With inflation above 8%, that means real wages have fallen at a 3% rate.

Fed's concern is only the part of inflation that

1) it can change, and

2) is self sustaining.

Only that part of inflation that goes trough wages is self sustaining for a long term. If wages don't increase, demand decreases when people can't afford to pay.

Sometimes demand doesn't decrease, but is replaced by low quality items. This applies to basic needs like food, hygiene etc...

All that is needed is monetary value of items to decrease.

8% is the monthly inflation (0.7%) annualized. We haven’t even had a full year of really high inflation.

I believe if you calculate it, inflation has been ~6%/yr over the last 2 years.

So a 5% rise in wages is almost keeping up with inflation this year.

Someone can check my math using the CPI-U numbers.

Like, the other commenter said, it's YoY, and a subtle mistake to think you can compartmentalize it to monthly is YoY / 12. Often what can happen is a sudden spike, like 8% inflation, where every month for the next year would turn out as 8% even though the month-to-month is flat every month except for the one sudden 8% jump.

Monthly = YoY / 12 iff inflation is linear and steady. (it almost never is)

Above 8% is YoY. Last release was May 22 at 1% MoM adjusted, which is 12.6% annualized.

CPI-U June 2020: 257.2

CPI-U May 2021: 268.6

CPI-U May 2022: 291.4

2020 to 2021 was 4.4%, 2021 to 2022 was 8.4%.

https://fred.stlouisfed.org/series/CPIAUCSL

Wage growth by itself means nothing if not compared with something else like inflation.