The latest inflation data was roughly in line with expectations , showing price increases continue to cool on an annual basis as investors debate when and how deeply the Federal Reserve should cut interest rates.

And while inflation was the reason the Federal Reserve began hiking interest rates, the central bank's other mandate, maximum employment, is now moving to the forefront amid the rate cut debate.

"These [job] payroll numbers are really where the action is going to be over the next couple of months," Citi global economist Nathan Sheets told Yahoo Finance . "That's where the Fed is going to be focusing by far the most of its attention."

Economists argue that with inflation now tracking below the Fed's 2% target on a three-month basis, the more concerning trend in economic data lies in the labor market, where the unemployment rate has been steadily rising and monthly job additions have been falling.

"We're at that kind of turning point right now," Nicholas Brooks, the head of economics and investment research at ICG, told Yahoo Finance. "Whereas I think most of the focus over the past six months and beyond was on the inflation numbers and getting them back down again, now that the headline [inflation] number and the core [inflation] number are getting back down ... to the levels where the Fed is more comfortable, I think now the focus is turning more to the growth data."

A weak July jobs report helped tilt the focus toward the slowing labor market. The report showed the second-weakest monthly job additions since 2020 and the highest unemployment rate in nearly three years. The report also triggered a commonly followed recession indicator that shows that on a historical basis, the recent rise in unemployment typically builds on itself as labor market dynamics worsen.

While Moody's chief economist Mark Zandi told Yahoo Finance the focus on inflation won't disappear, the risks in the labor market are more elevated than those in inflation.

"The trend line suggests even higher unemployment and even lower inflation," Zandi said.

If that trend continues, Zandi argued, further deterioration in the labor market would likely lead to more Fed easing than if just declining inflation prompted rate cuts.

While the labor market has clearly cooled off, economists have found solace in the current dynamics, where the unemployment rate is mainly rising because more workers are coming into the labor force while fewer companies are hiring new workers — and not because companies are conducting mass layoffs.

This puts elevated pressure on layoff data, which Zandi said will be the "key statistic."

"Businesses have already pulled back on their hiring and thus the slowing in job creation," Zandi explained. "But fortunately, so far they've not increased layoffs to any significant degree. But if that were to happen, then we're in a different ball game. Recession risks would rise much higher than I'm currently anticipating."

Zandi, who said he currently sees a roughly 33% chance of a recession in the next 12 months, noted that weekly jobless claims will be a key release to watch when tracking layoffs.

Last week, initial filings for unemployment insurance fell more than expected, offering some relief to markets worried about further signs of deterioration in the US labor market.

The next release of weekly claims is slated for Thursday morning. Economists expect 235,000 claims were filed, a slight uptick from the 233,000 claims filed a week prior.

Josh Schafer is a reporter for Yahoo Finance. Follow him on X @_joshschafer .