Thursday, April 17, 2014

Relative vs. Absolute Poverty Measures

In discussions over poverty and education policy in the United States, it is common to see international comparisons. These comparisons usually make the United States look quite bad -- i.e., 21% of our children are in poverty compared to 4% in Finland.

To be sure, childhood poverty is a serious problem in the United States, one that we should address in many ways (such as reforming the tax code so that poor people are not punished for getting married or taking low-paying jobs, increasing the EITC, or even instituting a child allowance). Nothing that follows should be misconstrued as denying any of that.

But in making international comparisons, we should also get the numbers right. 

What bothers me about the usual international comparisons of poverty rates is that they are relative to each country's median income. So people are counted as being in poverty if their income is under half of their own country's median. 

Such a measure is useful for thinking about inequality within countries. But the problem with making international comparisons is that countries differ in their median incomes. Indeed, in richer countries, people who have under half of that country's median income might actually be better off, in actual material terms, than people who are actually at or above the median income in poorer countries. 

Imagine two villages. In one, extreme wealth driven by oil wells has pushed the median income up to $200,000, but 30% of the people make $50,000 to $100,000; still, no one suffers from any material deprivation whatsoever (everyone has enough to eat, a place to live, etc.). In another village, everyone lives on a dollar per day and is in constant danger of hunger; half of children die in infancy from easily preventable diseases. 

The median income theory of poverty would say that there is a 30% poverty rate in the first village (despite its complete lack of material deprivation), compared to zero poverty in the second village (even though everyone is severely deprived). Yet who in the first village would trade places with the second? 

That said, we can say, accurately, that the first village suffers from much more inequality than the second. To the extent we care about inequality, separate and apart from material deprivation, we might worry about the first village's distribution of income too. But we shouldn't get confused and think that we're talking about poverty when we're really talking about inequality. 

What we need is a way to think about poverty and inequality separately, as two different concepts, without muddying the waters with a measure that conflates them for no apparent reason. 

Fortunately, there is an international measure of poverty that looks at what we should really care about when we say the word "poverty" -- that is, material living conditions. PPP, or purchasing power parity, is the usual term.

Poverty rates measured by PPP and by median income are not always the same. In fact, they can differ quite substantially. 

The following chart from a UNICEF paper on childhood poverty makes this clear. As you can see, the United States' "relative poverty rate" for children was 21-22% in 2004, compared to just over 10% when judged in terms of real income. 


Compare Poland -- a relative poverty rate of approximately 18% but a real poverty rate of nearly 80%. 

If we use the relative poverty rate to make international comparisons, we'd have to say that Poland is doing substantially better than the United States. But if we care about actual living conditions of people in poverty, we should give more weight to the much larger disparity in real poverty rates, by which nearly eight times as many kids are poor in Poland than in the U.S.

This is why the World Bank cautions, "If you are interested in a particular country, you should use national poverty lines, which are defined according to each country’s specific economic and social circumstances. The national poverty lines are typically lower in poorer countries and higher in richer countries. If you are interested in comparing poverty measures across countries, you should use international poverty lines. The international poverty lines attempt to hold the real value of the poverty lines consistent across countries by accounting for differences in purchasing power across countries."

To be sure, our real childhood poverty rate is still double that of several European countries, so none of the above should be read to deny that this is a significant problem. The point here is that it is possible to care deeply about poverty while not wishing to exaggerate the numbers.

Friday, March 07, 2014

Ravitch's math

In a recent post, Diane Ravitch decries the fact that Chicago charters expel a higher percentage of kids than do the other public schools:
The data reveal that during the last school year, 307 students were kicked out of charter schools, which have a total enrollment of about 50,000. In district-run schools, there were 182 kids expelled out of a student body of more than 353,000. That means charters expelled 61 of every 10,000 students while the district-run schools expelled just 5 of every 10,000 students.
She credits this pattern of expulsions with helping the charter schools have higher test scores:
It makes perfect sense. If a school can kick out the kids with low scores, the school will have higher scores and the public school that gets the low-scoring kids will have lower scores. How simple!
If you give all the Chicago kids a test on which public school students score an average of 70 and charter school kids score an average of 75, but then take 307 charter kids who score 50 (quite a bit lower than the overall average) and move them to the traditional public schools instead, what will happen to the overall test scores? Public schools will now have an average of 69.98 instead of 70, and charter schools will how have an average of 75.154 instead of 75.

