The CPI rose 0.1% in May as the core CPI rose 0.1% and energy rose 0.2%.
The real significance of the rise in energy prices shows up in this table that shows the composition of real average hourly earnings — the final column in the table.
In the fourth quarter real earnings rose sharply as oil prices collapsed from almost $150/bbl to some $30/bbl.. The large jump in real earnings is probably what drove the first quarter rise in real personal consumption expenditures.
But so far this year real average weekly earnings have fallen 0.6% as the drop in hours worked and rising inflation — largely oil prices — have more than offset a 0.8% gain in nominal average hourly earnings. This is the real threat to the recovery as rising oil prices offset the positive impact of the green-shoots and tax cuts that were apparent in the first quarter.