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These data concern school choice, an issue that most people feel strongly about in

one direction or another. True believers of school choice argue that their tax

dollars buy them the right to send their children to the best school possible.

Critics worry that school choice will leave behind the worst students in the worst

schools. Still, just about every parent seems to believe that her child will thrive if

only he can attend the right school, the one with an appropriate blend of

academics, extracurriculars, friendliness, and safety.

School choice came early to the Chicago Public School system. That’s because the

CPS, like most urban school districts, had a disproportionate number of minority

students. Despite the U.S. Supreme Court’s 1954 ruling in Brown v. Board of

Education of Topeka, which dictated that schools be desegregated, many black

CPS students continued to attend schools that were nearly all-black. So in 1980

the U.S. Department of Justice and the Chicago Board of Education teamed up to

try to better integrate the city’s schools. It was decreed that incoming freshmen

could apply to virtually any high school in the district.

Aside from its longevity, there are several reasons the CPS school-choice

program is a good one to study. It offers a huge data set—Chicago has the third-

largest school system in the country, after New York and Los Angeles—as well

as an enormous amount of choice (more than sixty high schools) and flexibility.

Its take-up rates are accordingly very high, with roughly half of the CPS students

opting out of their neighborhood school. But the most serendipitous aspect of the

CPS program—for the sake of a study, at least—is how the school-choice game

was played.

As might be expected, throwing open the doors of any school to every freshman

in Chicago threatened to create bedlam. The schools with good test scores and

high graduation rates would be rabidly oversubscribed, making it impossible to

satisfy every student’s request.

In the interest of fairness, the CPS resorted to a lottery. For a researcher, this is a

remarkable boon. A behavioral scientist could hardly design a better experiment

in his laboratory. Just as the scientist might randomly assign one mouse to a

treatment group and another to a control group, the Chicago school board

effectively did the same. Imagine two students, statistically identical, each of

whom wants to attend a new, better school. Thanks to how the ball bounces in

the hopper, one goes to the new school and the other stays behind. Now imagine

multiplying those students by the thousands. The result is a natural experiment

on a grand scale. This was hardly the goal in the mind of the Chicago school

officials who conceived the lottery. But when viewed in this way, the lottery

offers a wonderful means of measuring just how much school choice—or, really,

a better school—truly matters.

So what do the data reveal?

The answer will not be heartening to obsessive parents: in this case, school choice

barely mattered at all. It is true that the Chicago students who entered the

school-choice lottery were more likely to graduate than the students who

didn’t—which seems to suggest that school choice does make a difference. But

that’s an illusion. The proof is in this comparison: the students who won the

lottery and went to a “better” school did no better than equivalent students who

lost the lottery and were left behind. That is, a student who opted out of his

neighborhood school was more likely to graduate whether or not he actually

won the opportunity to go to a new school. What appears to be an advantage

gained by going to a new school isn’t connected to the new school at all. What

this means is that the students—and parents—who choose to opt out tend to be

smarter and more academically motivated to begin with. But statistically, they

gained no academic benefit by changing schools.

And is it true that the students left behind in neighborhood schools suffered? No:

they continued to test at about the same levels as before the supposed brain

drain.

There was, however, one group of students in Chicago who did see a dramatic

change: those who entered a technical school or career academy. These students

performed substantially better than they did in their old academic settings and

graduated at a much higher rate than their past performance would have

predicted. So the CPS school-choice program did help prepare a small segment

of otherwise struggling students for solid careers by giving them practical skills.

But it doesn’t appear that it made anyone much smarter.

Could it really be that school choice doesn’t much matter? No self-respecting

parent, obsessive or otherwise, is ready to believe that. But wait: maybe it’s

because the CPS study measures high-school students; maybe by then the die has

already been cast. “There are too many students who arrive at high school not

prepared to do high school work,” Richard P. Mills, the education commissioner

of New York State, noted recently, “too many students who arrive at high school

reading, writing, and doing math at the elementary level. We have to correct the

problem in the earlier grades.”

Indeed, academic studies have substantiated Mills’s anxiety. In examining the

income gap between black and white adults—it is well established that blacks

earn significantly less—scholars have found that the gap is virtually eradicated if

the blacks’ lower eighth-grade test scores are taken into account. In other words,

the black-white income gap is largely a product of a black-white education gap

that could have been observed many years earlier. “Reducing the black-white

test score gap,” wrote the authors of one study, “would do more to promote

racial equality than any other strategy that commands broad political support.”

So where does that black-white test gap come from? Many theories have been

put forth over the years: poverty, genetic makeup, the “summer setback”

phenomenon (blacks are thought to lose more ground than whites when school

is out of session), racial bias in testing or in teachers’ perceptions, and a black

backlash against “acting white.”

In a paper called “The Economics of ‘Acting White,’” the young black Harvard

economist Roland G. Fryer Jr. argues that some black students “have tremendous

disincentives to invest in particular behaviors (i.e., education, ballet, etc.) due to

the fact that they may be deemed a person who is trying to act like a white

person (a.k.a. ‘selling-out’). Such a label, in some neighborhoods, can carry

penalties that range from being deemed a social outcast, to being beaten or

killed.” Fryer cites the recollections of a young Kareem Abdul-Jabbar, known

then as Lew Alcindor, who had just entered the fourth grade in a new school and

discovered that he was a better reader than even the seventh graders: “When the

kids found this out, I became a target…. It was my first time away from home,

my first experience in an all-black situation, and I found myself being punished

for everything I’d ever been taught was right. I got all A’s and was hated for it; I

spoke correctly and was called a punk. I had to learn a new language simply to

be able to deal with the threats. I had good manners and was a good little boy

and paid for it with my hide.”

