Casey Mulligan is a very well respected economist - I should point out to those who don't realize - but he's done a lot of sloppy blogging, particularly in criticizing Keynesian understandings of the crisis, that I've drawn attention to several times on here. Sometimes his own data disproves his point (as in the summer employment post).
This time I'm outsourcing the critique of Mulligan's most recent post to Nick Rowe. People need to keep aggregate and disaggregated (i.e. - relative) effects distinct.
Nick also has this great warning at the end: "Of course, we could say that same thing about people who draw conclusions about macro fiscal multipliers from estimates of micro fiscal multipliers. They are mistaking shifts in relative demand for shifts in aggregate demand."
And there are a surprising amount of people who make this mistake. The most recent example I've seen is Matt Yglesias's intern goofing this blog post of an alleged example of Keynesianism in South Carolina (where I am now on a site visit, as it happens). I've also criticized several studies lately for doing the same thing with state-level estimation of fiscal multipliers. Fiscal multipliers need to be measured relative to a counterfactual of the same aggregate you are looking at. You cannot make relative comparisons. There are spillover concerns and there are also crowding out concerns (I think this is the sort of thing Nick has in mind at least).
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