essays on school choice and the returns to school quality · data from three cohorts of applicants...

Essays on School Choice and the Returns to School Quality

by

Kehinde Funmilola Ajayi

A dissertation submitted in partial satisfactionof the requirements for the degree of

Doctor of Philosophy

in

Economics

in the

Graduate Division

of the

University of California, Berkeley

Committee in charge:

Professor David Card, ChairProfessor Ronald Lee

Professor Edward MiguelProfessor David Levine

Spring 2011


Copyright c© 2011

by


Abstract


by


Doctor of Philosophy in Economics

University of California, Berkeley

Professor David Card, Chair

This dissertation consists of three studies which collectively seek to examine: what thebarriers are to receiving a high-quality education in a merit-based school choice setting; howpolicy reforms can address these barriers; and what benefits students gain from attending ahigh-quality school. Altogether, the papers focus on understanding the role of socio-economicbackground in explaining differences in education-related decisions and student outcomes.

Chapter 2 examines whether school choice programs increase opportunities for educa-tional mobility or reinforce initial disparities in schooling. I address this question in the con-text of the public education system in Ghana, which uses standardized tests and a nation-wide application process to allocate 150,000 elementary school students to 650 secondaryschools. As has been found in other settings, students from lower-performing elementaryschools in Ghana apply to less selective secondary schools than students with the same testscores from higher-performing elementary schools. I consider four potential explanations forthis behavior: differences in decision-making quality, imperfect information about admissionchances, costs and accessibility of schooling, and preferences for school quality. I use detaileddata from three cohorts of applicants to evaluate the relative importance of these explana-tions. My analysis suggests that differences in application behavior are largely due to poordecision-making and incorrect beliefs about admission chances, rather than differences inpreferences or the costs and accessibility of schools.

Building on the theoretical framework outlined in the preceding analysis, Chapter 3 eval-uates the impact of institutional reforms in school choice settings. Focusing again on thecase of Ghana, I estimate the effects of a series of reforms in the application process thatexpanded the number of choices students could list and encouraged students to select a di-versified portfolio of schools. I use a difference-in-differences approach to analyze the effectof each reform and find that both reforms decreased the difference in selectivity of schools

1

chosen by students from high-performing and low-performing elementary schools, which sug-gests that application and admission rules play a significant role in explaining differences inapplication behavior. Moreover, these results are consistent with a setting in which imperfectinformation has a strong impact on students’ choices and the effects can both be explainedas a consequence of uncertainty in the Ghanaian choice system.

Chapter 4 uses a unique dataset on Ghana’s education system to examine the effect ofschool quality on student outcomes. My analysis draws on exogenous variation in studentassignment due to the fact that admission of elementary school students into secondaryschool in 2005 was based on students’ ranking of their three most preferred choices and theirperformance on a standardized test. I compare students on different sides of the cutoff foradmission to their lowest-ranked choice and find that students who are not admitted to theirchosen school are assigned to schools of lower-quality and are less likely to complete secondaryschool. Additionally, these students are more likely to transfer out of their initially-assignedschools. However, those who do complete secondary school do not perform any worse onthe exit exam several years later. Thus, students’ behavioral responses to their admissionoutcomes appear to moderate the effects of school quality on educational attainment in thiscontext.

2

I have benefited from numerous discussions throughout this project and greatly appreci-ate everyone who took the time to share their ideas with me. I especially wish to thank DavidCard for being the best adviser a graduate student could hope for—and ever aspire to be. Ithank Nii Addy, Patrick Allen, Bryan Graham, Thembi Anne Jackson, Damon Jones, KellyJones, Maximilian Kasy, Patrick Kline, Ronald Lee, David Levine, Justin McCrary, EdwardMiguel, Glenda Oskar, Sarath Sanga, Harriet Somuah, Kenneth Train and my officematesin the labor field office for their invaluable contributions to my journey of discovery.

This research was supported by funding from a Spencer Dissertation Fellowship, UCBerkeley Institute for Business and Economic Research and Center of Evaluation for GlobalAction Dissertation Research Award, UC Berkeley Center for African Studies Rocca Pre-Dissertation Research Award, National Institute of Child Health and Human DevelopmentTraining Grant T32-HD007275-24, and UC Berkeley Chancellor’s Fellowship for GraduateStudy.

I am grateful to Ghana Education Service, the Computerised School Selection and Place-ment System Secretariat, Ghana Ministry of Education, SISCO Ghana, and the West AfricanExaminations Council for providing the data and background information which enabled meto pursue this study.

Finally, I thank my family and friends for their generous wisdom, patience and encour-agement. You continually inspire me.

i

To my teachers

ii

Contents

1 Introduction 1

2 Does School Choice Promote Educational Mobility? 3

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Institutional Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 School Choice Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.5 Decision-Making Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.6 Beliefs about Admission Chances . . . . . . . . . . . . . . . . . . . . . . . . 14

2.7 Preferences for School Characteristics . . . . . . . . . . . . . . . . . . . . . . 16

2.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 Can School Choice Reforms Provide More Equal Access to Education? 35

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 History of School Choice Reforms in Ghana . . . . . . . . . . . . . . . . . . 36

3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4 Difference-in-Differences Estimation . . . . . . . . . . . . . . . . . . . . . . . 38

3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

iii

4 Does Attending a Better School Improve Student Outcomes? 63

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.2 Institutional Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.4 Econometric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Bibliography 92

iv

Chapter 1

Introduction

Over the last decade, there has been growing emphasis on the importance of expanding accessto education in developing countries. Global commitments to initiatives such as the Millen-nium Development Goals have mobilized widespread support for improvements in schoolingbut with few guidelines on how to achieve these ideals in practice. Policy discussions andacademic research in this area have primarily focused on eliminating disparities in enrollmentrates, with less attention paid to differences in the quality of education that various studentsreceive. This dissertation examines several questions about the demand for and returns toschool quality, specifically: 1) what factors influence school choice? 2) do institutional fac-tors promote equal access to selective schools? and 3) does attending a high quality schoolimprove student outcomes?

Analysis of schooling choices can provide a powerful tool for understanding the market foreducation, particularly from a government’s perspective as a primary supplier of schooling.When faced with decisions about what types of schools to provide and how to ensure equalaccess to education, decision-makers must often consider the impact of various competingfactors. To illuminate this decision-making process, I examine the demand for schooling inGhana by analyzing secondary school applications. Ghana provides an ideal setting in whichto study this topic. Public education consists of six years of primary school, three years ofJunior High School (JHS), and three years of Senior High School (SHS). At the end of JHS(in 9th grade), students apply to SHS by submitting a ranked list of up to six programchoices. Admission is centrally coordinated through a Computerised School Selection andPlacement System (CSSPS) which places each qualified student in one school based on theirperformance on the Basic Education Certificate Exam (BECE). Thus, secondary schooladmission occurs through a highly competitive (but rather transparent) process.

My research draws on administrative data covering all students and schools which par-ticipated in the CSSPS between 2005 and 2009 (approximately 300,000 students, 10,000junior high schools and 700 senior high schools each year). School selection forms collectinformation on each candidate’s date of birth, sex, disabilities, and application choices. Ad-

1

Chapter 1. Introduction

ditionally, I observe BECE scores and admission outcomes for students admitted to SHS. Icombine this student information with data from the Ministry of Education on school char-acteristics (such as whether a school is public or private, single sex or coeducational, andwhat kinds of academic programs are offered). Finally, I measure secondary school qualityand academic outcomes using students’ performance on the Secondary School CertificateExamination (SSCE) which is a standardized exam taken at the end of secondary school andused for admission to university.

Beyond seeking to address the substantive issues raised, it is my hope that this projectillustrates the role of administrative records as a key resource for advancing research oneducation-related choices and academic outcomes. Given that education records providereadily available information on sizeable student populations and circumvent the costs asso-ciated with compiling survey data, they potentially provide valuable insights into meaningfulquestions concerning the demand for and returns to school quality.

2

Chapter 2

Does School Choice PromoteEducational Mobility?

2.1 Introduction

This chapter examines inequalities in access to education and analyzes whether merit-basedschool choice programs promote educational mobility or reinforce initial disparities in school-ing. I study this issue in the context of secondary school education in Ghana. Like manydeveloping countries, Ghana has a centralized application system in which admission to sec-ondary school is based on students’ academic merit. Consistent with findings from othersettings, I observe that students from low-performing elementary schools in Ghana apply toless selective secondary schools than students from high-performing schools with the sameadmission chances. I consider four potential explanations for this finding: differences indecision-making quality; incorrect beliefs about admission chances due to incomplete infor-mation; prohibitive costs and accessibility of attending high-quality secondary schools; anddifferences in preferences for school quality. Two features of the Ghanaian choice systempotentially magnify the importance of imperfect information. First, students can only applyto a limited number of schools. Second, students have to submit their applications beforethey know their test scores. Drawing on insights from a model of optimal portfolio choicedeveloped by Chade and Smith (2006), I use detailed data from three cohorts of applicantsto evaluate the relative importance of these distinct hypotheses and conclude that differ-ences in students’ application behavior largely result from imperfect information rather thandifferences in preferences.

I use three complementary strategies in my empirical analysis to investigate why studentswith the same academic potential make different application choices. First, I examine therole of decision-making quality: are students from low-performing schools making mistakes intheir application decisions? I explore this hypothesis by outlining a model of the school choiceproblem facing students and measuring whether students use the optimal choice strategy. I

3

Chapter 2. Does School Choice Promote Educational Mobility?

find that students from low-performing schools are less likely to use the optimal strategy andare subsequently less likely to gain admission to selective secondary schools. This analysissuggests that the complexity of the application process may be a key source of inefficiencyin the Ghanaian application system.

Next, I test whether differences in students’ beliefs about their admission chances canaccount for the differences in their application behavior: do students from low-performingschools under-estimate their admission chances? I present a normal learning model in whichstudents form expectations about their admission chances based on a signal of their indi-vidual ability and the average ability of students in their elementary school. Intuitively,high-performing students from low-performing schools will under-estimate their admissionchances while low-performing students from high-performing schools will over-estimate theiradmission chances. To test the explanatory power of this theory, I estimate students’ poste-rior beliefs about their ability using the assumptions of the normal learning model. I thencompare application decisions of students from low-performing and high-performing schoolswith the same beliefs about their ability and find that the differences in application behaviordiminish substantially. Thus, imperfect information about admission chances appears toaccount for a large part of why talented students from low-performing schools apply to lessselective secondary schools.

Finally, I examine the last two hypotheses: do schooling costs and distance prevent stu-dents from low-performing schools from applying to more selective schools; and do studentsfrom low-performing schools place a lower value on school quality? To investigate these twohypotheses, I use a discrete choice model to evaluate students’ preferences for a range ofschool characteristics including cost, proximity and academic performance. I find that stu-dents from lower-performing elementary schools are more likely to apply to schools withinclose proximity and to public schools instead of private ones. However, students from lower-performing schools are no less likely to apply to prestigious secondary schools. This analysisimplies that heterogeneity in preferences does not fully explain why talented students fromlow-performing schools do not apply to more selective schools. Rather, the first two expla-nations - differences in decision-making quality and beliefs about admission chances, seemto be relatively more important factors in accounting for differences in application behavior.

My analysis of the Ghanaian high school application system has direct implications forefforts to understand educational mobility in alternative contexts because it addresses aset of fundamental research and policy questions. The phenomenon that talented studentsfrom low-performing schools typically under-apply is evident across various settings and hasbeen particularly well-documented with regard to college applications in the United States(Manski and Wise (1983); Avery and Kane (2004); and Bowen, Chingos, and McPherson(2009) highlight this issue). This phenomenon raises concerns because there is substantialevidence that attending a more selective school may improve outcomes for high-achievingstudents and could reduce socio-economic differences in the long run (for examples study-ing the secondary school context, see Clark (2007), Pop-Eleches and Urquiola (2011), and

4


Jackson (2010) on the returns to peer quality in merit-based systems; Cullen, Jacob, andLevitt (2005), Cullen, Jacob, and Levitt (2006), Hastings, Kane, and Staiger (2008), andDeming (2010) in lottery-based systems; and Duflo, Dupas, and Kremer (forthcoming) onthe benefits of academic tracking).

This chapter also builds on a growing literature on school choice under constraints. Highschool admission in Ghana is based on students’ academic merit but there are two frictionsin the application process: 1) students can only submit a limited number of applicationsand 2) students have incomplete information about their admission chances.1 The result isthat students must solve a complex optimization problem under uncertainty. A set of recentstudies model this problem of constrained choice with incomplete information (Chade andSmith (2006); Chade, Lewis, and Smith (2008); Nagypal (2004); Haeringer and Klijn (2009)).Additionally, Calsamiglia, Haeringer, and Klijn (2010) test several theoretical predictions inan experimental setting. Altogether, these studies provide a useful foundation for furtherempirical work and this extension incorporates their insights into an analysis of observationaldata.

Finally, this study relates to discussions in the mechanism design literature on issues ofschool choice reform and student welfare. Studies in this literature have primarily evaluatedthe efficiency and stability of assignment mechanisms (see Roth and Peranson (1999) andPathak and Sonmez (2008) for representative examples). However, there is growing inter-est in analyzing issues of equity and the distribution of welfare for students from differentbackgrounds, particularly in choice mechanisms which reward strategic behavior but wherethe optimal strategy is unclear. In such cases, a policy reform which simplifies the choiceproblem could serve as an equalizing intervention and provide more equitable opportuni-ties for disadvantaged participants (see Abdulkadiroglu, Pathak, Roth, and Sonmez (2006)and Pathak and Sonmez (2008) for a discussion of strategic behavior under the assignmentmechanism originally used by Boston public schools and Lai, Sadoulet, and de Janvry (2009)for a related analysis of high school applications in Beijing). A complementary set of stud-ies demonstrate how information provision can lead to large changes in schooling choices(Hastings and Weinstein (2008); Jensen (2010)). Although these studies suggest that schoolchoice reforms can increase educational mobility, there is little direct evidence to support

1Similar conditions apply in several other settings. Comparable merit-based systems are used for sec-ondary school admission in other countries including Kenya, Romania, and Trinidad and Tobago and forcollege entry in Canada and Mexico. Students often apply to schools before knowing their test scores or canonly submit a fixed number of applications. Additionally, there are strong parallels between these contextsand the context of college choice in the US: students apply to a conservative number of schools because ofapplication costs (both in terms of time and money); and students are relatively uncertain about their admis-sion chances because admission is partly based on measures of students’ academic performance which maybe known at the time of applying (e.g. SAT/ACT scores and high school GPA), but also on assessments ofother background information (such as personal statements, extracurricular activities and recommendationletters).

5


this hypothesis in merit-based admission settings.2

The chapter proceeds as follows: Section 2 provides an institutional background on sec-ondary school admissions in Ghana. Section 3 describes the administrative data used inthis study and illustrates the differences in application behavior and admissions outcomes ofstudents from high-performing and low-performing elementary schools. Section 4 formalizesthe school choice problem in a theoretical model and motivates my empirical analysis. Thesubsequent three sections examine potential hypotheses for differences in application behav-ior: Section 5 compares the decision-making quality of students from high-performing andlow-performing elementary schools; Section 6 examines how imperfect information affectsapplication choices; and Section 7 evaluates whether students have heterogeneous prefer-ences for school characteristics. The final section concludes with a discussion of the resultsand their main implications.

2.2 Institutional Background

Compulsory education in Ghana consists of six years of primary school and three years ofjunior high school (JHS). At the end of junior high school, students compete for admissionto senior high school (SHS) 3. There are over 9,000 JHSs in the country but approximately650 SHSs with only half the capacity of JHSs. The government has made some efforts toincrease the number of SHSs in the country, but there remains substantial variation in schoolquality.

2.2.1 The Computerised School Selection and Placement System

Application to senior high school is centralized through a computerized school selectionand placement system (CSSPS) which was introduced in 2005 (Box 1 outlines the system).Admission of JHS students into SHS is based on students’ ranking of their preferred programchoices and their performance on the Basic Education Certificate Exam (BECE) which is anationally administered exam. Choices are often the result of discussions between studentsand their parents, teachers or friends. However, I refer to the student as the decision-makerthroughout this discussion for simplicity.

In practice, admission under the CSSPS occurs through the following process:

2MacLeod and Urquiola (2009) develop a theoretical model which predicts that competition in schoolchoice systems will lead to socio-economic stratification if admission is merit-based. This prediction isconsistent with the empirical patterns I find in the Ghana. Additionally, Avery (2009) presents resultsfrom a pilot study which offered guidance counseling to a randomly selected group of high-achieving low-income students and finds suggestive evidence that the intervention had positive effects in students’ collegeapplication choices and admission outcomes.

3I use the terms ”senior high school”, ”senior secondary school” and ”secondary school” interchangeablythroughout the remaining discussion.

6


1. Students submit a list of ranked choices (stating a secondary school and an academictrack within that school for each choice)

2. Students take the standardized entrance exam (BECE)

3. Students who perform well enough to qualify for admission to SHS are admitted to aschool4

On average, less than half of all candidates receive a sufficient grade in the BECE to qualifyfor admission to SHS. Qualified students are assigned in merit order to the first availableschool on their list and schools admit students up to their capacity. (See Appendix for amore detailed description of the deferred acceptance algorithm which the CSSPS uses forstudent assignment.) Students who do not gain admission to any of their chosen schools areadministratively assigned to an under-subscribed school with available spaces. Efforts aremade to place students in their home district or region wherever possible but there is limitedregard for students’ stated preferences.

A notable aspect of the Ghanaian school choice system is that students have to submittheir applications before taking the entrance exam. Therefore, students have incompleteinformation about their admission chances even though admission is based on test scores.Moreover, cutoffs are endogenously determined by the quality of applications to a givenschool since schools only define the number of spaces available that year, but not the ex-plicit test score required for admission. Thus, the application process is characterized by asubstantial amount of uncertainty.

Finally, students can only submit a limited number of choices. The number of permittedchoices has increased since the CSSPS began in 2005 but the number is still restricted.Students were allowed to list up to three choices in 2005 and 2006, this increased to fourchoices in 2007 and to six choices in 2008. Between 95 and 99 percent of students listed thefull number of choices in each year, which suggests that the constraint is indeed binding andthat a vast majority of students would prefer to list more schools if permitted.

2.2.2 The Application Decision

The CSSPS issues a handbook which provides limited advice to students about their se-lection of schools. First, the guidelines specifically instruct students to be truthful abouttheir ordering of choices, urging that “choices must be listed in order of preference” (p.5).However, the handbook also emphasizes that applicants should make a calculated applica-tion decision because they are only allowed to list a limited number of choices and are notguaranteed admission to any particular default school:

4The requirements for admission to SHS are that students receive a passing grade in the four core subjects(Mathematics, English, Integrated Science and Social Studies) as well as in the two additional subjectsrequired for the program they intend to pursue. Available programs include: General Arts, General Science,Agriculture, Business, Home Economics, Visual Arts and Technical Studies.

