WPS5638


Policy Research Working Paper                       5638




      Evaluating Public Per-Student Subsidies
           to Low-Cost Private Schools
       Regression-Discontinuity Evidence from Pakistan

                            Felipe Barrera-Osorio
                              Dhushyanth Raju




The World Bank
South Asia Region
Education Team
  &
Human Development Network
Education Team
April 2011
Policy Research Working Paper 5639


  Abstract
  This study estimates the causal effects of a public per-                          process of phase-4 test takers as a sharp RD design,
  student subsidy program targeted at low-cost private                              the authors find evidence of large positive impacts
  schools in Pakistan on student enrollment and schooling                           on the number of students, teachers, classrooms, and
  inputs. Program entry is ultimately conditional on                                blackboards. Modeling the entry process of phase-3 test
  achieving a minimum stipulated student pass rate (cutoff)                         takers as a partially-fuzzy RD design given treatment
  in a standardized academic test. This mechanism for                               crossovers, they do not find evidence of significant
  treatment assignment allows the application of regression-                        program impacts on outcomes of interest. The latter
  discontinuity (RD) methods to estimate program impacts                            finding is likely due to weak identification arising from a
  at the cutoff. Data on two rounds of entry test takers                            small jump in the probability of treatment at the cutoff.
  (phase 3 and phase 4) are used. Modeling the entry




  This paper is a product of the Education team, South Asia Region; and the Education Team, Human Development
  Network. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to
  development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://
  econ.worldbank.org. The authors may be contacted at fbarrera@worldbank.org and draju2@worldbank.org.




         The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
         issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
         names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
         of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
         its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.


                                                       Produced by the Research Support Team
    Evaluating public per-student subsidies to low-cost private schools:
             Regression-discontinuity evidence from Pakistan

                                            Felipe Barrera-Osorio
                                              Dhushyanth Raju




JEL classification codes: I21; I28; O10
Keywords: education; Pakistan; regression-discontinuity design; subsidies; private schools



Contact information: Barrera-Osorio: World Bank, fbarrera@worldbank.org; Raju: World Bank,
draju2@worldbank.org. We thank the staff of the Punjab Education Foundation, in particular Usman Tariq Bhatty,
Mian Kashif Ijaz, Shahid Hafiz Kardar, Allah Bakhsh Malik, Haroon Raheem, and Huma Rizvi, for extensive
discussions on program design and implementation and assistance with the program administrative data; Nabiha
Asghar, Hummayun Javed, Kashif Mahmood, and Sehar Sarah Sikander Shah for assistance with the follow-up data
collection; Corinne Saiens for assistance with the National Education Census data; Amit Dar, Michelle Riboud,
Sofia Shakil, and the Government of Punjab School Education Department/Project Management and
Implementation Unit for their encouragement and support of the research project; and Salman Asim, Elizabeth King,
Leigh Linden, and Quynh Nguyen for helpful comments and suggestions. Financial support for the follow-up data
collection from the World Bank’s Education Program Development Fund and Bank-Netherlands Partnership
Program Trust Funds is gratefully acknowledged. The findings, interpretations, and conclusions expressed herein are
our own and do not necessarily represent the views of the World Bank, its Board of Directors, or any of its member
countries. All remaining errors are our own.
1. Introduction

School participation in Pakistan is generally low in absolute terms, relative to other countries in

its region, and relative to developing countries at its level of per capita income. Given the present

trend, Pakistan is likely to fall significantly short of the United Nations’ Millennium

Development Goal of universal primary education by 2015. Thus, measures that produce sharp

and sustained gains in participation are viewed as pressing by development policymakers and

practitioners in the country.

       In this paper, we estimate the causal effects of a recently-instituted public subsidy

program to low-cost private schools in the province of Punjab, Pakistan on school enrollment

and inputs. Coined the Foundation Assisted Schools (FAS) program and administered by the

Punjab Education Foundation (PEF), a semi-autonomous intermediary organization, the rationale

behind the program is to leverage, essentially via public financing, the growing low-cost private

school system in Punjab to increase equitable access to schooling more efficiently than can be

achieved through the province’s public school system.

       Given the contracting modality, the program falls under the rubric of public-private

partnerships (PPPs) in education, a set of interventions which is increasingly perceived in

international policy circles as a promising mechanism for attaining key education goals (World

Bank 2009). In addition, opportunities for introducing PPP programs of medium to large scale

are emerging in several developing countries (e.g., India, Kenya, and Nigeria) as the private

education sector matures and becomes an important player in service delivery.

       The FAS program was initiated on a pilot basis in November 2005, and rapidly expanded

in phases. As of September 2008, the program had completed four phases of expansion and




                                                 2
covered 1,082 low-cost private schools (primary, middle, and secondary levels1) with roughly

474,000 students across 18 out of 35 districts in Punjab. In the districts with the highest

concentration of program schools, we estimate that the program covers approximately one-fifth

of all private schools. The program offers a monthly per-student cash subsidy strictly tied to,

among other things, free schooling for all enrolled children (thus, pricing program schools in line

with public schools which are officially free) and a minimum student pass rate in a specially-

designed standardized academic test administered semi-annually by PEF. Program schools have

free rein on how to spend the subsidy amount.2

          To the best of our knowledge, credible evidence on the impacts of public subsidies to

private schools is limited. The study by Kim et al. (1999) is particularly pertinent as they

evaluate a public subsidy program in Pakistan which shares some of the design elements of the

FAS program. They study the impact of a program that offered a low temporary per-girl student

subsidy conditional on free girls’ schooling to establish and operate private primary schools in a

randomly-selected subset of poor urban neighborhoods lacking public girls’ primary schools in

the province of Balochistan. Using a difference-in-differences approach, they find that the

program substantially increased girls’ as well as boys’ school participation in treatment

neighborhoods, and that these increases were obtained at lower costs than would have been

possible through the public school system. For other well-identified evaluation studies of subsidy

programs (as well as of other types of PPP interventions), see the recent review by World Bank

(2009).




1
  Primary schools are composed of grades 1–5. Middle schools are composed of grades 1–8 or 6–8. Secondary
schools are composed of grades 1–10, 6–10, or 9–10.
2
  In contrast, the standard subsidy program is designed to directly finance educational inputs (Gauri and Vawda
2003).

                                                      3
       Consistent with the objectives of the FAS program, we ask two questions in this study.

(1) What is the causal effect of the program on the number of students in program schools? (2)

What is the causal effect of the program on inputs, namely the number of teachers, classrooms,

blackboards, and toilets, and on student-teacher and student-classroom ratios in program

schools? To answer these questions, using school-level baseline and follow-up data on school

characteristics and outcomes obtained from program administrative records and telephone

interviews of school administrators, we fit appropriate regression-discontinuity (RD) designs to

the treatment assignment mechanism in order to obtain reliable nonexperimental estimates of

program impacts.

       In the last two entry phases preceding this study, phases 3 and 4, a standardized academic

test, called the Short Listing Quality Assurance Test (SLQAT), was administered by PEF as the

final step in the program entry screening process. In order for schools to enter the program in

these two phases, they had to apply to the program, pass a qualitative physical inspection, and

then pass the SLQAT. If the school achieves the stipulated minimum student pass rate (the

cutoff) in the SLQAT, then the school becomes eligible for the program, and not otherwise.

Furthermore, in practice, virtually all schools that become eligible elect to participate in the

program.

       At the time of the follow-up data collection in October 2008, as phase 4 was the last entry

phase, schools that took the phase-4 SLQAT were either untreated or treated based on their

SLQAT pass rate relative to the cutoff (i.e., the probability of treatment jumps from zero to one

at the cutoff). This structure allows us to apply a sharp RD design to these data. On the other

hand, schools that took the phase-3 SLQAT and failed found they had another opportunity to

seek entry when phase 4 was announced—some phase-3 SLQAT ―failers‖ reapplied to phase 4,



                                                4
recleared the physical inspection, retook the SLQAT, and passed it. We find that the probability

of treatment for phase-3 SLQAT takers also jumps at the cutoff but by less than one. This

structure allows us to apply a special case of a fuzzy RD design which accounts for what can be

viewed as equivalent to noncompliance by initially-untreated schools.

       Given these designs, the effects of the program are identifiable and estimable. In the case

of the sharp RD design, under some mild regularity conditions, the average causal effect of the

treatment on the treated at the cutoff is identified. In the case of our fuzzy RD design, under the

same regularity conditions, the average causal effect of the treatment on the untreated at the

cutoff is identified. Under both designs, the respective treatment effects at the cutoff are

estimated nonparametrically using local linear regressions.

       Our findings on the impacts of the FAS program differ by phase. For phase-3 SLQAT

takers, applying a partially-fuzzy RD design, we find no evidence of program impacts at the

cutoff on our outcomes of interest. We posit that this is likely due to weak identification arising

from a small jump in the probability of treatment at the cutoff. In contrast, for phase-4 SLQAT

takers, applying a sharp RD design, we find robust evidence of positive program impacts at the

cutoff on the number of students, teachers, classrooms, and blackboards. The program impacts

were sizeable both in absolute terms as well as relative to the baseline means for these outcomes

for phase-4 SLQAT takers near the cutoff: our most conservative estimates suggest that the

program expanded schools by roughly 85 students, and 3–4 teachers, classrooms, and

blackboards, which translate into relative increases of 27–47%, depending on the outcome of

interest. These impact estimates are particularly impressive when we consider that phase-4

program schools were exposed to only about ten months of treatment before the follow-up data

were collected. Our cost-effectiveness analysis suggests that the FAS program is among the



                                                5
cheapest interventions in developing countries for generating enrollment gains. Notwithstanding,

the estimated impact on enrollment needs to be interpreted cautiously as, given our data, we are

unable to establish the extent to which the enrollment gains translate into school participation

gains given that, among other things, the elimination of school fees in program schools is likely

to also attract students from non-program schools in the vicinity of program schools.