This is a somewhat artificial example, of course, but the point remains that even if every single kid expelled from charter schools had substantially lower test scores than everyone else, charter expulsions probably don't explain very much about the overall test score patterns.

Meat = Smoking?

Another day, another over-hyped scaremongering study in the news. The latest is this:
Eating a diet heavy on meat and cheese may be as harmful to you as smoking a cigarette, researchers claim. A new study, published in Cell Metabolism on March 4, shows that middle-aged people who eat a diet high in animal proteins from milk, meat and cheese are more likely to die of cancer than someone who eats a low-protein diet. The research also showed the people who ate lots of meat and dairy were more likely to die at an earlier age.
The actual study is here. Among the most obvious problems:

1. No good information on what people actually ate. 

The 6,381 people in the study were given a survey ONCE asking them about what they ate in the previous 24 hours. The authors then matched these people up with a database of death records 18 years later.

So you have to assume that:

 (a) these people told the truth about what they ate in that 24 hour period even though they only claimed to have eaten an average of 1,823 calories per day (which is completely implausible), and,

 (b) whatever they ate in that 24 hour period is the same thing that they ate for the next 18 years.

The authors themselves say in the “limitations” section: “First, the use of a single 24 hr dietary recall followed by up to 18 years of mortality assessment has the potential of misclassifying dietary practice.” No kidding.

2. The authors seem to have been cherry-picking amongst ways of subdividing the people in the study.

The overall conclusion, for all ages, is that “high and moderate protein consumption” were “not associated with all-cause, CVD, or cancer mortality when subjects at all the ages above 50 were considered.” The authors then subdivide people into ages 50-65 at baseline versus ages 66 and up at baseline.

When you split the data that way (and why did they pick 65 as the dividing line? who knows?), it turned out that high protein consumption appeared to be correlated with more cancer deaths for younger folks but REDUCED cancer deaths for the 66+ group. (Obviously this had to be the case – if there is no overall increased risk of cancer, then if you cleverly chop the sample such that one group has an increased risk, the other group has to have a decreased risk.) It is not clear why meat protein would “cause” a 4-fold increase in cancer at one age but a reduction in cancer at another age.

3. It’s just plain wrong to divide continuous variables up into simplistic categories such as high vs. low protein or over vs. under 65 years old. 

Age is a fairly continuous variable. So is protein consumption. Even if you have good information on protein consumption (which we don’t, see point 1), the correct way to model the risk of death at various ages versus protein consumption would be to use all the information at hand – people’s exact ages (not just whether they are over or under 65), and people’s exact protein consumption (not just whether they ate less than 10%, between 10% and 19%, or 20%+ of calories from protein).

Dividing these variables into large buckets like the authors did can cause completely spurious relationships to arise. There are innumerable articles warning NOT to do this. See here or here or here or here or here or here.

4. Correlation vs. causation. Even if we had good information on what people ate over the 18 year period, a correlation between meat and cancer deaths is just correlation unless we know for sure that the people who ate more meat were identical in every other way to people who ate less meat (or at least that the dataset measures everything that is different about them, such that we can control for it). But we don’t know this at all. Indeed, the authors did not control for some factors that might affect mortality, such as exercise levels, geography, or income.

To take one of many possibilities, perhaps poorer people eat more meat (fewer salads and the like) and also have less access to good cancer screening/treatment. This could cause a spurious correlation between meat and cancer to appear in the data (although even then, it’s not clear why the correlation would go in opposite directions depending on whether the person was over 65).

Thursday, September 19, 2013

The Case Against High-School Sports - Amanda Ripley - The Atlantic

The Case Against High-School Sports - Amanda Ripley - The Atlantic: "The Case Against High-School Sports
The United States routinely spends more tax dollars per high-school athlete than per high-school math student—unlike most countries worldwide. And we wonder why we lag in international education rankings?"

'via Blog this'

Saturday, September 14, 2013

Law School: Worth It?

I've been digesting the new paper "The Economic Value of a Law Degree," by Simkovic and McIntyre. It concludes:
"After controlling for observable ability sorting, we find that a law degree is associated with a 60 percent median increase in monthly earnings and 50 percent increase in median hourly wages. The mean annual earnings premium of a law degree is approximately $53,300 in 2012 dollars. The law degree earnings premium is cyclical and recent years are within historic norms."

