Mind The Poverty Gap

Last week, Michael Petrilli and Brandon Wright made an abortive attempt to "guesstimate" cross-country differences in child poverty at the National ReviewI criticized the effort here at Demos, pointing out that my own direct microdata analysis (not a guesstimate) from the LIS shows that children at the bottom of our society are much worse off than children at the bottom of the societies of our developed-nation peers.

Dylan Matthews also criticized the effort at Vox. In his piece, Matthews interviewed LIS data experts who described the effort variously as "garbage" (Timothy Smeeding) and "nonsensical" (Janet Gornick). He also had a current LIS researcher produce non-guesstimated figures using the LIS microdata and those figures not surprisingly show that child poverty rates (using absolute income) are much lower in Nordic countries than in the United States.

Attempt Number Two

Unphased, Petrilli and Wright are back in the National Review for another bite at the apple. In their new piece, Petrilli and Wright begin by claiming that these cross-country poverty calculations "are very hard calculations to make" (they are actually very easy to make provided you have access to the underlying data). Then they admit that they kind of made stuff up because they don't have access to the underlying microdata and had to rely upon summary data provided to them that doesn't allow for the kind of calculations they wanted to make.

Despite not having the data necessary to make the calculation they claimed to have made and despite people with access to the data showing that their estimate is totally incorrect, Petilli and Wright insist that their made up figures must be on to something because "[o]ur results looked strikingly similar to what Smeeding found using old data at the 125 percent level."

To borrow a phrase from Smeeding and Gornick, this defense is nonsense garbage. These authors initially claimed that in 2010, the US child poverty rate (at the 100 percent level) was similar to the poverty rate of these other countries. It was not and they didn't even do the right calculations to reach any such conclusion. Now they are claiming that these totally made up calculations are actually instructive because they sort of match the rates from 2000 at the 125 percent level.

Then, to make things worse, the authors go on to get mad that, in responding to their piece, "the Left" (defined as LIS data experts) used the 100 percent poverty level instead of the 125 percent poverty level. This choice was made, they claim, to make the US look worse, ignoring that actually this choice was made because it was the poverty level Petrilli and Wright used. Their post is literally a whine about how the debunkers on the Left actually generated the figure Petrilli and Wright said they had generated instead of generating a totally different figure based on a higher poverty threshold that Petrilli and Wright think (they don't know) would make their poverty parity claims look less ridiculous.

Income Percentiles and Poverty Rates

Though Petrilli and Wright still have not produced any actual figures favoring their conclusion, they are right about one thing: different absolute poverty lines will generate different disparities in poverty rates.

The best way to see this is to consider the following set of graphs. In the first graph, I have charted per capita child incomes (using real microdata, not guesstimates) from the 5th to 60th percentiles for the US and Denmark.

What you can see is that, at the 5th percentile, Danish children have much higher incomes than American children (80% more in fact). As we move up the income distribution, the Danish child income advantage slowly shrinks. And then, at the 40th percentile, the US catches up to Denmark and takes over. From the 40th percentile on up, US children have more income than their Danish counterparts.

For me, this percentile-based presentation tells you all you need to know about absolute child income patterns in the two respective countries. Bringing in child poverty "rates" doesn't actually add any more useful information. Nonetheless, Petrilli and Wright insist on finding rates for some reason. So what are the absolute child poverty rates of the two countries? Well, it really depends on where we draw the line.

Here is what the child poverty rates look like if we draw the poverty line somewhat low:

The orange line is the poverty line drawn at $6000 of per capita income (i.e. $24,000 family income for a family of four). At that poverty line, the Danish poverty rate is somewhere around 8% (notice the orange line intersects with the red line at around the 8th percentile). At that same line, the US poverty rate is around 18% (the orange and blue intersect at the 18th percentile). So, if we arbitrarily set the absolute poverty line there, we find the US has a much higher child poverty rate.

But what happens when we set the child poverty line somewhat higher? Consider the following graph with a "mid" poverty line:

For this graph I intentionally drew the poverty line at around $9800 (i.e. $39,200 for a family of four) because at that magic number, you could say the US and Denmark have identical child poverty rates. As you can see, the orange, blue, and red lines all intersect at aroud the 40th percentile, generating the conclusion that Denmark and the US both have a child poverty rate of 40%.

But we can make the child poverty line higher still! Here is what that looks like:

When we set the poverty line arbitrarily at $11,000, we find the US child poverty rate to be around 46% and the Danish child poverty rate to be around 55%. It turns out, then, that Danish child poverty is actually higher! I guess.

When Petrilli and Wright implore us to use higher poverty thresholds to define child poverty rates, they are trying to inch the threshold up in order to reach the mid-line and high-line conclusion. The higher you push up the income threshold, the better the US will look because egalitarian countries necessarily start to lose their income advantage the further up the income distribution you go. That's just the nature of having a much more equal distribution of income. Inching the poverty line up higher in order to try to make the poverty rate more equal doesn't actually tell us much about the degree of deprivation experienced by children at the bottom of society (for that, just look at the first graph standing alone), but it does serve certain purely rhetorical ends well.

Mind the Poverty Gap

While I don't think poverty rates are very helpful when doing cross-country comparisons of absolute income, if you insist on using them, you really need to make sure they are accompanied by estimates of the "poverty gap." The "poverty gap" refers to how far away the poor are from the poverty line. Coupling poverty rate analysis with poverty gap analysis, though inferior to simple percentile analysis, should at least tell you what you need to know about the degree of actual deprivation experienced by kids near the bottom of society.

To see what I mean by poverty gap, consider this hypothetical society with a poverty rate of 30%.

The pink part represents the poverty gap. It shows you just how far away people who are in poverty are from the poverty line.

Contrast that hypothetical society with this one:

This society also has a 30% poverty rate, but clearly its degree of poverty is much lower. That is, the pink area is much smaller in this graph than it is in the first one.

When it comes to comparing the poverty of the US to other countries (especially the Nordics), you can certainly arbitrarily draw the poverty line somewhere in order to ensure that both countries have similar poverty rates. But even when you do that, the countries will still have dramatically different poverty gaps. That is, the US poverty gap will look more like the first hypothetical country while the poverty gap of Nordic countries will look more like the second. The upshot of this poverty gap insight is the same as the upshot of the percentile insight: children near the bottom of the US society really do have much less than children near the bottom of other societies. To the extent that material resources help to determine educational outcomes, this means that children in the US really will do worse (all else equal) in school than children in peer nations.