The optimal taxation of Manhattanites

Matthew Yglesias dismisses the argument that $250,000 isn’t “really rich” in Manhattan:

Allison Schrager offers what is I think my least-favorite economic argument, the regional variant of the old people who buy expensive houses aren’t rich because their houses cost so much switcheroo…

“Perhaps fairness also requires that the tax code account for the higher cost of living in some areas. The income cut-off for tax increases floated by President Obama is $250,000. That sum buys you a lot more in Fargo than it does in Manhattan. Most high earners live in expensive areas. They command such high salaries, in part, to offset their high cost of living.”

But that’s not to say that $250,000 buys “more housing” in Fargo than it does in Manhattan, it’s to say that it buys worse housing. The people in those expensive Manhattan apartments are paying for the positive amenity value. They could move to the Bronx, but they don’t want to. Similarly, Manhattan is full of restaurants that don’t exist in Fargo. There are law firms in Manhattan and law firms in Fargo, but the Manhattan law firms are better. Service professionals move to New York to peddle their services because the city features a critical mass of well-heeled clients who can pay top dollar for the best hairstylists or dentists or architects in the world. Fargo’s not like that…

I’m with Yglesias about the $250,000: that income officially makes you rich everywhere. As a practical matter, I also agree that the tax code shouldn’t account for the “cost of living”. But from a theoretical perspective, there is some basis for the idea that Manhattan should have higher federal tax brackets than the rest of the country.

Let’s go back to a fundamental result in the theory of optimal taxation: the Atkinson-Stiglitz Theorem. This result demonstrates that if consumption and leisure are “separable in the utility function”, the optimal tax system should rely only on income taxation. Translated into English, this means that unless someone’s consumption decisions provide extra information about her underlying earning ability—information beyond what’s signaled by the level of income itself—it’s best to avoid taxing different goods at different rates.

As I pointed out in a earlier post, this result shows why some seemingly sensible propositions are wrong: the fact that demand for gasoline is highly inelastic doesn’t singlehandedly justify a higher gas tax. But Atkinson-Stiglitz is also useful in how it fails: it tells us when differential taxation might be reasonable after all.

In particular, if a certain type of consumption makes it easier to earn a high income (conditional on particular level of a ability), then the tax code should favor that type of consumption over others. The obvious candidate here is place of residence: it’s easier to earn a high income in Manhattan than Fargo. This doesn’t quite mean that we should set taxes based on the “cost of living”—a city might be more expensive because it has better amenities, not because it offers better income opportunities. (In practice, it’s usually a little of both.) But to the extent that cost of living is a proxy for income opportunities, it can play a useful role in the tax system.

Think about it this way: discouraging productive (but expensive) urban agglomeration is one of the efficiency costs of taxation. Normally, we think about the losses from income taxation along the labor/leisure margin: if the marginal tax rate on your labor income is too high, you’ll substitute away from labor and spend more time at home. (Perhaps you’ll retire sooner, or leave the labor force if you’re a secondary earner.) But the effect on decisions about where to live is also a source of inefficiency. Maybe after moving from Fargo to Manhattan, it’ll cost $50,000 more every year to maintain the same standard of living, and you’ll earn an extra $100,000. This should be a great tradeoff, but you’ll stay in Fargo if your marginal tax rate is higher than 50%.

In fact, if we change a few labels, we can think about this problem using another famous result in public economics: Diamond and Mirrlees’s demonstration that intermediate goods should not be taxed. Living in a high-powered city, after all, is just an “intermediate good” that makes labor more productive.

Now, in the real world I don’t think the tax code should discriminate according to place of residence. First of all, we don’t have any accurate measure for the extent to which cities improve productivity; we only have cost of living, which is an incredibly indirect proxy. Second, changing the tax code along these lines invites endless political manipulation—how long before the “cost of living” is mysteriously estimated to be highest in swing states? Finally, and most importantly, the high cost of living in the most expensive urban areas owes more to regulation-induced scarcity than economic fundamentals. Given the artificial supply constraint, lower taxes for Manhattan residents would be mainly a giveaway to incumbent property owners, not a way to encourage efficient concentration of labor.

But it isn’t ridiculous to think that a properly designed tax system might want to incorporate the fundamental differences between cities. In fact, in the lens of Atkinson-Stiglitz, it’s a lot more reasonable than most of the other breaks in the tax code.

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4 Comments

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4 responses to “The optimal taxation of Manhattanites

  1. ed

    I’m not sure this argument works if the amount of housing in Manhattan is limited. In the extreme case, assume housing is fixed. Then Manhattan is full, and anyone moving there will just drive someone else out (and indeed that’s why it costs so much, not because it is inherently expensive but because the prices are bid up by competition). Subsidizing Manhattan living like you seem to be suggesting cannot help if it is unable to increase the number of people in Manhattan. Am I missing something?

    Also, I believe Atkinson-Stiglitz says we should tax *labor* income, as taxing income from saving would have the effect of taxing current and future goods at different rates, when all goods should have the same rate.

    • Subsidizing Manhattan living like you seem to be suggesting cannot help if it is unable to increase the number of people in Manhattan. Am I missing something?

      You’re not missing anything. This was exactly my point in the second-to-last paragraph, where I said:

      “Given the artificial supply constraint, lower taxes for Manhattan residents would be mainly a giveaway to incumbent property owners, not a way to encourage efficient concentration of labor.”

      Also, I believe Atkinson-Stiglitz says we should tax *labor* income, as taxing income from saving would have the effect of taxing current and future goods at different rates, when all goods should have the same rate.

      Right—Atkinson-Stiglitz provides probably the cleanest theoretical explanation for why we should have zero capital taxation. Though I agree that it’s an important point, I didn’t want to get into this in the post (I feel that I go on for long enough already), which is why I elided the details a little and just said “income”.

  2. sunchaser

    I got a little lost in those papers, but I agree with your basic point. One point I would like to make (sorry if already made by Yglesias, I did not read his post) is that we have to think of costs of living in this case as a price signal. If we adjust tax code so as to offset those costs of living we are probably subsidizing inefficient city structure, size and (as you point out) regulatory environment. If cost of living is too high we need to let it serve as a signal that that city probably needs to shrink in size or change its regulations. There is some optimal city size for each city and nobody really knows what it is, so the best is to let the price mechanism decide what that is.

    On an unrelated matter, John Taylor wrote an interesting post on money multiplier on his blog, so maybe you can respond if you catch some time.

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