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# Raj Chetty's Non Sequitur

 DeLong on Scott's Seeing Like ... Modern Art and Occam's Razor...

Stanford economics professor Raj Chetty, who studies income inequality, has put out on the web a rich array of PowerPoints and videos as part of his Equality of Opportunity project. I haven't looked at them all yet--the sheer number of PowerPoints and videos is daunting.

But I did look at the first few slides in his Lecture 1 and the first few minutes of his YouTube video where he discusses these slides.

In them, there's an important non sequitur and a narrow definition of success.

Take a look at the PowerPoint for Lecture 1, slides 4 and 5. Slide 4 gives the probability of a child born to parents (and it's probably more accurate, although he doesn't say it, to use the singular form, "parent") in the bottom fifth of the income distribution making it to the top fifth. It's "only" 7.5 percent. The probability in my native Canada, by contrast, is a much-higher 13.5%. On slide 4, he says incorrectly, although, admittedly this usage has become common, that "Chances of achieving the 'American Dream' are almost two times higher in Canada than in the U.S." What he means of course, is that they are almost two times as high. They're actually 80 percent higher.

But everyone's used to that usage and that's not my main criticism.

Here's my main criticism: In the very next slide, his first statement is:

Central policy question: why are children's chances of escaping poverty so low in America?

See the problem? His slides showing nothing about a child's chance of escaping poverty in America. His slides, rather, show that a child has a 7.5% chance of making it to the top fifth, which is a multiple of the number that would get the child out of poverty.

Because the percent of households in poverty in the United States is typically about 13 to 14 percent, simply being in the top third of the bottom fifth would mean you are not poor. And being in the second fifth from the bottom would definitely mean you are not poor.

Wondering if I might see him make this point in the YouTube video, I went to that video and saw that he makes the same non sequitur: he treats the data as if he has shown the odds of an American child escaping poverty.

He also has a strange definition of success. At about the 2:50 point, he asks what we can do, policy-wise, to raise a poor child's chance of "succeeding." It's clear from context that to Raj Chetty, "succeeding" means making it into the top fifth. Yet I would wager that many, many children born to poor families in America would be thrilled to make it into the middle class. What's middle class? If we take the word "middle" seriously, it should mean the middle quintile plus, at most, the 2nd and 4th quintiles. I would wager also, that Chetty's data would show that well over half--and probably something like 70%--of children born into the lowest quintile make it into the next 4 quintiles.

HT2 Tyler Cowen.

CATEGORIES: Income Distribution

Emily writes:

80% would be if people born in the bottom quintile were not any more likely to wind up in the bottom quintile than people born in the top four. No? That seems very unlikely to me, although I agree with this criticism.

David R Henderson writes:

@Emily,
Oops. Yes. So I’m changing it to a more reasonable number. Thanks for catching the almost-certain error.

Jason writes:

His definition of success is also strange in the sense that by that definition, no more than 20% of the population can ever succeed. In fact, exactly 20% of the population succeed, and exactly 80% fail. By definition.

Phil writes:
In fact, exactly 20% of the population succeed, and exactly 80% fail. By definition.

Only if one takes exactly two measurements. If one recognizes income mobility is highly dynamic, everyone could potentially be in the top quintile at some time in their life.

Max writes:

Perhaps a stupid question, but is the top Quintil of canada comparable with the top Quintil of the US? There are probably many more ultra-rich Americans than Canada (given that usually people say that Canada is more equal & thus the distribution of incomes should be narrower & flatter).

To make a fair comparison it should be asked what is the chance in the US & in Canada to achieve the same income in US\$ (pick above poverty line income.. median?).

David R Henderson writes:

@Max,
Perhaps a stupid question, but is the top Quintil of canada comparable with the top Quintil of the US? There are probably many more ultra-rich Americans than Canada (given that usually people say that Canada is more equal & thus the distribution of incomes should be narrower & flatter).
Not a stupid question at all. An excellent question. Yes, I thought of that and should have mentioned it, but I wanted to keep this short. Also, Denmark comes out looking “better” than the U.S. by Chetty’s criterion, but the distribution there is more equal than, I think, the distribution in Canada, and certainly more equal than the distribution in the United States.

writes:

Excellent points! May I add that one of the elementary rules of statistics is that the sample sizes should be similar and the groups similar in all ways but the one being tested. Comparing the US with Canada violates both, as do all comparisons between the US and tiny European countries. I'm sure we could find a group of people in the US the same size, demographics and wealth.

One of the big differences between the US and Canada is that Canada doesn't have the huge amount of immigration from the poor south.

If I could address the issue of mobility, the book "The Bell Curve" has some insights. A lot of poverty is caused by being in the lower quintiles of IQ. If your parent come from the lower levels of IQ it's not likely that the children will do better. Socialists want us to believe that all poverty is caused by oppression of some kind.

