Real wages are not increasing. The ‘Real’ part of real wages means after adjustment for inflation. See link, we’ve been going straight down in real wages. We are already back below pre-COVID wages. That means we are back to wage levels around 3 years ago. In any job if you got no raise in 3 years then you should not look at that as a good thing - and that’s what has happened to everyone, on average after accounting for inflation. https://fred.stlouisfed.org/series/LES1252881600Q
That's arguing about leading/lagging indicators, though. Wages go up with inflation, more or less by definition. Wage increases due to inflation can't be measured until after the fact, though.
Short version: "inflation" is not remotely the same thing as "recession", which seems to be the point you're trying to make. If your only evidence for an economic slowdown is prices and not production or consumption, you're likely confusing factors.
Clearly the truth is that the labor market remains strong. Most people are working. Most people have multiple choices in jobs. Most people are making more money (yes, in nominal dollars) than they were last year. Those are all signs of a healthy economy. They are not the only signs of a healthy economy, and there can be other aspects (like inflation) which are less desirable[1]
[1] Though probably 80% of the people who like to yell about it don't really understand it well. Inflation, by reducing the size of existing investments and debts (i.e. "stuff wealthier people have") relative to the economy as a whole (i.e. "wage levels for everyone"), acts naturally to reduce income and asset inequality. It's not entirely a bad thing.
You are intentionally conflating nominal and real wages, most people are not making more money. In real wages they are declining as per the link in my previous comment. If you make $100K per year and your expenses are $100K you make zero. If you make $150K but your expenses are now $150K then you have not made any increase in wages in real dollars. Wages are not flat or going up with inflation as per my link, they are actually declining significantly since COVID.
And my point, which you missed, is that this is a confounded argument. "Real wages" are an after-the-fact metric, you can't measure it in immediate data because wage growth and inflation are highly correlated.
And the other point, which you skipped, was that this was a digression anyway from the upthread discussion about whether or not the labor market indicators are "strong" or not. And they are: wages are tracking labor demand and growing at the same time participation is growing. That means the market is operating well (and, FWIW, that typical models would expect wage growth to continue to match inflation, as it generally does in functioning markets).
Both inflation and wages are lagging indicators and thus can be used together to get real wages historically. Correlation to inflation does not mean anything other than inflation and wages both increased, you can be highly correlated but not exactly correlated. Real wages demonstrate both wages and inflation in a single metric and they are not increasing at the same rate, real wages have been declining continuously since 2020. The strength of a labor market (low unemployment) just means people that are looking for jobs can find them but doesn’t measure the wages or inflation, that is determined by real wages. You can pay anyone more but if it doesn’t buy more it is still a pay decline.
