Measuring Redistribution

I recently attended a workshop at Stanford for a paper on the redistributive effect of the US system of taxes and expenditures, to what degree it transfers from rich to poor. The paper’s conclusion, based on its analysis of data from three earlier papers:

In short, there is robust evidence across definitions and methodologies, that the tax system has become more redistributive.

My conclusion from attending the workshop, with which I do not think the author delivering the paper actually disagreed, was that we do not know, probably cannot know, how redistributive the system is or was. The purpose of this post is to explain why.

Distinguishing Rich from Poor

The main source of data on income is tax records which record what an individual’s income was in a particular year. Using those, individuals can be classified by where in the economic ranking they fell that year, making it possible to say which were in the bottom quartile of the income distribution, the top tenth, the top percent. The researchers can then try to figure out how much tax each group paid and how much was spent on benefits to them. The greater benefits received minus tax paid, the more that group was being redistributed to. The more redistribution is higher for higher income groups, the more redistributive the system is.

To see what is wrong with this approach, consider a successful surgeon. For the first seven years of his adult life he is in college and medical school, earning very little, so probably in the bottom quartile of the income distribution. Any money he was given, any money spent on him, classifies as a benefit to the bottom quartile.

At 25 he gets his medical license, begins to practice, soon find himself in the top quartile, very likely the top tenth, perhaps eventually the top one percent. Taxes he pays, money given to or spent on him, is classified accordingly.

At 65 he retires to live on his savings in a house whose mortgage is fully paid for. Assuming that he does not continue to practice or do consulting his income is now social security plus, perhaps, modest capital gains or dividends from his investments. He is back in the bottom quartile for the rest of his life, say another thirty years. He has lived the life of a rich man but for about half of it he was classified, for the purpose of measuring redistribution, as poor.

The same problem exists for someone with a job that varies between feast and famine, three hundred thousand one year, twenty thousand the next. He too, for statistical purposes, counts as poor for about half his life.

In principle the solution to the problem is to classify people by lifetime income. For a single person all of whose tax returns you have it could be done but in practice there is no way of doing it for the whole population and none of the papers attempted it.

Who Pays What Taxes

An income tax is paid to the IRS by a particular taxpayer but that does not tell us who bears the burden of the tax, for reasons I have explained elsewhere. What about the corporate income tax? A corporations is a person only by legal fiction; money it pays must come from real people, stockholders receiving lower dividends, employees paid less, customers paying more. The papers assumed that the corporate tax was born either entirely by the stockholders or three quarters by the stockholders, one quarter by the workers.

Either is an arbitrary assumption, neither a plausible one. If stockholders find that they receive a lower return by investing in a US corporation than by investing in something else, here or abroad, they will reduce their corporate investment until the return is the same as the return in other investments; to the extent that capital is mobile, it cannot be taxed. It is not perfectly mobile; there are advantages to investing in your own country, reasons you might prefer to invest in stock rather than in something else, but it is probably more mobile, at least internationally, than labor or consumers, probably bears less of the tax than labor or consumers.

A second example is the social security tax. Nominally it is paid half by employer, half by employee. The employer pays some amount of money, the employee receives a smaller amount, the difference goes to the government. What matters is how much it costs to employ the worker and how much the worker ends up with, not how much of the total is handed to the government by the employer, how much by the employee. Similarly for a sales tax paid by the seller compared to a consumption tax paid by the buyer.

The problem of incidence, of who must reduce his consumption in order that the government can increase its, exists for all taxes. These are only some of the obvious cases.

Who is Money Spent On?

The problem exists for the benefit side of the ledger as well. Some expenditures, welfare payments or the Earned Income Tax Credit, take the form of money handed over to someone, but most of the budget does not.

Consider Medicaid. The total is almost a trillion dollars, mostly spent providing medical services to poor people. That gets counted in the research on redistribution as a transfer to the poor but it is not clear how much of it should be. Medicaid substantially increases the demand for the services of medical personnel, bidding up their salaries and similarly for hospitals and medical drugs. How much of the total spent should be counted as going to the poor, how much to doctors, nurses, stockholders and employees of drug companies? There is no way to know.

Counting What We Don’t Know

Income reported to the IRS is not a perfect measure of income, even of taxable income. Some people fail to report income that the IRS has no easy way of observing or classify what is in fact consumption as a business expense. If the rich do it more, the calculations based on IRS figures will overstate the amount of redistribution, if the poor do it more, understate it.

