Consistency

I was looking at Andrew Gelman's blog and saw his discussion of Ray Fisman's piece on compensation. I was especially struck by this statement:

Yet this aversion to pay cuts isn't good for workers or the American economy more broadly. More people end up losing their jobs than if wages were more flexible, and there are serious long-term consequences for the workers who lose their monthly paychecks. The negative impact on a worker's earnings, health, and even the earning prospects of his children lasts decades beyond the pink slip's arrival. Creative solutions—like the furloughs that cut government salaries in California and elsewhere—might help to make lower pay more palatable, by presenting the cut as a temporary measure and by creating at least the illusion of a lower workload. If we can find other ways of overcoming the simmering resentment that naturally accompanies wage cuts, workers themselves will be better for it in the long run.

I wonder how this links with tax increases. Greg Mankiw seemed to be quite displeased by the prospect of tax increases (which are a form of reducing compensation).

If this relation works the same way, then there are two implications:

1) Tax cuts are a terrible idea as a way of providing economic stimulus as they will do little to increase output (3 hours according to Fisman's experiment) but will be greatly resented if they are rescinded

2) High taxes (like low pay) seems to have little effect on income so if you rise taxes then you should raise them by a lot so you only feel the pain of resentment once.

I am not sure that this position is correct, but it sure is thought provoking.

Tax Policy

Mark has been discussing the concerns about the hardship that tax increases would inflict on those with an income exceeding $250,000 per year. In part I think that this line of discussion began with Greg Mankiw trying to use himself as an example of a person who might do less labor if the marginal tax rate increased. There were a number of great points brought up as to why this example had issues: see here, here, and here.

There was a second economics professor who also made similar claims although I found them a bit harder to evaluate as the example was not as clear. This argument seemed to be more about how hard this person would find it to make cutbacks rather than a specific example of how he would become less productive.

Yesterday,Noahpinion linked to a great article by Karl Smith that went to the heart of this discussion. The argument was whether tax increases (at the sort of marginal rates we currently have) really depress productivity. Karl Smith made a number of arguments that were worth considering, including:

Third, high income people don’t seem to be working that much more than low income people despite the fact that a natural propensity towards work can make one high income.

Indeed, the data show us that low income folks used to work a little more, but now they work a little less than high income folks. Yet, if the income and substitution effects were balanced for each person we would still expect higher income people to work more.

That’s because working hard can lead to more education, more experience and more promotions. Being hard working is also associated with having a conscientious personality type which is itself more valuable.

So if someone was simply born with a stronger propensity to work, we would expect that person to earn more income per hour. Thus we when look at the data we should see that all these high income people are working lots of hours.

Yet, we actually don’t see that. We see only a mild effect and even then that effect is not robust over time. Sometimes, high income folks are working less.

But the piece is a must read in the entirety. The key argument here, though, is whether the extremely small tax increases that are under discussion (a raise in the marginal tax rate for the highest income bracket from 36% to 39.6%) is really likely to make high income Americans less productive. Because if these tax increases don't disincent work and we accept that government finances really are a mess then the tax hikes seem to be a logical way to "share the cost of these increases".

But I also think that these points don't necessarily go far enough. Are we really convinced that a small decrease in productivity among the wealthy will be that devastating? What is the source of productivity in the American economy? Is it highly paid CEOs, hedge fund managers, lawyers and medical doctors, or is it the majority of workers who drive productivity?

I think it is essential to get this correct. A top down model of an economy (where the people at the top make the key decisions and are responsible for the output) did poorly in Soviet Russia. A bottom up theory of economic gains seems to make a lot more sense and that suggests that small productivity losses among the wealthy are not a serious concern.

It is worth emphasizing that, at this time, I am aware of two proposals to increase the tax rates of the wealthy: increasing the amount of wages on which FICA can be charged and returning to Clinton-era tax rates. Neither of these increases is a vast change in the marginal tax rate of this group. Clearly there are tax increases that would cause issues, but we can handle those when they show up and not now when all of the possible rates under discussion are sane.

