The federal government has two main measures of inflation. They don’t agree.

The federal government produces two ways to measure inflation: There’s the consumer price index — the August reading comes Wednesday — and there’s the personal consumption expenditures price index, which is the gauge the Federal Reserve prefers to keep an eye on.

You might think they’d be about the same, but think again.

It turns out, the CPI shows consistently higher inflation than the PCE. That’s because the two measures put different emphasis or weight on different prices.

Take housing.

“For shelter, it’s around 36% in the CPI and a little less than half of that in the PCE,” said Carola Binder, an economics professor at the University of Texas at Austin.

So the high cost of a place to live pushes up CPI more than PCE, opening a gap between them. That gap turned into a chasm last spring when the core CPI, which excludes volatile food and energy, was a full percentage point higher than core PCE. Wow.

The two inflation yardsticks have narrowed their differences since then as housing prices have eased. But Sarah House, senior economist at Wells Fargo, said this gap hasn’t gone away. Hardly.  

“So right now, the gap is about twice as large as it has typically been,” she said.

The gap is also caused by differences in how data is collected: The CPI asks consumers, “Hey, what are you spending your money on?” while the PCE measures all money spent by consumers and businesses.

Skanda Amarnath, executive director of Employ America and a former Fed economist, said when there’s a huge spike in consumer prices the gap — or wedge — between the two inflation measures widens.

“That wedge tends to blow out pretty dramatically, which is to say, CPI drastically outperforms PCE in a big oil or food or any general energy price shock,” he said. Or, say, during a pandemic.

Amarnath said as inflation settles down, the gap (or wedge or whatever you want to call it) between the CPI and PCE will get back to normal. But it’ll never go away.