       The remainder of the paper is organized as follows. Section 2 describes the education

context in Pakistan at the time the FAS program was introduced. Section 3 describes the program

in detail. Section 4 lays out our identification and estimation strategies. Section 5 describes the

data and provides some summary statistics for SLQAT takers. Section 6 presents our impact and

cost-effectiveness findings. Section 7 summarizes and interprets our main findings, as well as

provides some concluding comments. These comments comprise of a discussion of external

validity and two specific potential threats to internal validity: treatment spillovers to non-

program low-cost private schools within the sphere of influence of program schools, and

behavioral changes in non-program schools in anticipation of future program entry.



2. The education context

The FAS program was conceived and introduced into an education landscape defined by three

features. One: equitable access to schooling is an acute, persistent challenge. Two: the public

sector, which remains the dominant provider of education, suffers from chronic weaknesses

which impair its ability to effectively address this challenge. Three: in the wake of this public

sector failure, the private sector has aggressively stepped in in recent years, growing dramatically

in size and reach, and now constitutes a major policy opportunity for addressing this challenge.




                                                 6
         The education situation of Pakistan is generally poor in absolute terms, relative to other

countries in its region, and relative to developing countries at its level of per capita income (see,

e.g., United Nations Educational, Scientific and Cultural Organization 2007 for a recent

comparative picture). Given the present trend, Pakistan is unlikely to meet the United Nations’

Millennium Development Goal of universal primary education by 2015. The education situation

of Punjab—Pakistan’s most prosperous and populous province and the site for the FAS

program—is by and large comparable to the rest of the country. As Panel A in Table 1 shows,

estimates using household sample survey data from 2004/05, which is just before the FAS

program was initiated, show that the participation rate in formal school (grade 1+) of children

ages 6–15 years was 65.7%, with a significantly lower share for children from the poorest

(bottom expenditure quintile) households.

         The public school system has been hampered in its ability to improve education outcomes

due to, in large part, the lack of effective accountability and incentive systems which promote the

legitimate and efficient use of allocated resources (Social Policy and Development Center

2003).3 While the public school system has struggled to enroll children and educate them, the

private school system has grown dramatically as reflected by the number of institutions and share

of enrollment. In addition, responding to the broad demand for greater access and better quality,

the system has evolved in character, becoming less elite and more egalitarian, increasingly



3
  Recent evidence on relative teacher performance in private and public schools in Punjab suggests this. Andrabi et
al. (2008a) find that, while public school teachers are on average significantly better paid and have higher levels of
education, training, and experience than their counterparts in private schools, the teacher absenteeism rate is 15% in
public schools compared to 8% in private schools. They also find that, whereas private school teacher salaries are
increasing in teacher competency (as measured by teacher test scores) and decreasing in teacher absenteeism, public
school teacher salaries do not exhibit similar correlation patterns and instead appear to be largely determined by
teacher credentials (education, training, and experience). Looking at child education outcomes, Andrabi et al. find
that private school teacher salaries are increasing in student test scores whereas public school teacher salaries are
not. The responsiveness of private school teacher salaries to these key behaviors and outcomes suggests the
influence of market discipline which the public school system is not subject to, at least directly.

                                                          7
reaching low-income and rural households.4 Using private school census data from 2000,

Andrabi et al. (2008b) find that there was an exponential increase in the number of private

schools over the 1990s, with over 50% of existing private schools established in or after 1996.

Furthermore, they find that while existing schools set up before 1990 were predominantly in

urban areas, the distribution since then has become increasingly rural.

        In line with this increase in institutions, the share of enrollment in private school has also

increased. As Panel B in Table 1 shows, in 2004/05, 15.8% and 18.5% of children ages 6–15

years were enrolled in private schools in all-Pakistan and Punjab, respectively; these shares

represent significant increases from 1998/99. The increases were particularly dramatic in rural

areas and for households in the poorest expenditure quintile. Similar evidence is provided by

Andrabi et al. (2008b) who find that the growth rate in private school enrollment over the 1990s

was highest among low-income households nationally, and among middle-income households in

rural areas, whereas the growth rate in public school enrollment over the same period was

negative in both urban and rural areas and across the household income distribution. They also

find that fees in private schools are generally low: median annual fees per student in 2000 in

Pakistan were 960 (US$23.45) and 751 rupees (US$18.3) in urban and rural areas, respectively,

and account for a small percentage of mean annual household expenditure. The corresponding

statistics for Punjab were lower, at 828 rupees (US$20.2) and 600 rupees (US$14.6).




4
  It is conceivable that much of the growth and metamorphosis in the private school system is in direct response to
the rigidities and shortcomings in the public school system.
5
  The exchange rate in 2000 was 41 rupees per US dollar.

                                                        8
3. The Foundation Assisted Schools program6

Institutional background: The FAS program is administered by PEF, a publicly-funded semi-

autonomous statutory organization established in 1991 which serves as the main institutional

mechanism for PPPs in education in Punjab. The organization’s primary aims are to enable

socioeconomically-disadvantaged households to access private education and to raise the quality

of education in low-cost private schools. To these ends, it employs an array of instruments such

as start-up and operational subsidies, vouchers to households in poor localities, school

management and teacher training, and specialist teacher services to promote private education.

The FAS program is PEF’s largest program. In fiscal year 2007–08, PEF spent 1.1 billion rupees

(US$12.9 million7) on FAS program benefits.8 This amount accounted for 61% of total

expenditures by the organization in that year.

Program coverage and timeline: The FAS program was initiated in November 2005 on a pilot

basis in 54 schools in five districts in Punjab. Since then, PEF has expanded the program in

phases to cover additional districts as well as more schools within program districts. (See Table 2

for a timeline of the program highlighting the start-dates of each of the phases as well as the

dates of other key events.) As of September 2008, the program has completed four entry phases

(the pilot phase represents phase 1), and covers 1,082 private primary, middle, and secondary

schools in 18 out of the 35 districts in Punjab.9 Of these, 945 schools (87%) are located in just

seven districts (see Table 3 for a district- and phase-wise disaggregation of the number of

program schools as well as Figure 1 for the location of program districts in Punjab). This number

6
  The information on the program presented in the paper reflects program design and administration until end 2008.
7
  In this and following sections, the exchange rate used for the conversions is 85 rupees per US dollar (effective
March 2011). When the program was introduced in 2005, the exchange rate was roughly 60 rupees per US dollar;
the rupee has steadily weakened since then.
8
  FAS program administrative costs are unavailable as PEF does not disaggregate administrative costs by program.
We however know that total administrative costs were less than 1% of total expenditures in fiscal year 2007–08,
suggesting that FAS program administrative costs are negligible relative to current FAS program benefit outlays.
9
  The FAS program also currently covers three higher secondary schools (schools with grades 11–12).

                                                        9
of program schools represents a significant share of all private schools in these seven districts:

using the 2005 National Education Census (NEC), a census of schools in Pakistan, we estimate

that the program covers 21% of private schools in these districts (see Table 4).10

Program location: The program was initially designed to be targeted at districts ranked lowest in

terms of adult literacy rates based on 2003/04 Multiple Indicators Cluster Survey data

(Government of Punjab 2004). However, in phases 1 and 2, this targeting decision was not

applied as PEF was limited in its institutional and logistical capacity at that time to effectively

administer the program in poorly-ranked districts that had physical environmental challenges and

limited transportation and accommodation options (Malik 2007). In contrast, in phases 3 and 4,

the targeting decision was effectively applied. Consequently, as Table 3 shows, 51% and 89% of

program schools are located in districts ranked among the bottom-quarter and bottom-half in

terms of adult literacy rates, respectively.

Program school characteristics: Table 5 presents the distribution of program schools by selected

characteristics measured in September 2008. Aggregating the phases together (Column 5), the

mean school size is 351 students. The majority of schools are middle level (59%), coeducational

(83%), registered with local government authorities (87%), and rural (55%). Disaggregating by

phase (Columns 1–4), the distribution of program schools by these characteristics is roughly

comparable except for the level of the school: in contrast to the pattern in the aggregate sample,

program schools that entered in phases 1 and 2 were mainly secondary schools (65–73%).

School size also appears to be monotonically decreasing with phase; the mean size of program

schools which entered in phase 1 is 561 students, whereas that of program schools which entered

10
   NEC’s coverage of private schools might be incomplete. According to the survey documentation, private schools
were identified in the field by interviewers with the assistance of local officials. It is conceivable that private schools
that are, for example, unregistered or very small, or operate in obscure locations are more likely to be missed by
interviewers. Thus, the estimate of 21% can be considered as an upper-end estimate of FAS program coverage of
private schools.

                                                           10
in phase 4 is 242 students. While there may be multiple (competing) explanations for this

pattern, length of exposure to the program is among them.

