Here's David (pulled from a longer comment):
I think where we disagree (assuming that we do disagree) is on where the burden of proof should lie. As an economist, and based on my reading of the theoretical and empirical literatures, the burden is on the individual who claims there are important plateaus and such. This requires showing empirically that they exist, and not in a general sense, but on the relevant margin of choice for those individuals. My general sense is that most economists would agree with this placing of the burden of proof, and your suggestion of the consensus of various economists is consistent with my impression as well. In other words, to assume that there are important plateaus on the margin requires empirical justification, and substantial justification because its very difficult to understand labor markets if we deviate generally even moderately from this productivity/wages relationship. So while you agree that “…if pundits' arguments are sufficiently robust or their assumptions are obviously true, they can do what Mankiw does.” I’d say that the consensus to me amongst economists supports the arguments and broader type of assumptions that I discussed previously. I suppose that’s an empirical question, for which I have not yet looked for data.
It's easy to get lost in the weeds here, so I'll try to get a few specific points out of the way then address the bigger issue of of the way we treat assumptions in the economic debate.
First, when it comes to robustness, it is sufficient to show that deviating from an assumption would cause the model to fail. There is no need to show that a particular deviation (such as the possible plateaus I suggested) occurs, only that if it occurs problems will follow. The world is full of perfectly good models that are not robust. As long as the real world lines up closely enough with the model's assumptions, the lack of robustness is not an issue.
Robustness is, however, an issue when we go out of the range of data, and, given these unique times, every policy proposal goes outside our range of data. At this point the burden falls on the proposer to be explicit with assumptions and make some kind of case that they are being met.
We also need to be carefully to distinguish between individual and aggregate relationships. We know that raises and promotions occur at discrete points and bonuses are frequently capped. That means, for many workers, the relationship between wages and productivity can't be linear. It is, however, possible that when aggregated that relationship is linear (or at least close enough for our purposes). The problem here is that proposals that assume individual level linearity can sound a lot like proposal that assumes aggregate linearity. Once again, we need more caution and clarity than we've been seeing.
All of which lead to the main point: much of the economic debate (particularly Greg Mankiw's corner of it) has been based on arguments that aren't all that robust and assumptions that aren't immediately self-evident. Many of these arguments reach conclusions that are difficult to reconcile with the historical record (such as Mankiw's prediction that a return to Clinton era taxes would have dire effects on the nation). Under these circumstances, assumptions should not be left implicit and they certainly should not be depicted as broad and obvious when they are highly specialized and non-intuitive (Freakonomics being the best known example with Levitt's go-to "people respond to incentives." formulation).
In other words, in this situation, I'd probably argue that the burden of proof is on Mankiw; I'd certainly insist the burden of clarity is.