The paper's introduction says: 



"The purpose of this article is to estimate, as closely as data permits, the causal effect on earnings of a particular type of education, the law degree. Rather than viewing law degree holders in isolation, we can get better estimates of the causal effect of education by comparing the earnings of individuals with law degrees to the earnings of similar individuals with bachelor’s degrees while being mindful of the statistical effects of selection into law school."

It's important for readers to know, however, that the article does not estimate the causal effect of law school. The authors are not running a randomized experiment, wherein otherwise identical college graduates are randomly assigned to go to law school or not. They do not rely on any exogenous shock to the availability of law school. They do not rely on any discontinuity in eligibility for law school, such that a regression discontinuity design would be possible. They do not have an instrumental variable that affects the availability of law school (but that has no effect on earnings through any other mechanism, which would mean the instrument violated the typical exclusion restriction).


Instead, they estimate the earnings of law school graduates compared to bachelor's degree holders that are similar in a number of observable ways. 


This is not sufficient to make a causal inference about the value of law school. The problem is the cliche that correlation is not causation. Even if one controls for observables, there may be quite significant differences between the people who attend law school and those who don't -- most notably, motivation and ambition, level of aggressiveness, and the like. Current datasets have no reliable way to control for these factors (self-reported answers to survey questions are not very useful given that it is socially unacceptable to answer, "I have zero ambition for my life" or "I am supremely committed to increasing my income at all costs," even if one of those is true). 


Take the two (hypothetical) people below, "John" and "Andrew." 
"John"



"Andrew"

Let's say that they are both English majors at the same university, with identical SAT scores, identical grades, identical family backgrounds, and the like. If you ask them what level of income they would like to make, they even give similar answers. 

But in terms of their revealed behavior, "John" works in a coffee shop after he graduates (he never even tries to do anything else), while "Andrew" goes to law school. It is a good guess that a group of 1,000 Andrews is more ambitious and will likely end up earning more than a group of 1,000 Johns, completely apart from any effect of law school attendance.

Another way of putting it is that to make a causal inference, we have to be able to get some idea of the counterfactual -- that is, how much income would the Andrews make if they were prevented from going to law school and had to do something else instead. The ideal way to get a counterfactual, of course, is random assignment. If we could randomly assign only half of the Andrews to attend law school, then we would actually see what the other half of the Andrews do with themselves when not allowed to attend law school.

A good guess, though, is that if law school were ruled out, the other half of the Andrews might not be content with just a bachelor's degree. Many of them might consider an MBA, or a master's in accounting, or even medical school. This means, however, that when Simkovic and McIntyre compare law school graduates to the pool of bachelor's-only degree holders, they are not looking at a good counterfactual. 

Indeed, the economic value of law school could be negative. What if ambitious young people went to business school instead of law school? In the long run, they might earn only $10,000 less per year on average (as Simkovic and McIntyre say in footnote 33). At a discount rate of 3%, 30 years' of $10,000 in extra real income would be worth about $196,000 in present value terms. But they would also save a year's tuition (which, if borrowed, could add to debt payments for decades) and a year's lost salary in the near present. 

It's not too hard to envision that for many young people -- those who have high borrowing costs and high opportunity costs in the present, but who have less than average chances of being a high-earning lawyer -- the actual value of law school could well be negative.  Notably, this can be true even if Simkovic and McIntyre are right that these people earn more after going to law school than do "similar" bachelor's degree holders.  

It is thus improper to suggest that law school "causes" the Andrews to have higher earnings. Law school might have some causal role, to be sure, but that cannot be determined.

All of which is to say, the title of this paper is wrong. Rather than being titled "The Economic Value of a Law Degree," the paper should more accurately be titled, "The Economic Value of a Law Degree Mixed In Unidentifiable Proportion With The Economic Value Of Being The Sort of Ambitious Person Who Chooses To Go To Law School."