Program benefits: The main program benefit is an enrollment-related subsidy: the school

receives a monthly per-student cash subsidy amount of 300 rupees (US$3.5) up to a maximum of

750 students (i.e., the total amount is capped at 225,000 rupees or US$2,647).11 Given a mean

school size of 215 students in phase-3 and phase-4 program schools at the time of application to

the program, the mean monthly subsidy payment is roughly 64,500 rupees (US$759) at program

entry. Enrollment information for determining the subsidy amounts is submitted by program

schools to PEF on a monthly basis using standardized reporting forms; if enrollment has

increased by 50 students or more over one month, PEF visits the school to verify the information

before raising the subsidy amount. PEF indicates that, when schools report large changes in

enrollment, these reports tend to be at the start of the academic year in April.

        PEF reports that the subsidy level was set low for two reasons. First, it confines the

attractiveness of the program to low-cost private schools. Second, it raises the political

palatability of the program as the per-student subsidy amount is less than half of the estimated

per-student expenditure in the public school system at the time the program was introduced.12

The subsidy benefit is paid for all twelve months of the year. To facilitate timely and regular

payments, starting in August 2007, the benefit amounts have been transferred electronically to

the bank accounts of program schools.

11
   The program also offers two cash bonus benefits. The first is a teacher bonus for a high level of school test
performance: once every academic year, a maximum of five teachers in each program school where at least 90% of
students in tested classes obtain a score of 40% or higher in the QAT receive an award of 10,000 rupees (US$118)
each. The second is a competitive school bonus for top school test performance: once every academic year, the
program school in each of the seven main program districts which has the highest share of students with a score of
40% or higher in the QAT is awarded 50,000 rupees (US$588).
12
   The exact subsidy amount was heavily guided by a survey conducted by PEF in 2005 in selected districts which
showed that the vast majority of private schools that operate in rural areas and disadvantaged urban neighborhoods
charge between 50–400 rupees per month (US$0.6–4.7) in fees. Based on this information, the subsidy amount was
set at the upper-segment of this price range (Malik 2007).

                                                       11
Initial benefit eligibility rules: School entry into the program follows a three-step process. In step

1, schools apply to the program when PEF issues a call for applications in newspapers.

Application eligibility is restricted to existing private primary, middle, and secondary schools

with a minimum enrollment of 100 students from the districts listed in the call. Except in a few

cases, only schools that submit properly filled-in applications by the announced deadline are

considered for step 2.

           In step 2, PEF inspection teams visit schools unannounced to verify the data provided in

the applications as well as assess the local reputation of the school and the quality of the physical

infrastructure and schooling environment. PEF provides a points and weighting scheme to its

inspection teams—this scheme primarily helps ensure that the same school attributes are

considered across schools and by different inspection teams. However, the screening exercise is

largely subjective: whether a school qualifies for step 3 depends principally on qualitative

impressions gathered by the inspection team on a given set of indicators.

           In step 3, which was introduced starting with phase 3, all students present in selected

grades in the school on the day of the physical inspection screening are offered a 55-minute,

written, curriculum-based test called the Short Listing Quality Assurance Test (SLQAT).13 The

SLQAT is a pared-down version of the Quality Assurance Test (QAT) which is used to

determine continuing benefit eligibility once schools enter the program. The SLQAT tests

knowledge and comprehension in three subjects: English, Urdu, and mathematics. It is designed

by the testing department of PEF, the Academic Development Unit (ADU). Each school is tested

on its own premises. Depending on the level of the school, two to three grades among grades 3,

4, 6, 7, and 9 are tested. Which grades are tested in a given school are not disclosed in advance

and are randomly selected by ADU. Furthermore, multiple test papers are prepared for each
13
     For schools that entered the program in phases 1 and 2, step 2 was the final entry step.

                                                            12
grade; ADU randomly selects which specific test papers are offered in a given school. The

SLQAT is transported in sealed envelopes and opened only in the presence of the school

administrator and teachers. At that time, both the PEF inspection team and the school learn

which grades are selected for the SLQAT. Test invigilation is coordinated by the ADU member

assigned to the PEF inspection team. The completed tests are transported back to PEF

headquarters and graded by ADU. The school passes the SLQAT if at least 67% of tested

students score 33% or higher.

        Figure 2 presents the numbers of schools which passed each step of the program entry

process. Out of the 1,070 and 1,430 schools that had submitted properly filled-in applications

and were inspected in phases 3 and 4, respectively, 799 (75%) and 872 (61%) schools were

offered the SLQAT. Of the schools that were offered the SLQAT, 514 (64%) and 431 (49%)

schools achieved the minimum pass rate and became eligible for the program.14 In terms of

program take-up, PEF reports that 482 (94%) and 425 (98%) of the schools that passed the

SLQAT in phases 3 and 4 respectively signed the formal program participation agreement.

Continuing benefit eligibility rules: The program participation agreement stipulates several

conditions for maintaining benefit eligibility. The conditions that are stringently applied by PEF

are (1) schooling is offered to students without charging them any fees (and displaying the free-

schooling status prominently on a PEF-issued signboard outside the school gate) and (2)

participation of the program school in the QAT and that at least 67% of the tested students score

40% or higher on the QAT. A one-time violation of these conditions typically results in a

warning and the capping of enrollment figures for the subsidy payment until the next QAT

round. A second violation results in the permanent disqualification of the school with immediate

14
   Our own tallies based on the SLQAT data deviate slightly from the above numbers: we find that 796 and 856
schools took the SLQAT and, out of these, 511 and 432 schools achieved the minimum pass rate in phases 3 and 4,
respectively.

                                                      13
effect. With the QAT-related condition, the school is permanently disqualified if it fails to

achieve the minimum pass rate in the QAT in two consecutive attempts.

        The QAT is a 65-minute, written, curriculum-based test designed by ADU, and

administered twice a year in October–November (in the first term) and February–March (in the

second term). It tests knowledge, comprehension, application, analysis, and synthesis. The

subject areas covered in the tests are English, Urdu, mathematics, and science (general science in

grades 1–8 and biology, chemistry, and physics separately in grades 9–10). The general test

administration procedures previously delineated with respect to the SLQAT are also followed

with the QAT.15 By the time of the follow-up data collection, PEF had conducted five QATs (see

Table 2 for the dates). Phase-3 program schools had been subject to two QATs and phase-4

program schools one.

        There are also other conditions for maintaining benefit eligibility. These include (1)

registering the school with the District Registration Authority within one year of joining the

program; (2) conducting only one class in a classroom in any period; (3) maintaining or

upgrading the quality of the school’s physical infrastructure (e.g., adequate classroom space,

properly-constructed rooms and buildings, sufficient ventilation, and sufficient artificial and

natural light); (4) acquiring and maintaining adequate furniture and teaching tools (e.g., benches,

desks, and blackboards); (5) providing monthly reports to PEF on enrollment counts; (6) keeping

student-teacher and student-classroom ratios below 35:1; (7) keeping enrollment above 100

students; and (8) not holding after-hours classes or tutoring services at the school. These

additional conditions are applied more leniently; typically, when PEF detects a violation among

this subset of conditions, schools are provided with a warning and a grace period within which to


15
   One important difference is that, unlike with the SLQAT, the school receives formal advance notices of the date
of the QAT, and at least 80% of its students are expected to be in school on the day of the test.

                                                       14
comply. As of the follow-up data collection, no program schools have been disqualified for

repeated violations of these conditions.

        Table 6 presents the number of program schools that were disqualified, disaggregated by

phase. The data are up until the time of the follow-up data collection. The number of schools that

have been disqualified for any reason is negligible: only 28 out of the 1,111 program entrants

(2.5%) have exited the program over time. In addition, in most cases, the reason for

disqualification is two consecutive failures to achieve the minimum pass rate on the QAT.

Importantly, for our analysis, only three schools that entered the program in phases 3 and 4 have

exited the program for any reason.16 Thus, program dropout has not been an issue with phase-3

and phase-4 program schools.

Direct impact channels: The structure of the program can be expected to have a positive effect

on enrollment via several direct channels. For example, setting the monthly subsidy as a linear

function of the number of children enrolled incentivizes program schools to draw in additional

students. Tying the receipt of program benefits to the elimination of school fees—which puts the

program school’s price at an advantage over other local non-program competitor private schools

and at par with public schools—is likely to raise the attractiveness of program schools,

particularly among households for which school fees serves as a major constraint to sending their

children to private school.17

        The structure of the program can also be expected to directly affect investments in the

quantity and quality of school inputs and resources. For example, increases in enrollment


16
   PEF reports that the three schools were problematical cases from the outset; the schools were ejected from the
program for general noncompliance and nonperformance.
17
   An increase in enrollment in program schools may not translate into a commensurate increase in participation
among children in areas where program schools operate. The lower price of schooling in program schools is likely to
induce both displacement and diversion effects: some share of the new enrollment in the program school will likely
come from students already enrolled in other schools or children that where initially considering enrolling
elsewhere.

                                                        15
induced by the per-student subsidy have to be met by increases in the number of classrooms and

teachers if the stipulated maximum student-teacher and student-classroom ratio conditions are to

be complied with. The maximum ratios encourage program entrants with preexisting ratios in

excess of the maximums to invest in additional classrooms and teachers. The physical

infrastructure and learning environment quality conditions encourage program schools to ensure

the proper design and construction of infrastructural expansions, and to invest in teaching tools

(e.g., blackboards) and basic facilities (e.g., toilets), in step with enrollment growth. These input-

related conditions encourage schools to schedule investments in school inputs and resources to

either lead or accompany enrollment increases. However, given that these conditions are not

stringently applied, it suggests that PEF might tolerate investments in school inputs and

resources that lag enrollment increases, although reportedly not by too long.