7


Parents should take the registration exercise seriously and select schools wheretheir wards chances of admission are brightest. Over-estimation and under-estimation of candidates’ academic capabilities should be avoided. (p.9)

In outlining the Roles and Responsibilities of Candidates, the document states that “[c]andidatesmust assess their chances of gaining admission into very competitive Senior Secondaryschools” and concludes that “[it] is therefore important to make realistic choices in orderto make the new system effective” (p.10-11). The CSSPS handbook therefore emphasizesthat certain students could benefit from choosing their set of listed schools carefully.

Thus, students receive two primary instructions: to carefully consider their admissionprospects when selecting schools and to rank selected choices truthfully.

2.3 Data

I use two main types of data to analyze application behavior in Ghana: 1) CSSPS ad-ministrative data on student background characteristics, entrance exam scores, choices, andadmission outcomes, and 2) supplementary data on school characteristics, including a stan-dardized measure of schools’ academic performance.

2.3.1 Student Information

CSSPS data cover the universe of students who applied to public and participating privatesecondary education institutions in Ghana between 2005 and 2009 and report each student’sranked list of secondary school choices.5 The data also include the aggregate BECE score andthe name and location of secondary school for the set of students who qualified for admission.The school selection forms collect limited background information on each candidate butprovide the name and location of the junior high school they attended. Table 1 presentssome descriptive statistics.

For the majority of my analysis, I focus on the 85 percent of students who attended publicjunior high schools because these students are most likely to comply with their senior highschool assignments instead of opting to attend one of the few elite private schools which haveindependent admission procedures but are substantially more expensive. I convert BECE

5The data are especially informative because virtually all students submit a complete list. This is aremarkably high participation rate compared to most school choice programs which have been studiedin the US. For example, less than 50 percent of students in Boston Public Schools listed the full num-ber of available choices (Abdulkadiroglu, Pathak, Roth, and Sonmez (2006)) and 40 to 60 percent did inCharlotte-Mecklenburg Public Schools (Hastings, Kane, and Staiger (2008)). This comprehensive coverageof applications allows me to compare students from a wide range of backgrounds and to examine the generalequilibrium effects of Ghana’s policy reforms.

8


scores into percentiles because a student’s relative performance in a given year determines heradmission chances. To examine the extent of educational mobility, I define higher-performingelementary schools as those where the average BECE score is above the median average forall schools in the country. Similarly, lower-performing schools are those with below-averageperformance. Evidence that students incorrectly estimate their admission chances can beseen in the prevalence of administrative assignments: 22 percent of students received anadministrative assignment in the first year of the program; however, this share decreasedover time and fell to 2 percent in 2009.

2.3.2 School Characteristics

I supplement the CSSPS student data with information on school characteristics. The Min-istry of Education maintains a register of schools which is updated each year to provideinformation on each school’s location and to indicate whether a school is public or privateand single sex or coeducational. The secondary school register also provides information onwhether schools are day or boarding, technical or academic, and lists the types of programsoffered and number of vacancies in each program. Finally, I obtained school-level distribu-tions of grades in the Secondary School Certificate Examination (SSCE) for each of the fourcore subjects (English, Mathematics, Social Studies and Integrated Science). The SSCE istaken at the end of secondary school and used for admission to university. It is also centrallyadministered to students at a national level so exam scores are therefore comparable acrossschools. Students must receive a grade of A to E in each of the four core subjects in orderto pass the exam. I use the average percentage of students receiving a grade of A to E ineach subject as an index of academic performance. There is substantial variation in schoolquality with some schools having a close to 100 percent pass rate and others producing nota single successful candidate. Table 2 summarizes the senior high school data.

2.3.3 Evidence of Systematic Differences in Application Behavior

As Figure 1 illustrates, there is a strong correlation between the choices of students whoattend the same junior high school. In particular, for a given test score, a student froma relatively high-performing JHS applies to a more selective school than a student froma relatively low-performing JHS. Additionally, students from high-performing schools areadmitted to more selective senior high schools than students from lower performing juniorhigh schools with the same test score. Overall, higher-performing students are less likelyto get an administrative assignment. However, students from higher-performing schools aremore likely to get an administrative assignment than students with the same test scores fromlower-performing junior high schools (Figure 2). To more systematically analyze decision-making behavior in the Ghanaian secondary school application system, I outline a formalmodel of the school choice problem in the next section.

9


2.4 School Choice Model

2.4.1 Setup

Following Chade and Smith (2006), I model the application decision in terms of a portfoliochoice problem. Consider a finite set of students I = {1, · · · , K} each with ability T ∗i whichis unknown to the student, and a finite set of schools S = {1, · · · , M} each with a knownselectivity level qs. Each student receives some utility Uis from attending a school.6 Giventhe uncertainty about her exam performance, each student has some subjective probabilityof being admitted to a given school, Pr (T ∗i > qs) ≡ pis ∈ [0, 1). Note that this setup impliesthat students’ subjective expectations of their admission chances are a rank-preserving trans-formation of their actual admission chances, such that qs = qt ⇐⇒ pis = pit ⇐⇒ pis = pit.Thus, each student has some expected value of applying to a school: zs = pisUis.

Students are faced with the task of selecting an application portfolio which is an orderedsubset A of schools. Finally, there is an application cost c (|A|) which is associated withselecting a portfolio of size |A| schools. In the CSSPS case, institutional restrictions permita fixed number of applications n, so c (|A|) = 0 if |A| ≤ n and c (|A|) =∞ if |A| > n.

In the resulting portfolio choice problem, each student chooses an application set Ai ={1, · · · , N} to maximize net expected utility:

maxA⊆S

f (A)− c (|A|) (2.1)

In particular, the optimal portfolio (A∗) consists of a ranked set of chosen schools andsolves:

maxA⊆S

f (A) = p1U1 + π2p2U2 + · · ·+ πN pNUN

where the subscript indicates the sth-ranked choice in the application set, and N ≤ n. Notethat ps denotes the unconditional probability of being admitted to school s, and πsps is theconditional probability of being admitted to school s given that a student is not admittedto any of her more preferred choices.7

6We can think of this utility as a comprehensive measure of the positive and negative factors associatedwith attending a school (including the costs of tuition payments and distance traveled as well as the benefitsof available facilities, peer quality, and the net present value of expected future income).

7This basic notion of conditional probabilities is sufficient for the present analysis. However, the moregeneral observation here is that merit-based assignment implies that a student’s admission chances at eachschool are correlated, so rejection from school s reduces the expected admission chances at all other schools.For example, a student who receives a negative shock and performs poorly on the BECE will have a lowerchance of gaining admission to all schools than if she had performed as well as expected. As such, herrealized admission outcome for a given school provides additional information on her admission chances forher lower-ranked choices.

10


2.4.2 Equilibrium Solutions

Denote the optimal application set for a student with beliefs B (p1, · · · , pM) by A∗(P ) andits sth element by s∗(P ). We can then consider three cases: 1) perfect information, 2)unconstrained choice, and 3) imperfect information with constrained choice. Examining allthree cases in turn illustrates how institutional features alter the school choice problem.

Case 1: Perfect Information In the case of perfect information, there is no uncertaintyabout admission prospects so students know that they are either guaranteed admission toa school or certain to be rejected. We can summarize the information set as follows: pis =pis ∈ {0, 1}. In this case, the student solves:

A∗(P)

= maxA⊆S

f (A) = max (Uis | pis = 1, Uis > 0) (2.2)

The optimal solution is to apply to the most preferred choice in the set of schools towhich admission is guaranteed. Thus, the application set consists of only one school - thatwhich gives the student the highest payoff for attending.

Case 2: Unconstrained Choice In the absence of constraints on the number of applicationsone can submit, the maximum application set is equivalent to the full set of available choices,n = M . Thus, the student chooses:

A∗(P)

= (1, 2, . . . , N∗) , where (Ui1 > . . . > UiN∗ > 0) (2.3)

The solution is to apply to all schools in the choice set which yield positive utility. Inpractice, this case is evident in school choice programs which have no limit on the number ofschools that students can list. Even with uncertainty about admission prospects, studentscan avoid the complex optimization problem because there is no cost to listing the full setof schools.

Case 3: Imperfect information with constrained choice In this case, there is uncertaintyabout admission prospects so that ps ∈ [0, 1). Additionally, there are some constraints onthe number of schools to which students can apply, which means that n < M . Under theseconditions, there is no simplification so the student must solve the full optimization problemoutlined in equation (1):

A∗(P)

= maxA⊆S

f (A)− c (|A|) (2.4)

In a recent paper, Chade and Smith (2006) demonstrate that this is a difficult problemto solve: “we find ourselves faced with the maximization of a submodular function of setsof alternatives—to be sure, a complex combinatorial optimization problem” (p. 1293). The

11


authors propose an intuitive solution concept which is computationally demanding yet pro-vides a means to derive the characteristics of the optimal portfolio.8 Their contribution iscentral to this analysis.

In essence, the optimal application strategy calls for three main factors:

1. Order schools based on utility

Ui1 > Ui2 > · · · > UiN

2. Order schools based on selectivity

pi1 < pi2 < · · · < piN

⇒ qi1 > qi2 > · · · > qiN

(Note that the second line follows from the earlier modeling assumption that students’subjective rankings of school selectivity have the same ordering and the actual rankingsof schools selectivity.)

3. Diversify selectivity of choices. Chade and Smith (2006) establish that the optimalportfolio is a diversified one. It is more aggressive than the optimal single choicesand not an interval of schools with similar selectivity levels. There are incentives to“gamble upward” and include a selective, high payoff school instead of an additionalschool of moderate selectivity and desirability.

2.4.3 Empirical Implications

The first implication of this theoretical model is that students are solving a complex optimiza-tion problem. Therefore, students who have weak decision making ability or lack guidancewill likely make poor choices. Second, the model demonstrates that students should maketheir application decisions based on the expected value of applying to a school, zs = pisUis.Thus, differences in observed application behavior for students with the same test scores willprimarily result from differences in three factors: their understanding of the school choiceproblem and ability to adopt the optimal application strategy, their beliefs about their ad-mission chances (pis), and their preferences for school characteristics (Uis). In the followingsections, I consider the relative importance of these theoretical insights in explaining observeddifferences in application choices.

8Most earlier theoretical discussions circumvent the complexity of this problem by reducing the choicespace to a set of two schools (see Nagypal (2004) and Chade, Lewis, and Smith (2008) for examples of collegechoice models with two college types).

12


2.5 Decision-Making Quality

One clear implication of the school choice problem facing Ghanaian secondary school appli-cants is that it is optimal for applicants to rank their chosen schools in order of selectivity.Consider student i who applies to two schools with admission chances pi1 < pi2 (let pi1 = 0.2and pi2 = 0.5, for example). If the student ranks school 1 below school 2, and is rejected fromschool 2, then she effectively wastes a spot by listing school 1 since admission chances arecorrelated so she has an even lower chance of gaining admission to school 1. Alternatively,if she lists school 1 above school 2, then she has a higher expected utility.

I do not observe students’ expected admission chances in the data, but I do observeschool selectivity, given by the performance distribution of students admitted to the schoolin previous years. Noting that admission chances (pis) are inversely correlated with schoolselectivity (qs), I use six measures to evaluate the quality of students’ decision making (seeSection A.2. in appendix for more detail).

Table 3 indicates the main predictors of the selectivity of the senior high school to whicha student gains admission. The table includes three panels for the years 2007, 2008 and2009. Each panel presents coefficients from a linear regression of following form:

SHSQualityij = α0 + α1BECEij + α2µj + α3DecisionMakingQualityij + εij (2.5)

where µj is the average test score in student i’s junior high school j. I use a measure ofwhether students rank their choices in order of selectivity as an indicator of the quality ofstudents’ decision-making.

If there was perfect educational mobility, a student’s exam performance would largelypredict the quality of her senior high school so that high-performing students would attendhigh quality senior high schools regardless of their educational backgrounds (i.e., irrespectiveof the quality of their junior high schools). A formal test of this would be to examine whetherα1 = 1 and α2 = 0. In 2007, the coefficient on a student’s performance was significantlylower than one (α1 = 0.50) and the quality of her junior high school played a significantrole in explaining her admission outcome (α2 = 0.17) as did the various indicators for thequality of her decision-making ability. By 2009, the coefficient on student performance hadincreased to 0.62. Moreover, 84 percent of students ranked their selected schools such thattheir first choice was more selective than their lowest-ranked school in 2007. This rose to93 percent of students in 2009. Thus, the results indicate that students’ individual abilityhas played an increasing role in explaining the quality of senior high school students attend,while the quality of a student’s junior high school has become decreasingly relevant and therehas been an improvement in the overall quality of students’ decision-making.

Overall, students from low-performing schools are more likely to make poor decisions (asdemonstrated by the fact that they are more likely to rank a more-selective school lowerthan an less-selective school even though the dominant strategy is to rank more selective

13


schools higher in the list). This implies that students from low-performing schools may notfully understand the application process or may lack guidance about the optimal applicationstrategy.

2.6 Beliefs about Admission Chances

A second explanation for differences in application choices is that students from low-performingschools may have incorrect beliefs about their admission chances. This section formalizes thenotion that differences in application choices may result from imperfect information becausestudents may incorrectly estimate their admission chances.

2.6.1 Normal Learning Model of Beliefs

To begin, assume that student i in school j has true ability T ∗ij. Further, assume that abilityis normally distributed within each junior high school, j:

T ∗ij ∼ N(µj, σ

2j

)Where µj is the mean ability level of students within school j. Given the timing of the

application process, the student does not know T ∗ij when she applies to secondary schools.Instead, she only knows the mean ability of students in her school, µj and she sees a signalof her individual ability (given by her relative performance in her school, for example):

sij = T ∗ij + εij

Assuming that µj and sij are both normal, the student will have a normal posterior beliefabout her ability, with mean:

Tij = λµj + (1− λ) sij

Finally, assume that students make application decisions based on their posterior expec-tations of their ability levels. Thus, two students with the same posterior Tij from the samejunior high school will apply to equally selective senior high schools as their first choice.9

(Even though they may not choose the same schools, their first-ranked choices should beequally as selective.)

We do not observe sij or Tij directly. However, we see a student’s BECE score which is

9Two specific cases under which this assumption would hold are: students have homogeneous preferences;or there is enough variation in the characteristics of schools within a given selectivity band such that twostudents with different preferences can both find schools which maximize their idiosyncratic utility but areequally as selective.

14


her true ability: BECEij = T ∗ij. Note that

E[Tij | T ∗ij, µj

]=E

[λµj + (1− λ) sij | T ∗ij, µj

]=E

[λµj + (1− λ)

(T ∗ij + εij

)| T ∗ij, µj

]=λµj + (1− λ)T ∗ij

It follows that if we know λ then we can form an expectation of the mean of the student’sposterior when she applied, and can then use this estimate to compare whether students withthe same posterior apply to schools of the same selectivity level.

2.6.2 Empirical Estimation of Beliefs

To estimate λ, note that if students i and k from school j choose equally selective schools astheir first choice, then

T ∗ij + εij =T ∗kj + εkj

εij − εkj = T ∗kj − T ∗ij =BECEkj −BECEij

Thus, using the differences in BECE scores for students in the same school who appliedto equally selective first choice schools, we can estimate

var [εij − εkj] = 2var [εij] = [BECEkj −BECEij]2

Effectively, an estimate of var [εij] is 0.5 times the mean squared difference in the actualscores of the pairs. Using this, we can then calculate

λ =var [εij]

var [εij] + σ2j

where σ2j is the variance in test scores for students in school j. The mean estimates from

the data for the 2007 to 2009 cohorts of applicants are σ2j = 0.39 and var [εij] = 0.33.

Figures 3 and 4 display the results from using this approach. I find that the differencesin selectivity of application portfolios virtually disappear when I compare students with thesame posterior Tij from high-performing and low-performing schools. This suggests thatstudents from low-performing schools under-estimate their admission chances and apply toless selective schools as a result. Conversely, students from high-performing schools tend toover-estimate their admission chances which would explain why they have a higher likelihoodof receiving an administrative assignment conditional on their BECE scores (as illustrated

15


in Figure 2). Taken together, it appears that differences in students’ expected admissionchances can potentially explain observed differences in application choices.

2.7 Preferences for School Characteristics

The two preceding sections have demonstrated that differences in decision-making qualityand imperfect information about admission chances are both plausible explanations for whystudents from low-performing elementary schools do not apply to more selective secondaryschools. In this section, I examine a third hypothesis - that students have different preferencesfor school characteristics.

The administrative data on students’ ranked application choices provides a natural op-portunity to analyze students’ revealed preferences for school characteristics using standardmethods of discrete choice analysis.10 However, estimation of student preferences throughdiscrete choice analysis is complicated by the fact that students applying to secondary schoolsin Ghana have incentives to be strategic in order to ensure that they gain admission to oneof their chosen schools. In particular, a student’s first-ranked choice may not necessarily bepreferred to all available schools because students may be taking their admission chancesinto account when selecting their application portfolios. To address this point, I draw on thefact that a student’s first-ranked choice is revealed preferred to schools that are equally asselective. The remainder of this section outlines my methodological approach more formally.

2.7.1 Demand for Schools

To estimate student preferences, I begin by assuming that student i’s expected utility fromattending school s, (Uis) depends on a set of observed and unobserved factors, where theobservable component is a linear function of school selectivity qs and a vector of student-specific school characteristics Xis.

• Assumption 1: Demand for school selectivity is additively separable from demandfor other school characteristics

U∗is = αqs + βXis + εis (2.6)

The error term in this utility function denotes students’ valuation of school characteristicswhich are unobserved by the researcher. The subscript “is” indicates that school character-

10The theoretical foundations of this econometric approach are reviewed in Train (2003). Several recentempirical studies have used application data to analyze revealed preferences in school choice settings, includ-ing: Avery, Glickman, Hoxby, and Metrick (2004); Griffith and Rask (2007); Hastings, Kane, and Staiger(2008).

16


istics result from an interaction between school attributes and student characteristics. Forexample, proximity to a given school varies across students.

Because students are constrained in their choice of what set of schools to apply to, wecannot necessarily conclude that a student applies to her most preferred school. However, ifwe assume that students rank selected schools in order of utilities - Ui1 > Ui2 > · · · > UiN ,then we can conclude that the first choice school is preferred to the other schools in a student’sapplication portfolio. Finally, recall that students pick schools based on zs = pisUis. Thissuggests that any school in the application portfolio is preferred to all other schools whichare equally or less selective.

