The other day I noted a San Francisco Fed study that claimed recent above-trend productivity growth in the U.S. likely reflects a fundamental upward shift in productivity, as opposed to an aberrant blip associated with employer caution in hiring plans (and hence an unsustainable squeezing of the existing labor force that may look like a permanent rise in productivity where there has been none). The evidence in favor of the fundamental shift story is the observation that productivity gains have been shared by states that have led the economy in employment gains, the idea being that these are the states with businesses that are no longer infected with employer malaise.
In response to the study's conclusion that the evidence is consistent with the fundamental productivity shift hypothesis, I closed my post with this comment.
"Consistent with" isn't exactly proof, of course, and a negative relationship between productivity growth and employment growth might emerge if other differences across states are controlled for.
In response to that, faithful reader godement asks what I might have in mind. That's a good question -- Bernard always asks good questions -- so here's an example.
Suppose that the "business caution" hypothesis is actually true, and suppose, for the sake of argument, that total U.S. employment is not growing at all. Now imagine that there is a third factor -- tax policy, say -- that is causing firms to migrate from one set of states to another. In this case, there will be no correlation between employment growth and productivity growth across states -- the "proof" offered in the article -- even though each firm is individually hoarding labor because of concern about future growth prospects, labor costs, or whatever. In fact, in my example there is no variation in the data that would allow any inference to be drawn if the econometric exercise appropriately controls for the remixing of employment from one state to another.
I'm not, to be sure, arguing that this is the case. I'm generally sympathetic to the conclusion that the San Francisco folks draw. But I don't think the case is quite closed.