4. Empirical strategy

Identification

Following the exposition in van der Klaauw (2008) and Todd (2007), let yi denote the outcome

of interest (e.g., enrollment) in school i, and let the indicator variable d i  0,1 denote treatment

assignment, where one denotes that the school is covered by the FAS program (treated), and zero

if not (untreated). In addition, let y0i and y1i denote the potential outcomes of school i in the

untreated and treated states, respectively. The actual outcome observed for school i is given by

                       yi  di y1i  1  di  y0i  y0i   y1i  y0i  di  y0i  i di ,        (1)

where  i denotes the treatment effect for school i.




                                                       16
        Unless treatment is randomly assigned, simply comparing mean outcomes of treated

schools and untreated schools, E  yi1 | di  1  E  yi 0 | di  0 , would not yield an unbiased

estimate of the average causal effect of the treatment: E  i  . In general,

          E  y1i | di  1  E  y0i | di  0  E i | di  1  E  y0i | di  1  E  y0i | di  0.   (2)

The first term on the right-hand side of (2) is the average treatment effect on the treated (ATT)

and the second term (in braces) is the selection bias arising from differences in potential average

untreated outcomes between treated and untreated schools. Selection is clearly plausible in our

case. For example, if, ex ante, program schools have higher levels and better quality inputs and

resources relative to non-program schools, then the selection bias term will be positive and

generate an upward bias in our estimate of the ATT.

        The potential selection bias problem can however be overcome by using the institutional

feature that program eligibility is ultimately determined by the student pass rate obtained by the

school in the SLQAT relative to the known pass rate cutoff of 67%. Given that virtually all

schools that become eligible to participate in the program also choose to participate in the

program, in practice, the cutoff determines actual program participation. Thus, program

participation status is assigned based on the decision rule

                                               di  zi   1 zi  c ,                                        (3)

where z i denotes school i’s pass rate which is perfectly observed (z will be more generally

referred to as the assignment variable), c the known distinct cutoff pass rate, and 1 an indicator
                                                                                      

function. This design for treatment assignment based on a completely deterministic function is

referred to as a sharp regression-discontinuity (RD) design.




                                                         17
        The SLQAT pass rate z might be correlated with our outcomes of interest. Thus, the

treatment assignment mechanism is clearly not random and comparing schools that receive the

treatment ( d i zi   1 ) to schools that do not ( d i zi   0 ) will yield a biased estimate of the ATT.

If, however, we consider schools with pass rates near the cutoff to be comparable, then the

treatment assignment mechanism in the neighborhood of the cutoff can be viewed as if it was

―almost random‖.

        More formally, let e  0 denote an arbitrarily small number. Comparing the outcomes of

schools with pass rates just below the cutoff (marginal failers) with the outcomes of schools with

pass rates at or just above the cutoff (marginal passers), yields

E  y1i | zi  c  e   E  y0i | zi  c  e   E i | zi  c  e  E  y0i | zi  c  e  E  y0i | zi  c  e . (4)

Under the assumptions that (1) the limit lim E y0i | zi  c  e is well defined; (2) E y0i | zi  c
                                                      e0



is continuous in the assignment variable z at the cutoff (i.e., the conditional expectations of the

outcome variable exhibits local smoothness at the cutoff in the absence of the treatment); and (3)

the density of the assignment variable z is positive in the neighborhood of the cutoff, the

difference in the mean outcomes between marginal passers and marginal failers identifies

                        E i | zi  c   lim E  y1i | zi  c  e   lim E  y0i | zi  c  e  .                   (5)
                                            e 0                         e 0



This object is interpreted as the ATT at the cutoff (Hahn et al. 2001; Todd 2007).

        A sharp RD design neatly fits the phase-4 SLQAT taker data, as the school’s pass

(eligibility) versus fail (ineligibility) status remains fixed given that phase 4 was the last entry

phase before the follow-up data collection. A variant of the above framework will however be

required for phase-3 SLQAT takers given that some phase-3 failers reapplied to the program in

phase 4 and passed the SLQAT at that time. As a result, our set of phase-3 SLQAT takers can be


                                                            18
divided into three distinct subsets: (1) phase-3 failers who did not enter the program any time

later; (2) phase-3 failers who entered the program later in phase 4 (crossover schools); and (3)

phase-3 passers who entered the program at that time (as noted before, the treatment take-up rate

by passers was virtually 100%, and there have been no dropouts to date). While the pass rate

cutoff rule strictly determines program eligibility status for phase-3 SLQAT takers, the processes

and factors behind the phase-4 application decision of phase-3 failers are unobservable to us and

likely to be nonrandom. Given this, the eventual participation status of this group of schools is

also considered to be driven partly by selection on unobservables.

       In our data, we find that the probability of program participation as a function of the pass

rate in the phase-3 SLQAT, Edi | zi   Prdi  1 | zi , consists of a positive but smaller jump than

one at the cutoff. The probability of program participation will still be discontinuous in the

assignment variable z at the cutoff. This feature implies that the phase-3 SLQAT taker data are

more appropriately fitted with a fuzzy RD design. Under this design, apart from the identifying

assumptions for the sharp design, if we assume that treatment d i is nondecreasing in the

assignment variable z at the cutoff (local monotonicity) and that potential outcomes are

independent of treatment conditional on the assignment variable z at the cutoff (local conditional

independence), then the average causal effect of the treatment is identified by

                                            lim  y1i | zi  c  e  lim  y0i | zi  c  e
                      E  i | zi  c     e 0                       e 0
                                                                                                  ,   (6)
                                            lim  d1i | zi  c  e  lim  d 0i | zi  c  e 
                                            e 0                       e 0


where the denominator of (6) is nonzero given the discontinuity in the probability of treatment at

the cutoff (Hahn et al. 2001; Todd 2007).

       This treatment parameter represents the RD analog to the local average treatment effect

(LATE) (Imbens and Angrist 1994; Angrist et al. 1996). It can be interpreted as the average


                                                          19
treatment effect for schools in the neighborhood of the cutoff who are induced to take up

treatment when their pass rates are at or above the cutoff d i zi   1 but not so when they are

below d i zi   0 .

         The general fuzzy design setup above allows for partial (or imperfect) compliance for

both treatment-eligible and treatment-ineligible groups; that is, it allows for both crossovers

(treatment-ineligibles taking up treatment) and no-shows (treatment-eligibles not taking up

treatment) (Bloom 1984). In our case, the problem is essentially one of one-way partial

compliance: we have the equivalent of crossovers over time from treatment-ineligible to

treatment-eligible status, with all treatment-eligible schools choosing to take up treatment.

Hence, the probability of program participation for phase-3 SLQAT passers is one, while the

probability for failers lies between zero and one.

         Battistin and Rettore (2008) describe the other one-way partial compliance case, where

treatment-ineligible agents are not exposed to treatment and treatment-eligible agents self-select

into treatment. They formally show that the LATE at the cutoff can be identified simply under

the conditions required for identifying the ATT at the cutoff under the sharp RD design, thus

labeling their framework as a ―partially‖ fuzzy RD design. Their framework straightforwardly

applies to our case of one-way partial compliance as well. However, whereas in their specific

setup, they identify the ATT at the cutoff ( lim E i | zi  c  e ), by applying the smoothness
                                                    e0



condition to obtain the counterfactual average outcome for the untreated ( lim E yi1 | zi  c  e ),
                                                                                  e0



we instead identify the average treatment effect on the untreated ( lim E i | zi  c  e), by
                                                                            e0



applying the smoothness condition to obtain the counterfactual average outcome for the treated (

lim E  yi 0 | zi  c  e ) (Duflo et al. 2007).
 e0




                                                     20
Estimation

Choice of estimator: Given that we are interested in estimating the treatment effects at a single

point using observations in its neighborhood, one suitable approach is local smoothing using

nonparametric regression. Following Hahn et al. (2001), we opt for local linear regression (a

local polynomial of order one). In the case of the sharp RD design, which applies to our phase-4

SLQAT takers, the application of local linear estimation entails individually estimating the

conditional expectations of the outcome y at the cutoff from below (denoted by  y ) and above
                                                                                ˆ

the cutoff (denoted by  y ) and then subtracting the two estimates. Under the sharp RD design, a
                        ˆ

consistent estimate of the ATT at the cutoff is given by

                                           y   y  y .
                                          ˆ     ˆ ˆ                                         (7)

       In the case of the fuzzy RD design, the application of local linear regression entails

estimating the ratio of two differences. Given our particular problem related to phase-3 SLQAT

takers, we individually estimate the conditional expectations of the outcome y at the cutoff c

from above and below (  y and  y , respectively), and the conditional expectation of treatment
                       ˆ      ˆ

d from below only (denoted by  d ). Note that the conditional expectation of treatment d from
                               ˆ

above is one by definition. Under our particular partially-fuzzy RD design, a consistent estimate

of the LATE at the cutoff is given by

                                           y  y  y
                                          ˆ    ˆ ˆ
                                                      .                                      (8)
                                          d
                                          ˆ    1 d
                                                   ˆ




                                                21
        To perform statistical inference, empirical standard errors for (7) and (8) are obtained

using the standard i.i.d. nonparametric bootstrap with paired sampling  yi , zi  , resampling from

the original data 500 times.