Every year the IRS selects a small random sample of returns to intensively audit. If we assume that that turns up most of the unreported income it gives us an estimate of how the amount unreported varies with income. Judging by that evidence, rich and poor are about equally successful in tax evasion, understate the amount of their income by about the same percentage.

If you accept that conclusion, as some of the researchers do, you do not have to worry too much about the income that isn’t reported on your calculations of redistribution. But you don’t have to accept it; the authors of one of the three papers did not, believed that rich taxpayers succeeded more than poor in concealing income from even the intensive audits. That turned out to have a substantial effect on their conclusions.

The Conceptual Problem

So far I have been talking about problems that could, in principle, be solved with enough data. A deeper problem is that it is not clear what question we are asking. Redistribution compares the result of the existing pattern of taxes and expenditures with an alternative, evaluates how different it is in the effect on different sorts of people. But what is the alternative?

The obvious answer is “the US as it is but with no taxes and no expenditures.” But with no taxes and no expenditures we would also have no courts and no police and no national defense and … . That would be a very different US. It might be a US with no security of person or property, in which case we should measure redistribution relative to that world. It might be a world where rights protection and dispute settlement were handled privately, perhaps along the lines sketched in my first book, in which case we would have to know what that world would be like, what the incomes would be of the people in our world. Things the government does affect people’s welfare in a wide variety of ways, all of which would stop.

The approach actually used, implicitly, by economists trying to answer these questions is to take the alternative US as the present US minus all taxes and all benefits, ignoring the internal contradictions in that picture. Everyone has the same job, the same private income, the same level of security of person and property he now has. That makes the question one that could be answered with enough data but it is not clear what the answer to that question would be relevant to.

The Distribution of Income

A lot of concern with how redistributive the existing system is or isn’t is motivated by concern with inequality of wealth and income, widely believed to be increasing. Whether it is increasing and by how much involves statistical issues that I do not know enough to comment on but I can offer some possible reasons why it might be increasing, reasons that have little to do with how redistributive the tax and expenditure system is.

The simplest is the change over time in the value of different abilities. Being physically strong is still useful in some jobs but less valuable and in fewer than it was a century or more ago. Intellectual ability, on the other hand, has probably become more valuable and relevant to more skills than it was a century, even a few decades, ago. Since brains and brawn are not closely correlated, a world in which both are valuable is likely to have a more equal income distribution than one in which only one of them is. And as intellectual ability becomes more important its uneven distribution produces an increasingly uneven distribution of income.

Another possible cause of increasing income inequality is the rise of the welfare state, at least if measured income does not include benefits in cash or in kind. The better the life of a poor person, the less the incentive to do difficult and unpleasant things to become less poor.

A third possible cause is the divergence between the lives of richer and poorer people, discussed at some length by Charles Murray in Coming Apart: The State of White America, 1960–2010:

Murray goes on to provide evidence that religiosity, work ethic, industriousness, family, etc., have either remained strong or have weakened minimally in the New Upper Class, whereas these same attributes have either weakened substantially or have become almost nonexistent in the New Lower Class. Much of his argument is centered on a notion of self-selective sorting that began in the 1960s and 1970s, when he argues that cognitive ability became the essential predictor of professional and financial success, and people overwhelmingly began marrying others in the same cognitive stratum and living in areas surrounded largely by others in that same stratum, leading to not only an exacerbation of existing economic divides, but an unprecedented socio-cultural divide that had not existed before in America. (Wikipedia)

The point about assortative mating, raised earlier in The Bell Curve by Murray and his coauthor, suggests a fourth possibility. To the extent that our society has become increasingly meritocratic, sorting by ability, smart people are increasingly likely to marry smart people. The lawyer or business executive marries his Harvard classmate instead of his secretary. That increases income inequality in the short run by combining incomes, in the longer run by making intellectual ability, in large part heritable, more unequal.¹

I do not know which of these played what role in changes in the income distribution over recent decades but it is worth considering causes unrelated to how much the government does to affect it.

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1. A commenter points me at a paper that tried to measure assortative mating for education across countries and times, concluded that:

The United States had a non-linear trend in assortative mating for educational attainment, as it decreased from 1875 to 1926, increased from 1926 to 1945, decreased from 1945 to 1958, increased from 1958 to 1977, and decreased from 1977 onwards.