Here is Noah Smith summarizing the implications that Brad Delong draws from Robert Lucas’s defense of microfoundations as theoretical assumptions:
This leaves modern macro defenders in the odd position of saying that it’s crucially important to model agents’ decisions, but totally unimportant to model them in a realistic way.
This is interesting—well, to me at least—because it speaks to a longtime interest I’ve had in the very different ways that contemporary political science and contemporary economics understand the term “microfoundations” (see, in chronological order, here, here, here, and here). In short, when political scientists use the term microfoundations, they tend to mean individual data. When economists use microfoundations, they mean assumptions about optimizing behavior.
I spell out the implications of this more fully in this comment in International Interactions (ungated preprint here).
It’s tempting to see Brad and Noah as advocating a position that is closer to the political science view of microfoundations as data. But I don’t think that’s actually right, they are just objecting to one particularly inaccurate set of assumptions, about “one infinitely-lived hyper-rational representative price-taking agent.” Put otherwise, they would probably not find it particularly revealing to “test the microfoundations” of a New Keynesian macroeconomic model, they would just advocate different ways of modeling individual and aggregate behavior. (But perhaps I’m wrong on that.)