Choice of kernel and bandwidth: Implementation of local linear estimation requires the

specification of the kernel k, the weighting function, and bandwidth h  0 , the window width in

which the kernel function is applied. We opt for the triangular kernel given that it is boundary

optimal and thus well suited to RD problems (Cheng et al. 1997).18

        The choice of bandwidth is a relatively more important decision given the trade-off

between estimation bias and variance. Consensus in the literature on valid and robust methods

for bandwidth selection for RD problems is lacking.19 Given this, we discount the specific

method used to select the optimal bandwidth and instead emphasize checking the robustness of

our findings to reasonable deviations in bandwidth from the optimal bandwidth choice.

        To select the optimal bandwidth, we rely on the default bandwidth choice in Nichols’

(2007) rd program for Stata which assigns positive weight to at least 30 observations on each

side of the cutoff, and applies the same bandwidth for the local linear estimators of the

conditional mean outcomes (and probabilities of treatment) above and below the cutoff (i.e.,

h   h   h ). In our case, the default choice translates to a bandwidth of three or four percentage

points for our RD impact estimations. We believe that this is a conservative choice, and


18
   As Imbens and Lemieux (2008) note, while more sophisticated kernels are available, they do not provide any
significant gain in asymptotic bias reduction. Furthermore, they note that, in general, parameter estimates appear to
be robust to the choice of kernel.
19
   This is, in large part, due to two reasons. First, standard automated procedures for bandwidth selection for
nonparametric regression have been developed with the estimation of functions at interior points in mind; the nature
of the trade-off between bias and variance at interior points may differ from the nature of the trade-off at boundary
points (Ludwig and Miller 2005). Second, the literature on the development of bandwidth selectors customized to
the RD context is an emergent one (e.g., McCrary and Royer 2006; Imbens and Lemieux 2008; Imbens and
Kalyanaraman 2009). In addition, the relative finite sample performances of the proposed bandwidth selection
methods for RD designs have yet to be rigorously assessed.


                                                         22
acceptably balances restricting estimation to a local neighborhood around the cutoff against

having sufficient statistical power to yield informative estimates of treatment effects.

Notwithstanding, we examine whether our RD impact estimates and statistical inference results

are sensitive to increasing the optimal bandwidth by 50% and 100%, potentially trading off

increased bias for reduced variance.



5. Data and sample

Data

Baseline data: The baseline data come from the program application records and SLQAT test

records collected and maintained by PEF. In phase 3, properly filled-in application forms

received by PEF before the announced deadline of April 2007, as well as forms filled out by

schools solicited by PEF inspection teams on their way to inspect applicant schools were

considered. In phase 4, only properly filled-in forms received by PEF before the announced

deadline of July 2007 were considered. PEF collected 1,070 and 1,430 properly filled-in

application forms in phases 3 and 4, respectively.20

        PEF constructed a school-level application electronic database for each phase which

contains information on school characteristics (location, gender type, level, physical

infrastructure, and registration status), total school enrollment separately by gender, total number

of teachers and administrative staff separately by gender, and the minimum and maximum

monthly teacher salaries in the school.21 These databases serve as the source of baseline data on

the following outcomes measured at the school-level: number of students, teachers, classrooms,

20
  The total number of unique applications received by PEF is unknown as all rejected applications were discarded.
21
   As part of this inspection, the data provided by the school in the application form are verified. These inspection
data would have been useful for checking the accuracy of the application data; they were however collected in paper
form and not entered into an electronic database. Consequently, these data are unavailable for the purposes of this
study.

                                                         23
blackboards, and toilets. The school-level outcomes of student-teacher and student-classroom

ratios are constructed by us using the data on total number of students, teachers, and classrooms.

These databases also serve as the source of baseline data on school-level covariates, namely

location, gender type, level, and registration status.

        The SLQAT serves as the source of data on the school’s student pass rate, our treatment

assignment variable z. Separate electronic databases have been constructed by PEF for phase-3

and phase-4 SLQAT takers. These databases contain the total score for each student that took the

test. In the databases, student test scores are organized by school and, within school, by grade.

The school identification information provided in the databases comprise of the school’s name

(at times, with some address elements) and location (tehsil22 and district). Although PEF

constructed the SLQAT pass rate for each school, we used the student test score data in order to

construct our own measure of school SLQAT pass rates. The match rate between their

calculation of school SLQAT pass rates and ours’ in both phases is nearly perfect at 99.5%.

While it makes virtually no difference, we use our measure of school SLQAT pass rates as the

treatment assignment variable

        Constructing a single electronic database for our analysis required that the application

data are linked with the SLQAT data at the school level. Unfortunately, the same unique school

identification variable was not used across databases. Consequently, we linked the application

databases to the SLQAT databases using an iterative visual-matching process. First, schools were

matched across databases using the district name and school name variables.23 Exact matching

failed in a number of cases as PEF did not maintain consistency in the spelling, word ordering,


22
  Tehsil is the spatial unit of government administration one tier below district. There are 127 tehsils in Punjab.
23
   Although information on the school’s tehsil was also available in both the application and test databases, this
information was error-ridden. Consequently, we did not use this information in the cross-database matching
exercise.

                                                        24
and completeness of the school’s name across the two databases; hence, matching on school

name frequently required matching on key words and word patterns. In cases where we

suspected that the combination of district name and school name (even with keyword and word

pattern matching) did not yield a unique school record in a database, where possible, the set of

matching variables was extended to include school address. This extension helped resolved a

number of cases where we were tentative. On the basis of this exercise, 94% and 97% of school

records in the SLQAT databases were linked with school records in the application databases for

phases 3 and 4, respectively. Only the linked school records are used in our analysis, which yield

sample sizes of 747 and 830 schools in phases 3 and 4, respectively. We refer to these samples as

the SLQAT samples.

Follow-up telephone interview data: We collected follow-up outcome data via telephone in

October 2008 from phase-3 and phase-4 schools with SLQAT pass rates between  /  15

percentage points of the cutoff. This information was gathered by a small team of independent

interviewers. We were able to collect the data using this mode as schools were required to

provide the telephone number of the school owner or administrator when they applied to the

program, and the information was included in the school application electronic databases for

both phases.

        We obtained data on the following outcomes: the number of students, teachers,

classrooms, blackboards, and toilets (the data on the last two outcomes were collected only for

the phase-4 schools). 24 We also obtained information on the program participation status of the

schools, and crosschecked this information against PEF’s records of program schools as of

September 2008. The school sample sizes within the selected pass rate range from the cutoff are

24
  We are unable to speculate on the accuracy of these data vis-à-vis the same data collected through, for example,
face-to-face interviews in the field, as we are unclear what context factors might lead to differences in accuracy
across survey modes.

                                                       25
268 and 319 schools in phases 3 and 4, respectively. These numbers constitute 36% and 38% of

the respective SLQAT samples. We refer to these samples as the cutoff neighborhood samples.

       The period of the follow-up data collection was roughly 14 and 10 months after the

receipt of the first subsidy payment by phase-3 and phase-4 program schools, respectively. The

treatment exposure period under investigation roughly covers the second half of the 2007/08

academic year and first half of the 2008/09 academic year.

Unit nonresponse analysis: Despite repeated attempts by the interviewers, not all schools in the

cutoff neighborhood samples were contactable over the telephone. Unit nonresponses were

mainly due to wrong numbers or unattended telephone calls; when reached, refusals were rare.

There were no cases of item nonresponse. Roughly 28% and 22% of schools have missing data

due to unit nonresponse in the phase-3 and phase-4 cutoff neighborhood samples, respectively.

These large percentages are expected to reduce the study’s statistical power (which does pose

some concern given that our study is low-powered to begin with) but do not necessarily

introduce sample selection bias.

       To investigate the presence of systematic bias, we estimate simple bivariate correlations

between unit nonresponse and selected covariates, separately by phase. The covariates that we

examine comprise of indicator variables for (initial) treatment assignment (i.e., whether the

school’s SLQAT pass rate is above the cutoff) as well as baseline measures of the school’s

registration status, level, gender type, and location. Table 7 presents nonresponse counts and

rates (Panel A) and the estimated correlations (Panel B). It appears that the probability of

nonresponse is not significantly associated with treatment assignment: the estimated correlation

coefficients are .03 and .07 and the associated standard errors are .06 and .05 for the phase-3 and

phase-4 cutoff neighborhood samples, respectively. In addition, as Columns 3 and 6 in the table



                                                26
show, barring a few exceptions—which could arise simply due to random chance—the

probability of nonresponse does not appear to be significantly associated with the selected school

covariates. Thus, the evidence suggests that we cannot reject the null hypothesis that

nonresponse rates are generally comparable for marginal failers and marginal passers across the

selected dimensions measured at baseline.

         Even if nonresponse rates are similar between marginal failers and passers, it is still

possible that the selection process for nonresponding marginal failers differs from the selection

process for nonresponding marginal passers (Duflo et al. 2007). Table 7 also reports bivariate

correlations between unit nonresponse and selected covariates measured at baseline separately

for marginal failers and marginal passers (Columns 1 and 2 for phase 3 and Columns 4 and 5 for

phase 4). The evidence generally suggests that we cannot reject the null hypothesis that the

underlying selection processes for nonresponse for both marginal failers and marginal passers are

random. Based on these collective findings, we assume that the nonresponse rate is locally

smooth in the assignment variable at the cutoff.



