I wasn't trying to differentiate between growth and improvement, I meant to use them interchangeably, apologies for the confusion. What I meant is the relative amounts in the BLS chart are prone to being misinterpreted because that growth is compounding and the time periods depicted don't correspond to the time period we are interested in.

I realize the findings from these studies are tentative; in such a short timeframe such conclusions have to be. But I don't really see much open contention regarding the key question here, which I think is "Has AI had an impact on national level labor statistics?"

E.g. the conclusion you quoted simply says that it is not clear if this is a temporary uptick or a sustained boom. But it agrees that there has been a significant positive impact on labor productivity already, even if the impact on TFP is more modest. Which is what the St. Louis study looking at survey data, and corroborated by various other data sources, finds too.

If the question is whether this is a sustained "productivity boom", I agree that we don't know that yet. But if the question is whether there has been any productivity impact at all, I would say there are multiple indications of that.