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How the school choice mechanisms affect the welfare of students WANG Tong 講師

China and many other countries adopt centralized school assignment mechanisms, in which students and their parents express their preferences over schools, and the government goes through a complicating task of matching as many students to their stated preferred schools as possible. Each student’s score in school entrance exam should also be considered.

The design of an efficient student-placement mechanism is thus the key for establishing a fair and vigorous education system. Many papers are discussing advantages and shortcomings of various algorithms, but often with contradictory results.

In a joint research with Congyi Zhou, we have developed a unique dataset to compare the welfare of students under three popular mechanisms: the so-called Boston Mechanism (BM) which had been used in a Chinese coastal city until 2007, the Chinese Parallel (CP) mechanism introduced in 2008, and the Deferred Acceptance (DA) mechanism.

Our research, based on a survey of more than 8,000 students and large administrative data, provided evidence that the average social welfare is higher when a mechanism is “less manipulable” – that is students do not have to maneuver their lists of preferred schools to be sent to the authorities.

The biggest beneficiary of a switch to a less manipulable mechanism is students from low socioeconomic background, our data analysis showed.

Of the three mechanisms, BM is the most vulnerable to manipulation of preference revelations by students. Under BM, students face a bigger risk of ending up in least desirable schools should they fail to get into their top priority schools. Therefore, they have the incentive to avoid ranking competitive schools as their first choice and manipulate the lists of preferred schools using the best of their and their parents’ knowledge.

But as DA assigns students more in line with their test score, there is not much room for students to manipulate. CP is more manipulable than DA, but less so than BM.

This is the first paper to use observational data that links administrative data and survey data to study the Chinese Parallel mechanism. The survey result enabled us to recover students’ true preferences over schools, compare them with their lists of preferred schools sent to the authorities (Rank Order Lists; ROL) and analyze how they are manipulating the mechanism. The data also allowed us to evaluate the welfare performance of three mechanisms including DA, which has not been done in previous studies.

DATA AND MECHANISM

In a survey conducted in 2014 in the Chinese city that had employed BM, we asked more than 8,000 middle-school students their true preferences over high schools, among others. That covers almost two-thirds of the total exam takers in that year.

Of that, 7,865 students’ data was successfully merged with their corresponding administrative data such as the score in high school entrance exam, home address, ROLs and eventually in which school they were enrolled. The administrative data covers all middle-school graduates from 2006 through 2014.

It was found students behave very strategically in submitting their “preferred” schools. Their true preferences were far from what they had told the government in ROLs: only 2 percent of the survey respondents wrote their true preferences on ROLs.

Whether a mechanism is manipulable or not has important social implications because the ability to do so can hinges on students’ socioeconomic background. Students need to be very sophisticated in submitting ROLs to get assigned to schools closer to their preference, but those from poor family background may lack the relevant information or ability to manipulate. In that case, students who scored high in exams but not skillful in strategizing the mechanism, could face a smaller chance of breaking the intergenerational poverty.
The Chinese city switched to CP from BM in 2008 after seeing some students being assigned to low-quality schools despite their high-test scores as their strategy to manipulate ROLs backfired.

Shortly after sending ROLs, students take high school entrance exam. The test scores will serve as their unique priority score: Every school favours students with higher score to those with lower score. Then the matching begins as follows:

BM:
In the Round 1, each school considers all the students who rank it first and assigns the seats to students according to their test scores until either there are no seats left or no such students left. In Round 2, the second-choice of the students who have not yet been assigned will be considered.

Under the system, a student who was rejected in Round 1 will be considered by his second-choice school in Round 2, but only when the school still has available seats.

CP:
In the Round 1, students will be assigned in a similar way as BM but only temporarily. Every student who was rejected in Round 1 applies for the school of his second choice. Each school pools new applicants together with those held from Round 1 and ranks them altogether according to their test score. Therefore, manipulating the mechanism is less important under CP than BM.

DA:
Every student is assigned temporarily in every round. The process terminates when there were no students left. Each school is then matched with students it is holding according to their test score. With less need for working strategy, students are expected to fill in the ROL according to their true preferences.

SURVEY STATISTICS

We divided the surveyed city into four districts, calculated the average incomes and sorted them into two groups: higher socioeconomic status and lower socioeconomic status.

We also analyzed whether students with high test scores are assigned to schools farther from their homes, among others.

Some of the results from our survey /administrative data are as follows:
● There are higher variations in incoming students’ quality under BM. This could mean low test-score students   who are good at manipulation can get into better schools under BM. The variation is smaller in high education quality schools under CP. This could mean the correlation between students’ test scores and the education quality of students’ admitted school is higher under less manipulable mechanisms;
● Under CP, higher test-score students are more likely to be assigned to schools with higher education quality. Students from lower-income districts tend to gain from the switch to CP. This can be viewed as an evidence that those from the low socioeconomic background are not good at manipulation;
● Higher-test score students are more likely to be assigned to schools farther from home, an indication the education quality is positively correlated with average distance from students’ home.

CONCLUTION

So, will able students from poor family background have a bigger chance of getting assigned to good schools when the mechanism switches to DA from CP?

We changed mechanisms in our simulations to see what happens. Our conclusion is that the total welfare changes under different mechanisms and there is redistribution of welfare when the mechanism switches to DA from CP. The less manipulable the mechanism is, the higher average social welfare it yields, it showed.

This is probably because under DA, no one needs to strategize their preferences, and that it is almost not possible to make strategic mistakes.

FUTURE WORK

I had a chance to work with a non-governmental organization in Hong Kong ten years ago and looked into the education problems of migrant workers’ children. The early exposure to the issues of inequality and public policy prompted me to study distribution of welfare and issues like who benefit most from an increase of welfare in the U.S.

How the society can design a mechanism that prompts people to behave in a certain way and increases the total welfare is an interesting subject, with particularly large implications in the area of education.

We found students tend to make so many strategic mistakes in submitting ROLs that we are interested in documenting such mistakes in our future work.

取材・構成:井上裕子
協力:早稲田大学大学院政治学研究科J-School

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