Sample

Table 8 presents statistics on the distribution of schools by selected characteristics measured at

baseline, separately by phase and for the SLQAT and cutoff neighborhood samples. We

highlight two patterns. First, across both phases and samples, the distributional patterns across

characteristics are broadly comparable. For example, the majority of schools are (1) middle

schools (63–72%), (2) coeducational (82–87%), (3) officially-registered (81–88%) and (4) rural

(53–59%). Second, comparing the phase-3 SLQAT sample to the phase-4 SLQAT sample

(Columns 1–3), pairwise t-tests of the equality of proportions show significant differences in the



                                                   27
distribution of schools across several characteristics. It appears that, among other things, the

shares of secondary schools, single-sex schools, urban schools, and registered schools are larger

in the phase-3 SLQAT sample than in the phase-4 SLQAT sample. These distributional

differences across phases lose their statistical significance when we restrict our attention to the

cutoff neighborhood samples (Columns 4–6). Some part of the explanation for the loss in

significance is likely due to reduced statistical power resulting from the smaller sample sizes for

the cutoff neighborhood samples relative to the SLQAT samples.

       Table 9 presents means and standard deviations for selected outcomes measured at

baseline, again separately by phase and for the SLQAT and cutoff neighborhood samples. In the

phase-3 SLQAT sample (Column 1), we find that schools on average have 253 students; 10

teachers, classrooms, and blackboards; and 3 toilets. Mean student-teacher and student-

classrooms ratios are 25:1 and 28:1, respectively, which, to begin with, are below the stipulated

maximums for program benefit maintenance. The differences across phases in the SQLAT

samples (Columns 1–3) lose their statistical significance when we restrict our attention to the

cutoff neighborhood samples (Columns 4–6). Again, some part of the explanation for the loss in

significance is likely to be the lower statistical power of the cutoff neighborhood samples relative

to the SLQAT samples. Notwithstanding, the sizes of the inter-phase differences in the cutoff

neighborhood samples are generally substantially smaller than the corresponding differences in

the SLQAT samples. In sum, the phase-3 and phase-4 cutoff neighborhood samples appear to be

similarly composed with respect to mean outcomes measured at baseline.




                                                28
6. Results

Before presenting our RD estimates of the impacts of the FAS program, we discuss results from

a couple of model specification tests. First, we show that there is a discontinuous change in the

conditional probability of treatment at the SLQAT pass rate cutoff, as the suitability of the RD

model hinges on this feature of the data. Second, we examine whether the density function of the

SLQAT pass rate exhibits local smoothness at the cutoff. This test is particularly useful if data

are unavailable to directly test whether the conditional mean untreated outcomes at the cutoff

exhibit local smoothness. However, in our case, we can directly test the identifying condition for

the RD design by using our baseline data on outcomes. Thus, we perform the density test mainly

to check whether the result of this test is consistent with the result of the test of the identifying

condition.



Discontinuity in the probability of treatment at the cutoff

Figure 3 plots the local linear regression functions estimated separately above and below the

cutoff, separately for the phase-3 and phase-4 cutoff neighborhood schools with follow-up data

on, among other things, program participation status (the optimal bandwidth is six percentage

points for both samples). The jump in the probability of treatment is clearly visible for both

samples. For the phase-3 sample, as expected, the probability of treatment is one above the cutoff

and positive but less than one below (with 42% of marginal failers in phase 3 gaining

participation status in phase 4). Furthermore, we observe that the probability of treatment is

increasing as we approach the cutoff from below. A plausible and likely explanation for this

pattern is that phase-3 marginal failers closer to the cutoff have a greater chance of passing the

phase-4 SLQAT and entering the program than marginal failers farther away. For the phase-4



                                                 29
sample, as expected, the probability of treatment jumps discontinuously from zero to one at the

cutoff. These patterns in the conditional probabilities of treatment motivate our selections of

partially-fuzzy and sharp RD designs for the phase-3 and phase-4 SLQAT samples, respectively.



Local smoothness in the density function of SLQAT pass rates

Rejection of local smoothness in the density function of the assignment variable at the cutoff

may suggest manipulation of the assignment variable z (McCrary 2008). Manipulation is

plausible in our case as the SLQAT pass rate cutoff for program participation was advance

public knowledge, and schools and perhaps even program managers may have an interest in a

particular treatment outcome. The pass rate that the school actually received on the SLQAT may

be subject to partial manipulation, which is typically benign.25 However, PEF staff exercise full

control over the calculation of SLQAT pass rates, as well as their reporting, thus, introducing the

risk of complete manipulation.26 Given that we use SLQAT pass rates calculated by us based on

the individual student test score data as our measure of the assignment variable, and these

calculations nearly always match the pass rates calculated by PEF, manipulation would have to

occur at the individual student level. Manipulation at this level is less straightforward;

nonetheless, we cannot rule out the possibility.

        Figures 4 and 5 present frequency histograms of schools with bins equal to the integer

values of SLQAT pass rates for the SLQAT and cutoff neighborhood samples, respectively,

separately by phase. A simple visual inspection of the SLQAT pass rates for both the phase-3


25
   The day the SLQAT is offered, the classes which are tested, and the specific SLQAT papers offered at the school
are stochastic elements from the perspective of the school and outside its control.
26
   PEF staff may face incentives to manipulate the pass rates of marginal passers downwards (to just below the
cutoff) if, for example, the program budget limits the number of schools that the program can be offered to. Given
that PEF reports that they were flush with funds during this period, we can probably discount downward
manipulation due to this reason. Alternatively, sympathetic PEF staff might manipulate the pass rate of marginal
failers upwards (to just above the cutoff), so that these schools become eligible to participate in the program.

                                                       30
and phase-4 samples suggests the presence of discontinuities in their densities in the immediate

neighborhood of the cutoff. This is confirmed by formally testing for discontinuities in the

densities at the cutoff by applying a test proposed by McCrary (2008) involving separate kernel

density estimations below and above the cutoff.27 However, this pattern is not unique to the

cutoff location; the histograms show multiple sharp frequency peaks and troughs (at times, at

adjacent pass rates) across the SLQAT pass rate support.



Local smoothness in conditional mean outcomes at baseline

As a direct test of the identifying assumption, we examine whether mean outcomes measured at

baseline satisfy local smoothness at the cutoff using two approaches: by (1) examining

differences in simple means between marginal failers and passers for alternative cutoff

neighborhood sizes and (2) estimating the discontinuity in the conditional means at the cutoff via

local linear regressions at the selected alternative bandwidths. Table 10 presents the simple mean

outcomes at baseline for marginal failers and differences from these means for marginal passers

for two cutoff neighborhood sizes:  /  15 percentage points and  /  5 percentage points. The

evidence suggests that, for both phase 3 and 4, by and large, there are no statistically-significant

differences between marginal failers and passers in mean outcomes measured at baseline.

           Table 11 presents sharp RD estimates of baseline mean outcomes at the cutoff using local

linear regressions, separately by phase and for the selected alternative bandwidths (the optimal

bandwidth is four and three percentage points for the phase-3 and phase-4 cutoff neighborhood

samples, respectively). In addition, Figures 6a–6c depict the estimated local linear regression

functions for the phase-3 and phase-4 cutoff neighborhood samples, using their respective

optimal bandwidths. In general, the evidence suggests that we can reject local smoothness in
27
     Results from the tests are available from the authors upon request.

                                                            31
baseline mean outcomes at the cutoff more frequently than what our earlier simple comparisons

of baseline mean outcomes between marginal failers and passers would have led us to state, as

well as more frequently than we would have expected by random chance given standard

significance levels.

       Out of the 42 individually-estimated RD parameters across phases, outcomes, and

selected bandwidths, seven estimates (17%) are statistically-significant. Virtually all the

statistically-significant RD estimates are negative in sign, suggesting that program schools tend

to be smaller and have lower levels of inputs at baseline. The inference results are however not

robust to the selected alternative bandwidths. Given this sensitivity in inference, we consider the

results to generally satisfy the identifying condition.



RD impact estimates

Table 12 presents our RD impact estimates based on local linear regressions, separately by phase

and for the selected alternative bandwidths (the optimal bandwidth is six and three percentage

points for the phase-3 and phase-4 cutoff neighborhood samples, respectively). Figures 7a–b plot

the estimated local linear regression functions using the optimal bandwidth choice for the phase-

4 cutoff neighborhood sample.

       For the phase-3 cutoff neighborhood sample (Columns 1–3), whose data are subject to a

partially-fuzzy RD design, we find no evidence of significant program impacts across the

outcomes of interest. The magnitudes of the impact estimates also appear to be sensitive to the

selected alternative bandwidths. In addition, the empirical standard errors associated with the

impact estimates are inordinately large, suggesting weak identification.




                                                  32
       For the phase-4 cutoff neighborhood sample (Columns 4–6), whose data are subject to a

sharp RD design, we find evidence of significant positive impacts on the number of students,

teachers, classrooms, and blackboards in marginal passers; furthermore, their significance is

robust to the selected alternative bandwidths. The accompanying figures show a discernible

structural change in the mean levels for these outcomes marginally above and below the cutoff.