The last example that people tend to bring up is innovation and how important it is to reward innovators. Now, as part of a first principle I would like to point out that the innovator is not always the person who profits the most from an invention (consider Nikola Tesla). But it is also worth noting, as Mark points out, that copyright law already provides enormous rewards for intellectual property holders.

So I think we should look to balance harms. Recent events have included layoffs of government workers into a economy with an extremely high unemployment rate. Are we sure that the consequences of a large body of long term unemployed workers will be better than that of small increases in tax rates?

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.

Hoisted from comments -- more on Mankiw's assumptions

David had this to say about my post critiquing the way Greg Mankiw and many other economist who defend the magic of the market don't spell out the highly restrictive assumptions they use in their arguments:

An often neglected aspect of these standard assumptions is that they are *sufficient* not necessary conditions. Perfect information, for example, might not exist, but that doesn't mean there won't be an equilibrium capturing all the potential gains from exchange.

These statements may well form a set of conditions that are sufficient but for the most part not necessary to support Mankiw's conclusions. You could say the much same foe some list of statements in most intellectually mature movements. With Mankiw, I'd go even further and say that if these statements don't have to be true; they just have to approximate reality to a sufficient degree in order to make his case.

But we're talking about something slightly but significantly different. In this context, these assumptions are part of the arguments that Mankiw is making. It is, of course, possible for invalid argumnts to lead to correct conclusions and you can have a trivially valid argument that starts with a false premise, but (putting aside those old logic lessons about the implications of the existence of unicorns) you can't have a valid and meaningful argument based on false assumptions.

It's important to put this in context. Mankiw is arguing that, in addition to being immoral, a return to Clinton era tax rates would cause a sharp drop in productivity and economic growth. It is possible that he's right, but there is considerable historical evidence and any number of counterarguments (many by Nobel Prize winners) that contradict his conclusions. Under those circumstances, I think the burden of proof should rest with the guy who's saying this time it will be different.

'Standard' does not mean 'sound'

Eric Schoenberg is raising some important points:

[Greg] Mankiw concisely summarizes the theory underlying the ethical argument for market capitalism: "under a standard set of assumptions... the factors of production [i.e., workers] are paid the value of their marginal product... One might easily conclude that, under these idealized conditions, each person receives his just deserts." Mankiw's long-standing opposition to higher taxes on the wealthy suggests that he thinks these conditions usually pertain in the real world, too.

Consider me skeptical. The list of "standard assumptions" open to question is long... I believe, progressives must directly challenge the claim that unfettered markets create just deserts. This won't be easy. Free market fundamentalists have the advantage of a simple message -- ending bailouts will deliver just deserts -- and of nearly limitless funds from rich folks who benefited from the bailout but are happy to claim that it should never happen again.

Mankiw's assumptions may all be correct, but they are not all self-evident. Some are at odds with experience. Some are in conflict with findings from related fields like psychology and behaviorial economics. Some are just hard to buy. These are the kind of assumptions that need to be stated and supported.

As mentioned before, the way language is used in the debate compounds the problem. The 'free-market fundamentalists' (to use Schoenberg's phrase) often affect a folksy, plain-spoken tone. They make common-sense statements like "people are rational" or "people respond to incentives." They generally don't add that they are using these terms in a technical, highly specialized sense.

Tax increases as landscape perturbation?

Over at Felix Salmon's site, Justin Fox presents an interesting counter-argument to Greg Mankiw:

[T]here’s a really fascinating tale in [Sam Howe Verhovek’s Jet Age: The Comet, the 707, and the Race to Shrink the World] involving tax incentives. During the Korean War, Congress enacted an excess profits tax meant to keep military contractors from, well, profiteering. In its infinite wisdom, Congress defined excess profits as anything above what a company had been making during the peacetime years 1946-1949.

Boeing was mostly a military contractor in those days (Lockheed and Douglas dominated the passenger-plane business), and had made hardly any money at all from 1946 to 1949. So pretty much any profits it earned during the Korean conflict were by definition excess, and its effective tax rate in 1951 was going to be 82%. This was unfair and anti-business. If similar legislation were enacted today, you could expect U.S. Chamber of Commerce members to march on Washington and overturn cars on the streets.

