### A 0.82% Tax Rate

8/12/2012 06:09:00 PM
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Just passing along an interesting fact: vice-presidential candidate Representative Paul Ryan's proposed tax changes, Mitt Romney's tax liabilities in 2010 (the year for which he disclosed his tax returns) would have been equal to 0.82% of his \\$21 million dollar income. He actually paid about 14% that year. The reason for the difference is that Ryan's proposal calls for elimination of the capital gains tax.

There are two issues that this raises: one is just a practical policy consideration I want to mention, and the other is a hat-tip to the extensive economic theory on optimal taxation policies.

First, the policy issue. We have long segregated income from so-called "capital gains" from other types of income. We tax the latter at progressive rates, to try to ensure that poorer people do not pay as high a percentage of their income in taxes as the rich. But we have almost always insisted on a flat tax rate on income from capital gains. Why? The classic argument (which Romney uses often) is that a particular sale of an asset such as a stock or a house represents income earned over several years, but is only counted in a single year. If we taxed that at a progressive rate, then your tax liabilities would increase the longer you own an asset, which discourages long-term investment strategies. This is unfair. If you are lost, here is what I mean:
Suppose choose to become a real estate investor for the next two years. I have \\$100,000 to invest in 2012. Suppose that house prices go up 5% every year. I have a I have a choice between two investment strategies: one is to buy a house now for \\$100,000 and sell it in 2014 for \\$110,250--call this strategy A. The other is to buy the house now for \\$100,000, sell it in 2013 for \\$105,000, buy a different house in 2013 for \\$105,000 and sell it in 2014 for \\$110,250--call this strategy B. Either way, I earn a total capital gains over two years of \\$10,250. If we have a flat tax rate of, say, 20%, then I owe the exact same amount of taxes under both strategies: a total of \\$2,050 over two years. But if taxes are progressive, then it makes a difference. Suppose income under \\$6,000 is taxed at 10% and income over \\$6,000 is taxed at 20%. Then strategy A means you owe a total of \\$1,450, while under strategy B you owe a total of \\$1,025.
Since the income in 2014 under strategy A was in fact earned over two years, just like in B, you could argue that the \\$10,250 income in 2014 under A should be taxed at the lower rate of 10% even though it is larger than the \\$6,000 threshold chosen for this example. This is exactly the argument Mitt Romney has made to justify his low 14% tax rate--his income comes from investments he has held for many years. But there is a huge problem with this reasoning, which is that Romney makes roughly that amount every year. That is, unlike the example above where, if you look at the average income over the two years it is less than the tax bracket threshold, Romney's average income from investments is way, way above the highest tax bracket. So we simply cannot argue that he deserves a lower rate because it is income over several years--he would be in the highest tax bracket no matter what kind of investment strategy he chose.

This brings me to the economic theory behind capital gains taxes. In macroeconomics, it is common to solve what is known as the "Ramsey Problem" to derive the optimal tax plan needed to finance the government's (pre-determined) budget constraint. I thought wikipedia would have a good page to send readers to, but apparently not, so just looking at the first couple results on google, I would recommend you check out section 2 of this set of class notes from UC San Diego (I'm a Cornellian, so I won't vouch for these--but I'd be surprised if there were major errors) for further details. Anyway, the point is that when the government's powers of taxation are "complete" meaning that it can accurately measure and tax any factor of production as it pleases, then the Ramsey problem says that in the long run, it is optimal to eventually set the capital gains tax rate equal to zero. Maybe I am naively overstating the influence of economics, but I suspect that this result is the main reason why some people want to abolish the capital gains tax.

I wonder, however, whether they aren't misinterpreting the implications of the Ramsey result. It arises because the tax on capital gains violates the zero-arbitrage condition on the model, meaning that the government could potentially make more money by borrowing funds to buy up the capital stock, and then finance the government through the returns it earns on capital, allowing it to set all taxes equal to zero. That's quite a bit different than the story you hear from, say, John Taylor, which argues that the Ramsey problem says that taxing capital is inefficient--in fact, the Ramsey problem says nothing of the sort, since it has nothing to say about whether the government can manage capital more or less efficiently than households. The Ramsey result especially does not say that taxing capital won't generate much revenue, which is what Taylor has argued in the past.

Now, even if we suppose that, for whatever reason, we oppose the idea of the government engaging in financial arbitrage. On that basis, I have three objections to the Ramsey result as it is typically formulated:
1. The arbitrage condition is already broken, and not just by government taxation. The fact is that study after study shows a pervasive pattern of market's failing to eliminate arbitrage opportunities--investors, for some as yet unknown reason, are leaving billions worth of potential profits untapped. I'd like to see the tax implications for an economy in which prices are not arbitrage free. Unfortunately, I will have to wait, since while there are many theories on the arbitrage puzzle (or puzzles rather, there are tons), none is yet convincing.
2. The government's taxing power is not really complete. This goes back in part to the point about Romney's taxes--the fact is that a lot of that investment income is actually income from labor disguised as capital gains. This is a growing problem in the economy because increasingly, the labor supplied by CEOs, and executives like Romney is being compensated with stock options and dividends rather than wages. This completely reverses the Ramsey result--we have inputs into production (labor from executives) that can't be taxed directly by the government (because firms do not record their labor compensation as wages). Thus, since capital and executive labor are complements in production, solving the Ramsey problem says that we should tax capital gains, at least somewhat (the amount, of course, would also depend on the pervasiveness of the problems critiqued in 1 and 3).
3. The Ramsey problem typically assumes a single representative household. That is how we are able to claim that one tax system is "better" than another that allows the same level of government spending. But in reality we have heterogeneous households. This is highly relevant to the optimal tax rate on capital gains, since a disproportionate amount of capital gains income accrues to only a small percentage of households (the very rich one). The tax, then, affects different households differently, so it may well be possible to construct a capital gains tax that is non-zero and welfare improving, if the non-wealthy represent a significant portion of the aggregate "social welfare function" used in the Ramsey problem. This is essentially an offshoot to 2, since this does depend on what assumptions you make on the powers of taxation--we would not need to tax capital to achieve this welfare outcome if we allow for lump-sum taxation of the rich households. But a selective "head tax" would  be hard to implement (what is a "rich" household, any way?), and definitely unconstitutional (equal protection of the laws!).