The harder question is what happens when the shelter lag finally converges. Does headline CPI drop sharply as lagged data catches up to current reality? Or has the composition of inflation shifted enough that services keep the number elevated regardless?
If the lag was masking disinflation, the catch-up will look like a sudden soft print. If wage-driven service inflation has structurally replaced goods inflation, the headline might stay sticky even after shelter normalizes. Both are plausible. Neither is fully priced in.
What constraint am I missing?