One more exchange on Mankiw's assumptions

More from the ongoing debate.

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.

David,

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.

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.

The indispensable Professor Thoma

Having spent a lot of time recently on the issue of compensation, this post by Mark Thoma caught my eye:

Greg Mankiw complains that if taxes go up for people with incomes as high as his, he won't work as hard and that means he won't be able to leave as much for his kids. Incentives matter he says. If that's the case, I wonder why someone who is trying to take away the incentive for his kids to work hard and be successful on their own doesn't leave academia and become a high paid consultant.

I'm sure Greg Mankiw could clean up as a consultant. The same effort he puts into academics would be much more highly compensated somewhere else. The fact that he decided to become an academic in the first place indicates that it's not all about the money.

As Greg Mankiw makes clear every chance he gets, he's at Harvard. That tells me that the return to his ego is every bit as important as the financial return. I'd further guess that even if the New York Times stopped paying him for his column, he'd write it anyway. It's a boost to his ego and reputation that he'd want even without whatever small payment he gets for each column (he could make more by using the time to prepare a talk "to a business group, consulting on a legal case, [or] giving a guest lecture," so the opportunity cost of the column is quite high).

I have only anecdotal evidence for the following statement (but it is pretty damned extensive anecdotal evidence so here goes):

When it comes to assumptions, statisticians and economists (particularly freshwater economists) tend to take opposite approaches. Statisticians generally insist on running through more assumptions than the listener has any interest in hearing about, often including those of no relevance to the situation you're in. (A former manager of mine once joked that it was easy being a statistician -- whatever the question, you just answered "it depends.") Economists tend to leave assumptions unsaid, even the really important ones that probably aren't being met.

I can give you plenty of examples of these buried assumptions (if you can make it through a chapter of Freakonomics without finding a few you're not paying attention), but there are also economists who do their best to unearth these assumptions, to bring them back into the debate where they belong. One of the best and most diligent of those diggers is Mark Thoma.

Which brings us back to Greg Mankiw's recent column. On one level, Mankiw's argument is sound. Every product that reaches the marketplace did start with the producer asking "Is this worth my while?" Tax rates do factor into that calculation, so, yes, there can a situation where dropping the Bush tax cuts would cause someone to decide not to make a product.

But there are a couple of big assumptions here. First, since we're talking about a return to Clinton (not Eisenhower) era tax rates here, a product would have to be just barely worth doing now -- the drop in returns under the proposed change is very small. Since this is known economic territory, we know that Clinton's tax increase caused at most a trivial number of products and services to be dropped for the reason Mankaw suggests and the Clinton rates were as high or higher than anything proposed by Obama. (Mankiw gets around this by starting out talking about the income tax increases for people making over 250K then slipping in the estate tax about half a page down, leaving most readers with the impression that making the income tax slightly more progressive will cut his take home pay in half but that's more a case of lying through misdirection than of burying the assumption).

The second, and more important assumption is where Thoma really shines. The idea that a producer will stop making a product if the tax rate passes a certain point assumes that primary return on that product is taxable, an assumption that is in no way justified here. As Thoma points out, the compensation Mankiw receives in the form of ego-stroking and reputation-building far exceed the $650 he gets for each column. I would add to that the satisfaction of influencing the debate. Conservative groups spend millions of dollars getting anti-tax arguments in the papers. When Mankiw does it, the papers send him the check.

When the compensation for a product or service is overwhelmingly non-taxable, an increase in tax rates will almost never cause a provider to drop that product or service. Mankiw is smart enough to be aware of this (he is at Harvard, after all); he just doesn't want the rest of us to realize it.