Taken together, these observations imply that the first ranked choice is preferred to allother schools in which a student has equal admission chances:

pi1Ui1 > pitUit ∀ t s.t. pit = pi1 (2.7)pi1pitUi1 > Uit (2.8)

Ui1 > Uit (2.9)

where Uis = βXis+εis because there is no variation in school selectivity given that all schoolsin the choice set are equally selective.

We can specify a discrete choice estimation framework for the selection of a first choiceschool based on the fact that student i chooses the most preferred school s out of the set ofall schools with equal selectivity (Sp). The dependent variable of interest is defined by:

yis =

{1 iff Uis > Uit ∀ t ε SP

0 otherwise

Thus, the probability that student i lists school s as a first choice is:

Pi (s) = Pr(Uis > Uit ∀ tε SP

)Focus on the subset of alternatives in this restricted choice set (Sp) yields a valid estimateof student preferences due to the independence from irrelevant alternatives (IIA) propertyof the multinomial logit model. If we assume that the error term εis is independently andidentically distributed (i.i.d.) extreme value, then the probability that student i choosesschool s as a first choice can be written as:

Pi (s) = Pr(Uis > Uit ∀ t ∈ SP

)(2.10)

=eXisβ∑tεSP eXitβ

(2.11)

17


This yields the log-likelihood function:

LL (X, β) =N∑i=1

SP∑s=1

yislneXisβ∑tεS e

Xitβ(2.12)

2.7.2 Beliefs

Since I do not observe students’ subjective probabilities of admission (pis), I assume thatthey are systematically related to students’ actual admission chances, pis.

• Assumption 2: Students form expectations about their admission chances based onthe selectivity of schools in the previous year so that pis = g (pis) where the functiong (·) is a rank-preserving transformation which ensures that pis = pit ⇐⇒ pis = pit.

The key requirement of this assumption is that students should be able to accurately gaugewhich set of schools are equally as selective as their first choice. Although this assumptionis somewhat restrictive, it allows for students to have different beliefs about their absoluteadmission chances and only imposes that students have correct beliefs about their relativechances of admission into various different schools. (I.e. certain students may be more orless confident than others, but they must be uniformly biased about their chances of gainingadmission to all schools.) This condition permits a wide range of functional forms for g (·)such as pis = pis + ci , pis = ci · pis or pis = (pis)

2, where students consistently over or underestimate their admission chances in a systematic manner. However, it does not allow formore flexible cases such as pis = cis · pis, where the degree of bias (cis) varies for a givenstudent across schools.

In practice, I use the five nearest neighbors to a students first choice school in order toconstruct the set of ”equally selective” schools.

2.7.3 Heterogeneity

To examine heterogeneity in preferences, I estimate the model outlined in Section 7.1 andallow the estimates of β to vary by student performance (percentile ranking) and JHS quality,µij (the average percentile ranking of peers in a student’s 9th grade class), by interactingschool characteristics with these two student characteristics. The formal test is effectivelyto estimate:

Uijs = β1Xis + β2(Xis ×BECEi) + β3(Xis × µij) + εijs

and evaluate whether β3 6= 0. Finally, I cluster standard errors at the junior high schoollevel to allow for correlation in preferences for students in a given school.

18


2.7.4 Results

I estimate the model using students’ choices in 2008 when they faced the fewest number ofconstraints. I restrict the sample to focus on students who demonstrate an understanding ofthe optimal school choice strategy by ensuring that their first choice school is more selectivethan their lowest-ranked school (condition (6) in Appendix section A.2). Furthermore, Ilimit my analysis to public school students since these are the students who are most likelyto comply with their admission outcomes instead of opting out into the set of elite privateschools which have an independent admissions process. Additionally, private JHS studentsmay have stronger preferences for attending private senior high schools even within thecentralized application system. Lastly, I split the sample by gender and focus on the set ofstudents who qualify for admission to senior high school since I only observe test scores forthese students.

Tables 4 presents summary statistics for the full 2008 cohort and Tables 5 and 6 reportestimates from a multinomial logit regression using data from the restricted 2008 sample ofpublic school students. Out of the terms interacted with JHS quality, the coefficients onschool distance for both male and female students and the indicator for a public secondaryschool for males are statistically significant. However, the indicator for whether a schoolwas established before Ghana gained independence (a measure of historical prestige) is notsignificant. Additionally, there is no significant difference in students’ preferences for singlesex schools or schools with boarding facilities.

Taken together, this analysis suggests that distance and costs of attending a higher-quality school may be more important determinants of application behavior than preferencesfor school quality per se. These results are consistent with findings from Burgess, Greaves,Vignoles, and Wilson (2009) who study school choice in England. The authors find that pref-erences for academic performance do not substantially vary across different socio-economicgroups and largely attribute educational inequality to differences in access to high qualityschools.

2.8 Conclusions

This study set out to examine why there is limited educational mobility in school choicesettings. I find that low expectations about admission chances and poor decision-makingquality explain a substantial part of why students from low-performing schools do not ap-ply to higher-quality schools. I also find that students have different preferences for certainschool characteristics but seem to place equal value on school quality. Altogether, the theo-retical models and empirical evidence presented in this chapter demonstrate that merit-basedschool choice systems can promote educational mobility if there is perfect information andunconstrained choice. These findings suggest that changes in application or admission rulesshould lead to sizeable changes in application behavior. Consequently, policy measures which

19


provide information and guidance on application strategies could greatly increase the equityand efficiency of school choice systems by enabling talented students from low-performingschools to exercise their preferences for attending higher quality schools. I document thedifferential effects of two school choice reforms which support this prediction in the nextchapter.

20


Table 2.1: Student Summary Statistics (2005-2009)

2005 2006∗ 2007 2008 2009

Student characteristicsAge (mean) 17.01 17.10 17.17 17.13 17.25Male 55.40 54.80 54.62 54.90 54.26Attended a public JHS 83.71 82.17 83.80 83.03 84.32Number of JHS classmates (mean) 77.43 63.86 63.44 62.88 67.62

Application choicesNumber of choices permitted (total) 3 3 4 6 6Listed maximum number of choices 98.34 98.79 99.91 94.80 99.98

Admission outcomesAdmitted to a school 55.49 - 51.97 47.22 46.24Number of admitted students (total) 162,077 - 167,279 160,936 183,484

Admitted to first choice 24.57 - 22.72 22.36 29.74Administratively assigned 22.76 - 16.60 9.19 2.13Admitted to school in JHS district 41.18 - 39.32 36.97 33.41Admitted to school in JHS region 76.13 - 76.46 75.64 74.74Admitted to boarding school 56.32 - 67.15 65.72 61.75

Observations 292,070 309,911 321,891 340,823 396,832Notes: Table reports percentages except when alternative measures are indicated inparentheses.∗Data on admission outcomes for 2006 are incomplete.

21


Table 2.2: Senior High School Summary Statistics (2005-2009)

2005 2006 2007 2008 2009

School characteristicsPublic 93.86 81.74 81.20 78.58 80.59Mixed 91.68 91.60 91.50 91.58 90.53Males only 3.70 3.66 3.71 3.55 3.73Females only 4.62 4.73 4.79 4.87 5.75Technical or vocational institute 12.29 12.33 12.33 12.26 12.36Has boarding facilities 44.24 50.39 51.34 51.44 51.45Programs per school (mean) 3.62 3.62 4.04 4.01 4.31

Vacancies reportedVacancies per program (mean) 66.48 63.86 75.38 65.01 88.03Vacancies per school (mean) 246.24 241.79 313.03 260.81 366.23Number of vacancies (total) 160,590 159,157 204,340 176,566 235,849

Academic performanceSSCE pass rate in core subjects 53.39 63.37 68.94 71.12 70.41SSCE pass rate in mathematics 45.17 66.81 54.03 60.48 50.81

Observations 651 657 649 677 644

Notes: Table reports percentages except when alternative measures are indicated in parentheses.

22


Tab

le2.

3:F

acto

rsP

redi

ctin

gth

eS

elec

tivi

tyof

aS

tude

nt’s

Sen

ior

Hig

hS

cho

ol

2007

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Stud

ent’

sB

EC

Esc

ore

perc

enti

le0.

649

0.50

90.

509

0.50

20.

500

0.49

50.

499

0.50

10.

491

(0.0

01)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

Ave

rage

scor

ein

stud

ent’

sJH

S0.

213

0.17

70.

175

0.17

30.

168

0.17

30.

175

0.16

8(0

.002

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)D

ecis

ion-

mak

ing

qual

ity

inde

x(I

)0.

037

0.03

90.

047

0.03

70.

038

0.01

2(0

.001

)(0

.001

)(0

.001

)(0

.001

)(0

.001

)(0

.000

)D

istr

ict

fixed

effec

tsN

oN

oY

esY

esY

esY

esY

esY

esY

es%

ofst

uden

tsw

ith

I=

119

.39

25.7

649

.94

32.0

483

.59

2008

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Stud

ent’

sB

EC

Esc

ore

perc

enti

le0.

713

0.58

40.

583

0.57

80.

576

0.57

00.

574

0.57

30.

560

(0.0

01)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

Ave

rage

scor

ein

stud

ent’

sJH

S0.

201

0.14

90.

143

0.14

10.

136

0.14

10.

146

0.12

9(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)D

ecis

ion-

mak

ing

qual

ity

inde

x(I

)0.

068

0.06

20.

053

0.04

40.

068

0.02

1(0

.002

)(0

.002

)(0

.001

)(0

.001

)(0

.001

)(0

.000

)D

istr

ict

fixed

effec

tsN

oN

oY

esY

esY

esY

esY

esY

esY

es%

ofst

uden

tsw

ith

I=

14.

587.

7127

.38

21.9

489

.72

2009

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Stud

ent’

sB

EC

Esc

ore

perc

enti

le0.

729

0.64

60.

645

0.63

90.

639

0.63

20.

629

0.63

70.

623

(0.0

01)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

02)

Ave

rage

scor

ein

stud

ent’

sJH

S0.

132

0.06

70.

063

0.06

20.

057

0.06

00.

065

0.05

4(0

.002

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)(0

.003

)D

ecis

ion-

mak

ing

qual

ity

inde

x(I

)0.

041

0.04

10.

044

0.04

00.

065

0.01

7(0

.001

)(0

.001

)(0

.001

)(0

.001

)(0

.002

)(0

.000

)D

istr

ict

fixed

effec

tsN

oN

oY

esY

esY

esY

esY

esY

esY

es%

ofst

uden

tsw

ith

I=

19.

9911

.15

35.3

440

.10

92.7

0N

otes

:In

dica

tors

ofde

cisi

onm

akin

gqu

alit

yus

edin

colu

mns

(4)

to(8

)co

rres

pond

toin

dica

tors

1,2,

3an

d6

inA

ppen

dix

A.2

..D

ecis

ion-

mak

ing

qual

ity

mea

sure

used

inco

lum

n(9

)is

anin

dex

ofin

dica

tors

1to

6.A

llco

effici

ents

are

stat

isti

cally

sign

ifica

ntat

the

0.1

perc

ent

leve

l.

23


Table 2.4: Summary Statistics for Discrete Choice Sample (2008)

Male FemaleQuality of Junior High School Low High Low High

Student characteristicsBackground information

Age 17.28 16.47 16.67 16.03Has a disability 0.02 0.01 0.03 0.02Attended a public JHS 90.75 59.45 89.15 57.26Average BECE score percentile in JHS 13.95 62.07 15.70 63.31Student’s BECE score percentile 34.33 69.13 29.25 65.70

Application behaviorListed maximum number of choices 94.46 92.22 94.29 92.63Listed SHSs only 70.25 73.78 90.70 91.34Listed same program for all choices 7.72 13.86 10.96 18.41Listed same school for all choices 0.05 0.03 0.04 0.03First choice more selective than last 79.39 83.59 79.37 84.23

Characteristics of first choice program and schoolAcademic performance

SSCE Pass rate 80.36 89.87 80.95 89.25Average BECE score of admits (2007) 62.94 80.83 64.04 81.87Historically prestigious 15.95 36.97 13.78 31.96

Other school characteristicsPublic 1.00 1.00 1.00 1.00Mixed sex 88.61 65.09 84.78 59.21Technical or vocational institute 1.99 1.71 0.23 0.10Has boarding facilities 82.32 90.62 82.32 91.54Located in student’s JHS district 40.10 31.30 42.61 29.25Located in student’s JHS region 81.45 67.31 81.19 62.49Number of vacancies 426.02 448.78 414.02 410.76

Program choiceGeneral Arts 36.76 34.17 47.06 47.03General Science 14.79 18.96 7.95 10.58

Admissions OutcomesAdministratively assigned 9.60 5.73 14.76 8.21Admitted to first choice school 27.16 38.26 20.67 29.28Admitted to school in JHS district 42.78 32.30 41.90 30.63Admitted to school in JHS region 83.95 69.90 81.88 66.19Admitted to boarding school 56.17 76.62 54.04 75.33

Number of students 50,976 42,704 29,388 37,776

24


Table 2.5: Discrete Choice Model Estimates (Males)

School characteristics [1] [2] [3] [4]

Historically prestigious 0.323 0.433 0.389 0.437(0.034) (0.069) (0.052) (0.068)

SSCE Pass Rate -0.001 -0.001 -0.007 -0.003(0.001) (0.002) (0.002) (0.002)

Public 2.821 4.808 5.157 5.141(0.622) (1.777) (1.396) (1.611)

Single sex 1.942 0.841 1.525 0.857(0.040) (0.087) (0.064) (0.086)

Boarding facilities 0.654 0.578 0.565 0.545(0.038) (0.057) (0.051) (0.060)

Distance -3.755 -4.859 -4.463 -4.866(0.048) (0.088) (0.069) (0.085)

BECE score*Historically prestigious -0.209 -0.152(0.125) (0.134)

BECE score*SSCE Pass Rate 0.001 -0.018(0.005) (0.005)

BECE score*Public -3.861 -0.108(2.901) (1.982)

BECE score*Single sex 1.761 1.956(0.154) (0.174)

BECE score*Boarding facilities 0.256 0.154(0.123) (0.120)

BECE score*Distance 2.156 1.437(0.146) (0.144)

JHS Quality*Historically prestigious -0.227 -0.119(0.129) (0.147)

JHS Quality*SSCE Pass Rate 0.025 0.038(0.007) (0.008)

JHS Quality*Public -5.443 -5.381(2.336) (1.914)

JHS Quality*Single sex 0.901 -0.339(0.152) (0.182)

JHS Quality*Boarding facilities 0.333 0.248(0.180) (0.195)

JHS Quality*Distance 2.030 1.041(0.163) (0.180)

Notes: Dependent variable is an indicator for the student’s first choice school. Regressions also include indicators for distance

squared, number of vacancies and programs offered. Standard errors clustered at junior high school level. All coefficients

significant at the 5 percent level except those in italics. 25


Table 2.6: Discrete Choice Model Estimates (Females)

School characteristics [1] [2] [3] [4]

Historically prestigious 0.522 0.129 0.284 0.123(0.032) (0.069) (0.060) (0.070)

SSCE Pass Rate 0.005 0.007 0.005 0.007(0.002) (0.002) (0.002) (0.002)

Public 1.816 6.728 5.014 6.575(0.583) (1.867) (1.295) (1.691)

Single sex 1.388 0.850 1.092 0.855(0.044) (0.085) (0.071) (0.085)

Boarding facilities 0.845 0.695 0.683 0.658(0.044) (0.068) (0.064) (0.072)

Distance -3.331 -4.723 -4.308 -4.753(0.053) (0.091) (0.082) (0.092)

BECE score*Historically prestigious 0.715 0.667(0.111) (0.134)

BECE score*SSCE Pass Rate -0.004 -0.010(0.005) (0.006)

BECE score*Public -8.542 -5.977(2.721) (2.307)

BECE score*Single sex 0.809 0.840(0.144) (0.176)

BECE score*Boarding facilities 0.482 0.264(0.167) (0.166)

BECE score*Distance 2.679 2.077(0.154) (0.147)

JHS Quality*Historically prestigious 0.542 0.072(0.120) (0.148)

JHS Quality*SSCE Pass Rate 0.003 0.011(0.006) (0.008)

JHS Quality*Public -6.622 -2.816(2.258) (1.953)

JHS Quality*Single sex 0.512 -0.058(0.139) (0.172)

JHS Quality*Boarding facilities 0.586 0.388(0.197) (0.215)

JHS Quality*Distance 2.368 0.831(0.185) (0.202)

Notes: Dependent variable is an indicator for the student’s first choice school. Regressions also include indicators for distance

squared, number of vacancies and programs offered. Standard errors clustered at junior high school level. All coefficients

significant at the 5 percent level except those in italics. 26


Box 1: Timeline for School Selection and Placement in Ghana (2005-2008)

1. Students Submit Choices

• October: West Africa Exam Council (WAEC) registers students for Basic Edu-cation Certification Exam (BECE)

– Collects students’ lists of program choices

– Provides CSSPS Secretariat with data on student backgrounds and choices

2. Schools Declare Vacancies

• January: Ministry of Education supplies CSSPS Secretariat with

– register of all JHSs

– register of all SHSs (with numbers of program vacancies)

3. Student Quality Revealed

• April: Students take the BECE exams

4. Students Admitted to Schools

• July/August: WAEC sends scores to CSSPS Secretariat which then

– Assigns each student an aggregate score based on performance in 4 core and2 best subjects

– Places qualified students in schools according to ranked choices and deferredacceptance algorithm, with priority determined by aggregate BECE scores

• A few weeks after CSSPS Secretariat receives BECE results:

– Placement results released and displayed in junior and senior high schools orretrieved by text messaging candidate IDs to the CSSPS Secretariat

27


Figure 2.1: Exam Performance and Application Choices (2008)

4050

6070

80m

ean

sele

ctiv

ity o

f cho

sen

seni

or h

igh

scho

ols

0 20 40 60 80 100student's BECE score percentile

high performing JHS low performing JHS

Notes: This figure illustrates differences in application choices for students with the same testscores but from low and high-performing junior high schools (JHSs). The x-axis is indexed bystudent percentiles in the standardized high school entrance exam (BECE). The y-axis illustratesthe mean selectivity of the senior high schools to which a student applied. The solid linerepresents students who attended a high-performing JHS. The dashed line represents studentswho attended a low-performing JHS.

28


Figure 2.2: Exam Performance and Administrative Assignments (2008)

0.2

.4.6

.81

adm

inis

trat

ive

assi

gnm

ent (

shar

e of

stu

dent

s)

0 20 40 60 80 100students' BECE score percentile


Notes: This figure illustrates differences in admission outcomes for students with the same examscores, but from different junior high schools. The x-axis is indexed by student percentiles in thebasic education certification exam (BECE). The y-axes illustrates the share of students receivingan administrative assignment. The solid line represents students who attended a high performingJHS. The dashed line represents students who attended a low-performing JHS.

