Hoisted from comments -- still more on Mankiw's assumptions

Following this and this, here's the latest in my ongoing debate with David over Mankiw's use of assumptions.

Drawn from a longer comment, here's David:

Assumptions may be very sensitive in a model such that if they deviate even slightly, then the results change substantially. And, of course, some assumptions are robust to substantial changes. It would seem that this is the language that Mankiw is speaking in, according to the few short quotes in the past post.

This seems to me to be a different question when evaluating the policy conclusion. For example, I don't believe that all workers earn their Marginal Product (and in some sense there's no way that we could ever tell). In this sense, Mankiw is mostly likely wrong. However, I do strongly believe that there is an important relationship between productivity and wages. The more productive a worker is, the more he or she will likely be paid. This latter formation is much less precise than the former, but I would submit that they carry very similar policy conclusions. Importantly, the assumptions necessary to make the latter statement are much more robust than the former.

Here's my reply (adapted from a previous comment):

David,

Everything you've said is correct but here's the problem: at the level of generality you're talking about, everyone from Mankiw to Paul Krugman to Dan Ariely is in agreement, but many of Mankiw's arguments seem to require much more specific definitions. Rather than being robust, they are so sensitive that making small, common-sense changes can do great damage.

Keep in mind I'm a statistician, not an economist, so I may be getting some of this wrong but let's assume (except for workers on commission -- I'll grant you linearity for that one) the relationship between a worker's productivity and wages is generally monotonic but with plateaus and possibly even the occasional local optimum. I'm not saying this is the case but I suspect it's a pretty good description of what's going on. More importantly, I wouldn't be comfortable assuming this isn't the case.

I'm pretty sure some of Mankiw's arguments break down if you make this assumption. There's a luck factor now as to whether a change in productivity will result in an increase in wages. You also have an asymmetry problem -- the employer has a better idea where the plateaus are.

Or look at his statements about the inheritance tax. He assumes that one component of money's value to a worker is the pleasure of leaving money to an heir (so far, so good) and that the value of that component holds its value even as the inheritance gets well into the millions. If parents start to worry progressively less about each dollar after, say, the first million then the other value components (such as spending, bragging, charitable giving) will swamp the inheritance component long before the inheritance taxes kick in. If this is true, Mankiw's policy arguments simply collapse.

In other words, if pundits' arguments are sufficiently robust or their assumptions are obviously true, they can do what Mankiw does. Unfortunately, neither case applies here.