Thursday, December 8, 2011

Inequality and Taxation

This seems what everyone is focused on - occupiers, partiers, people who want to stay in office, people who want to kick those people out of their offices, etc. Plenty has been written on this, but I'll extract a small sample here in an attempt to sharpen the ideas.

Let's start with the series that Robert Frank recently contributed to Slate. If you're unfamiliar with Frank, his view of the world is dominated by externalities. Why is inequality bad? That's because the filthy rich make the poor feel so bad that the poor will do any number of reprehensible things in an attempt to consume more. Frank is concerned with "habit."

Economists like to think about two kinds of habit - internal and external. With internal habit I care not only about my current consumption, but about my current consumption relative to my past consumption. I'm better off with more current consumption, but more past consumption makes me currently worse off. With preferences like these, I become accustomed to a high standard of living. I'm much happier if I have always been poor than if I am poor today and rich yesterday. Internal habit is used a lot in macroeconomics. You see it in estimated New Keynesian models, for example Christiano/Eichenbaum/Evans, and in work on asset pricing. I think this has more to do with adding free parameters to fit the data than any micro evidence to support the idea, but there you are.

In any case, internal habit is not going to help the arguments of people who want to redistribute income from rich to poor. Internal habit will tend to favor the status quo, as there will be large transition costs in terms of lost welfare from making the rich poorer. Further, if everyone in the economy has preferences with internal habit, I'm not sure what is Pareto efficient, or if anyone has even solved that problem. For all I know, you solve the problem and it looks completely goofy.

Frank is concerned with external habit - envy, essentially. This is an externality, sometimes called "keeping up with the Joneses." I am worse off the better off my neighbor is. In Frankworld the poor are so overcome by envy that we might as well take the wealth of the rich and throw it away. This would make the poor feel immensely better. Something like kicking a banker in the nuts. Conversely, the rich get some of their happiness from having more possessions than the poor, and flaunting all that stuff. Seymour Cray, for example, liked to build a sailboat every year, but apparently did not sail it. Each year, he would burn the old boat to make room for the new one. However, it's not clear we want to think of Seymour Cray as an example of the typical behavior of rich people. His Wikipedia entry tells us:
Another favorite pastime was digging a tunnel under his home; he attributed the secret of his success to "visits by elves" while he worked in the tunnel: "While I'm digging in the tunnel, the elves will often come to me with solutions to my problem."


Frank seems to think that external habit implies that we should all consume the same quantity. Thus, no more envy. Let's explore this idea further. External habit tells us something about the types of neighbors we like to have. Frank says that the best neighbor the richest person in the population could have is the poorest one in the population, as that makes him or her feel really good. But there is a problem, which is that the best neighbor the poorest person can have is the next poorest one. If you let everyone choose their neighbors, what will they do? This problem has actually been solved. Some of Ken Burdett's marriage models with search fit this exactly. The result is that there is positive assortative matching. Like types tend to match - poor with poor and rich with rich. Frank's theory thus explains neighborhood stratification, something which happens everywhere, and with a vengeance in St. Louis. So far, the theory looks pretty good.

However, note that you would also get positive assortative matching if the externality goes the other way. If any individual feels happier the richer their neighbor is, then we get exactly the same outcome, with the same neighborhood stratification. Similarly, suppose in the marriage matching story that every individual prefers a taller partner to a shorter one. Then, there will tend to be matching of tall types with tall types, and short types with short types. But if each individual prefers a short partner to a tall one, you get the same result.

So, which do you think it is? Do I prefer having a rich neighbor or a poor neighbor? If it's the former, and we follow Frank's logic, he has a lot of explaining to do. Given the conclusions he makes in the latter case, in the former case it would be a better society if we made one person enormously rich, with the rest of us living at subsistence.

What does Frank think explains the recent increase in income dispersion in the United States? The received explanation for this is basically "supply, technology, and trade." Changes in technology have changed the relative demands for high-skill and low-skill workers, high-skill workers are scarce because it is very costly to acquire the skills, and low-skill-intensive goods can be produced more cheaply abroad than used to be the case. A small amount of the increase in dispersion in income is due to the US income tax becoming less progressive. But Frank has a different idea. This also has something to do with technology, though.

Frank uses the example of music. Everyone in the world can now hear the best guitar player in the world, without going out of the house. So why should I pay any attention to the second-best guitar player in the world? Ultimately, the best guitar player in the world gets a huge market share, and second best gets close to nothing. Society then consists of a small number of stars getting enormous salaries and the rest of us getting close to nothing. But surely if second-best is willing to work for a little less, I might prefer that. Or seeing #500 guitar player in the local bar for a $5 cover charge could dominate paying $200 to sit in a nosebleed seat in Madison Square Garden to see #1.

