# Is Income Inequality Rising, and Are a Lot of Feathers Heavy?

New data on income inequality in the United States were just released. And they provide a useful teaching moment. The graph below, which comes from the Census Bureau, shows the evolution of the Gini coefficient since 1967. It’s pretty clear that this measure of inequality has been rising pretty much through this whole period.

But here’s how the Census Bureau chose to describe these data:

Based on the Gini index, income inequality increased by 1.6 percent between 2010 and 2011; this represents the first time the Gini index has shown an annual increase since 1993, the earliest year available for comparable measures of income inequality.

Say what?

It turns out that they’re looking only at year-to-year changes. And they’re counting a year-to-year change as positive only if it measures inequality this year as being statistically significantly larger than it was last year. And while inequality rose in most years, it may not have risen by enough over any one year to be called statistically significant.

Yet while the Census Bureau may be right that no individual year-to-year change was statistically significant, the accumulation of positive changes is. That is, since 1993, the number of times inequality has risen, is itself statistically significant. Alternatively, if you compare inequality today with that more than a year or two earlier, the rise both this year and in most years is statistically significant.

Over on Twitter, **Alex Tabarrok** had a nice way of summarizing the mistaken logic that led the Census Bureau to make such a misleading statement:

Census: Feathers are light therefore lots of feathers are also light.

His point: Each year-to-year change in inequality may not be that significant of a burden, but accumulating a bunch of them over decades really is.

Bottom line: Your eyes don’t deceive you, inequality is rising. And think hard about what statements about statistical significance are really testing.

## Justin S.

The technical name is fallacy of composition

## Justin S.

I'm most curious about the motive for the misinformation.

## Jason

Remember that this is the government and therefore at least 10 people edited that announcement before it went out. Could mean any number of things, but my theory is that somewhere along the line someone added:

- "The increase was so great this year that it was statistically significant for the first time since 1993."

That became:

"this represents the first time the Gini index has shown a STATISTICALLY SIGNIFICANT annual increase since 1993."

And finally a public affairs officer said, "Readers don't like complex words like statistically significant," and promptly cut them out.

## Gabe Kotter

This is a bit off-topic about the statistical relevance of the data discussed above.

I keep hearing about income inequality, but no one can tell me why it is bad. I can see if evil land barons kept all the gold in their tower and didn't let the peasants have anything but gruel, but in a free, capitalist society, isn't income inequality the point, or if not the point exactly, at least the result of the system working?

If we all are pursing our own individual best interests, and assuming that there are laws and rules and that people by and large follow them, isn't income inequality evidence that those who create value are yielding the benefits of that value? And that those who do not are therefore not?

My income/wealth has stayed roughly the same year over year but Sergey Brin has gone from his Stanford dorm room (and the Soviet Union) to being worth $18 Billion. Isn't that how it should work? Or if a guy who sells copy machines sells a bunch of them while his counterpart sells none, shouldn't there be income inequality between the two? Sergey Brin and sales guy 1 created value, so they should make more money.

In order to reduce income inequality, we can make Sergey Brin give me some a few million (he won't miss it), or make sales guy 1 give sales guy 2 some of his well-earned commissions. Alternatively, I could sit down with sales guy 2 and figure out how the two of us can go out and create something of value.

It's not bad for me if someone else gets rich, unless somehow it makes me poor. No one is making the case that the poor are poorer than they used to be because Mark Zuckerberg invented Facebook.

I think the emphasis on this is simply (and sadly) effective politics for ill-informed people.

## Paul in VA

Well said Gabe! It would further be interesting to look at all those people who we here about who are "voluntarily" leaving the work force, and so are no longer included in unemployment data. How many of these people have looked at rising Gov't benefits and decided that the difference that they make by working Versus just staying on the dole is not worth it and so they "drop down". Is this data skewed both by a few ultra zillionares on one side, and people "dropping down" on the other?

## TexCIS

If you want income equality, then you want your doctor to make the same salary as your hamburger flipper.

How many doctors would we have then?

Or what would the price of hamburgers be?

## Jeff

Because the only two options are the system we have now or communism.

## dan donoghue

It is the degree of inequality. No one earns millions of dollars by themselves. There must be other stakeholders who were shortchanged. The system is unfair.

## Nick

What statistical test were they using to determine significance? Because if it's just comparing year-to-year, then they're assuming independence of years, which is clearly not a valid approach for time series data.

## frankenduf

lots of feathers are light- duh