For more than two years, the economy's big problem was inflation — it was the key irritant for policymakers, the White House and American consumers.

• Today's Consumer Price Index report confirms that is no longer the case: Prices are no longer rising rapidly, which means the battle to kill inflation appears all but over.

Why it matters: Inflation looked to be coming down alongside a still-flourishing economy — until recently. The string of upbeat inflation data is all but certain to allow Fed officials to more comfortably shift their attention to the weakening labor market and lower interest rates.

What they're saying: "[T]he cumulative improvement in the overall inflation data over the past year now gives the Federal Reserve cover to move into risk management mode with the intent of protecting and preserving the soft landing," Joe Brusuelas, chief economist at accounting firm RSM, wrote today.

By the numbers: Overall CPI rose 2.9% in the 12 months ending in July, dropping below 3% for the first time since 2021.

• Core CPI, which excludes food and energy prices, rose 3.2% — the smallest increase in three years.
• By a different measure, inflation looks more benign. Over the last three months, core CPI rose 1.6% on an annualized basis, down from 2.1% in June.

Zoom in: Prices for many key items increased more slowly — or, in some cases, got cheaper over the month.

• Grocery costs have been rising at a mild pace since February, including a 0.1% increase in July. Prices are up just 1% compared to the same time last year.
• Used vehicle costs fell 2.3% in July, a bigger drop than that seen the previous month. New vehicle prices fell 0.2%, the sixth-straight month of price decreases.

The intrigue: The bad news was in the housing sector, where prices have kept upward pressure on inflation.

• The shelter index is a huge component. It accounted for over 70% of core CPI's 12-month increase through July, the government said.
• The sector is "solely responsible for core inflation remaining above the Fed's 2% target," Preston Caldwell, senior U.S. economist at Morningstar, wrote today.

In the CPI report, the rent index rose 0.5%, up from 0.3%. Owner's equivalent rent, which the government uses to account for inflation in homes that people own, rose 0.4% after slowing in June.

What to watch: The question in recent weeks has been how drastic of a cut the Fed will make at the conclusion of its next policy meeting in September — rather than whether it will do so at all.

• The odds that the Fed would cut by a quarter of a percentage point rose to 54% after the inflation report, according to CME's FedWatch tool.
• As of yesterday, odds of a half-percentage point cut looked slightly more likely.

The bottom line: The incoming data about the health of the labor market will ultimately determine that call.

• "This is now a labor data-first Fed, not an inflation data-first Fed, and the incoming labor data will determine how aggressively the Fed pulls forward rate cuts," economists at Evercore wrote in a note this morning.

The number of Americans applying for a mortgage just hit its highest level since January 2023, while the number of refinance applications surged to a level not seen since May 2022.

Why it matters: The number of Americans taking out new mortgages is still extremely low — but at least it's growing.

The big picture: Lower long-term interest rates means lower mortgage rates, and an opportunity for folks who took out expensive mortgages to refinance and get a little bit of relief on their monthly payments.

By the numbers: The average new 30-year fixed-rate mortgage is now 6.5%, which is still higher than the overwhelming majority of outstanding mortgages.

• That's depressing both purchases of homes and refinance activity.

The bottom line: Even at its 19-month high of 251, the composite index of mortgage applications remains lower than at any point between January 2000 and September 2022.