Heckman is Wrong

James Heckman (Chicago, Nobel prize winner) has been arguing that society should offer universal preschool for youngsters. His main evidence for this claim -- which I agree with, by the way -- is a couple of extremely small studies from the 1970s. What bothers me, however, is how he depicts these studies. To wit, here's what he writes in the New York Times:
Also holding back progress are those who claim that Perry and ABC are experiments with samples too small to accurately predict widespread impact and return on investment. This is a nonsensical argument. Their relatively small sample sizes actually speak for — not against — the strength of their findings. Dramatic differences between treatment and control-group outcomes are usually not found in small sample experiments, yet the differences in Perry and ABC are big and consistent in rigorous analyses of these data.
Contrary to what Heckman says, dramatic differences between treatment and control groups are MOST likely to show up in small samples. This is one of the most basic facts that any empirical scholar learns: when the sample size is small, sampling error will be the largest (for example, if a particular small sample happens to include a few outliers, that can swing the results in either direction rather dramatically). When the sample is large, that's when you'd expect to see smaller effects (e.g., in large samples, there's not as much opportunity for a few outliers to swing the results).

It's disturbing that Heckman seems to say the opposite of such a basic point.

Pascal Junod » An Aspiring Scientist’s Frustration with Modern-Day Academia: A Resignation

Friday, August 16, 2013

Riddle of the script: how the world's most difficult puzzle was solved - Telegraph

Music I Like

The Boxer Rebellion, "Diamonds."

 

Amy Holford, "I Won't Wait." Move over, Adele:
 

The Boxer Rebellion, "Caught by the Light."
 

 The Boxer Rebellion, "Both Sides Are Even."
 

 Haim, "The Wire."

 

 Matthew Koma, "Years" (acoustic):
 

 Parade of Lights, "We're the Kids."
 

 Kitten, "Cut it Out."

 

Monday, August 12, 2013

Why the World Is Smarter Than US - The Daily Beast

Why the World Is Smarter Than US - The Daily Beast:



In all of these nations, sports have little or nothing to do with public schooling. If kids want to play hockey or basketball, they organize pick-up games, join a community program, or take private lessons. Children are held to high academic expectations and allowed to fail, so they come to understand the importance of school.

'via Blog this'

Friday, July 26, 2013

Obama's Preschool Proposal is Not Based on Sound Research | Brookings Institution

Sunday, July 21, 2013

Unhappy Truckers and Other Algorithmic Problems - Issue 3: In Transit - Nautilus

Unhappy Truckers and Other Algorithmic Problems - Issue 3: In Transit - Nautilus:

"Modeling a simplified version of a transportation problem presents one set of challenges (and they can be significant). But modeling the real world, with constraints like melting ice cream and idiosyncratic human behavior, is often where the real challenge lies. As mathematicians, operations research specialists, and corporate executives set out to mathematize and optimize the transportation networks that interconnect our modern world, they are re-discovering some of our most human quirks and capabilities. They are finding that their job is as much to discover the world, as it is to change it.

"

'via Blog this'

Saturday, July 20, 2013

Science Prodigy Zhao Bowen Wants to Crack a Genetic Mystery: What Makes Some People So Smart? - Wired Science

Science Prodigy Zhao Bowen Wants to Crack a Genetic Mystery: What Makes Some People So Smart? - Wired Science

Now, at 21, he oversees his own research project at BGI Shenzhen—the country’s top biotech institute and home to the world’s most powerful cluster of DNA-sequencing machines—where he commands a multimillion-dollar research budget.
Zhao’s goal is to use those machines to examine the genetic underpinnings of genius like his own. He wants nothing less than to crack the code for intelligence by studying the genomes of thousands of prodigies, not just from China but around the world. He and his collaborators, a transnational group of intelligence researchers, fully expect they will succeed in identifying a genetic basis for IQ. They also expect that within a decade their research will be used to screen embryos during in vitro fertilization, boosting the IQ of unborn children by up to 20 points. In theory, that’s the difference between a kid who struggles through high school and one who sails into college.

Friday, July 12, 2013

The Shocking Truth About Doug Engelbart: Silicon Valley's Sidelined Genius -SVW

The Shocking Truth About Doug Engelbart: Silicon Valley's Sidelined Genius -SVW: "Tributes to the genius of computer pioneer Doug Engelbart are flooding the web following the announcement of his death at the age of 88. Yet in the final four decades of his life no one would fund him and he felt he had wasted the last years of his life."

'via Blog this'

Carrot Facts (RealCarrotFacts) on Twitter

From Carrot Facts (RealCarrotFacts) on Twitter:

"To add carrot taste to anything just add a carrot to it"