29


Figure 2.3: Expected and Actual Exam Performance (2008)

4050

6070

80m

ean

sele

ctiv

ity o

f cho

sen

seni

or h

igh

scho

ols


actual BECE score expected BECE score

Students from high-performing junior high schools

Notes: The figure focuses on students who attended a high-performing Junior High School. They-axis illustrates the mean selectivity of the senior high schools to which a student applied. Thesolid lines indicate the relationship between students’ application decisions and their actualBECE scores. The dashed lines indicate the relationship between students’ application decisionsand their expected BECE scores. Students’ expected BECE scores are calculated by using ashrinkage estimator to weight students’ individual BECE performance by the averageperformance in their junior high school (see Section 6 for more detail).

30


Figure 2.4: Expected and Actual Exam Performance (2008)

4050

6070

80m

ean

sele

ctiv

ity o

f cho

sen

seni

or h

igh

scho

ols


actual BECE score expected BECE score

Students from low-performing junior high schools

Notes: The figure focuses on students who attended a low-performing Junior High School. They-axis illustrates the mean selectivity of the senior high schools to which a student applied. Thesolid lines indicate the relationship between students’ application decisions and their actualBECE scores. The dashed lines indicate the relationship between students’ application decisionsand their expected BECE scores. Students’ expected BECE scores are calculated by using ashrinkage estimator to weight students’ individual BECE performance by the averageperformance in their junior high school (see Section 6 for more detail).

31


Figure 2.5: Expected Exam Performance and Application Choices (2008)

3040

5060

7080

mea

n se

lect

ivity

of c

hose

n se

nior

hig

h sc

hool

s

0 20 40 60 80 100students' expected BECE score percentile


Notes: This figure illustrates differences in application choices for students with the sameexpected ability but from low and high performing junior high schools (JHSs). Students’ expectedability level is calculated by using a shrinkage estimator to weight students’ individual BECEperformance by the average performance in their junior high school. The y-axis illustrates themean selectivity of the senior high schools to which a student applied. The solid line indicatesstudents who attended a high-performing JHS. The dashed line indicates students who attended alow-performing JHS.

32


Appendix

A.1: Student Optimal Stable Matching Mechanism

The CSSPS uses a deferred-acceptance algorithm (or Student-Optimal Stable Matchingmechanism) for school placement (Gale and Shapley (1962) provide a more detailed descrip-tion). Under this algorithm, students are placed in schools according to their preferencesand priority is determined strictly by academic merit as follows:

• Step 1 : Each student i proposes to the first school in her ordered list of choices,Ai. Each school s tentatively assigns its seats to proposers one at a time in order ofpriority determined by students’ academic performance (measured by aggregate BECEscores). Each school rejects any remaining proposers once all of its seats are tentativelyassigned.

In general, at

• Step k : Each student who was rejected in a previous round proposes to his or her kthchoice school. Each school compares the set of students it has been holding with theset of new proposers. It tentatively assigns its seats to these students one at a time inorder of students’ academic performance and rejects remaining proposers once all ofits seats are tentatively assigned.

The algorithm terminates when no spaces remain. Each student is then assigned to his orher final tentative assignment. Rejected students remain unassigned. The mechanism hasbeen shown to be stable and strategy proof. It is not Pareto efficient, however, it is Paretooptimal relative to all other stable matching algorithms (Haeringer and Klijn (2009)).

Note that academic performance is the ultimate determinant of school assignment in theCSSPS and no preferential treatment is given to students for listing a school as a first choice.Thus, there is no penalty for ranking schools in true preference order within the set of listedchoices. This contrasts with the Boston mechanism (formerly used by Boston public schoolsand several other school districts in the United States) which assigns students based on theirfirst choices in the same way but then keeps these initial assignments for all subsequent roundsand does not allow higher priority students to displace students already assigned to a schoolin a preceding round. There are clear incentives for making a strategic first choice under theBoston mechanism which do not apply under the deferred-acceptance algorithm. The CSSPStechnical working committee produced a handbook outlining a set of “Guidelines for Selectionand Admission into Senior Secondary Schools and Technical/Vocational Institutes” (MOES(2005)). The publication highlights the issue of “Displacement of 1st choice candidates and2nd choice candidates as a matter of merit or better performance” and emphasizes the notionthat placement priority is based on “merit not choice”. (p.4)

33


The deferred-acceptance algorithm has several desirable properties when students areallowed to rank all schools - it is student optimal, strategy proof and eliminates “justi-fied envy”11 (Gale and Shapley (1962); and Abdulkadiroglu and Sonmez (2003)). The at-tractiveness of this mechanism decreases only slightly when students are forced to make aconstrained choice with an opportunity to rank only a limited number of schools (Abdulka-diroglu, Pathak, and Roth (2009), p.1975). However, the CSSPS’s merit-based priority maycreate incentives for strategic behavior because students are encouraged to select schoolsaccording to their anticipated BECE scores and expected admission chances.

A.2: Measures of Decision-Making Quality

I do not observe students’ expected admission chances in the data, but I do observe schoolselectivity, given by the performance distribution of students admitted to the school inprevious years. Noting that admission chances (pis) are inversely correlated with schoolselectivity (qs), I use six measures to evaluate the quality of students’ decision making:

1. qi1 > qi2 > . . . > qiN : choices are strictly ranked in order of selectivity

2. qi1 ≥ qi2 ≥ . . . ≥ qiN : choices are weakly ranked in order of selectivity

3. qi1+10 ≥ qi2, qi2+10 ≥ qi3, . . . ≥ qiN : choices are weakly ranked in order of selectivity,allowing for a band of 10 percentile points around the selectivity level of each school

4. qi1 +20 ≥ qi2, qi2 +20 ≥ qi3 . . . ≥ qiN : choices are weakly ranked in order of selectivity,allowing for a band of 20 percentile points around the selectivity level of each school

5. qi1 ≥ qi2, . . . qiN and qiN ≥ qiN−1, . . . q1 : the highest-ranked choice is the most selectiveschool and the lowest-ranked choice is least selective

6. qi1 ≥ qiN : the highest-ranked choice is weakly more selective than the lowest-rankedchoice

Finally, I also construct a decision-making index which assigns a value of 6 to students whosatisfy condition (1), a value of 5 to those who satisfy condition (2), and so on, assigning avalue of 1 to students who satisfy condition (6) and a value of 0 to those who fail to satisfyany of the six conditions. The final row in each panel of Table 6 indicates the share ofstudents who satisfy each condition in a given year. For the most part of my analysis, I usecondition (6) as my preferred measure of decision-making quality since it predicts the largestchange in the selectivity of senior high schools to which students gain admission.

11This requires that there should be no unmatched student-school pair (i, s) where student i prefers schools to her final assignment and has higher priority than another student who is assigned to school s.

34

Chapter 3

Can School Choice Reforms ProvideMore Equal Access to Education?

3.1 Introduction

A testable prediction of the preceding analysis and earlier research findings is that simplifyingthe application process or providing additional information and guidelines should encouragestudents from low-performing elementary schools to apply to a more selective set of secondaryschools. To validate this prediction, I use variation from two recent policy reforms in Ghanato examine the effect of changing the application process. The first reform increased the num-ber of secondary schools that each student could list. The second reform assigned secondaryschools into four categories based on their available facilities and restricted the number ofschools that a student could select from each category. These restrictions effectively encour-aged students to apply to a more diversified set of schools. Using a difference-in-differencesapproach to analyze the effect of each reform, I find that both reforms decreased the differ-ence in selectivity of schools chosen by students from high-performing and low-performingelementary schools, which suggests that application and admission rules play a significantrole in explaining differences in application behavior. Moreover, these results are consistentwith a setting in which imperfect information has a strong impact on students’ choices.

Chapter 2 provided a theoretical discussion of potential explanations for observed dif-ferences in application behavior. A complementary approach to understanding why certainstudents fail to apply to selective schools is to evaluate whether students from different ed-ucational backgrounds respond differently to school choice reforms. If changes in featuresof the assignment mechanism lead to a decrease in the distinctions between students fromhigh-performing and low-performing schools, then this would suggest that part of the differ-ence in application behavior may be due to the application rules governing the school choicesystem and not to preferences alone.

35

Chapter 3. Can School Choice Reforms Provide More Equal Access to Education?

3.2 History of School Choice Reforms in Ghana

The nature of the CSSPS has changed since it was established in 2005. Firstly, the numberof permitted choices has increased over time. Students were allowed to list up to threechoices when the CSSPS began in 2005, this increased to four choices in 2007 and to sixchoices in 2008. Moreover, Ghana Education Service introduced an additional reform in2009 which was designed to improve the decision-making ability of students. (Box 2 detailsthese changes.)

The noteworthy characteristics of the 2009 reform are as follows:

1. Public secondary schools were assigned into four categories based on their “availablefacilities” and students were restricted in their selection of schools from each category.In particular, students could only pick one Category A school, two Category B schools,and no more than five Category C or D schools.

2. Students were allowed to list up to six program choices as they had been in the past,but were no longer allowed to pick more than one program from any given school.

This categorization only affected choices in 2009 since it was not available in earlier years.Students in the 2008 cohort submitted their lists of choices in September 2007 and thecategories were not publicized until February 2009 when students in the 2009 cohort weresubmitting their choices, so there is no possibility that the categorization had a causal effecton choices prior to this.

The categorization of schools under this new scheme is positively correlated with schoolage (historical prestige) and academic performance. Figure 5 provides some descriptivestatistics and illustrates the distribution of selectivity for schools in each category. Onaverage, the median BECE percentile of students admitted in the year preceding the reformwas 76.87 for Category A schools but 18.03 for Category D schools. However, correlationbetween school quality and categorization is not perfect. In particular, some schools whichwere assigned to Category A were obviously elite but others were not of high quality by anyobservable measures. Discussions with Ghana Education Service revealed that schools werecategorized based on their capacity to admit students, their historical selectivity, as well asthe concern for spatial variation by ensuring that each region contains at least one schoolfrom each category.

The complexity of the choice problem and features of the optimal portfolio naturallysuggest the use of a rule of thumb as an alternative to explicitly solving the optimizationproblem. Although this may not always be optimal, a rule of thumb provides an easy meansto approximate the optimal portfolio choice when agents are hampered by decision-makingcosts or limitations. In particular, suppose that schools lie on a continuum of desirabilityand selectivity. On one end of this spectrum, a reach school represents a highly preferredschool which is highly selective. The safety school is at the other end of the spectrum and

36


reflects a less preferred option but one which has lower admission standards and so ensuresa successful application. In the middle lie a set of match schools where admission chancesare favorable and there is strong appeal. Students can approximate the best portfolio byapplying to at least one reach, one match, and one safety school.1 Additionally, it is optimalto rank schools based on payoffs and admission standards.

The new conditions imposed by the Ghanaian categorization reform are similar in spiritto the reach, match and safety school rule of thumb. Category A primarily consists ofmore selective “reach” schools, Category B of less selective schools and Categories C and Dconsist of the least selective schools. The key restriction in the program, however, is thatthese categorizations are specified in absolute terms and not in relation to an individualstudent’s expected admission chances.

3.3 Data

I use two main types of data to analyze the impact of Ghana’s categorization reform: 1)CSSPS administrative data on student background characteristics, entrance exam scores,choices, and placement outcomes, and 2) supplementary data on school characteristics, in-cluding a standardized measure of schools’ academic performance. These data cover theuniverse of students who applied through the CSSPS between 2005 and 2009. I focus inparticular on three cohorts: the 321,891 students who applied to senior secondary schoolin 2007 when they could list only four choices, the 340,823 students who applied in 2008with six unrestricted choices, and the 395,844 who applied in 2009 under the reformed cat-egorization system. There were no default school assignments in any of these three years,so students were not guaranteed admission to any particular school if they left their formsblank or if they were not admitted to any of their listed choices. Thus, 95 percent of studentssubmitted a complete list of all choices even in the years when they were permitted to selectup to six choices. Another benefit of this centralized admission system is that I am able toobserve application choices as well as admission outcomes for the full sample of applicantseach year.2

1This rule of thumb is a commonly accepted guideline for college choice in the US. The websitewww.go4ivy.com recommends that the following thresholds be used to define school types - Reach/Stretch: 1to 49 percent admission chance, Match/Likely: 50 to 85 percent admission chance, Safety: 86 to 99 percentadmission chance. They provide the following additional guidance: “We recommend that you choose atleast two colleges in each category (stretch, likely, safety) to help maximize your chances of getting in. Tryto minimize the number of schools in the outer ranges. For example, consider applying to no more thanone single-digit stretch school (i.e. 7%) because such schools do not match your background well. You canprobably find an equally prestigious school where you have a better chance of getting in.”Go4ivy (2010)

2Similar studies of college choice in the US have used administrative data on SAT score-sending behavioras a proxy for students’ college application decisions, however, it is difficult to obtain a large sample ofstudent-level data on admission outcomes and matriculation decisions. Survey data are often used, whichlimits the feasible sample size as well as the researcher’s ability to observe general equilibrium effects (see

37


3.3.1 Establishing the Impact of Categorization Constraints

To illustrate the impact of the categorization reform, I focus on two groups of students -those who could potentially have benefitted and those who could potentially have experiencedutility losses. (See Table 5 for a summary and A3 in the appendix for more detailed examplesof how the reform could have impacted students’ outcomes.) Students who potentiallybenefitted from the program are those who previously would have applied to no selectiveschools and received an administrative assignment. Following the reform, they are forced toapply to no more than 1 Category A and 2 Category B schools so that they must includesome non-selective schools in their portfolio. I estimate that 4.36 percent of students fall intothis category. Another group of students who could benefit is those who would have appliedto six C or D schools, but could have gained admission to a more selective A or B school.Under the new reform, they are forced to select at least one A or B school, and subsequentlygain admission to one of these schools. I estimate that 0.45 percent of students fall into thiscategory. Note that admission to a more selective school is not an automatic result of thereform even when constraints are binding, because students who genuinely did not want toattend an A or B school could simply list it as their sixth choice. Similarly, students whodid not want to attend a selective school could apply to one of the few non-selective A orB schools. Finally, the majority of students who applied to only one A or B did not gainadmission to this school and so ended up in a C or D school as the likely would have in theabsence of the program.

Students who may have been negatively affected by the program are those who wouldhave liked to apply to more than one A school or more than two B schools. These students arenow forced to apply to C or D schools when they could have gained admission to an A or Bschool if they had been allowed to rank more than the number permitted under the reformedpolicy. I estimate that 8 to 12 percent of students fall into this category. Additionally, asmall share of students (0.1 percent) applied to the maximum of 5 C or D schools and didnot gain admission to any of their chosen schools. These students received an administrativeassignment which may have been avoided if they had been allowed to apply to a sixth Cor D school. To more systematically evaluate the welfare impact of Ghana’s school choicereform, I outline a formal model of the school choice problem in the next section.

3.4 Difference-in-Differences Estimation

In the remainder of this section, I evaluate the effects of two policies which may have encour-aged educational mobility in Ghana: 1) increasing the number of permissible choices and2) providing information and a set of guidelines on school choice strategies. I estimate the

Avery, Glickman, Hoxby, and Metrick (2004), Griffith and Rask (2007), and Dale and Krueger (2002) forexamples of analysis using survey data.)

38


impact of the first policy by observing changes following the increase from 4 choices in 2007to 6 choices in 2008. I estimate the impact of the second policy by observing the changesfollowing the categorization reform in 2009.

More specifically, I evaluate the effect of the reforms by estimating the following regres-sion:

Yi = α0 + α1BECEi + γh + δa + ηah + εi (3.1)

Where γh indicates a student who attended a high-performing JHS, δa denotes the periodafter a reform and ηah is the interaction of these two terms. This difference-in-differencesframework allows me to compare the change in application behavior for students from lowerperforming schools relative to the change for students from higher performing schools. Asearlier, I define students from lower performing schools as those who come from a schoolwhere the average performance of students in the BECE is below the median average for allschools. Conversely, students from higher performing schools are those who attend a JHSwhere the average score of students is above the median average for all schools.

Policy reforms such as these are likely to have substantial distributional effects (Bitler,Gelbach, and Hoynes (2006)). As an extension of the basic difference-in-differences estima-tion, I examine whether the reforms had heterogeneous effects on students across the perfor-mance distribution by estimating a separate parameter for each BECE score percentile. I dothis by introducing a percentile indicator variable βp and estimating the following regression:

Yi = β0 + βp + γh + δa + ηah + θph + θpa + θpah + εi (3.2)

The θ parameters capture individual changes for students at each BECE score percentile.

3.5 Results

Table 7 illustrates the results for the mean coefficients estimated from equation (13). I finda decrease in the difference in selectivity of schools to which students from high-performingand low-performing schools applied following the reforms. Both groups of students appliedto more selective first choices, and less selective sixth choices but the gap between theirchoices decreased.3 With regard to admission outcomes, I find a decrease in administrativeassignments following each reform and a slight increase in the difference-in-difference be-tween students from high-performing and low-performing schools (indicating that the shareof administrative assignments decreased, for low-performing students more than for high-performing students). Moreover, I find that the difference in the selectivity of schools towhich students from lower-performing junior high schools were admitted increased follow-ing both reforms, but I find that the difference in differences also increased following the

3Pallais (2010) finds a similar result in her analysis of the effect of increasing the number of free scorereports provided for ACT-takers.

39


reforms. These changes in admission outcomes capture two opposing forces: on one hand,the decrease in administrative assignments implies an increase in the selectivity of schoolsto which low-performing students from high-performing schools are admitted; on the otherhand, the changes in selectivity of choices implies a decrease in the advantage of attendinga higher performing school to begin with. The effect of decreased administrative assign-ments outweighs the changes in application choices so the net impact of these two factors isthat students from high-performing schools ended up getting into more selective schools onaverage following the reforms.

Beyond these general changes, there is some degree of heterogeneity in the difference-in-difference estimates for students across the BECE performance distribution. Figures 6 and7 display the results from estimating a separate coefficient for each BECE score percentileusing equation (14) with the mean selectivity of chosen schools and the selectivity of thesecondary school to which a student was admitted as the outcomes of interest. The dashedline in each figure illustrates the mean effect (estimated using equation (13)), while the solidline indicates the individual coefficients for students at each percentile of BECE performance.Notably, the difference in admission outcomes for students from high-performing and low-performing schools is slightly more pronounced at the tails of the distribution, althoughnot at a statistically significant level. Furthermore, the general effect of increasing studentchoices is to increase the selectivity of admissions for students in the middle of the testscore distribution, while imposing restrictions on choice lowered the quality of schools forhigh-performing and low-performing students and additionally increased the selectivity levelof schools for students in the middle of the distribution. Finally, there was no systematicvariation in the difference-in-difference estimates along the test score distribution.