Ram writes:

It would seem that a more interesting quantity is the expected present value of a child's consumption over the life cycle, given their parents' consumption. This has the virtue of measuring something relevant to quality of life, takes into account length of life, and isn't relativized to a given country's distributional idiosyncrasies. We perhaps want to know if there are segments of the (lifetime) consumption distribution in which we expect children not to enjoy greater consumption than their parents.

James writes:

The chances are lower for a child form a first-quintile family end up above any percentile, not just the 80th, therefore Chetty's statement is correct.

Equal opportunity means that the percentage from the bottom quintile getting above a certain percentile = (100 - that percentile). Anything below that means that opportunities are not equal. 7.5

So, equality of opportunity would mean that the chance for kids from the bottom 13 percent to escape poverty is 87%. That is not true at all and it is what Chetty seems to mean. I think most readers understand that.

T Boyle writes:

David Henderson, you said

"Yes, I thought of that and should have mentioned it, but I wanted to keep this short."

I have often read this statistic. It has always been assumption that the primary thing wrong with it is that the quintiles are farther apart in the United States. If the quintiles differed by only \$1/year, the chance of a child born in the bottom quintile reaching the top quintile in their lifetime would be ~100%.

So, to keep it short, that's the reason that statistic, beloved of the left, means nothing - or, certainly, does not mean what they think it means.

David R Henderson writes:

@Jason,
His definition of success is also strange in the sense that by that definition, no more than 20% of the population can ever succeed. In fact, exactly 20% of the population succeed, and exactly 80% fail. By definition.
Good point.
@Phil,
If one recognizes income mobility is highly dynamic, everyone could potentially be in the top quintile at some time in their life.
Good point also.
@Roger D. McKinney,
One of the big differences between the US and Canada is that Canada doesn't have the huge amount of immigration from the poor south.
I think that’s right.
@Ram,
It would seem that a more interesting quantity is the expected present value of a child's consumption over the life cycle, given their parents' consumption. This has the virtue of measuring something relevant to quality of life, takes into account length of life, and isn't relativized to a given country's distributional idiosyncrasies. We perhaps want to know if there are segments of the (lifetime) consumption distribution in which we expect children not to enjoy greater consumption than their parents.
Interesting point. My guess is that we don’t have the data. Also, if we did, it would be difficult to choose a discount rate to compute the present value. But you’re right that this would be a better measure.
@James,
The chances are lower for a child form a first-quintile family end up above any percentile, not just the 80th, therefore Chetty's statement is correct.
Wrong. You need to look at his statement. HIs statement is about escaping poverty: his data are all about getting into the top quintile. He gives literally no data on escaping poverty. See the problem?
Equal opportunity means that the percentage from the bottom quintile getting above a certain percentile = (100 - that percentile). Anything below that means that opportunities are not equal.
Yes, but then it’s about equal opportunity, not what he claims it to be about, which is escaping poverty.
So, equality of opportunity would mean that the chance for kids from the bottom 13 percent to escape poverty is 87%. That is not true at all and it is what Chetty seems to mean. I think most readers understand that.
Again, you’re going back to equality of opportunity. Given the name of his project, it’s quite likely that he is concerned about equality of opportunity. But then that’s what he should talk about. If he wants to talk about escaping poverty, which he clearly does also, then he should give data on escaping poverty. He doesn’t.

David R Henderson writes:

@T Boyle,
I have often read this statistic. It has always been [my] assumption that the primary thing wrong with it is that the quintiles are farther apart in the United States. If the quintiles differed by only \$1/year, the chance of a child born in the bottom quintile reaching the top quintile in their lifetime would be ~100%.
Good point.

Brian writes:

"Equal opportunity means that the percentage from the bottom quintile getting above a certain percentile = (100 - that percentile)."

James,

That's not equal opportunity at all. That's randomization, independent of ability or hard work. That's a mere lottery. Equal opportunity means unbiased outcomes within the constraints of ability and hard work.

David R Henderson writes:

@Brian,
That's not equal opportunity at all. That's randomization, independent of ability or hard work. That's a mere lottery. Equal opportunity means unbiased outcomes within the constraints of ability and hard work.
Oops, you’re right. I shouldn’t have accepted James’s statement at face value. Early morning sleepies.

James writes:

The statement that the proportion of children growing up in the bottom x percentile (where x can be 13 or whatever you want), and end up in the top (100-x) percent of the distibution themselves is smaller than 100-x is true.

Therefore the statement that it is hard for kids to escape poverty is true.

Given what we know from the literature, this proportion is smaller in the US than in most other countries with gdp/capita in the same range.

Therefore it is harder for kids to escape poverty in the US than elsewhere.

David, your comments here would only have value if you could disprove these claims.

Brian writes:

David,

Nice post pointing out an inconsistency in how Chetty views the issue of inequality. I think this points to a bias on his part, which prevents him from seeing the inconsistency.

