labor Statistics.
This matters because rents are driven by a qualitatively different dynamic than most other prices. They depend largely on the ease of building and shortages of land, rather than rising wages. By slowing new construction, higher interest rates are more likely to increase rather than decrease rents, unless the rise goes far enough to lead to a recession and thereby substantially reduce demand.