However, as with the partially-fuzzy RD estimates for the phase-3 cutoff neighborhood sample,

the magnitudes of the impacts appear to be sensitive to bandwidth. In particular, the estimates

drop fairly sharply when we increase the bandwidth from the optimal choice of 3 percentage

points by 50% to 4.5 percentage points. The most conservative impact estimates at the cutoff on

the number of students, teachers, classrooms, and blackboards are 85, 3.4, 4, and 2.8,

respectively. Relative to the baseline means for these outcomes in the phase-4 cutoff

neighborhood sample, the absolute impact estimates translate into percent impact estimates of

roughly 37%, 37%, 47% and 27%, respectively. These impacts are substantial. They are

particularly impressive given the short treatment exposure under investigation: the follow-up

telephone interview data were collected only some ten months after phase-4 program schools

received their first subsidy payment.

       Notwithstanding, we do not find evidence of impacts at the cutoff on the number of

toilets and student-teacher and student-classroom ratios. This finding is robust to the selected

alternative bandwidths. The lack of evidence of a positive effect on the number of toilets is

concerning given the large expansion in enrollment in marginal passers and its potential negative

bearing on the use and maintenance of the facility. The finding may reflect that PEF does not

encourage the adequate provision of this facility to the same degree as the provision of other

types of physical infrastructure (such as classrooms). Given the expansion in enrollment in



                                               33
marginal passers, the absence of effects on the ratios suggests that program schools have

expanded the number of teachers and classrooms (which we find) in lock-step with this

expansion. This behavior may be driven in large part by PEF’s condition that program schools

maintain these ratios below stipulated levels.



Falsification test: RD estimates at false cutoffs

Table 13 presents sharp RD estimates for our outcomes of interest based on local linear

regressions for the phase-4 cutoff neighborhood sample at two arbitrarily-selected false cutoffs:

57% and 77%. The false cutoffs are equidistant from the true cutoff of 67%. We expect to find

local smoothness in the conditional mean outcomes at these cutoffs. The subsample for the

investigation at 57% is schools with SLQAT pass rates between 52% and 66%. Likewise, the

subsample for the investigation at 77% is schools with SLQAT pass rates between 67% and

82%. The optimal bandwidths for the lower and upper samples are six and three percentage

points, respectively. At both cutoffs, the evidence suggests that we cannot reject the null

hypothesis of local smoothness in the conditional mean outcomes. The inference results are

robust to the selected alternative bandwidths.



Cost-effectiveness estimates

We estimate the cost-effectiveness of the program in relation to enrollment gains using two

alternative approaches. Using the conservative estimate of the sharp RD impact on enrollment

for the phase-4 cutoff neighborhood sample (85 students), a first way that we estimate the

program’s cost-effectiveness is by deriving the annual rupee cost of one additional student in a

program school induced by the program. Given a baseline mean school size of 232 students for



                                                    34
schools in the phase-4 cutoff neighborhood sample (which we treat as the number of children

that would have attended the program school in the absence of the treatment) and an annual

subsidy amount of 3,600 rupees (US$42.4) per student,28 it costs 13,426 rupees (=3,600 

(232+85)/85) (US$157.7) to induce an additional student per year. In comparison, this cost is

roughly half of the cost of inducing an additional student per year through conditional cash

transfers to female students in public secondary schools in Punjab (Andrabi et al. 2008a).

        Following the approach by Evans and Ghosh (2008), a second way we calculate the

program’s cost-effectiveness is by deriving the annual per-student cost of increasing enrollment

in program schools by 1%. Using an annual subsidy amount of 3,600 rupees per student and the

sharp RD impact estimate on enrollment of 37%, we estimate a cost-effectiveness ratio of 97

rupees (=3,600/37) (US$1.1). This estimate compares extremely favorably with the estimated

cost-effective ratios of other evaluated education interventions across the developing world

which generated enrollment gains as reported in Evans and Ghosh. In fact, the FAS program’s

ratio ranks among the very lowest.29 What is more, our cost-effectiveness estimate surprisingly

neighbors Evan and Ghosh’s estimate of the cost-effectiveness of the per-student subsidy

program in Balochistan, Pakistan evaluated by Kim et al. (1999) and noted in Section 1.



7. Conclusion

In this paper, we estimate the causal effects of the FAS program, a recently-instituted public

subsidy program to low-cost private schools, in the province of Punjab, Pakistan on student

enrollment and schooling inputs. Our findings on the impacts of the program differ by phase. For

28
   The annual subsidy amount per student is roughly equal to the annual program amount per student, as the per-
student amounts for program administrative costs and the teacher and school bonuses add less than 1% to the
amount. This is principally due to the large number of students currently covered under the program.
29
   This result remains qualitatively unaltered if we precisely follow the currency conversion and inflation
adjustments steps taken by Evans and Ghosh to fix all ratios in 1997 US dollars.

                                                      35
phase-3 SLQAT takers, applying a partially-fuzzy RD design, we find no evidence of program

impacts at the cutoff on our outcomes of interest. We posit that this is likely due to weak

identification arising from a small jump in the probability of treatment at the cutoff. In contrast,

for phase-4 SLQAT takers, applying a sharp RD design, we find robust evidence that the

program significantly increased the number of students, teachers, classrooms, and blackboards in

marginal passers. The impact estimates at the cutoff were sizeable: our conservative estimates

indicate that the program expanded marginal passers by roughly 85 students, and 3–4 teachers,

classrooms, and blackboards. These impact estimates are also large relative to the mean baseline

values for these outcomes for phase-4 SLQAT takers near the cutoff. What is more, they are

particularly impressive given that phase-4 program schools were exposed to only about ten

months of treatment before the follow-up telephone interview data were gathered. Finally, our

cost-effectiveness estimates suggest that the program is among the cheapest interventions in

developing countries for inducing enrollment gains.

       Two potential threats to the internal validity of our impact estimates are however present.

These threats arise from specific design and implementation features of the program. The first

threat is program spillovers to non-program schools (of which marginal failers are but a specific

subset) that operate in the same local schooling markets as program schools. Design features of

the program such as the free-schooling condition for program benefit maintenance can alter the

terms of local market competition, providing program schools with a competitive edge vis-à-vis

non-program schools. The altered terms could result in impact estimates being upwardly biased

if, for example, they induce the flow of students (and accompanying them, teachers) from non-

program to program schools leading to the shrinking (or, at an extreme, the shutdown) of non-

program schools and/or they discourage investments in the quantity and quality of inputs. On the



                                                36
other hand, the altered terms could result in impact estimates being downwardly biased if they

induce non-program schools to adapt to more effectively compete in the new local market

environment created by the program such as by ratcheting up their investments in the quantity

and quality of inputs and/or altering their fee structures to retain their existing student bodies and

attract new students. Both types of effects could be present simultaneously; consequently, the

direction of the net effect is theoretically ambiguous.

       The second threat arises from anticipation of future treatment. Program entry is not a one-

off event. To date, there have five calls for applications over a three-year period. Given this

pattern, it is conceivable that non-program schools interested in joining the program might alter

their behavior in anticipation of a future call for applications and in an effort to increase the

likelihood of program entry. These actions could, for example, take the form of non-program

schools investing in more and better quality inputs and resources. Anticipation in this case would

result in impact estimates being downwardly biased. In particular, behavioral changes due to

anticipation might be most applicable to non-program schools who just failed to achieve the

SLQAT pass rate cutoff in an earlier phase of entry (our marginal failers), as we would expect

that the marginal costs of investments and efforts required for failers from a previous phase to

gain program entry are likely to be decreasing as one approaches the cutoff from below.

       While when the RD model is applied to the right data designs, it yields internally-valid

estimates, the generalizability of these impact estimates is likely to be limited as they are in

principle only valid for narrowly-defined subpopulations. In the case of the phase-4 SLQAT

taker data, which are fitted using a sharp design, the RD impact estimates are valid for low-cost

private schools that successfully applied to the program, cleared the physical inspection, and

obtained pass rates near the SLQAT cutoff. Even if we generalize our estimated treatment effects



                                                 37
to be average treatment effects over the full range of SLQAT pass rates, the further

generalizability of the estimated effects is limited by sample selection, as the SLQAT pass rate is

only available for low-cost private schools in the seven main program districts that learned about

the call for applications, applied to the program, passed the inspection screening, and took the

SLQAT. This group of schools may not be representative of the population of low-cost private

schools in the program districts, leave alone the population of low-cost private schools more

widely. Given what we know about the steps that precede taking the SLQAT, the extent to which

the population of SLQAT takers diverges from the broader population of low-cost private

schools in the program districts is largely determined by how demanding PEF’s physical

inspection screening is. Evidently, this screening has bite: as mentioned before, only 75% and

61% of schools that were inspected by PEF cleared it and took the SLQAT in phases 3 and 4,

respectively.




