Wednesday, February 26, 2014

Some Income Inequality and Redistribution Facts (And Why to Take Them Not Quite So Seriously)

In all walks of life, there are facts and then there are “facts”. I’ve used quotes to indicate things that may actually be true, but don’t say what we think they do.

There are few facts about income inequality. The reason is that the data we’re talking about is not really inequality, but rather the distribution of income. And that’s an empirical statistical distribution (ooooh, nasty stuff to some people) with over a hundred million data points (one for each household). And those households aren’t very forthcoming about how much they make. Put those together, and most of what we have are “facts” not facts.

So, there’s a lot of “facts” floating around, and the Obama administration has been pushing them lately. But conservatives have their own “facts”. A good example of this is the op-ed piece from the February 13 issue of The Wall Street Journal entitled “Here's What 'Income Equality' Would Look Like”. It’s by Scott Hodge, President of the Tax Foundation. This is a D.C. think tank that is nominally non-partisan, but which for practical purposes tends to line up with conservatives.

One statistical fact we need to deal with up front is that the distribution of income is severely positively skewed (most economic and financial data is). This means that if you were to graph the entire distribution, it should have a long tail on the right hand side. The reason for that long tail on the right hand side is that there’s a floor on how low incomes can go (at zero), but there’s no ceiling on how high they can go (some incomes are over a billion dollars per year).

The thing is … no one has the entire distribution in front of them. So we guesstimate. But our guesstimates need to preserve that positive skew. The way this works out in practice leads to some weirdness with the numbers.

One immediate implication of positively skewed data is that the average will be higher than the median. You can see how this works with some simple data sets. If we have the data set:


It should be clear that a) the data is symmetric and not skewed, b) the average is 2, and c) the median is 2 as well.

But if our data set is:


It should be clear that a) the data is no longer symmetric and that it is positively skewed, b) the average is now 3, but c) the median is still 2.

Household income data looks like the second data set, so average income is likely to be larger than median income. This also means that the majority earn less than the average.

Most of our data on income inequality is divvied up into 5 quintiles. Within those quintiles, we’ll see the same problem. So when Hodge says:

A typical American family in the lower income quintile, on the other hand, has an average market income of $9,560 …

He’s also saying that the median family in the lowest quintile earns less than this. Inferring medians is just about impossible without seeing the whole data set, but you could take a stab at this and figure that the median income of the lowest fifth is in the $6-8K range.

Hodge also says:

… Those in the bottom fifth, or quintile, of the income scale received $9.62 in federal spending for every $1 they paid in federal taxes of all kinds.

Again, this is true, but it’s a “fact”. In that quintile, most taxes are probably paid by people at the top end, and most benefits are brought in by the people at the bottom. So the 9.62 to 1 ratio is kind of comparing apples to oranges: it’s infinity to one for some and probably zero for others. But … it’s what we’ve got, so it’s what we use … even if it’s a “fact”.

At the other end of the spectrum the weirdness gets worse. Households in the top quintile average $311K in income, but because of the skewness this must be much higher than the median. The same follows with net taxes, which are $65K for households in this quintile. Those are facts. But his assertion that you’d need to take $164K from each of these households to bring that quintile to average income is a “fact”. This amount is ridiculous (and borders on inflammatory) because that would put the majority of the households in that quintile below the average; the factual version would be much smaller. And that’s presupposing that such a scheme would be worthwhile.

The bottom line of all this is that you should be on the lookout for innumeracy from D.C. types on both sides of the issue.

FWIW: Hodge does site two useful, fact rich, summaries of income and tax data: The Distribution of Federal Spending and Taxes in 2006 from the CBO and The Distribution of Tax and Spending Policies in the United States from the Tax Foundation.

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