What's particularly mind boggling to me is that he doesn't even seem to understand his own data. A completely random distribution would be distributed equally across all quintiles. Any effect of ability on income will appear to reduce mobility, since ability is partially inherited from one's parents. Taking this into account, it's easy to show that the U.S. has nearly perfect income mobility.

Here's how it works. Assume that heredity accounts for just under 50% of one's quintile position. This is in line with twin studies, often cited by Bryan Caplan, that genes acoount for about 45% of outcomes, with 5% for environment and 50% for undetermined individual characteristics. Based on this simple assumption, here's the predicted likelihood of 1st quintile person moving up, compared to Chetty's data.

_________1st Q__2nd Q___3rd Q___4th Q___5th Q

Model_____36%____28%_____20%_____12%_____4%

Data______33.7%__28.0%___18.4%___12.3%___7.5%

In other words, U.S. mobility data implies that economic mobility in the U.S. is almost perfectly unbiased once heredity is taken into account. The only bias is a small effect of making 1st quintile people more likely to jump all the way to the top. These data imply, then, that the U.S. offers almost perfectly equal opportunity while rewarding ability. It's hard to argue with that.

When Chetty asks "why are children's chances of escaping poverty so low in America?," he's really asking "Why can't America's economic opportunity be more random and capricious?" The obvious response is "Why would we want that?"

James writes:

@brian: because we want rewards based on effort not endowments. We don't want to punish or reward people for things they cannot affect. See the equality of opportunity literature

Brian Delaney writes:
@brian: because we want rewards based on effort not endowments. We don't want to punish or reward people for things they cannot affect. See the equality of opportunity literature

In Reality, there are no "rewards". There are only consequences.

We pay people (mostly) based on what they achieve. Not how hard they tried. If we paid people based on their efforts, rather than their results, we would pay amateurs more than experts, since they would be working hardest to overcome their lack of experience and skill.

And we'd pay more for food grown on poor soil than on good soil.

I may *admire* someone who has overcome great handicap to become a pilot or brain surgeon. But I'm still going to pay them according to their actual results. I'm paying for results, not a morally uplifting story.

I'm not *rewarding* somebody when I cut them a paycheck. I'm not their mom, patting them on the head and giving them a cookie when they do something I approve of.

I'm *compensating* them for their (presumably) objective productivity. In which case, as long as they didn't break any rules achieving that productivity, I don't care how they achieved it.

Likewise, when I fire someone for non-performance, it's not a "punishment". There is absolutely zero moral judgement involved. It's just a result.

Neil S writes:

@James If that is indeed what the literature says then i want no part of it. Rewarding "effort" has no place in a rational economic system. Who measures effort? How do you compare the efforts of a brain surgeon and a construction worker?

I want an economic system that rewards the generation of value, as measured by what others freely choose to exchange for that result.

Brian writes:

"because we want rewards based on effort not endowments."

James,

Even if this were true (and it's not true from an economics perspective), you are failing to understand that even one's "effort" is partially a hereditary endowment. Some people work hard because they're good at it or they like it, just like their parents. Others are lazy because their parents were lazy (i.e., their genes predispose them for it.

In any case, economics is about putting scarce resources in the hands of those who will use them most productively. That's why we reward productivity, which is some combination of ability and effort, rather than just one or the other. In fact, evolution selected the right proportion of genes and random luck to maximize biological productivity. The point is that Chetty's data shows that the U.S. distributes income in the same way--to maximize productivity. It is otherwise unbiased, which is precisely what we mean equal opportunity. That's different than equality of outcome. Please don't confuse the two.

James writes:

You guys have chosen a very weird social welfare function to optimize

Brian writes:

"You guys have chosen a very weird social welfare function to optimize"

James,

Who's talking about a social welfare function? The Chetty data is about income mobility--how likely is someone raised in a family at the bottom of the income scale to later earn an income at the higher level? There's nothing to "choose" here. People make incomes from their jobs, and employers hire them based on their ability to be productive and create value for the company. These are the things that drive income mobility because they drive job opportunities. This is just reality, and there's no way it could be otherwise unless the government controls a sizable share of production.

My point in my earlier post is that the data imply that the U.S. does this in a nearly unbiased way. People are getting paid for the value they produce and not for other reasons. And that is equal opportunity by definition. Everyone gets an equal and unbiased chance to create as much value as they want and get compensated fairly for it. Other countries don't do this nearly as well.

David R Henderson writes:

@Brian,
Very nice comment with your table above. And also your subsequent responses are excellent. I got busy with the second last day of my day job (I retire today--yay!) and so am now just catching up.

Brian writes:

David,

Congratulations on your retirement. I'm sure you'll enjoy a well-deserved break from the necessity of work and use it to work only when you want to. :) Best of luck in all your endeavors.

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