You may already be aware of this, from the July edition of the Cleveland Fed's Economic Trends ...
OER—the costs that homeowners would assume if they rented their homes instead of owning them— accounts for nearly one-quarter of the CPI market basket. Monthly growth in OER has accelerated since the beginning of the year. OER jumped 6.8% in May, well above its 3.1 average monthly percent change. Some of the recent rise can be tied to decelerating utilities costs, which are subtracted from this housing cost measure, but some part of the rise seems to come from a rental market that is growing stronger after several years of relative softness.
... but I'm not so sure this is widely appreciated:
The recent pressure on the OER component of the CPI may be with us for the summer. Since 1995, the monthly OER index has been computed from six-month rent changes, a procedure that reduces its monthly volatility but also causes the measure to exhibit some persistence. In other words, monthly changes in OER tend to influence the CPI’s behavior over a period of several months.
Emphasis added. Of course, today we saw another northward run in oil prices, duration unknown. As suggested above, and noted in the June issue of Economic Trends:
Because residential leases often include utilities provided by the landlord, the Bureau of Labor Statistics subtracts these utility costs from rents when calculating OER. During periods of rising energy prices, the growth in OER may be understated until these higher energy costs are reflected in higher rents.
So, it may be a challenge to figure out how rising rents and the effects of averaging in the BLS' calculations of OER -- both of which will be working in the direction of maintaining higher levels of CPI growth -- might combine with yet more energy-price increases -- which can temporarily depress the OER part of the CPI -- in driving the near-term evolution of core inflation measures (ex food and energy versions, especially). It surely is not getting any easier.