The Elite Illusion

kwai chang caine: I seek not to know the answers, but to understand the questions.

Kung Fu, Season 1, Episode 14

The Boston and New York City public school systems include a handful of selective exam schools. Unlike most other American public schools, exam schools screen applicants on the basis of a competitive admissions test. Just as many American high school seniors compete to enroll in the country’s most selective colleges and universities, younger students and their parents in a few cities aspire to coveted seats at top exam schools. Fewer than half of Boston’s exam school applicants win a seat at the John D. О’Bryant School, Boston Latin Academy, or the Boston Latin School (BLS); only one-sixth of New York applicants are offered a seat at one of the three original exam schools in the Big Apple (Stuyvesant, Bronx Science, and Brooklyn Tech).

At first blush, the intense competition for exam school seats is understandable. Many exam school students go on to distinguished careers in science, the arts, and politics. By any measure, exam school students are well ahead of other public school students. It’s easy to see why some parents would give a kidney (perhaps a liver!) to place their children in such schools. Economists and other social scientists are also interested in the consequences of the exam school treatment. For one thing, exam schools bring high – ability students together. Surely that’s a good thing: bright students learn as much from their peers as from their teachers, or so we say at highly selective institutions like MIT and the London School of Economics.

The case for an exam school advantage is easy to make, but it’s also clear that at least some of the achievement difference associated with exam school attendance reflects these schools’ selective admissions policies. When schools admit only high achievers, then the students who go there are necessarily high achievers, regardless of whether the school itself adds value. This sounds like a case of selection bias, and it is. Taking a cue from the far-sighted Oregon Health Authority and its health insurance lottery, we might hope to convince Stuyvesant and Boston Latin to admit students at random, instead of on the basis of a test. We could then use the resulting experimental data to learn whether exam schools add value. Or could we? For if exam schools were to admit students randomly, then they wouldn’t be exam schools after all.

If selective admissions are a necessary part of what it means to be an exam school, how can we hope to design an experiment that reveals exam school effectiveness? Necessity is the mother of invention, as revered philosophers Plato and Frank Zappa remind us. The discrete nature of exam school admissions policies creates a natural experiment. Among applicants with scores close to admissions cutoffs, whether an applicant falls to the right or left of the cutoff might be as good as randomly assigned. In this case, however, the experiment is subtle: rather than a simple on-off switch, it’s the nature of the exam school experience that changes discontinuously at the cutoff, since some admitted students choose to go elsewhere while many of those rejected at one exam school end up at another. When discontinuities change treatment probabilities or average characteristics (treatment intensity, for short), instead of flicking a simple on-off switch, the resulting RD design is said to be fuzzy.

Fuzzy RD

Just what is the exam school treatment? Figures 4.6-4.8. which focus on applicants to BLS, help us craft an answer. BLS applicants, like all who aspire to an exam school seat in Boston, take the Independent Schools Entrance Exam (ISEE for short). The sample used to construct these figures consists of applicants with ISEE scores near the BLS entrance cutoff. The dots in the figures are averages of the variable on the Y-axis calculated for applicants with ISEE scores in bins one point wide, while the line through the dots shows a fit obtained by smoothing these data in a manner explained in a footnote.- Figure 4.6 shows that most but not all qualifying applicants enroll at BLS.

Enrollment at BLS

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Notes: This figure plots enrollment rates at Boston Latin School (BLS), conditional on admissions test scores, for BLS applicants scoring near the BLS admissions cutoff. Solid lines show fitted values from a local linear regression estimated separately on either side of the cutoff (indicated by the vertical dashed line).

BLS is the most prestigious exam school in Boston. Where do applicants who miss the BLS cutoff go? Most go to Boston Latin Academy, a venerable institution that’s one school down in the Boston exam school hierarchy. This enrollment shift is documented in Ligure 4.7. which plots enrollment rates at any Boston exam school around the BLS cutoff. Ligure 4.7 shows that most students who miss the BLS cutoff indeed end up at another exam school, so that the odds of enrolling at some exam school are virtually unchanged at the BLS cutoff. It would seem, therefore, that we have to settle for a parochial-sounding experiment comparing highly selective BLS to the somewhat less selective Boston Latin Academy, instead of a more interesting evaluation of the whole exam school idea.


Peer quality around the BLS cutoff


Notes: This figure plots average seventh-grade peer quality for applicants to Boston Latin School (BLS), conditional on admissions test scores, for BLS applicants scoring near the admissions cutoff. Peer quality is measured by seventh – grade schoolmates’ fourth-grade math scores. Solid lines show fitted values from a local linear regression, estimated separately on either side of the cutoff (indicated by the vertical dashed line).

Or do we? One of the most controversial questions in education research is the nature of peer effects; that is, whether the ability of your classmates has a causal effect on your learning. If you’re lucky enough to attend high school with other good students, this may contribute to your success. On the other hand, if you’re relegated to a school where most students do poorly, this may hold you back. Peer effects are important for policies related to school assignment, that is, the rules and regulations that determine where children attend school. In many American cities, for example, students attend schools near their homes. Because poor, nonwhite, and low-achieving students tend to live far from well-to – do, high-achieving students in mostly white neighborhoods, school assignment by neighborhood may reduce poor minority children’s chances to excel. Many school districts therefore bus children to schools far from where they live in an effort to increase the mixing of children from different backgrounds and races.

Exam schools induce a dramatic experiment in peer quality. Specifically, applicants who qualify for admission at one of Boston’s exam schools attend school with much higher-achieving peers than do applicants who just miss the cut, even when the alternative is another exam school. Figure 4.8 documents this for BLS applicants. Here, peer achievement is measured by the math score of applicants’ schoolmates on a test they took in fourth grade (2 years before they applied to exam schools). As in the charter school investigation discussed in Chapter 3. test scores in this figure are measured in standard deviation units, where one standard deviation is written in Greek as 1 o. Successful applicants to BLS study with much higher-scoring schoolmates, enjoying a jump in peer math achievement of.8o, equivalent to the difference in average peer quality between inner city Boston and its wealthy suburbs. Such dramatic variation in treatment intensity lies at the heart of any fuzzy RD research design. The difference between fuzzy and sharp designs is that, with fuzzy, applicants who cross a threshold are exposed to a more intense treatment, while in a sharp design treatment switches cleanly on or off at the cutoff.

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