## Same Income, Varying Taxes: ERP #4

This is the fourth of four posts based on figures from the 2012 Economic Report of the President. For the first post and an overview, start here.

Amid the complexity and confusion of the U.S. income tax code, it\’s quite possible for people with similar levels of income to pay widely varying level of tax. For illustration, consider the table. The rows of the table divide up the U.S. income distribution into fifths, or quintiles. The last row shows results for the top 1% of the income distribution.  For each quintile–and for the top 1%–the columns of the table then tell about the distribution of taxes for that group.

For example, if one looks at the distribution of average tax rates for the bottom quintile, households at the 10th percentile of that distribution have a federal tax rate of -13.7% (that is, they receive refundable tax credits from the government). In the bottom quintile of the income distribution, those at the median pay 5.4% of income in federal taxes. (These calculations include income taxes and payroll taxes.)

Or look at the top 1%. Given the distribution of federal taxes for that group, the household at the 10th percentile of tax payments for this group pays 8.7% of income in federal taxes (presumably due to substantial tax-free investments, or perhaps to carrying forward losses from a previous tax year that count against income in this year). However, a household in the top 1% of the income distribution and the 90th percentile of the tax distribution for this group pays an average federal tax rate of 34.6%.

At least for me, there is something of a tendency when looking at tables like this one to feel as if some of those with high income are paying too little, and some of those with low incomes are paying too much. And maybe that quick reaction is correct. But the tax code has so many rules and provisions and exceptions and situations, that it\’s s also possible that if I knew the actual details of some of these taxpayers, the outcome would seem fairly reasonable to me.

The broader point here is that when a tax code becomes enormously complex and lengthy, it is also going to allow the possibility of considerable variation in taxes paid even for those with similar incomes. Even if all the individual provisions of such a tax code are defensible (an enormous \”if\”!), the tax code as a whole is likely to end up appearing arbitrary and unfair.

## Should the Top Income Tax Rate be 48% or 73%?

How high should the top marginal tax rate be: that is, how much should those with the highest incomes pay in tax not on average, but out of any additional marginal dollars they earn? In the Fall 2011 issue of my own Journal of Economic Perspectives, \”The Case for a Progressive Income Tax: From Basic Research to Policy Recommendations,\” Peter Diamond and Emmanuel Saez argue that a top marginal tax rate of 73% is justifiable. For comparison, they estimate that the current top marginal tax rate–combining federal income tax rates, Medicare payroll taxes, and average state and local income taxes–is about 42.5%.

The Diamond-Saez 73% top tax rate has occasioned some controversy in the blogosphere. For example, Scott Sumner expresses his disagreement in \”Saez and Diamond explain taxes in the Journal of Economic Propaganda.\” Brad De Long expresses his approval in \”The 70% Solution: Taxing the Rich Department.\” Paul Krugman also expresses approval in \”Taxing Job Creators.\”

To me, the most thought-provoking counterpoint to the Diamond-Saez paper is an article published two years ago in the Fall 2009 issue of JEP. In \”Optimal Taxation in Theory and Practice,\” N. Gregory Mankiw, Matthew Weinzierl, and Danny Yagan make a case that the top marginal tax rate should be around 48%–roughly the current level.

My goal in this post is not to take sides between these papers, and get shot in the crossfire. I have proud parental feelings toward all of the articles that appear in my own \”Journal of Economic Propaganda\”–er, \”Perspectives.\” But even a proud parent can note the ways in which his offspring differ from each other.

Both sets of authors start with the standard optimal tax theory, which is built on two pillars. First, taxing those with high incomes at a higher rate makes sense if the marginal utility from income declines as income rises. But second, raising the marginal tax rate will reduce the incentive to work. So any gains from greater equality must be balanced against reductions in incentives to work. But even when two papers use a fundamentally similar framework, they can reach different conclusions. I\’m still trying to work through the fine print of the two papers, but at this point, here are some of the underlying differences.

1) How does one value the marginal dollar to someone with a high-income as opposed to the marginal dollar of someone with a low income? Diamond and Saez, for example, apply a formula such that the marginal value of a dollar of consumption for the average household in the top 1% of the income distribution, with about \$1.3 million in income on average, is worth 3.9% of the marginal dollar of consumption for a family with median income of about \$52,000. The lower the value put on marginal dollars for those with high incomes, the higher the implied marginal tax rate. But any such comparisons involve some dose of value judgment.

2) How much do high marginal tax rates discourage work effort? This effect is quite difficult to estimate accurately, because what we usually observe in the real world is a change in tax rates and a change in level of income reported–which is not the same thing as work effort. For example, if higher top tax rates cause a number of taxpayers to find ways to take more of their compensation in the form of employer perks or deferred benefits or lower-taxed capital gains, the data may show that higher tax rates lead to less current income–but how much of this is due to shifts in the form of compensation and how much is due to less work effort is hard to dig out of the data. Especially at the top of the very tip-top of the income distribution, most workers don\’t fill out time cards, and they often have considerable flexibility in the form in which they are paid. Of course, if higher marginal tax rates are highly discouraging to work effort, then there is a case for holding down those top rates.

3) As one simulates tradeoffs between equality and output, it\’s necessary to model the distribution of wages at the top of the income distribution. It turns out that how you describe that distribution matters. For the statisticians out there, Diamond and Saez argue that a Pareto distribution is a good fit, while Mankiw, Weinzeirl and Yagan argue that something between a lognormal and a Pareto distribution is a better fit. For the non-statisticians, imagine a graph of how many households have any given level of income. The right-hand tail of this graph, describing incomes of the very rich, will be getting \”thinner\” as income levels rise. The Pareto and lognormal distributions are two different formulas for how quickly the right-hand tail of income thins down. A \”fatter\” tail of high-income people tends to favor a higher marginal tax rate. The two sets of papers have a variety of other differences, too, like the extent to which capital income should be taxed and how this equity-incentive tradeoff should apply to the marginal tax rates of those with low incomes.

It is also fair to note that political beliefs probably play a role in these differences. Greg Mankiw is a Republican-leaning economist: he was chair of the Council of Economic Advisers in the George W. Bush administration and has been an adviser to Mitt Romney. On the other side, Peter Diamond is a Democratic-leaning economist: Barack Obama attempted to appoint him to the Federal Reserve Board of Governors, and when he was blocked by Republican senators, his name was rumored as a possibility for Obama\’s Council of Economic Advisers. To be clear, I\’m not suggesting that either author would consciously shade his analysis to fit pre-existing political beliefs. But I do believe that when working through a complex model with a number of discretionary choices, we all have a tendency to come out with what seems a \”reasonable\” answer–which often happens to be not too far from our preexisting beliefs.

For noneconomists, this difference in answers about top tax rates is frustrating. There\’s often a belief that economics is like an arithmetic problem–even if it\’s a complicated arithmetic problem–and it should have a right answer. But the study of economics isn\’t a cookbook with a set of ready-made answers. Instead, economics is a way of thinking that can be used by all political persuasions.

John Maynard Keynes once wrote (in the introduction to the Cambridge Econonomic Handbooks): \”[Economics] is a method rather than a doctrine, an apparatus of the mind, a technique of thinking which helps its possessor to draw correct conclusions.\” Indeed, debates among economists often seem odd to outsiders, because the shared framework is to use economic analysis to break down the arguments into their components, and then to use additional analysis and data to argue over the components. Frankly, I don\’t expect the Diamond-Saez and Mankiw-Weinzierl-Yagan authorial teams ever to reach agreement. But the ways in which they specify the components of their disagreement will be the basis of research in this area for years to come.