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.
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).