The case for raising interest rates has a specific shape. Prices rise because wages rise; wages rise because the labor market is too tight; a central bank cools the labor market by making money expensive. Every part of that chain has to hold for the conclusion to follow.

The Employment Cost Index is the government's broadest measure of the second link, covering wages, salaries and benefits across private industry and state and local government. The second-quarter reading landed at 0.9 percent, the same as the first quarter, a tenth above the 0.8 percent forecast. Wages and salaries rose 0.9 percent, benefits 1.0 percent. [1]

The number that matters for the argument is the annual one, and it did not move: total compensation growth is 3.4 percent year over year, unchanged. [1]

June PCE inflation was 3.7 percent.

Subtract, and real compensation is running three tenths of a point behind prices. Not accelerating. Not spiraling. Losing.

This week the Federal Open Market Committee held its target range at 3.50 to 3.75 percent for the fifth consecutive meeting, with three of twelve members dissenting in favor of an increase: Beth Hammack of Cleveland, Neel Kashkari of Minneapolis, and Lorie Logan of Dallas. [2] Chair Kevin Warsh's framing was conditional: "If inflation continues to be elevated through the forecast period, interest rates could well be part of that solution." [2]

Part of what solution, though, is the question the committee's own statement answers. Inflation "remains elevated relative to the Committee's 2% goal," it reads, "in part reflecting supply shocks that have driven price increases in certain sectors, including energy." [2] The supply shock in that sentence is a closed strait and crude above 80 dollars. A federal funds rate does not reopen a shipping lane.

The steel-man for the hawks is real and worth stating: 3.7 percent is nearly twice the target, expectations can unanchor regardless of what causes the initial shock, and a central bank that waits out a supply disruption can find the disruption has become general inflation. That is a genuine risk and a defensible reading.

What the ECI removes from that argument is the wage channel. Whatever is keeping prices at 3.7 percent, it is not workers extracting compensation faster than output, because compensation is not keeping up with prices at all.

The market has already priced the hawks. Freddie Mac's 30-year fixed mortgage hit 6.66 percent this week, a fourth consecutive weekly increase and a one-year high, with applications down 6.4 percent. [3] Anthony Smith, senior economist at Realtor.com, put the connection plainly: "With the Fed signaling that its next move is more likely a hike than a cut, near-term rate relief looks unlikely." [3]

The household arithmetic reads like this. Pay up 3.4 percent. Prices up 3.7. Gas up 96 cents a gallon on the year. Mortgage at a one-year high because three officials would like money to cost more. We reported the income and PCE halves of this squeeze yesterday; the ECI is the third leg, and it points the same direction.