The implications of this analysis are that the applications choices of students from high-performing and low-performing schools became increasingly similar following each reformon average. However, students from high-performing schools continued to apply to moreselective schools even after the categorization reform. Additionally, administrative assign-ments fell following each reform, but students from high-performing schools ended up gainingadmission to more selective schools than students from low-performing schools on average,emphasizing the substantial re-distributional effects of these reforms.

3.6 Conclusions

The aim of this analysis was to estimate the welfare changes associated with restrictions onstudents’ application choices. Altogether, the findings suggest that institutional reforms inGhana may have improved outcomes for students at risk of over-estimating their admissionchances, but at the cost of utility for students who were able to identify the optimal applica-tion portfolio on their own. Moreover, these findings suggest that changes in application oradmission rules can lead to sizeable changes in application behavior and varied changes in

40


admission outcomes depending on the general equilibrium effects of student assignment toavailable spaces. Consequently, policy measures which provide information and guidance onapplication strategies can greatly increase the equity and efficiency of school choice systemsby enabling talented students from low-performing schools to exercise their preferences forattending higher quality schools. I document the differential effects of two school choicereforms which support this prediction.

This research has broader implications for other contexts in which policy makers seek toencourage high-performing students from underprivileged backgrounds to apply to more se-lective schools. First, these findings suggest that the elimination of school choice constraintscould potentially lead to decreases in student sorting along socio-economic characteristicsand to increases in sorting along academic dimensions. Practical steps in this direction in-clude: the introduction of the common application for college admissions in the US, increasesin the number of free reports for standardized test scores, and the elimination of limits onthe numbers of applications students can submit in centralized choice-systems. Notably,however, these interventions benefit all students uniformly so may not necessarily decreaseadvantages for students from high-performing schools. Second, students’ application behav-ior seems to rely heavily on students’ ability to understand the school assignment mechanismand to implement an effective school choice strategy, so reforms will likely have only a lim-ited impact on expanding students’ educational opportunities unless they are accompaniedby targeted efforts to improve the level of guidance and information available to studentsin lower-performing schools. Lastly, schooling choices also appear to be driven by consid-erations about non-academic factors (especially cost and proximity) so that socio-economicdifferences in application behavior will likely persist unless there are complementary effortsto increase access and affordability.

This study also highlights some limitations of school choice programs which impose re-strictions on decision-makers’ behavior. On the whole, these findings suggest that the elimi-nation of market frictions could potentially lead to decreases in student sorting along socio-economic characteristics and to increases in sorting along academic dimensions. However,students’ application behavior seems to rely heavily on students’ actual preferences, so in-stitutional reforms will likely have only a limited impact on expanding access to educationalopportunities unless these reforms are accompanied by efforts to improve the attractivenessof schools’ non-academic characteristics.

41


Table 3.1: Potential Positive Impact of Reform (2008 data)

Potential Beneficiaries

Unsuccessfula High Achieving All

Low-Aimingb

Applicants Applicants

Potential Beneficiaries

As percentage of all admits 9.19 8.31 17.13

(total number) (14,787) (13,372) (27,574)

Potential Impact of Reform

Potentially binding constraint ≤1 A and ≤2 B ≤5 C or D

Students not in compliance


(total number) (7,014) (727) (7,741)

As percentage of admits who are

Unsuccessful Applicant 47.43

High Achieving, Low Aiming 5.44

Either 28.07

Notes: a Unsuccessful applicants are those who were administratively assigned because they didnot get admitted to any of their chosen schools. b High achieving, low aiming applicants are thosewho were admitted to a non-selective school but whose scores were higher than the median scorein a selective Category A or B school.

42


Table 3.2: Estimated Positive Impact of Reform

Binding Constraint (Positive Outcome)

Choose 1 A and 2 B Choose 5 C or D Either

(Admitted to (Admitted to

Pre-reform 6th Choice) Selective A or B)

At constraint


(total number) (13,720) (22,620) (36,340)

At constraint, get positive outcome


(total number) (791) (1,371) (2,162)

As percentage of admits who

choose 1 A and 2 B 2.08

choose 5 C or D 6.06

were at either constraint 4.56

Post-reform

At constraint


(total number) (85,478) (20,038) (105,516)

At constraint, get positive outcome


(total number) (8,744) (1,762) (10,506)

As percentage of admits who

choose 1 A and 2 B 10.23


were at either constraint 9.96

Reform Impact

Change in % at constraint with positive outcomes 4.70

Note: This table illustrates the change in the number of students who were at a constraint andexperienced a positive admissions outcome.

43


Table 3.3: Potential Negative Impact of Reform (2008 data)

Potentially Affected Students

Admitted to A B C or D All

Relevant Population

As percentage of all admits 17.79 19.35 40.71 96.61

(total number) (28,632) (31,138) (95,714) (155,484)

Potential Impact of Reform

Potentially binding constraint ≤1 A ≤2 B ≤5 C or D

Students at risk

As percentage of all admits 6.17 1.72 0.10 7.99

(total number) (9,934) (2,770) (162) (12,866)

As percentage of admits who are

admitted to A 34.70

admitted to B 8.90

admitted to C or D 0.17

admitted to A, B, C or D 8.27

Notes: Students who are potentially bound by the constraint are those who: were admittedto a category A school which was ranked 2nd to 6th on their list; admitted to a category Bschool which was ranked 3rd to 6th on the list; admitted to a category C or D school whichwas ranked 6th on their list.

44


Table 3.4: Estimated Negative Impact of Reform

Binding Constraint (Negative Outcome)

Choose 1 A Choose 2 B Choose 5 C/D Any

(rejected (rejected (Admin.

Pre-reform from A) from B) Assignment)

At constraint

As % of all admits 9.33 5.38 14.06 12.30

(total number) (15,016) (8,653) (22,620) (41,921)

At constraint, negative outcome

As % of all admits 3.44 1.14 0.75 5.10

(total number) (5,538) (1,831) (1,203) (8,201)

As % of admits who

choose 1 A 36.88

choose 2 B 21.16


were at any constraint 19.56

Post-reform

At constraint

As % of all admits 30.05 26.40 11.52 20.10

(total number) (52,271) (45,920) (20,038) (76,230)

At constraint, negative outcome

As % of all admits 16.08 5.93 0.17 17.41

(total number) (27,960) (10,320) (289) (30,274)

As % of admits who

choose 1 A 53.49

choose 2 B 22.47


were at any constraint 39.71

Reform Impact

Change in % at constraint with negative outcomes 12.31

Note: This table illustrates the change in the number of students who were at a constraintand experienced a negative admissions outcome. The vulnerable populations are studentswho score higher than the median score at a selective Category A or B school and who choose1 A school as their first choice and/or choose 2 B schools in their top three choices.

45

Chapter 3. Can School Choice Reforms Provide More Equal Access to Education?T

able

3.5:

Mea

nD

iffer

ence

sin

App

licat

ion

Cho

ices

and

Adm

issi

onO

utco

mes

Bef

ore

and

Aft

erR

efor

ms

Sele

ctiv

ity

ofC

hoic

esA

dmis

sion

Out

com

es20

07-2

008

Fir

stL

ast

Por

tfol

ioA

dmin

istr

ativ

eSe

lect

ivit

yP

eer

Qua

lity

(inc

reas

efr

om4

to6

choi

ces)

Cho

ice

Cho

ice

Ave

rage

Ass

ignm

ent

ofSH

Sin

SHS

Stud

ent’

sB

EC

Esc

ore

perc

enti

le0.

311

0.12

60.

234

-0.3

710.

550

0.60

5(0

.003

)(0

.004

)(0

.003

)(0

.006

)(0

.004

)(0

.004

)H

igh-

perf

orm

ing

JHS

2.09

15.

484

3.51

50.

025

0.88

91.

241

(0.3

62)

(0.3

82)

(0.3

09)

(0.0

05)

(0.2

58)

(0.2

12)

Aft

erre

form

4.19

7-3

.321

-0.7

41-0

.071

3.29

2-1

.439

(0.2

46)

(0.1

99)

(0.1

71)

(0.0

03)

(0.1

26)

(0.1

07)

Aft

erre

form×

Hig

h-pe

rfor

min

gJH

S-0

.699

-6.9

71-2

.174

0.00

62.

826

1.59

1(0

.456

)(0

.458

)(0

.383

)(0

.006

)(0

.393

)(0

.313

)Se

lect

ivit

yof

Cho

ices

Adm

issi

onO

utco

mes

2008

-200

9F

irst

Las

tP

ortf

olio

Adm

inis

trat

ive

Sele

ctiv

ity

Pee

rQ

ualit

y(c

ateg

oriz

atio

nan

dre

stri

ctio

ns)

Cho

ice

Cho

ice

Ave

rage

Ass

ignm

ent

ofSH

Sin

SHS

Stud

ent’

sB

EC

Esc

ore

perc

enti

le0.

292

0.01

50.

186

-0.1

800.

618

0.64

7(0

.003

)(0

.003

)(0

.002

)(0

.004

)(0

.004

)(0

.004

)H

igh-

perf

orm

ing

JHS

1.92

12.

837

2.76

6-0

.004

1.22

81.

626

(0.3

54)

(0.2

53)

(0.2

53)

(0.0

04)

(0.2

16)

(0.1

79)

Aft

erre

form

2.12

3-8

.062

-0.4

41-0

.086

-0.3

440.

793

(0.2

22)

(0.2

02)

(0.1

41)

(0.0

03)

(0.1

26)

(0.0

97)

Aft

erre

form×

Hig

h-pe

rfor

min

gJH

S-1

.755

-4.1

84-1

.938

0.03

20.

757

-0.1

07(0

.378

)(0

.409

)(0

.281

)(0

.004

)(0

.277

)(0

.218

)N

otes

:T

able

sre

port

the

diffe

renc

ein

mea

nsfo

rap

plic

atio

nde

cisi

ons

and

adm

issi

onou

tcom

es.

The

top

pane

lan

alyz

esth

e20

08re

form

whi

chin

crea

sed

the

max

imum

num

ber

ofap

plic

atio

nsfr

omfo

urto

six

choi

ces.

The

bott

ompa

nel

anal

yzes

the

2009

refo

rmw

hich

impo

sed

ash

iftfr

omsi

xun

rest

rict

edch

oice

sto

six

rest

rict

edch

oice

sun

der

the

new

cate

gori

zati

onsy

stem

.T

hepe

riod

“bef

ore”

are

form

isth

epr

eced

ing

year

,th

epe

riod

“aft

er”

isth

eye

arof

the

refo

rm.

Out

com

eof

inte

rest

isin

dica

ted

atth

eto

pof

each

colu

mn.

All

coeffi

cien

tsar

esi

gnifi

cant

atth

e1

perc

ent

leve

lex

cept

for

thos

ein

ital

ics.

46


Figure 3.1: Categorization and Quality of Public Senior High Schools

School QualitySelectivitya Pass Rateb Prestigiousc Total

Available FacilitiesCategory A 76.87 73.23 % 22 65Category B 70.26 66.71 % 10 72Category C 40.05 48.07 % 2 178Category D 18.03 41.19 % 0 178

Mean (Total) 41.37 52.87 % (34) (493)

020

4060

8010

020

08 s

elec

tivity

0 20 40 60 80 1002007 selectivity

Category A (Prestigious) Category A (Less Prestigious)Category B (Prestigious) Category B (Less Prestigious)Category C or D

Notes: School selectivity indicates the median BECE percentile of students admitted to a schoolin a given year. Historically prestigious schools are those which were constructed before Ghanagained independence in 1957.

47


Figure 3.2: Differences-in-Differences Regression Estimates (Application Choices)

Differences between students from low and high performing schools2007-2008 2008-2009

-30

-15

015

30di

ffere

nce

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


-30

-15

015

30di

ffere

nce

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


Differences between before and after a reform2007-2008 2008-2009

-30

-15

015

30di

ffere

nce

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


-30

-15

015

30di

ffere

nce

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


Difference in differences between students from low and high performing schools, before and aftera reform

2007-2008 2008-2009

-30

-15

015

30di

ff-in

-diff

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


-30

-15

015

30di

ff-in

-diff

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


Notes: These figures illustrate results from difference-in-difference regressions estimated with interactionterms for each percentile in the performance distribution.

48


Figure 3.3: Differences-in-Differences Regression Estimates (Admission Outcomes)


-40

-20

020

40di

ffere

nce

in s

elec

tivity

of s

enio

r hi

gh s

choo

l


-40

-20

020

40di

ffere

nce

in s

elec

tivity

of s

enio

r hi

gh s

choo

l



-40

-20

020

40di

ffere

nce

in s

elec

tivity

of s

enio

r hi

gh s

choo

l


-40

-20

020

40di

ffere

nce

in s

elec

tivity

of s

enio

r hi

gh s

choo

l



2007-2008 2008-2009

-40

-20

020

40di

ff-in

-diff

in s

elec

tivity

of s

enio

r hi

gh s

choo

l


-40

-20

020

40di

ff-in

-diff

in s

elec

tivity

of s

enio

r hi

gh s

choo

l


Notes: These figures illustrate results from difference-in-difference regressions estimated with interactionterms for each percentile in the performance distribution. The outcome variable is the selectivity level thesenior high school to which a student is admitted. 49


Figure 3.4: Differences-in-Differences Regression Estimates (Application Choices)


-30

-15

015

30di

ffere

nce

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


-30

-15

015

30di

ffere

nce

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s



-30

-15

015

30di

ffere

nce

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


-30

-15

015

30di

ffere

nce

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s



2007-2008 2008-2009

-30

-15

015

30di

ff-in

-diff

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


-30

-15

015

30di

ff-in

-diff

in a

vera

ge s

elec

tivity

of c

hose

n sc

hool

s


Notes: These figures illustrate results from difference-in-difference regressions estimated with interactionterms for each percentile in the performance distribution. The outcome variable is the average selectivity ofschools to which a student applied. 50


Figure 3.5: Differences-in-Differences Regression Estimates (Admission Outcomes)


-40

-20

020

40di

ffere

nce

in s

elec

tivity

of s

enio

r hi

gh s

choo

l


-40

-20

020

40di

ffere

nce

in s

elec

tivity

of s

enio

r hi

gh s

choo

l



-40

-20

020

40di

ffere

nce

in s

elec

tivity

of s

enio

r hi

gh s

choo

l


-40

-20

020

40di

ffere

nce

in s

elec

tivity

of s

enio

r hi

gh s

choo

l



2007-2008 2008-2009

-40

-20

020

40di

ff-in

-diff

in s

elec

tivity

of s

enio

r hi

gh s

choo

l


-40

-20

020

40di

ff-in

-diff

in s

elec

tivity

of s

enio

r hi

gh s

choo

l


Notes: These figures illustrate results from difference-in-difference regressions estimated with interactionterms for each percentile in the performance distribution. The outcome variable is the selectivity level thesenior high school to which a student is admitted. 51


Box 2: History of School Choice Reforms in Ghana

• 2005: Computerization

– shift from a manual admission system

– students can apply to 3 choices anywhere in the country (no longer constrainedto apply to three schools in the same region)

– schools have limited input in admission process

• 2007: Increase in number of permitted choices, from 3 to 4

• 2008: Increase in number of permitted choices, from 4 to 6

• 2009: School categorization reform (“CSSPS Guidelines for Selection of Schools forPlacement”)

1. All second cycle institutions have been grouped into categories as follow:

– Senior High Schools: four (4) categories namely A, B, C, and D depending onavailable facilities (e.g. single sex, boarding and day, geographical location).

– Technical Institutes (T).

– Private Schools (P).

2. Before making any selection of schools and programmes offered in these schools,parents are advised to note the following:

– All schools selected (1st to 6th) are considered in the placement of candidates

– Placement in schools is based on scores obtained by candidates (Merit)

3. Conditions for Selection of Schools

– Candidates must choose six schools (1st - 6th choice).

– Candidates must select programmes and accommodation in each school ofchoices.

– Candidates must not choose one school twice.

– Candidates cannot choose more than one (1) school in category A.

– Candidates cannot choose more than two (2) schools in category B.

– Candidates may choose a maximum of 5 schools from category C or D.

4. Note: Regardless of the categories, candidates must arrange their choices in orderof preference.

52


Appendix

A.2: Descriptive Analysis of Categorization Reform

A.2.1: Student Choices

Throughout this analysis of the categorization reform, I restrict the sample to the set ofstudents who qualify for admission to senior secondary school and who submitted a full listof six choices. I present students’ performance in terms of the share of all students whoreceived an equal or lower score. Performance is reported on a scale from 0 to 1, where thehighest scoring student receives a rank of 1.4 Figures 6 to 8 illustrate the impact of thereform on students’ application behavior by comparing portfolio choices in 2008 and 2009.The figures demonstrate two main observations: 1) students largely comply with the newconditions, and 2) the average student applies more conservatively following the reform.

Figure 6 illustrates the change in students’ compliance with each of the reform’s condi-tions, namely: 1) students can apply to a school no more than once, 2) students can apply tono more than one Category A school, 3) students can apply to no more than two CategoryB schools, and 4) students can apply to no more than five Category C or D schools. A fifthimplicit condition is that students must apply to at least three Category C or D schools. In2008, only 28.46 percent of students selected portfolios that would have been in compliancewith the conditions outlined by the 2009 reform. In 2009, there was 93 percent compliance.Additionally, lower performing students were more likely to have selected portfolios thatfilled the categorization conditions prior to the reform and average-performing students wereleast likely to comply after the institution of the reform.

Figure 8 illustrates the aggressiveness of students’ application behavior as indicated bythe selectivity of schools in a student’s portfolio. I measure selectivity by the median per-formance of students admitted to a school in the previous year. This analysis indicates thathigher performing students generally applied to less selective schools following the reformand lower performing students typically listed a more selective school as their first choicebut applied to a portfolio of six schools which were equally as selective on average as theschools chosen before the reform. Students across the distribution applied to a less selectivesixth choice school.

A.2.2: Admission Outcomes

Figures 9 and 10 illustrate the impact of the reform on students’ admission outcomes. Mostnotably: 1) there are fewer administrative assignments, and 2) higher performing students areadmitted to less selective schools than previously and vice versa (resulting in less academic

4This scale provides a direct translation to a student’s percentile. For example, students with a rankabove 0.99 are in the 99th percentile while students with a rank of 0.50 received the median score.

53


sorting). Administrative assignments are concentrated among students at the bottom ofthe performance distribution and decreased overall from 9 percent to 2 percent. For thelowest performing students, the chances of receiving an administrative assignment fell from20 percent to 8 percent.

