Back when inflation really started to take hold of the economy in 2021, many people were worried about a wage-price spiral. This means that wages were going up, and businesses would have to increase prices, which would lead to more wage increases, and so on.

Now, a new paper from the Federal Reserve Bank of San Francisco finds that didn’t happen. Rising wages, the paper concludes, are only responsible for about a tenth of a percentage point of the increase in the Fed’s preferred personal consumption expenditures price index.

So, not much at all. Why?

The PCE measures inflation in three categories: goods, housing services — like rent — and the very broad “nonhousing services,” according to Adam Shapiro, vice president of macroanalysis and economic geography at the San Francisco Fed.

“Hotels, restaurants, and then smaller categories, such as airlines, public transportation, haircuts and things like that,” he said.

And that’s where most of the inflation has been happening lately. Labor makes up a huge portion of costs in that category, but Shapiro found that “when a business’s cost structure changes — so if their labor costs increase — they don’t necessarily have to pass on those costs to consumers.”

So, as wages at the low end of the spectrum have risen, some companies have swallowed those higher labor costs by reducing their own profits.

Others have changed their offerings.

“For example, we don’t make decorated cookies anymore,” said Nancy Boehm, co-owner of Pint Size Bakery & Coffee in St. Louis. “They take a ton of time. You can’t really charge what they’re worth.”

Boehm’s been paying more lately for packaging like coffee cups and ingredients. The same goes for labor: she estimates she’s paying about 25% more. Her staff includes four bakers, three full-time baristas and one part-timer.

But she’s only raised her prices by around 10%. That may be about the most she can get away with, said Brad Hershbein, senior economist at W.E. Upjohn Institute for Employment Research.

“If you’re a local bakery and there’s another bakery down the road, you’re in more trouble if you try to raise prices,” he said.

But if you’re a well-known brand with a lot of loyalty, Hershbein said you might be able to raise prices by much more.