Wednesday, January 6, 2010

Summers on Tax Incidence

I've long been "meaning" to read and critique more Larry Summers papers...

Finally, I was assigned to read one in a course I'm auditing, entitled "Tax Incidence" with Larry Kotlikoff.

On some level, the paper is basically fine. However, it falls into the category of what I like to call "pre-Modern" Economics, as the premise of the paper is that "we" know nothing about human behavior except that humans are uber-rational machines. It is a paper chalk full of obviously erroneous assumptions such as "all agents are the same" and "Production exhibits Constant Returns to scale" while maintaining innocence that the conclusions are a product of the assumptions...

Take the first (seemingly harmless) insight that tax incidence need bear no correlation with who bears the legal incidence of a tax. And that who bears the legal incidence will make no difference to the equilibrium price or quantity. It's a fascinating insight! Except it's not true in the real world case.

Theoretically, fine. But as Larry Summers himself would be wont to say "There are idiots. Look around..." If the government taxes each carton of milk, and charges the company directly, so that a consumer sees only the post-tax price when they walk into the grocery store, there will be a different equilibrium outcome than if the tax is not levied until the consumer gets to the cash register... Should there be? No. But, people are, well, people. $1.99 with 5% tax later looks like a better deal than $2.09. The milk-producing folks might well be better off with the tax incidence falling on the consumer...

But, whatever, you say, you can't expect someone to theorize about everything at once. Fine. The next section in the paper deals with factor taxes. Summers & Kotlikoff just consider the homogenous-worker tax incidence case. Some things, such as "a tax on capital doesn't affect the real wage in the short run" are obviously conclusions that will not extend to the real world case (although I suspect, in this case, the authors realize it).

More strikingly though, the basic conclusion that, when taxing factors, the more elastically demanded and inelastically supplied factor will bear the burden of the tax, does not hold if we start relaxing some of our assumptions (which nobody believes anyway). Let's assume everyone, and every job is not the same. Let's look at NFL teams -- clearly the quarterback position is the most important on the team. The Colts demand for Peyton Manning is clearly more inelastic than Peyton Manning's supply of labor to the Colts. If the Colts unilaterally announced they would cut his salary to $5 million, Peyton could threaten to sign w/ Tennessee and could easily get way more (in which case, how many seconds would it take the Colts to come crawling back?). On the other hand, for lineman and/or wide receivers, especially the second-stringers, its quite plausible that the Colts demand for these guys is quite elastic (second-stringers are easy to replace), while at the same time, the Colts have an inelastic demand for some second string lineman.

Summers' theory suggests that, when we tax Peyton Manning, the incidence should not primarily fall on Peyton Manning. But if Peyton were taxed by declaring all income over $5 million taxed at a 99% rate, Peyton would likely just settle for $5 million since it's not the Colts organization which is insulting him. Now, with more room under the salary cap, the lineman, receivers, and second stringers would be getting more. The incidence falls completely on Peyton Manning, even though he's the guy, according to Summers' analysis, who can't be touched by taxes.

Am I cheating here by relaxing so many assumptions? And, isn't the NFL a special case? Well, in a sense yes, and in a sense no. Summers' didn't mention that there isn't just one labor supply curve, that if the Colts offer Peyton less or more he'll react differently than if the government taxes Peyton less or more (even if it's the city of Indianapolis which taxes him to pay for inner-city education). Or that Peyton Manning will have a different supply curve if the Colts offer him $5 million, but promise to sign a pro-bowl lineman with the proceeds. And Peyton's labor supply curve for playing for the Colts is different than his supply for playing football at all.

In the last section, he considers an OLG model, which implies that a higher tax on capital reduces the capital stock and the real wage.

How might we tweak this model? Instead of assuming everyone is the same, we could merely assume two types of Agents. The first type is the Walton family, and the second type are workers who work at Wal-mart. The ultra-rich tend to do the lions share of saving, so let's assume the workers all have tight budget constraints, while the Walton family all goes to grad school until they are 40 and then soothe their soles working on humanitarian projects in between ski trips to Aspen. In other words, let's assume the Waltons are rich enough they are at or near a satiation point.