A.3: Examples of Student Responses to Reform

Example 1 - A Non-Selective Portfolio The Table below illustrates three potential out-comes for a student who would have selected a portfolio consisting of 6 C or D schools underthe old system, but is forced to apply to at least one Category A or B school after the reform.Column 1 indicates the portfolio that a student could have chosen under the unrestrictedsystem. For each choice, I list the category of a school followed by the admission standardin parentheses. Columns (2) to (4) illustrate three modified portfolios which would complywith the new conditions - the student lists a more selective A school as her first choice (2),the student lists a non-selective A school as her first choice (3), the student lists a selectiveB school as her sixth choice (4). Finally, the last three rows indicate admission outcomes fora high performing student with a score of 0.88, an average performing student with a scoreof 0.34 and a low performing student with a score of 0.22.

Note that admission to a more selective school is not an automatic result of the reform,students who genuinely did not want to attend an A or B school could simply list it as theirsixth choice. Similarly, students who did not want to attend a selective school could applyto one of the few non-selective A or B schools. Finally, low-performing students who whocan not gain admission to an A or B school would still end up in a C or D school even ifthey are forced to apply to at least one A or B.

Example 2 - A Selective Portfolio The Table below illustrates three potential outcomesfor a student who would have selected a portfolio consisting of 6 C or D schools under theold system, but is forced to apply to at least one Category A or B school after the reform.Column 1 indicates the portfolio that a student could have chosen under the unrestrictedsystem. For each choice, I list the category of a school followed by the admission standardin parentheses. Columns (2) to (4) illustrate three modified portfolios which would complywith the new conditions - the student her most selective A and B schools as her top choices(2), the student lists her less selective A and B schools as her top choices (3), the studentlists a new set of non-selective A and B schools as her top choices (4). Finally, the last tworows indicate admission outcomes for a high performing student with a score of 0.84 and alow performing student with a score of 0.32.

54


Table 3.6: Potential Impact of Reform for Students with Selective Portfolios

unrestricted new (risky) new (neutral) new (safe)(1) (2) (3) (4)

Application Portfolio1st choice A (0.90) A (0.90) A (0.85) A (0.70)2nd choice A (0.85) B (0.70) B (0.70) B (0.65)3rd choice B (0.70) B (0.65) B (0.50) B (0.45)4th choice B (0.65) C (0.40) C (0.40) C (0.40)5th choice B (0.50) C (0.35) C (0.25) C (0.25)6th choice C (0.40) C (0.30) C (0.20) C (0.20)

Admission Outcome by Student PerformanceHigh (0.88) 2nd - A (0.85) 2nd - B (0.70) 1st - A (0.85) 1st - A (0.70)Average (0.60) 5th - B (0.50) 4th - C (0.40) 3rd - B (0.50) 3rd - B (0.45)Low (0.22) Admin Admin 6th - C (0.20) 6th - C (0.20)

Note: boldface indicates new schools which have been added to the unrestricted portfolio inresponse to the reform.

Table 3.7: Potential Impact of Reform for Students with Non-Selective Portfolios

unrestricted new new new(selective) (non-selective) (low rank)

(1) (2) (3) (4)

Application Portfolio1st choice C (0.40) A (0.70) A (0.30) C (0.40)2nd choice C (0.35) C (0.40) C (0.40) C (0.35)3rd choice C (0.30) C (0.35) C (0.35) C (0.30)4th choice D (0.25) C (0.30) C (0.30) D (0.25)5th choice D (0.30) D (0.25) D (0.25) D (0.30)6th choice D (0.20) D (0.30) D (0.20) B (0.4)

Admission Outcome by Student PerformanceHigh (0.88) 1st - C (0.40) 1st - A (0.70) 1st - A (0.30) 1st - C (0.40)Average (0.34) 3rd - C (0.30) 4th - C (0.30) 4th - C (0.30) 3rd - C (0.30)Low (0.22) 6th - D (0.20) Admin 6th - D (0.20) Admin

Note: boldface indicates new schools which have been added to the unrestricted portfolio inresponse to the reform.

55


Figure 3.6: Compliance with Categorization Reform

0.2

.4.6

.81

shar

e co

mpl

ying

with

cat

egor

izat

ion

rest

rictio

ns

0 .2 .4 .6 .8 1student's relative performance

2008 2009

Compliance with New Categorization System

0.2

.4.6

.81

shar

e co

mpl

ying

with

cat

egor

izat

ion

rest

rictio

ns


2008 2009

Compliance with Choosing a School Once Only

0.2

.4.6

.81

shar

e ch

oosi

ng n

o m

ore

than

one

Cat

egor

y A

sch

ool


2008 2009

Compliance with Choice of Category A Schools

0.2

.4.6

.81

shar

e ch

oosi

ng n

o m

ore

than

two

Cat

egor

y B

sch

ools


2008 2009

Compliance with Choice of Category B Schools

0.2

.4.6

.81

shar

e ch

oosi

ng n

o m

ore

than

five

Cat

egor

y C

& D

sch

ools


2008 2009

Compliance with Choice of Category C & D Schools

0.2

.4.6

.81

shar

e ch

oosi

ng a

t lea

st th

ree

Cat

egor

y C

& D

sch

ools


2008 2009

Compliance with Choice of Category C & D Schools

Figures display how compliance with criteria of the categorization reform varies by student perfor-mance, before and after the reform. Student performance is reported as the share of all studentswho received an equal or lower score (e.g., the highest scoring student has a rank of 1 and themedian performing student has a rank of 0.5). Students who did not submit all six choices areexcluded.

56


57


Figure 3.7: Characterization of Portfolios

0.2

.4.6

.81

shar

e ch

oosi

ng a

t lea

st o

ne A

sch

ool


2008 2009

Choice of an A School

0.2

.4.6

.81

shar

e ch

oosi

ng a

t lea

st o

ne C

or

D s

choo

l


2008 2009

Choice of a C or D School

0.2

.4.6

.81

shar

e ch

oosi

ng a

sen

sibl

e po

rtfo

lio

0 .2 .4 .6 .8 1standardized exam score

2008 2009

Sensible Portfolio Choice (A>B>C/D)

0.2

.4.6

.81

shar

e ch

oosi

ng a

non

-sen

sibl

e po

rtfo

lio


2008 2009

Non-sensible Portfolio Choice (H<L)

0.2

.4.6

.81

shar

e ch

oosi

ng a

bal

ance

por

tfolio


2008 2009

Balanced Portfolio Choice (A & C/D)

0.2

.4.6

.81

shar

e ch

oosi

ng a

n op

timal

por

tfolio


2008 2009

Optimal Portfolio Choice(balanced & sensible)

Figures display how the composition of application portfolios varies by student performance, beforeand after the reform. Portfolio definitions: sensible - Category A schools are ranked higher thanCategory B schools, and Category B schools are ranked higher than Category C or D schools; non-sensible - a Category A school is ranked lower than a Category C or D school; balanced - containsat least one Category A school and at least one Category C or D school; optimal - both balancedand sensible.

58


Figure 3.8: Selectivity of Chosen Schools

0.2

.4.6

.81

sele

ctiv

ity o

f firs

t cho

ice

scho

ol


2008 2009

Selectivity of First Choice Schools

0.2

.4.6

.81

sele

ctiv

ity o

f six

th c

hoic

e sc

hool


2008 2009

Selectivity of Sixth Choice Schools

0.2

.4.6

.81

aver

age

sele

ctiv

ity o

f cho

sen

scho

ols


2008 2009

Mean Selectivity of Chosen Schools

.1.1

5.2

.25

.3st

d de

v in

sel

ectiv

ity o

f sch

ools

in p

ortfo

lio


2008 2009

Variation in Selectivity of Chosen Schools

Figures display how the selectivity of chosen schools varies by student performance, before andafter the reform. The figures illustrate the selectivity of the 1st and 6th choice schools as well asthe average and standard deviation in selectivity of all chosen schools. A school’s selectivity isgiven by the median performance of students admitted in the previous year. Student performanceis reported as the share of all students who received an equal or lower score (e.g., the highest scoringstudent has a rank of 1 and the median performing student has a rank of 0.5). Students who didnot submit all six choices are excluded.

59


Figure 3.9: Admission Outcomes

0.1

.2.3

.4.5

shar

e re

ceiv

ing

an a

dmin

istr

ativ

e as

sign

men

t


2008 2009

Probability of Administrative Assignment

12

34

56

aver

age

choi

ce r

ecei

ved


2008 2009

Choice Received

-.2

-.1

0.1

dist

ance

to m

edia

n st

uden

t


2008 2009

Student Quality Relative to Peer Quality

Figures display how admission outcomes vary by student performance, before and after the reform.Students who do not gain admission to one of their six chosen schools are administratively assignedto an under-subscribed school with remaining vacancies. “Student quality relative to peer quality”is measured by the difference between a student’s performance and the median performance ofstudents who are admitted to the same school. Students who did not submit all six choices areexcluded.

60


Figure 3.10: Admission Outcomes (by quality of JHS attended)

0.1

.2.3

.4.5

shar

e re

ceiv

ing

an a

dmin

istr

ativ

e as

sign

men

t

0 .2 .4 .6 .8 1average performance of Junior High School peers

2008 2009

Probability of Administrative Assignment

12

34

56

aver

age

choi

ce r

ecei

ved


2008 2009

Choice Received

-.15

-.1

-.05

0.0

5di

stan

ce to

med

ian

stud

ent


2008 2009

Student Quality Relative to Peer Quality

61


Figure 3.11: Sorting in Senior High Schools

0.2

.4.6

.81

aver

age

exam

sco

re o

f Sen

ior

Hig

h S

choo

l pee

rs


2008 2009perfect sorting

Sorting in Ghanaian Secondary Schools

Figures display how the extent of sorting in senior high schools varies by student performance, beforeand after the reform. The dashed 45-degree line in the first figure illustrates the hypothetical caseof perfect sorting, in which students are distributed into schools based on their exam performanceonly, so that each student is admitted to a school along with other students of equal performance.The blue and red lines plot actual data from 2008 and 2009 and indicate that higher performingstudents are admitted to schools with lower performing peers and lower performing students gainadmission to schools with relatively higher performing peers. Student performance is reported asthe share of all students who received an equal or lower score (e.g., the highest scoring student hasa rank of 1 and the median performing student has a rank of 0.5). Students who did not submitall six choices are excluded.

62

Chapter 4

Does Attending a Better School ImproveStudent Outcomes?

4.1 Introduction

This chapter estimates the academic returns to school quality by analyzing whether studentswho gain admission to a more selective secondary school have better educational outcomes.The merit-based admission rule that governs admissions to senior high schools in Ghanaleads to a discontinuous change in school quality for similarly qualified students who aredirectly above or below the cutoff for admission to a given school. This cutoff is particularlysalient for students who are on the threshold of gaining admission to the last school ontheir selected list because students can only submit a limited number of choices. Qualifiedstudents who are not placed in any of their chosen schools are administratively assigned toan under-subscribed school with available spaces. Efforts are made to place students in theirhome district or region wherever possible but there is limited regard for students’ statedpreferences. I focus on applications from the 2005 cohort where the students were permittedto list up to three choices. Thus, I focus on the cutoff between gaining admission to thethird choice on a student’s list and receiving an administrative assignment.

I use data from the centralized secondary school application system in Ghana whereadmission to secondary school is based on students’ ranking of their preferred choices andperformance on a standardized test. To account for any endogenous selection of studentsinto schools, I use an instrumental variables approach which focuses on students who areon opposite sides of the threshold for gaining admission to their lowest-ranked choice. Theidentifying assumption is that two students with similar initial test scores who applied to thesame school would have had similar outcomes later in their academic careers if they had bothbeen on the same side of an admission cutoff. If instead, one student gains admission to theirselected choice while the other student is narrowly rejected and assigned to a less selectivealternative school then we can attribute differences in their future outcomes to the differences

63

Chapter 4. Does Attending a Better School Improve Student Outcomes?

in their school assignments. Using this empirical approach, I analyze the cohort of studentswho were admitted to Ghanaian secondary schools in 2005 and evaluate completion ratesand academic performance at the end of secondary school several years later. 98 percentof students listed the full number of choices, which suggests that the constraint was indeedbinding and that a vast majority of students would have preferred to list more schools ifpermitted. Additionally, 23 percent of students received an administrative assignment thatyear. I find that students below the cutoff for admission to their lowest-ranked choice areadministratively assigned to schools with lower-performing peers peers on average and thatthese schools were typically further away. However, these students are slightly less likely tocomply with their initial secondary school assignment which suggests that they may incurcosts of moving but ultimately respond in ways that appear to counteract the potential long-term academic consequences. In particular, these students are less likely to complete theexit exam at the end of secondary school but those who do complete it have similar examscores to students who narrowly escaped receiving an administrative assignment.

This chapter builds on a growing literature on the effects of school quality which hasfocused on comparing the outcomes of students who gained admission to high performingschools to the outcomes of those who narrowly missed admission. The key empirical challengein this literature concerns finding an exogenous assignment rule. Several studies have adopteda similar discontinuity design that identifies the effect of attending a higher performingschool relative to the next best alternative: Clark (2007), Pop-Eleches and Urquiola (2011)and Jackson (2010) examine the academic returns to school quality in the UK, Romaniaand Trinidad and Tobago. All three settings have admissions procedures which are quitesimilar to the one used in Ghana. The findings have been mixed, at best suggesting marginaleffects on educational performance. Additionally, most studies find that there is substantialheterogeneity in effects for students at different points in the performance distribution. Thesesmall effect sizes could be due in part to the fact that the “treatment” in many cases is asmall one. Limited results are in some regard to be expected given that the alternativeoutcome in many cases is admission to a slightly less selective school. Thus, the differencebetween one school and the next is often negligible. To overcome this factor, I examine aslightly different initial treatment by comparing students who gain admission to a schoolof their choosing to students who are assigned to a school without much consideration forpreferences.1

The effect of school quality on student outcomes has also been extensively documentedusing various alternative empirical strategies in other settings. Several researchers haveexploited random variation generated by lottery-based assignment mechanisms in Chicagopublic schools (Cullen, Jacob, and Levitt (2005), Cullen, Jacob, and Levitt (2006)) andthe Charlotte-Mecklenburg school district in North Carolina (Hastings, Kane, and Staiger

1Ozier (2011) estimates the effect of attending secondary school at all using a discontinuous change in thelikelihood of admission to secondary school in Kenya for students with exam scores above a given threshold.He finds positive effects on cognitive ability and labor market outcomes.

64


(2008), Deming, Hastings, Kane, and Staiger (2010) and Deming (2010)). These studies findsimilarly marginal improvements in test performance but document significant benefits inacademic attainment and performance on non-academic indicators such as engagement incriminal activity. Moreover, there is some evidence of large labor market returns to schoolquality (see for example Card and Krueger (1992)). Finally, results from a randomized fieldexperiment study suggest that homogeneity in peers’ test scores may also have a causaleffect on student outcomes. Duflo, Dupas, and Kremer (forthcoming) find positive effects ofability-based tracking on student outcomes in a randomized study which suggest that theremay be benefits to being in an environment where there is homogeneity in peers’ test scores.

This chapter contributes to existing studies by investigating the primary mechanismsthrough which students respond to their treatment status. One of the peculiar aspects ofestimating school quality effects in school choice settings is that students are keenly awareof the “treatment” that they receive. As such, we might expect students to respond totheir treatment assignment - students who are rejected from a high performing school maywork harder to compensate for their misfortune or might be more aggressive in seekingalternative educational opportunities. Similarly, students who are admitted to selectiveschools might become complacent given their privileged position. Most studies estimate thecombined impact of the pure treatment effect and any behavioral responses to the treatmentassignment. I demonstrate that this reduced-form approach might understate the true effectsof school quality if students respond in ways that offset the impact of their initial schoolassignments.

The remainder of the chapter is structured as follows: Section 2 provides an institutionalbackground on education in Ghana. Section 3 describes the data and sample construction.Section 4 outlines the methodology. Section 5 presents results and the final section concludes.

4.2 Institutional Background

Ghana inaugurated a computerized school selection and placement system (CSSPS) inSeptember 2005 with the aim of increasing transparency and enhancing the efficiency ofthe school transition process. In the first year of the new system, admission of JSS studentsinto SSS was based on students’ ranking of their top three choices and their performanceon the BECE. Students who were qualified for admission but were rejected from all threeof their chosen schools were administratively assigned to an under-subscribed school whichhad spaces available at the end of the initial placement process. The CSSPS administra-tors tried to place students in a school in their local district wherever possible but therewas no guarantee about the location of the school and these schools tended to consist oflower-performing students since they were non-selective.

In the first year of the program, 22 percent of students received an administrative as-signment. This was a particularly large share of students who qualified for admission to a

65


school but were rejected from all three of their listed choices. This large share was due to thelimited number of choices that students were allowed to submit and to the fact that studentswere uncertain about their admission chances (because students had to submit their list ofschools before knowing their exam score).

At the end of secondary school, students sit the Secondary School Certification Exam(SSCE). Like the BECE, the SSCE is also centrally administered by the West African Exam-inations Council (WAEC), so performance is comparable across schools. Less than a quarterof candidates pass the SSCE and qualify for admission to university. Normative time forcompletion of senior secondary school is 3 years. Approximately 80 percent of students whoenter SHS complete it.

4.3 Data

To study the effect of school quality, I construct a linked dataset which allows me to trackthe secondary school performance of students who completed the BECE and applied tosenior high school in 2005. My analysis draws on two main sources of data: 1) CSSPSadministrative data on student characteristics, application choices, admission outcomes andBECE performance for applicants to secondary school; and 2) examination results fromthe West African Examination Council (WAEC) which report student performance on thestandardized Secondary School Certification Exam (SSCE) at the end of secondary school.The data cover the universe of applicants to public senior secondary schools in Ghana in2005 and the universe of students who completed senior secondary schools in 2008 and 2009.

Senior high school is three years long, so students who entered SHS in 2005 should sitthe SSCE in 2008 if they completed SHS in normative time. I use WAEC information onstudents from the 2008 and 2009 cohorts to allow students who entered secondary school in2005 to complete in the normative time of three years or to delay secondary school completionby one additional year. Students do not have a unique identifier so I link individuals acrossthe CSSPS and WAEC samples using their name, sex, and date of birth. I am able to linkBECE students to their SSCE results for 60 percent of the 2005 cohort. Aggregate dataon the total number of BECE and SSCE candidates suggest that 80 percent of senior highschool admits complete the SSCE. Thus, my linked sample covers approximately 75 percentof the target population.

For the purposes of this study, I limit the resulting sample to focus on students whoapplied to a program where the capacity constraint was binding (i.e., where the numberof applications exceeded the number of available spaces). This allows me to examine casesin which there was a discontinuous change in admission outcomes for students with similarBECE scores on either side of the admission cutoff. Finally, I focus on are students who are onthe cutoff for admission to their third choice program. This is because my primary objectiveis to examine the effect of attending a selective school and there is a substantial drop in

66


the selectivity of schools for student who are administratively assigned because the schoolswhere they receive admission are schools which are under-subscribed and so, therefore, arenon-selective.