Fryer is also one of the authors of “Understanding the Black-White Test Score

Gap in the First Two Years of School.” This paper takes advantage of a new trove

of government data that helps reliably address the black-white gap. Perhaps

more interestingly, the data do a nice job of answering the question that every

parent—black, white, and otherwise—wants to ask: what are the factors that do

and do not affect a child’s performance in school?

In the late 1990s, the U.S. Department of Education undertook a monumental

project called the Early Childhood Longitudinal Study. The ECLS sought to

measure the academic progress of more than twenty thousand children from

kindergarten through the fifth grade. The subjects were chosen from across the

country to represent an accurate cross section of American schoolchildren.

The ECLS measured the students’ academic performance and gathered typical

survey information about each child: his race, gender, family structure,

socioeconomic status, the level of his parents’ education, and so on. But the study

went well beyond these basics. It also included interviews with the students’

parents (and teachers and school administrators), posing a long list of questions

more intimate than those in the typical government interview: whether the

parents spanked their children, and how often; whether they took them to

libraries or museums; how much television the children watched.

The result is an incredibly rich set of data—which, if the right questions are

asked of it, tells some surprising stories.

How can this type of data be made to tell a reliable story? By subjecting it to the

economist’s favorite trick: regression analysis. No, regression analysis is not

some forgotten form of psychiatric treatment. It is a powerful—if limited—tool

that uses statistical techniques to identify otherwise elusive correlations.

Correlation is nothing more than a statistical term that indicates whether two

variables move together. It tends to be cold outside when it snows; those two

factors are positively correlated. Sunshine and rain, meanwhile, are negatively

correlated. Easy enough—as long as there are only a couple of variables. But

with a couple of hundred variables, things get harder. Regression analysis is the

tool that enables an economist to sort out these huge piles of data. It does so by

artificially holding constant every variable except the two he wishes to focus on,

and then showing how those two co-vary.

In a perfect world, an economist could run a controlled experiment just like a

physicist or a biologist does: setting up two samples, randomly manipulating one

of them, and measuring the effect. But an economist rarely has the luxury of such

pure experimentation. (That’s why the school-choice lottery in Chicago was such

a happy accident.) What an economist typically has is a data set with a great

many variables, none of them randomly generated, some related and others not.

From this jumble, he must determine which factors are correlated and which are

not.

In the case of the ECLS data, it might help to think of regression analysis as

performing the following task: converting each of those twenty thousand

schoolchildren into a sort of circuit board with an identical number of switches.

Each switch represents a single category of the child’s data: his first-grade math

score, his third-grade math score, his first-grade reading score, his third-grade

reading score, his mother’s education level, his father’s income, the number of

books in his home, the relative affluence of his neighborhood, and so on.

Now a researcher is able to tease some insights from this very complicated set of

data. He can line up all the children who share many characteristics—all the

circuit boards that have their switches flipped the same direction—and then

pinpoint the single characteristic they don’t share. This is how he isolates the true

impact of that single switch on the sprawling circuit board. This is how the effect

of that switch—and, eventually, of every switch—becomes manifest.

Let’s say that we want to ask the ECLS data a fundamental question about

parenting and education: does having a lot of books in your home lead your

child to do well in school? Regression analysis can’t quite answer that question,

but it can answer a subtly different one: does a child with a lot of books in his

home tend to do better than a child with no books? The difference between the

first and second questions is the difference between causality (question 1) and

correlation (question 2). A regression analysis can demonstrate correlation, but it

doesn’t prove cause. After all, there are several ways in which two variables can

be correlated. X can cause Y; Y can cause X; or it may be that some other factor is

causing both X and Y. A regression alone can’t tell you whether it snows because

it’s cold, whether it’s cold because it snows, or if the two just happen to go

together.

The ECLS data do show, for instance, that a child with a lot of books in his home

tends to test higher than a child with no books. So those factors are correlated,

and that’s nice to know. But higher test scores are correlated with many other

factors as well. If you simply measure children with a lot of books against

children with no books, the answer may not be very meaningful. Perhaps the

number of books in a child’s home merely indicates how much money his

parents make. What we really want to do is measure two children who are alike

in every way except one—in this case, the number of books in his home—and see

if that one factor makes a difference in his school performance.

It should be said that regression analysis is more art than science. (In this regard,

it has a great deal in common with parenting itself.) But a skilled practitioner can

use it to tell how meaningful a correlation is—and maybe even tell whether that

correlation does indicate a causal relationship.

So what does an analysis of the ECLS data tell us about school-children’s

performance? A number of things. The first one concerns the black-white test

score gap.

It has long been observed that black children, even before they set foot in a

classroom, underperform their white counterparts. Moreover, black children

didn’t measure up even when controlling for a wide array of variables. (To

control for a variable is essentially to eliminate its influence, much as one golfer

uses a handicap against another. In the case of an academic study such as the

ECLS, a researcher might control for any number of disadvantages that one

student might carry when measured against the average student.) But this new

data set tells a different story. After controlling for just a few variables—