What happens now when we increase the tax on savings? Well, nothing really changes, especially if the taxes get refunded, lump-sum. The workers weren't saving anyway, and the Waltons are basically satiated enough to the point where they are just giving money away... Now, probably the real world is somewhere in between my story and their story, but, nevertheless, the conclusion of Summers and Kotlikoff "Thus, an interest income tax compensated in the second period unambiguously reduces capital intensity. This means that the pre-tax return to capital rises and the wage falls. The tax is thus at least partially shifted to labor." only follows because of the authors assumptions, assumptions which do not happen to hold in the real world case...

Of course, there are dozens of ways we could relax the assumptions and reverse tweedle-dee and tweedle-dum's results. We could assume, for the poor group, that their consumption largely consists of education, food, and health care expenditures, and that productivity in the second period depends on consumption in the first. In this case, the larger the tax on capital, the higher productivity is, and the higher the steady-state capital stock. But, of course, if the capital stock mostly consists of the Waltons' vacation homes, this might not even be a good thing!


  1. A little off topic but I have been thinking a lot about your interest in development economics and whether one economics textbook is better than the other.

    Most of these economics texts are damn near worthless (at best) and misleading and pernicious nonsense (at worst.) The fatal flaw most of them share is that they seem so clueless about how the industrial superpowers got the way they did. And face it, if you don't understand the "successes", there is NO possibility you can understand the "failures." And so a book on sub-Saharan problems of development is about as useless as the views of Victorian Protestant missionaries.

    Which leads to recommendation #1. Get your arms around the basic facts of the Industrial Revolution. Yes, this is a HUGE topic but there are two utterly delightful books to use as a starting point. Jacob Bronowski's "The Ascent of Man" and James Burke's "Connections." Both are companion volumes to documentaries done for BBC / PBS. Yes they are British, but when it comes to the history of industrial development, it's a fine place to start. You can fill in the German and Japanese gaps later.

    Then read Veblen's "Instinct of Workmanship." It was his magnum opus--by his own description his best book (by far!) And what I find so interesting about it is that he turns the newly-invented tools of cultural anthropology on the industrial explosion of capability that was happening all around him. Sort of a 1914 Burke and Bronowski from POV of the son of successful American pioneers.

    And not to be too immodest, but I believe the first eight chapters of my "Elegant Technology" is a damn fine effort to describe industrial development. I have devoted most of my adult life to understanding how the industrialization of North America happened--mostly out of pure curiosity. A one point, I was actually granted a 19-claim product-by-process patent for my attempts to add a little bit to the industrial heritage of USA.

    "Elegant Technology" is available as a .pdf file at my web site.

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  3. Jon -- Many thanks for the info! I'll confess I've never read Jacob Bronowski's "The Ascent of Man" and James Burke's "Connections", I haven't got Veblen's "Instinct of Workmanship" or your "Elegant Technology"...

    That's something I'm going to have to remedy!

  4. «It is a paper chalk full of obviously erroneous assumptions such as "all agents are the same" and "Production exhibits Constant Returns to scale"»

    Those absurd assumptions are essential to proving the central truthiness of Economics, that the distribution of income is justified by productivity and creativity.

    «while maintaining innocence that the conclusions are a product of the assumptions...»

    That's the principal tool of Economics in ensuring that the central truthiness is endorsed: ensuring that the assumptions are a product of the conclusions.

    Economists who are going to have a rewarding, well paid career figure out which conclusions the market for Economics opinions demands, and then ensure that the assumptions are a product of those conclusions. It is a simple demand-supply example.

    What matters then is that the conclusions be quotable sententiously in the mass media, which do not bother mentioning how absurd the assumptions are or broken the math is.

    For example Greg Mankiw very approvingly mentioned some time ago a paper proving that 70% of the incidence of corporate taxes is on employees:

    He did not mention at all that the assumptions were manufactured to reach that conclusion as it does not matter; what matter is reaching the "right" conclusion so it can be quoted sententiously by Economics professors and their sponsors in the corporate propaganda machine.

  5. «Jacob Bronowski's "The Ascent of Man" and James Burke's "Connections", I haven't got Veblen's "Instinct of Workmanship" or your "Elegant Technology"»

    I'll have a look at some of these. For development economics I like "The wealth and poverty of nations" of Landes, which is from a fairly conservative/rightist point of view, but an informative, interesting one.

    Also, old-style European (and Italian) development political economics tends to be far more interesting than Usian Economics.

  6. I loved Landes, despite the fact he's hopelessly Euro-centric. He's occasionally on to something, and a masterful storyteller...

    Do you have any specific recommendations for old-style European or Italian development policitical economists? and what is "Usian" Economics?

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