This selection criteria results in a sample of 33831 students who applied to a total of576 programs. In order to pool the data for applicants across the individual programs, Iredefine students’ BECE scores relative to the admission cutoff for their third choice schoolsuch that the marginal admitted student has a score of 0. Identifying the appropriate cutoffto use for each program is somewhat challenging. Although admission is merit-based, thereis a slight complication in the resulting assignments because of the way the CSSPS dealswith unclaimed spaces. Students are informed of their assignments and are given thirtydays to report at their assigned school once the school year begins. Students who receivea placement may choose not to enroll in the school for several reasons - wealthy studentsmay opt out of the public school system and instead enroll in an elite private school, lessaffluent students may choose not to enroll if they do not have sufficient financial resourcesto fund their secondary education, and some students defer enrollment for health reasons.Thus, not all assigned spaces are filled. Schools are required to report any unfilled placesto the Ministry of Education so that the spaces can be allocated to previously unplacedstudents in a supplementary round of placement. These are often students who are fromthe lower end of the performance distribution, because higher performing students wouldhave been placed in schools in the first round. I only observe final student assignments anddo not observe the explicit cutoff for each school before the supplementary assignments, soI replicate the initial admission outcomes by applying the deferred acceptance algorithmused by the CSSPS administrators to the data on students’ choices and BECE performanceaccording to schools’ declared vacancies.

A final data-related factor to note is that I am missing baseline (BECE) test scores forabout 10 percent of students in the 2005 cohort. This is because in the first year of theCSSPS, students were allowed to request a transfer from their initial placement as a result ofthe large share of students being rejected from all three of their choices. For those studentswho successfully transferred, I no longer observe initial test scores but instead observe a codeindicating that they received an alternative placement. I am, however, still able to observeoutcome variables for these students in cases where they complete secondary school and takethe SSCE.

Altogether, the administrative data pose three challenges for implementing a discontinu-ity design to study the effect of school placement on academic performance: 1) non-perfectcompliance with the assignment rule which leads to a ”fuzzy” discontinuity in admissionstatus, 2) missing outcomes for students who I do not observe taking the SSCE (40 percentof the sample), and 3) missing baseline test scores for students who successfully petition outof their initial school placement (10 percent of the sample). The first two of these issuesare relatively common and have been addressed in related literature. The third point issomewhat less studied but could also arise in other settings. I discuss potential strategies for

67


dealing with these issues in more detail in the following section which outlines my empiricalapproach.

4.4 Econometric Model

I use a two stage least squares estimator to evaluate the effect of attending a selective schoolon students’ academic performance. In the first stage, I estimate the effect of the admissionrule on students’ school assignment, Ti. In particular, I examine how much a student’schances of escaping an administrative assignment (and instead gaining admission to one oftheir chosen schools) improves as a result of scoring above the test score cutoff. In particular,I estimate the following equation:

Ti = α1{θi ≥ θs}+ a(θi) + νi

where 1{θi ≥ θs}is an indicator for whether student i’s score exceeds the cutoff for admissionto school s and a(θi) is a control function for exam scores. Since the data are pooled acrossseveral programs, I include school fixed effects and robust standard errors clustered at theprogram level.

The second stage of my analysis estimates the effect of this initial assignment on stu-dents’ future academic outcomes Yi (e.g., secondary school completion or performance onthe secondary school certification exam). A reduced form approach to this question wouldbe to estimate the following regression:

Yi = β1{θi ≥ θs}+ a(θi) + νi

The instrumental variables specification for this analysis is:

Yi = δE (Ti | θi) + a(θi) + µi

E (Ti | θi) = γ1{θi ≥ θs}+ a(θi) + ηi

The identifying assumption underlying this empirical approach is that two students withsimilar initial test scores who applied to the same school would have had similar outcomeslater in their academic careers if they had both been on the same side of an admission cutoff.

My baseline specification focuses on linked students for whom I observe both baseline(BECE) and future (SSCE) outcomes. However, I then perform several additional analysesto address the data issues I raised in the previous section.

68


4.4.1 Fuzzy RD

First, I consider the fact that I do not observe the initial admission cutoffs. I deal with thisin two ways - my preferred approach is to replicate the placement procedure described inthe CSSPS handbook and retrieve the cutoffs that would have occurred if the procedure hadbeen implemented strictly. I am able to replicate admission outcomes for 90% of students.The error likely arises from the splitting of ties (I split ties arbitrarily, while the actualimplementation split ties using subject-specific scores to which I do not have access) andfrom schools which do not report vacancies. I exclude these schools from my analysis,however. As a robustness check, I also perform my analysis using the lowest observed scoreof students admitted to each school as the cutoff (see Table in Appendix). One might expectthis cutoff to be endogenous if students were able to influence their likelihood of gaining anadministrative assignment. The issue of non-compliance has been addressed in other studiesand is commonly refered to as a “fuzzy” regression discontinuity (see Jackson (2010) forexample).

4.4.2 Missing Outcomes

As I mentioned in the data section, I do not have a unique identifier for students so I linkBECE candidates from the 2005 cohort to SSCE candidates in 2008 and 2009 using theirnames and birthdates. I am able to get a strong link for 60 percent of the sample. I thereforedo not observe outcomes for the remaining set of students. I deal with this missing data onoutcomes in two main ways. First, I assume they drop out of school and do not completethe SSCE. In which case, I assign a score of 0 to them and include them in my analysis. Inan alternative specification, I drop these students from the analysis altogether and calculatethe effects using only the linked sample. These approaches allow me to construct a set ofbounds on the estimated treatment effect.

4.4.3 Missing Baseline Scores

For 10 percent of the sample who successfully petitioned to transfer, I am missing baseline testscores. From their observable characteristics, these students seem to be positively selected.I perform a series of robustness checks to examine whether this selection out of placementassignment is responsible for the effects I observe. First, I assume that test scores follow anormal distribution. I then calculate the missing density from each point in the distribution.I assign BECE scores to students who successfully petitioned based on the distributions thatwould be observed under three scenarios: 1) missing at random (no relationship betweenBECE scores and resulting SSCE performance), 2) strong unobserved selection in which casethe best SSCE performers had the worst BECE scores (upper bound), and 3) no selectioneffect in which case the best SSCE performers had best BECE scores (lower bound).

69


4.5 Results

Figure 1 displays the distribution of student test scores around the admission cutoffs andillustrates that there is a discontinuous decrease in density below the cutoff point. Thischange in density suggests manipulation of the running variable which is students’ relativeBECE scores (McCrary (2007)). Indeed, as I mentioned earlier, 10 percent of students weregranted a request to have an alternative placement. I do not observe BECE scores forthese students but do observe certain background characteristics. These students appear tobe positively selected as indicated by the fact that there is a discontinuous change in thequality of junior high schools attended for students who are on both sides of the admissioncutoffs (Figure 3). This suggests that the assumption of exogenous assignment is not validsince students across the thresholds do not appear to have similar observable characteristics.I deal with this issue subsequently but begin by examining outcomes for the initial samplefor whom I observe BECE scores.

Figure 4 illustrates the discontinuous change in admission chances for students on oppo-site sides of the threshold for admission to their third choice school. In particular, studentsexperience a 70 percentage point increase in their admission chances if their test scores isabove the admission threshold. This increase in admission chances translates into improvedschool quality - students above the threshold end up with peers who have test scores that are2 standard deviations higher than peers for students below the threshold. Moreover, theyattend schools which have a 5 percentage point higher pass rate on the SSCE at the end ofsecondary school.

As a result of these significant differences in exposure to school quality, there is some ev-idence that receiving an administrative assignment has lasting effects on students’ academicperformance. Figures 5 and 6 display the differences in students’ academic attainment andperformance on the SSCE. Specifically, I find that students who receive an administrativeassignment appear to be less likely to comply with their school assignment and more likelyto transfer into a different school by the time they complete secondary school (Figure 5).These new schools are generally closer to a student’s junior high school district but not ofsignificantly higher quality than their initially assigned schools. However, among the stu-dents who do complete senior high school, there are only marginal differences in academicperformance (with the exception of performance in English language, where students whogained admission to one of their chosen schools have a substantial advantage over the averagescore for students on the opposite side of the admission threshold).

Tables 2 to 11 present regression estimates. Apart from the regression discontinuityestimates, there are some interesting overall differences based on gender and school quality.In particular, boys are less likely to complete senior secondary school (after controlling forinitial BECE scores). Additionally students from high performing junior high schools aremore likely to complete SHS but have lower performance on the SSCE. This suggests thatfamily background may be a strong factor in ensuring school retention but less impact on

70


academic achievement. With regard to the effects of attending a third choice school, boysare more likely to benefit in terms of having higher chances of high school completion andboth boys and girls have increased chances of finishing in three years and staying in thesame school. Moreover, students seem to have greater gains if they secure admission to arelatively selective third choice school.

4.6 Conclusions

This chapter focuses on measuring academic outcomes for students who attend schools ofdiffering quality. I find that the effects of school quality are meaningful. One limitationof this study is the focus on academic outcomes which may overlook important changes innon-cognitive ability. The findings are consistent with similar discontinuity design studieswhich find limited gains in academic performance but measurable gains in non-cognitiveoutcomes (such as career aspirations or propensity for crime). Thus, a natural area forfuture research would be to extend this study to examine non-academic outcomes. Further,I find some evidence of a behavioral response to treatment status in that students who receivean administrative assignment are more likely to transfer out of their assigned school. A nextstep in exploring the implications of this finding would be to bound the size of the pure effectof school quality by focusing on students who comply with their initial school assignment.Altogether, this study highlights the potential importance of taking a comprehensive viewof the effects of admission outcomes in school choice settings.

71


Figure 4.1: Density Smoothness at Cutoff

050

010

0015

00F

requ

ency

of S

tude

nts

-200 -100 0 100 200BECE Points Above or Below the Admission Cutoff

Figure 4.2: Density Test for Smoothness at Cutoff

0.0

02.0

04.0

06.0

08.0

1

-200 -100 0 100 200

72

Chapter 4. Does Attending a Better School Improve Student Outcomes?F

igur

e4.

3:D

istr

ibut

ion

ofC

ovar

iate

sar

ound

Cut

off

-.10.1.2.3Academic Performance in Junior High School

-20

-15

-10

-50

510

1520

BE

CE

Poi

nts

Abo

ve o

r B

elow

Adm

issi

on C

utof

f

Loca

l Ave

rage

Qua

drat

ic R

egre

ssio

n

0.2.4.6.81Attended a Public Junior High School

-20

-15

-10

-50

510

1520

BE

CE

Poi

nts

Abo

ve o

r B

elow

Adm

issi

on C

utof

f

Loca

l Ave

rage

Qua

drat

ic R

egre

ssio

n

15.51616.517Age in Years

-20

-15

-10

-50

510

1520

BE

CE

Poi

nts

Abo

ve o

r B

elow

Adm

issi

on C

utof

f

Loca

l Ave

rage

Qua

drat

ic R

egre

ssio

n

0.2.4.6.81Male

-20

-15

-10

-50

510

1520

BE

CE

Poi

nts

Abo

ve o

r B

elow

Adm

issi

on C

utof

f

Loca

l Ave

rage

Qua

drat

ic R

egre

ssio

n

73


Figure 4.4: First Stage - Admission Discontinuity

0.2

.4.6

.81

Adm

issi

on R

ate

-20 -15 -10 -5 0 5 10 15 20BECE Points Above or Below the Admission Cutoff

Figure 4.5: First Stage - Fuzzy Admission Discontinuity

0.2

.4.6

.81

Adm

issi

on R

ate

-20 -15 -10 -5 0 5 10 15 20BECE Points Above or Below Admission Cutoff

Local Average Quadratic Regression

74


Figure 4.6: Outcomes - Academic Attainment

0.2

.4.6

.81

Pro

babi

lity

of A

chie

ving

Out

com

e


Take BECE Complete in 3 YearsStay in Same School Quadratic Regression

Figure 4.7: Outcomes - SSCE Performance

010

2030

40S

SC

E E

xam

Per

form

ance


Selected Average Local AverageLocal Median Quadratic Regression

75


Table 4.1: Summary Statistics

Characteristic Mean SD N

age 16.425 1.635 33817male .523 .499 33831avg BECE percentile in JHS .012 .744 33814JHS public .693 .461 33830cutoff 301.342 46.233 33831distance from cutoff .555 .71 33509admitted to third choice .274 .446 33831take ssce .580 .494 33831finish in 3 years .796 .403 19611stay in same school .540 .498 19611performance on SSCE core subjects 13.231 6.02 19603

76


Table 4.2: Performance on Core SSCE Subjects (Baseline Specifications)

OLS OLS OLS IV IV

rdadmitboth 0.904 0.986 1.283 1.873 1.553(0.177)*** (0.275)*** (0.317)*** (0.714)*** (0.802)*

scoreuse 0.090(0.003)***

jmdnscore -1.938 -1.612 -1.621 -1.635 -1.627(0.189)*** (0.201)*** (0.211)*** (0.201)*** (0.212)***

male -0.554 -0.584 -0.418 -0.588 -0.419(0.190)*** (0.205)*** (0.221)* (0.205)*** (0.221)*

rddist est 0.088 0.080 0.047 0.067(0.020)*** (0.022)*** (0.037) (0.043)

rdadmitdist est -0.028 -0.037 -0.006 -0.028(0.031) (0.034) (0.035) (0.042)

Cutoff Fixed Effects No Yes Yes Yes YesCutoff Cluster-Robust SEs Yes Yes Yes Yes YesExclude Fuzzy Range No No Yes No YesAdj. R2 0.150 0.188 0.188 0.187 0.188N 8634 8634 7771 8634 7771

Notes: The Core SSCE Subjects are English, Maths, Social Science and Integrated Science. Grades foreach subject have been converted to a scale of 1 to 10. * denotes significant at the 10% level, ** denotessignificant at the 5% level, and *** denotes significant at the 1% level. Tables produced by estout (Jann

(2005) and Jann (2006)).

77


Table 4.3: Performance on All SSCE Subjects

All Subjects Linked SampleOLS OLS IV OLS OLS IV

rdadmitboth 2.411 3.168 4.213 0.864 2.003 0.312(0.392)*** (0.694)*** (1.780)** (0.421)** (0.763)*** (1.916)

scoreuse 0.180 0.200(0.007)*** (0.006)***

jmdnscore -3.737 -3.377 -3.401 -5.879 -6.281 -6.241(0.405)*** (0.454)*** (0.456)*** (0.321)*** (0.384)*** (0.383)***

male -1.915 -1.296 -1.300 -0.240 0.144 0.153(0.399)*** (0.476)*** (0.476)*** (0.361) (0.403) (0.405)

rddist est 0.182 0.129 0.158 0.249(0.047)*** (0.094) (0.054)*** (0.111)**

rdadmitdist est -0.105 -0.070 -0.025 -0.092(0.073) (0.092) (0.072) (0.105)

Cutoff Fixed Effects No Yes Yes No Yes YesCutoff Cluster-Robust SEs Yes Yes Yes Yes Yes YesExclude Fuzzy Range No Yes Yes No Yes YesAdj. R2 0.138 0.169 0.169 0.266 0.333 0.332N 8634 7771 7771 4630 4189 4189Notes: * denotes significant at the 10% level, ** denotes significant at the 5% level, and *** denotes

significant at the 1% level.

78


Table 4.4: Performance on Core SSCE Subjects - Differences by Gender

Male FemaleOLS OLS IV OLS OLS IV

rdadmitboth 1.383 1.861 2.075 0.330 0.364 1.234(0.262)*** (0.479)*** (1.127)* (0.236) (0.455) (1.227)

scoreuse 0.089 0.091(0.004)*** (0.005)***

jmdnscore -2.117 -1.946 -1.953 -1.769 -1.275 -1.284(0.248)*** (0.281)*** (0.281)*** (0.265)*** (0.335)*** (0.337)***

rddist est 0.092 0.081 0.092 0.048(0.034)*** (0.060) (0.032)*** (0.068)

rdadmitdist est -0.078 -0.072 -0.024 0.007(0.049) (0.058) (0.049) (0.066)

Cutoff Fixed Effects No Yes Yes No Yes YesCutoff Cluster-Robust SEs Yes Yes Yes Yes Yes YesExclude Fuzzy Range No Yes Yes No Yes YesAdj. R2 0.144 0.193 0.193 0.162 0.198 0.197N 4739 4257 4257 3895 3514 3514Notes: * denotes significant at the 10% level, ** denotes significant at the 5% level, and *** denotes

significant at the 1% level.

79


Tab

le4.

5:P

erfo

rman

ceon

Cor

eS

SC

ES

ubje

cts

-D

iffer

ence

sby

SH

SQ

ualit

y

Bot

tom

Qua

rtile

Mid

dle

Hal

fT

opQ

uart

ileO

LS

OL

SIV

OL

SO

LS

IVO

LS

OL

SIV

rdad

mit

both

0.23

8-0

.249

0.85

00.

925

1.46

41.

450

0.63

81.

993

2.02

1(0

.290

)(0

.464

)(1

.903

)(0

.231

)***

(0.3

90)*

**(1

.125

)(0

.516

)(0

.973

)**

(1.4

12)

scor

euse

0.06

80.

079

0.15

8(0

.009

)***

(0.0

07)*

**(0

.015

)***

jmdn

scor

e-0

.807

-0.9

79-1

.024

-1.8

42-1

.535

-1.5

35-2

.436

-2.0

49-2

.049

(0.3

66)*

*(0

.417

)**

(0.4

24)*

*(0

.255

)***

(0.2

68)*

**(0

.267

)***

(0.3

58)*

**(0

.425

)***

(0.4

25)*

**

mal

e-0

.107

0.25

00.

240

-0.6

04-0

.265

-0.2

65-1

.059

-1.3

47-1

.347

(0.3

63)

(0.4

06)

(0.4

08)

(0.2

42)*

*(0

.280

)(0

.281

)(0

.429

)**

(0.5

24)*

*(0

.524

)**

rddi

stes

t0.

118

0.06

30.

062

0.06

20.

087

0.08

6(0

.037

)***

(0.0

98)

(0.0

29)*

*(0

.061

)(0

.056

)(0

.074

)

rdad

mit

dist

est

-0.1

06-0

.060

-0.0

36-0

.036

0.01

90.

020

(0.0

57)*

(0.0

93)

(0.0

45)

(0.0

57)

(0.0

80)

(0.0

84)

Cut

offF

Es

No

Yes

Yes

No

Yes

Yes

No

Yes

Yes

Rob

ust

SEs

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Exc

l.Fu

zzy

No

Yes

Yes

No

Yes

Yes

No

Yes

Yes

Adj

.R

20.