What seems to make Frank's argument fall apart is congestion and scale economies. You can see this when he gets to his other examples. Frank wants to think of his university president, David Skorton, as one of these superstars. First, contrary to what Frank seems to think, my guess is that Skorton earns something in the range $500K-$600K. An odd characteristic of the market for university presidents is that the high-paid ones are mostly at schools you have never heard of. There may be a theory that explains that, but I don't think it's the one Frank has in mind. Second, Skorton was my university president once as well. People at the University of Iowa thought of Skorton as a good guy, but I don't recall the word "superstar" floating around.

Frank wants to dismiss corporate governance explanations for high executive compensation, but I'm not sure he's right. Small differences in the ability of a CEO may indeed make huge differences in corporate outcomes, but it's very difficult for a Board to discern those differences. How do you tell a good one from a bad one? Thus, you can't rely on those small differences to explain huge differences in compensation.

Finally, Frank gives us his solution to inequality, which is a progressive consumption tax. A consumption tax is sometimes thought to have some virtues relative to the income tax as a means for generating revenue, but as typically envisioned, it would also be less progressive than the income tax. Replace the current federal income tax with flat-rate value-added tax generating the same revenue (I'm neglecting the issue of deductions), and income dispersion will increase.

The problem is that, if the consumption tax is collected at the point of sale, it has to be a proportional tax. We can't have retailers checking their customers' total consumption, and even if they could there would be ways to game the system. Frank's suggestion is that consumers report their incomes and net asset positions, from which we can determine individual consumption, which we then tax progressively.

Frank thinks that a progressive consumption tax will cure all our problems. Frankly, I don't see it. First, Frank has not thought through the tax evasion problem. How easy would it be to cheat in this system, relative to the current one? The cheating one would want to do is to under-report income and over-report asset accumulation. The income under-reporting problem is one that exists currently, so that is no different. However, over-reporting of assets is something new altogether. One could imagine that over-reporting could be quite easy. This might amount to shady appraisals or asset valuation that could be very difficult to check.

Second, even if you can solve the evasion problem, what do you gain relative to a progressive income tax? With a progressive consumption tax, individuals have a greater motive for consumption smoothing over time. This works like an increase in risk aversion - not clear this is a good thing. Also, the consumption tax does not actually promote savings relative to the income tax, except because people are effectively more risk averse and will self-insure by saving more. Again, this is hardly a good thing. Otherwise, saving is just postponed consumption. If my current consumption is taxed and my future consumption is taxed, that's a wash in terms of the effect on savings. Indeed, ultimately the distortion shows up in labor supply.

Next, some people have shown interest in this paper by Diamond and Saez. A key result that seemed to get these people excited is the calculation of a top optimal marginal tax rate (including all taxes) of 73%, relative to the current rate of 42.5%. There are two key assumptions that Diamond and Saez make to come up with the 73% optimal rate. First, we should not care about the welfare (at the margin) of the rich people. This argument is based solely on the notion that marginal utility of income is low for the top income-earners. Second, Diamond and Saez use a "behavioral elasticity" of tax revenue with respect to the tax rate of 0.25. To see how this matters, if you use their formula and an elasticity of one, you get an optimal top tax rate of 40%.

Now, I know it is fashionable to dump on rich people, but I'm not sure we want to discount their welfare as much as Diamond and Saez want to. Preferences will matter here. For example, if we take internal habit persistence seriously, as some people like to, that could make us want to weight the rich and poor equally, by Diamond and Saez's logic. I'm not committed to habit persistence, but there may be some features of behavior that are not consistent with log utility, for example. Further, Diamond and Saez are thinking in static terms. In reality, there is mobility within the income distribution, and how much mobility is an important issue here. Given mobility within the income distribution, we all care, for selfish reasons, about how the rich are treated, as we all could be rich some day, or our descendants could be rich.

Finally, I have no idea where that "behavioral elasticity" is coming from, and I don't trust it. My best guess is that it includes none of the factors that I think are important in addressing the problem. What we need here is a dynamic general equilibrium model that can take account of the short run and long run effects of a change in the income tax schedule. My best guess is that "behavioral elasticity" means that Diamond and Saez are measuring the effects of tax evasion and the intensive margin of labor supply, and that's all. If so, I think they miss most of what is important:

1. There's also an extensive margin. Tax people at a higher rate, and some drop out of the labor force.
2. Taxes affect occupational choice. Some work by Manuelli/Seshadri/Shin says that the effect of taxes on human capital is big time. Why do I want to undertake a costly and risky investment for a very small payoff?
3. Entepreneurial activity has to be very elastic with respect to tax rates at the top end. Why would I want to risk my own wealth or that of my close family for a very big payoff with very low probability, if that big payoff is taxed at 73%?
4. The United States is highly dependent on highly-skilled labor that migrates here from other countries. With a top tax rate of 73%, the Indian engineers might prefer to work in India, and the Canadian professors might prefer Canada.

Thus, I think it is likely that tax revenue is much more elastic with respect to the tax rate, particularly in the long run, than Diamond and Saez are letting on. To evaluate this properly, you need a serious model, and they have not provided one.

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