It being 1951, Boeing instead sucked it up and let the tax incentives inadvertently devised by Congress steer it toward a bold and fateful decision. CEO Bill Allen decided, and was able to persuade Boeing’s board, to plow all those profits and more into developing what became the 707, a company-defining and world-changing innovation. Writes Verhovek:

Yes, it was a huge gamble, but for every dollar of the dice roll, only eighteen cents of it would have been Boeing’s to keep anyway. For Douglas and Lockheed, both in a much lower tax bracket, that was not so easy a call.

So that’s it! High tax rates—confiscatory tax rates—spur innovation! Well, at least once in a blue moon they do. Which is an indication that there might be some important stuff missing from the classic economists’ view of taxation, as summed up by Greg Mankiw a few weeks ago:

Economists understand that, absent externalities, the undistorted situation reflects an optimal allocation of resources. It is crucial to know how far we are from that optimum. To be somewhat nerdy about it, the deadweight loss of a tax rises with the square of the tax rate.

Somehow I don’t think that formula held true in Boeing’s case.

This leads me to wonder if this reminds anyone else of algorithms that locate superior optima by slightly perturbing fitness landscapes (processes closely related to simulated annealing). Mankiw complains that certain taxes distort the economic landscape, but if local optimization is an issue (as was apparently the case with Boeing), then mild distortion from time to time is likely to lead to a better performing economy.

For background, here's an excerpt from a post on landscapes. The subject was lab animals but the general principles remain the same:

And there you have the two great curses of the gradient searcher, numerous small local optima and long, circuitous paths. This particular combination -- multiple maxima and a single minimum associated with indirect search paths -- is typical of fluvial geomorphology and isn't something you'd generally expect to see in other areas, but the general problems of local optima and slow convergence show up all the time.

There are, fortunately, a few things we can do that might make the situation better (not what you'd call realistic things but we aren't exactly going for verisimilitude here). We could tilt the landscape a little or slightly bend or stretch or twist it, maybe add some ridges to some patches to give it that stylish corduroy look. (in other words, we could perturb the landscape.)

Hopefully, these changes shouldn't have much effect on the size and position of the of the major optima,* but they could have a big effect on the search behavior, changing the likelihood of ending up on a particular optima and the average time to optimize. That's the reason we perturb landscapes; we're hoping for something that will give us a better optima in a reasonable time. Of course, we have no way of knowing if our bending and twisting will make things better (it could just as easily make them worse), but if we do get good results from our search of the new landscape, we should get similar results from the corresponding point on the old landscape.


* I showed this post to an engineer who strongly suggested I add two caveats here. First, we are working under the assumption that the major optima are large relative to the changes produced by the perturbation. Second our interest in each optima is based on its size, not whether it is global. Going back to our original example, let's say that the largest peak on our original landscape was 1,005 feet tall and the second largest was 1,000 feet even but after perturbation their heights were reversed. If we were interested in finding the global max, this would be be a big deal, but to us the difference between the two landscapes is trivial.

Greg Mankiw's reply -- dishonesty or just bad prose?

From Mankiw's follow-up to his NYT editorial:

Aren't you motivated by more than money? Of course. I have never suggested that money is my, or anyone's, sole motivation in choosing a lifestyle.

The phrase "sole motivation in choosing a lifestyle" is going to cause us some problems; it's difficult to rebut this kind of practiced vagueness, but we were talking about the choice to do certain work. If we read choice of lifestyle to mean choice of work, then yes, he did suggest exactly that.

Let's roll the tape:

By contrast, without the tax increases advocated by the Obama administration, the numbers would look quite different. I would face a lower income tax rate, a lower Medicare tax rate, and no deduction phaseout or estate tax. Taking that writing assignment would yield my kids about $2,000. I would have twice the incentive to keep working.

If doubling the money you're paid doubles your incentive, doesn't that suggest that your incentive is solely pecuniary?

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.