043

0.09

30.

090

0.06

30.

093

0.09

30.

095

0.13

60.

136

N20

0817

8017

8043

7539

3539

3522

5120

5620

56N

otes

:*

deno

tes

sign

ifica

ntat

the

10%

leve

l,**

deno

tes

sign

ifica

ntat

the

5%le

vel,

and

***

deno

tes

sign

ifica

ntat

the

1%le

vel.

80


Table 4.6: Educational Attainment - Take SSCE

All Male FemaleProbit IVP IVP IVP

goodmatchrdadmitboth 0.181 0.278 0.329 0.231

(0.053)*** (0.123)** (0.165)** (0.192)

rddist est 0.010 0.001 0.005 -0.005(0.004)** (0.007) (0.009) (0.011)

rdadmitdist est -0.011 -0.005 -0.014 0.007(0.006)* (0.007) (0.009) (0.010)

jmdnscore 0.046 0.210 0.192 0.229(0.033) (0.026)*** (0.034)*** (0.033)***

male -0.152 -0.127(0.039)*** (0.033)***

rdadmitbothrddist est 0.030 0.030 0.030

(0.001)*** (0.002)*** (0.002)***

rdadmitdist est -0.028 -0.027 -0.029(0.002)*** (0.002)*** (0.002)***

jmdnscore 0.003 0.007 -0.001(0.006) (0.008) (0.007)

male -0.003(0.007)

rdadmit est 0.466 0.458 0.477(0.021)*** (0.028)*** (0.032)***

Cutoff Fixed Effects Yes No No NoCutoff Cluster-Robust SEs Yes Yes Yes YesExclude Fuzzy Range Yes Yes Yes YesN 7613 7771 4257 3514

Notes: * denotes significant at the 10% level, ** denotes significant at the 5% level, and *** denotessignificant at the 1% level.

81


Table 4.7: Educational Attainment - Finish in 3 Years


Aontimerdadmitboth 0.351 0.422 0.359 0.511

(0.059)*** (0.127)*** (0.167)** (0.196)***

rddist est 0.007 -0.004 0.005 -0.015(0.004) (0.007) (0.009) (0.011)

rdadmitdist est -0.004 0.003 -0.007 0.016(0.006) (0.007) (0.009) (0.011)

jmdnscore 0.032 0.236 0.224 0.248(0.033) (0.027)*** (0.035)*** (0.034)***

male -0.225 -0.174(0.041)*** (0.035)***


(0.001)*** (0.002)*** (0.002)***

rdadmitdist est -0.028 -0.027 -0.029(0.002)*** (0.002)*** (0.002)***

jmdnscore 0.003 0.007 -0.001(0.006) (0.008) (0.007)

male -0.003(0.007)

rdadmit est 0.466 0.458 0.477(0.021)*** (0.028)*** (0.032)***



82


Table 4.8: Educational Attainment - Stay in Same School


Asameschoolrdadmitboth 0.933 0.925 0.814 1.067

(0.063)*** (0.135)*** (0.180)*** (0.200)***

rddist est 0.005 -0.003 0.004 -0.011(0.005) (0.008) (0.010) (0.012)

rdadmitdist est -0.005 -0.002 -0.009 0.007(0.007) (0.007) (0.010) (0.012)

jmdnscore -0.035 0.113 0.091 0.138(0.034) (0.031)*** (0.039)** (0.038)***

male -0.238 -0.172(0.043)*** (0.039)***


(0.001)*** (0.002)*** (0.002)***

rdadmitdist est -0.028 -0.027 -0.029(0.002)*** (0.002)*** (0.002)***

jmdnscore 0.003 0.007 -0.001(0.006) (0.008) (0.007)

male -0.003(0.007)

rdadmit est 0.466 0.458 0.477(0.021)*** (0.028)*** (0.032)***



83


84


Table 4.9: Educational Attainment - Take SSCE

All Bottom Middle TopProbit IVP IVP IVP IVP

goodmatchrdadmitboth 0.181 0.278 0.396 0.245 0.280

(0.053)*** (0.123)** (0.412) (0.173) (0.180)

rddist est 0.010 0.001 -0.001 0.005 -0.003(0.004)** (0.007) (0.022) (0.010) (0.010)

rdadmitdist est -0.011 -0.005 -0.004 -0.012 0.010(0.006)* (0.007) (0.021) (0.009) (0.012)

jmdnscore 0.046 0.210 0.151 0.069 0.101(0.033) (0.026)*** (0.079)* (0.036)* (0.046)**

male -0.152 -0.127 -0.168 -0.162 -0.105(0.039)*** (0.033)*** (0.073)** (0.048)*** (0.057)*

rdadmitbothrddist est 0.030 0.038 0.031 0.019

(0.001)*** (0.003)*** (0.002)*** (0.003)***

rdadmitdist est -0.028 -0.039 -0.029 -0.014(0.002)*** (0.003)*** (0.002)*** (0.003)***

jmdnscore 0.003 0.027 0.016 0.019(0.006) (0.026) (0.008)* (0.007)***

male -0.003 0.001 -0.002 0.010(0.007) (0.019) (0.009) (0.010)

rdadmit est 0.466 0.303 0.446 0.647(0.021)*** (0.047)*** (0.028)*** (0.039)***

Cutoff Fixed Effects Yes No No No NoCutoff Cluster-Robust SEs Yes Yes Yes Yes YesExclude Fuzzy Range Yes Yes Yes Yes YesN 7613 7771 1780 3935 2056


85


Table 4.10: Educational Attainment - Finish in 3 Years


Aontimerdadmitboth 0.351 0.422 0.545 0.464 0.312

(0.059)*** (0.127)*** (0.397) (0.183)** (0.187)*

rddist est 0.007 -0.004 -0.003 -0.004 -0.000(0.004) (0.007) (0.022) (0.010) (0.010)

rdadmitdist est -0.004 0.003 0.005 0.000 0.011(0.006) (0.007) (0.021) (0.009) (0.012)

jmdnscore 0.032 0.236 0.211 0.039 0.141(0.033) (0.027)*** (0.083)** (0.038) (0.041)***

male -0.225 -0.174 -0.232 -0.229 -0.121(0.041)*** (0.035)*** (0.080)*** (0.048)*** (0.060)**


(0.001)*** (0.003)*** (0.002)*** (0.003)***

rdadmitdist est -0.028 -0.039 -0.029 -0.014(0.002)*** (0.003)*** (0.002)*** (0.003)***

jmdnscore 0.003 0.027 0.016 0.019(0.006) (0.026) (0.008)* (0.007)***

male -0.003 0.001 -0.002 0.010(0.007) (0.019) (0.009) (0.010)

rdadmit est 0.466 0.303 0.446 0.647(0.021)*** (0.047)*** (0.028)*** (0.039)***



86


Table 4.11: Educational Attainment - Stay in Same School


Asameschoolrdadmitboth 0.933 0.925 0.800 0.974 0.950

(0.063)*** (0.135)*** (0.441)* (0.187)*** (0.216)***

rddist est 0.005 -0.003 -0.001 -0.006 0.004(0.005) (0.008) (0.025) (0.010) (0.012)

rdadmitdist est -0.005 -0.002 0.001 -0.005 0.004(0.007) (0.007) (0.025) (0.010) (0.013)

jmdnscore -0.035 0.113 0.100 -0.021 0.018(0.034) (0.031)*** (0.087) (0.044) (0.046)

male -0.238 -0.172 -0.202 -0.229 -0.121(0.043)*** (0.039)*** (0.090)** (0.053)*** (0.067)*


(0.001)*** (0.003)*** (0.002)*** (0.003)***

rdadmitdist est -0.028 -0.039 -0.029 -0.014(0.002)*** (0.003)*** (0.002)*** (0.003)***

jmdnscore 0.003 0.027 0.016 0.019(0.006) (0.026) (0.008)* (0.007)***

male -0.003 0.001 -0.002 0.010(0.007) (0.019) (0.009) (0.010)

rdadmit est 0.466 0.303 0.446 0.647(0.021)*** (0.047)*** (0.028)*** (0.039)***



87


Appendix

Dealing with Attrition

To illustrate the approach that I would use to bound the effects of selection, I focus onone school which has both a high share of transfer students as well as a high number ofapplications. I first simulate a normal distribution using the density of students to the righthand side of the cutoff and to the low end of the left tail as moment conditions. Thiseffectively assumes that there is no selective attrition to the right hand of the cutoff and atthe very low end of the left tail, so all of the selective transfer occurs in the region within75 points below the admission cutoff. I then fit a normal distribution which satisfies theseconditions and calculate the distribution of missing students given the disparity between theexpected and observed density of students in the middle-range of the distribution. Finally, Iassign scores to students who applied to the school but transferred out under three scenarios:1) no selection (students’ SSCE scores are unrelated to their initial BECE scores); 2) upperbound (students with the highest SSCE scores are assumed to have had the lowest initalBECE scores); and 3) lower bound (students with the highest SSCE scores are assumed tohave had the highest inital BECE scores). I then run the same regression analysis presentedearlier under each of these scenarios, to examine the estimated effects. Table xx presents theresults from an analysis of the effect on finishing in 3 years.

88


Table 4.12: Regression Results using Observed Cutoffs

OLS OLS OLS IV IV

rdadmitboth 0.904 0.978 1.123 1.075 1.516(0.177)*** (0.275)*** (0.306)*** (0.515)** (0.880)*

scoreuse 0.090(0.003)***

jmdnscore -1.938 -1.613 -1.571 -1.615 -1.578(0.189)*** (0.200)*** (0.205)*** (0.201)*** (0.207)***

male -0.554 -0.584 -0.467 -0.584 -0.468(0.190)*** (0.206)*** (0.219)** (0.206)*** (0.219)**

rddist emp 0.089 0.077 0.084 0.055(0.021)*** (0.024)*** (0.031)*** (0.054)

rdadmitdist emp -0.026 -0.016 -0.023 0.002(0.029) (0.032) (0.032) (0.051)

Cutoff Fixed Effects No Yes Yes Yes YesCutoff Cluster-Robust SEs Yes Yes Yes Yes YesExclude Fuzzy Range No No Yes No YesAdj. R2 0.150 0.188 0.194 0.188 0.194N 8634 8634 7924 8634 7924


89


Table 4.13: Bounding Selection Effects (Timely Completion)

Compliers Random Upper Bound Lower BoundProbit IVP IVP IVP IVP

Aontimerdadmitboth 2.603 4.609 3.251 4.829 2.772

(1.011)** (1.048)*** (1.436)** (1.294)*** (1.509)*

jmdnscore -1.399 -0.827 -0.300 -0.207 -0.616(0.778)* (0.748) (0.281) (0.336) (0.360)*

male -0.409 -0.382 0.155 0.062 0.224(0.646) (0.567) (0.365) (0.390) (0.430)

rdadmitbothrdadmit est 0.519 0.819 0.820 0.808

(0.141)*** (0.096)*** (0.096)*** (0.096)***

jmdnscore -0.052 0.001 -0.007 -0.011(0.069) (0.038) (0.039) (0.042)

male -0.027 -0.020 -0.020 -0.048(0.075) (0.049) (0.048) (0.050)

Impute Missing Scores No No Yes Yes YesExclude Fuzzy Range Yes Yes Yes Yes YesN 42 42 71 71 71


90


Figure 4.8: Observed and Imputed Scores for Sample School

05

1015

Num

ber

of S

tude

nts

-100 -50 0 50BECE Points Above or Below the Admission Cutoff

Observed Imputed

91

Bibliography

Abdulkadiroglu, A., P. Pathak, and A. Roth (2009): “Strategy-Proofness versusEfficiency in Matching with Indifferences: Redesigning the NYC High School Match,”American Economic Review, 99(5), 1954–78.

Abdulkadiroglu, A., P. Pathak, A. Roth, and T. Sonmez (2006): “Changing theBoston Mechanism: Strategyproofness as Equal Access,” National Bureau of EconomicResearch Working Paper, (11965).

Abdulkadiroglu, A., and T. Sonmez (2003): “School Choice: A Mechanism DesignApproach,” American Economic Review, 93(3), 729–747.

Avery, C. (2009): “The Effects of College Counseling on High-Achieving, Low-IncomeStudents: Results of a Pilot Study with a Randomized Controlled Trial,” Working Paper.

Avery, C., M. Glickman, C. Hoxby, and A. Metrick (2004): “A Revealed Prefer-ence Ranking of U.S. Colleges and Universities,” National Bureau of Economic ResearchWorking Paper, (10803).

Avery, C., and T. Kane (2004): “Student Perceptions of College Opportunities. TheBoston COACH Program,” in College Choices: The Economics of Where to Go, Whento Go, and How to Pay For It, ed. by C. M. Hoxby, pp. 355–394. National Bureau ofEconomic Research.

Bitler, M., J. Gelbach, and H. Hoynes (2006): “What Mean Impacts Miss: Dis-tributional Effects of Welfare Reform Experiments,” American Economic Review, 96(4),988–1012.

Bowen, W., M. Chingos, and M. McPherson (2009): Crossing the Finish Line. Prince-ton University Press.

Burgess, S., E. Greaves, A. Vignoles, and D. Wilson (2009): “What Parents Want:School Preferences and School Choice,” Department of Quantitative Social Science Uni-versity of London Working Paper, (0901).

92

BIBLIOGRAPHY

Calsamiglia, C., G. Haeringer, and F. Klijn (2010): “Constrained School Choice:An Experimental Study,” American Economic Review, 100(4), 1860–74.

Card, D., and A. Krueger (1992): “Does School Quality Matter? Returns to Educa-tion and the Characteristics of Public Schools in the United States,” Journal of PoliticalEconomy, 100(1), 1–40.

Chade, H., G. Lewis, and L. Smith (2008): “A Supply and Demand Model of the CollegeAdmissions Problem,” University of Michigan, mimeo.

Chade, H., and L. Smith (2006): “Simultaneous Search,” Econometrica, 74(5), 1293–1307.

Clark, D. (2007): “Elite Schools and Academic Performance,” Institute for the Study ofLabor (IZA), Discussion Paper 3182.

Cullen, J., B. Jacob, and S. Levitt (2005): “The Impact of School Choice on StudentOutcomes: An Analysis of the Chicago Public Schools,” Journal of Public Economics,89(5-6), 729–760.

(2006): “The Effect of School Choice on Participants: Evidence from RandomizedLotteries,” Econometrica, 74(5), 1191–1230.

Dale, S. B., and A. Krueger (2002): “Estimating The Payoff To Attending A MoreSelective College: An Application Of Selection On Observables And Unobservables,” TheQuarterly Journal of Economics, 117(4), 1491–1527.

Deming, D. (2010): “Better Schools, Less Crime?,” Working Paper.

Deming, D., J. Hastings, T. Kane, and D. Staiger (2010): “School Choice andCollege Attendance: Evidence from Randomized Lotteries,” Working Paper.

Duflo, E., P. Dupas, and M. Kremer (forthcoming): “Peer Effects and the Impactsof Tracking: Evidence from a Randomized Evaluation in Kenya,” American EconomicReview.

Gale, D., and L. Shapley (1962): “College Admissions and the Stability of Marriage,”The American Mathematical Monthly, 69(1), 9–15.

Go4ivy (2010): “Strategy for Choosing, Visiting and Applying to Top Selective U.S. Col-leges and Universities,” http://www.go4ivy.com/planstrategy.asp.

Griffith, A., and K. Rask (2007): “The Influence of the US News and World ReportCollegiate Rankings on the Matriculation Decision of High-Ability Students: 1995-2004,”Economics of Education Review, 26(2), 244–255.

93

http://www.go4ivy.com/planstrategy.asp

BIBLIOGRAPHY

Haeringer, G., and F. Klijn (2009): “Constrained school choice,” Journal of EconomicTheory, 144(5), 1921–1947.

Hastings, J., T. Kane, and D. Staiger (2008): “Heterogeneous Preferences and theEfficacy of Public School Choice,” National Bureau of Economic Research Working Paper,(No. 12145 and No. 11805 combined).

Hastings, J., and J. Weinstein (2008): “Information, School Choice, and AcademicAchievement: Evidence from Two Experiments,” The Quarterly Journal of Economics,123(4), 1373–1414.

Jackson, C. K. (2010): “Do Students Benefit from Attending Better Schools? Evi-dence from Rule-based Student Assignments in Trinidad and Tobago,” Economic Journal,120(549), 1399–1429.

Jann, B. (2005): “Making Regression Tables from Stored Estimates,” The Stata Journal,5(3), 288–308.

(2006): “Making Regression Tables Simplified,” The Stata Journal, 7(2), 227–244.

Jensen, R. (2010): “The (Perceived) Returns to Education and the Demand for Schooling,”The Quarterly Journal of Economics, 125(2), 515–548.

Lai, F., E. Sadoulet, and A. de Janvry (2009): “The Adverse Effects of Parents’ SchoolSelection Errors on Academic Achievement: Evidence from the Beijing Open EnrollmentProgram,” Economics of Education Review, 28(4), 485–496.

MacLeod, W. B., and M. Urquiola (2009): “Anti-Lemons: School Reputation and Ed-ucational Quality,” NBER Working Papers 15112, National Bureau of Economic Research,Inc.

Manski, C., and D. Wise (1983): College Choice in America. Harvard University Press.

McCrary, J. (2007): “Manipulation of the Running Variable in the Regression Disconti-nuity Design: A Density Test,” NBER Technical Working Papers 0334, National Bureauof Economic Research, Inc.

MOES (2005): Computerised School Selection and Placement System (CSSPS) Guidelinesfor Selection and Admission into Senior Secondary Schools and Technical/Vocational In-stitutes. Ministry of Education and Sports.

Nagypal, E. (2004): “Optimal Application Behavior with Incomplete Information,” Work-ing Paper.

94

BIBLIOGRAPHY

Ozier, O. (2011): “The Impact of Secondary Schooling in Kenya: A Regression Disconti-nuity Analysis,” Working Paper.

Pallais, A. (2010): “Small Differences that Matter: Mistakes in Applying to College,”Working Paper.

Pathak, P., and T. Sonmez (2008): “Leveling the Playing Field: Sincere and Sophisti-cated Players in the Boston Mechanism,” American Economic Review, 98(4), 1636–52.

Pop-Eleches, C., and M. Urquiola (2011): “Going to a Better School: Effects andBehavioral Responses,” NBER Working Papers 16886, National Bureau of Economic Re-search, Inc.

Roth, A., and E. Peranson (1999): “The Redesign of the Matching Market for AmericanPhysicians: Some Engineering Aspects of Economic Design,” American Economic Review,89(4), 748–780.

Train, K. (2003): Discrete Choice Methods with Simulation. Cambridge University Press.

95

essays on school choice and the returns to school quality · data from three cohorts of applicants...

Documents