                                                38
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                                              40
Table 1. Selected education statistics for Pakistan and Punjab province, 1998/99 and 2004/05
                                                                                        % change,
                                          1998/99                 2004/05
           Sample                                                                   1998/99–2004/05
                                  Pakistan      Punjab     Pakistan     Punjab     Pakistan   Punjab
                                      (1)         (2)         (3)          (4)        (5)       (6)
                          Panel 1: School participation rate, ages 6–15 years
All                                  51.6        54.2        60.9         65.7       18.1      21.2
Rural                                45.3        48.9        54.6         60.9       20.5      24.5
Female                               43.0        48.1        53.7         61.2       24.7      27.3
Poorest quintile                     30.2        32.6        45.0         48.7       49.1      49.4

                         Panel 2: Public school participation rate, ages 6–15 years
All                                  38.8        39.0         43.7         45.5               12.5          16.9
Rural                                38.7        40.0         44.7         47.4               15.5          18.5
Female                               31.6        33.7         37.6         42.0               18.7          24.8
Poorest quintile                     27.2        28.5         39.3         41.1               44.5          44.2

                        Panel 3: Private school participation rate, ages 6–15 years
All                                  11.2        13.5         15.8         18.5      40.7                   37.4
Rural                                 5.2        7.4           8.7         12.1      66.9                   64.8
Female                               10.2        13.0         14.9         17.8      45.2                   36.9
Poorest quintile                      2.0        2.9           4.5         6.4      119.2                  120.2

Notes: Statistics for Pakistan actually represent statistics for the four provinces of Pakistan (unit data for the
territories were not available). All statistics are corrected for sampling weights. The selected age group for
measuring participation (ages 6–15 years) is one year removed from the official ages for primary and secondary
schooling (ages 5–14 years) as this range is more consistent with when children typically attend school. The
private and public school participation rates do not necessarily added up to the school participation rate as school
participation also includes religious and NGO/community school participation, with are treated as separate school
types.
Data sources: 1998/99 Pakistan Integrated Household Survey (PIHS); 2004/05 Pakistan Social and Living
Standards Measurement Survey (PSLM). Fieldwork for the 2004/05 PSLM was conducted between September
2004 and March 2005, preceding the FAS program start date.




                                                        41
Table 2. FAS program timeline
Phase 1 application deadline                                October 2005

Phase 1 school agreements signed                            November 2005–January 2006 (52/54)

Phase 1 first monthly subsidy payment                       January 2006

QAT 1                                                       March–April 2006

Phase 2 application deadline                                June 2006

Phase 2 school agreements signed                            September–December 2006 (143/150)

Phase 2 first monthly subsidy payment                       October 2006

QAT 2                                                       October–November 2006

First payment of annual teacher bonus                       January 2007

QAT 3                                                       March–April 2007

Phase 3 application deadline                                April 2007

Phase 3 school agreements signed                            July–August 2007 (473/482)

Phase 3 first monthly subsidy payment                       August 2007

Phase 4 application deadline                                July 2007

QAT 4                                                       October–November 2007

Phase 4 school agreements signed                            November 2007 (424/424)

Phase 4 first monthly subsidy payment                       December 2007

Second payment of annual teacher bonus                      February 2008

First payment of annual school bonus                        February 2008

QAT 5                                                       March–April 2008

Phase 5 application deadline                                April 2008
Notes: The statistics in parentheses represent the number of schools that signed agreements in those months relative
to the number of schools that entered the program in that phase.




                                                         42
Table 3. District- and phase-wise frequency distribution of FAS program schools
                                                                                                    Adult literacy rate rank                                  Phase
                  District                           Adult literacy rate (10+ years)
                                                                                                  (Low number = high rank)                   1           2             3           4         Total
Rawalpindi                                                         78                                           1
Lahore                                                            70 a                                          2                            7           11                                    18
Sialkot                                                            70                                           3                            7            9                                    16
Chakwal                                                            69                                           4                            9           17                                    26
Jhelum                                                             68                                           5
Gujranwala                                                         67                                           6
Gujrat                                                             65                                           7                                        15                                    15
Faisalabad                                                         60                                           8
Narowal                                                            60                                           9                                        6                                     6
Sargodha                                                           58                                          10
Toba Tek Singh                                                     58                                          11
Attock                                                             57                                          12
Mandi Bahauddin                                                    57                                          13
Mianwali                                                           56                                          14                                        12                                    12
Hafizabad                                                          55                                          15
Sahiwal                                                            54                                          16
Khushab                                                            52                                          17                           10           19                                    29
Sheikhupura                                                        50                                          18                            2                                                 2
Khanewal                                                           49                                          19
Jhang                                                              47                                          20                                                     44          48           92
Layyah                                                             46                                          21
Multan                                                             46                                          22                                                      58         80          138
Bahawalnagar                                                       44                                          23                                        14           115         43          172
Okara                                                              43                                          24
Vehari                                                             43                                          25                                        1                                     1
Kasur                                                              42                                          26
Pakpattan                                                          42                                          27
Rahim Yar Khan                                                     42                                          28
D. G. Khan                                                         40                                          29
Bahawalpur                                                         37                                          30                           10           16           114         88          228
Bhakkar                                                            37                                          31                                        11                                    11
Lodhran                                                            37                                          32                                                     42          49           91
Muzaffargarh                                                       36                                          33                                        1            72          81          154
Rajanpur                                                           34                                          34                                                     35          35           70
Nankana Sahibb                                                     --                                          --                                         1                                    1
                                                                                                                  Number of districts        6           13            7          7            18
                                                                                        Number of program schools (as of June 2008)         45          133           480        424          1082

                                                                                                                                                      High presence
                                                                                                                                                      Low presence
                                                                                                                                          Bold        Program district
Notes: District-level adult literacy rates obtained from Government of Punjab (2004) based on data from the 2003-04 Multiple Indicators Cluster Survey (MICS). bThe literacy rate for Nankana Sahib
was unavailable. aThe statistic for Lahore district is a simple mean of the literacy rates for towns and cantonments in Lahore.



                                                                                                43
44
Table 4. FAS program coverage of private schools in selected program districts
                               (1)                          (2)                                    (3)
                                                   Number of primary,
  Program district     Number of program
                                                  middle and secondary                       Program share
                             schools
                                                      private schools
Bahawalnagar                   172                           447                                  0.38
Bahawalpur                     230                           871                                  0.26
Jhang                           93                           686                                  0.14
Lodhran                         93                           284                                  0.33
Multan                         139                         1,411                                  0.10
Muzaffargarh                   157                           690                                  0.23
Rajanpur                        71                           226                                  0.31
Total                          955                         4,615                                  0.21
Notes: Numbers of private schools provided by Corinne Siaens using the 2005 National Education Census (NEC)
data. Column (2) reports numbers of relevant schools strictly classified as private in the NEC.



Table 5. Mean characteristics of FAS program schools
                                   (1)          (2)                    (3)              (4)               (5)
       Characteristic
                                Phase 1       Phase 2                Phase 3          Phase 4         All phases
Total number of students         561.40       547.42                 373.83           241.66           351.18

Level
Primary                              0.02             0.05             0.05             0.11             0.07
Middle                               0.24             0.31             0.60             0.69             0.59
Secondary                            0.73             0.65             0.35             0.20             0.34

Gender type
Coeducational                        0.69             0.86             0.83             0.82             0.83
Girls-only                           0.20             0.11             0.09             0.11             0.11
Boys-only                            0.11             0.03             0.07             0.07             0.07

Registration status
Registered                           0.91             0.97             0.89             0.81             0.87
Unregistered                         0.09             0.03             0.11             0.19             0.13

Location
Urban                                0.36             0.45             0.48             0.42             0.45
Rural                                0.64             0.55             0.52             0.58             0.55

N                                     45               133              480              424             1,082
Notes: The statistics exclude the three higher secondary schools that are program schools. The statistics are
constructed from administrative data from September 2008, one month before the follow-up data collection.




                                                        45
                 Met application               Passed physical                  Passed                 Joined FAS
                  requirements                   inspection                     SLQAT                    program

Phase 3:              1,070                           799                         514                       482

Phase 4:              1,430                           872                         431                       425

      Figure 2. Numbers of schools which cleared the different FAS program entry steps


Table 6. FAS program school participation status, by phase
                      (1)                     (2)                  (3)                                  (4)
   Phase                                Disqualified,         Disqualified,                          Current
                   Entrants
                                         all reasons       double QAT failure                      participation
     1                  54                     9                    7                                     45
     2                 150                    16                   13                                    133
     3                 482                     2                    0                                    480
     4                 425                     1                    0                                    424
   Total            1,111                     28                   20                                 1,082
Notes: Disqualification also includes voluntary exits. Statistics reflect program school participation status at the
time of the follow-up data collection in October 2008.




                                                         46
Table 7. Correlates of nonresponse in follow-up telephone interview data
                            Phase-3 cutoff neighborhood sample Phase-4 cutoff neighborhood sample
                                (1)          (2)         (3)          (4)       (5)         (6)
                            Marginal      Marginal                 Marginal Marginal
                                                        All                                All
                              failers      passers                  failers  passers
                                 Panel A: Nonresponse counts and rates
Number of nonresponses          29           47          76           26        45          71
Nonresponse rate               0.27          0.29       0.28          0.20     0.24        0.22

                               Panel B: Bivariate correlation estimates
Above cutoff                   --           --          0.03          --            --          0.04
                                                       (0.06)                                  (0.05)
Baseline characteristics
Registered                    –0.14         0.01        –0.04        –0.06         0.00        –0.01
                             (0.16)       (0.11)        (0.09)       (0.12)       (0.07)       (0.06)
Coeducational                  0.06        –0.03         0.01        –0.03        –0.10        –0.06
                             (0.12)       (0.11)        (0.08)       (0.14)       (0.08)       (0.07)
Girls-only                    –0.10         0.19         0.07         0.03         0.05         0.02
                             (0.13)       (0.13)        (0.10)       (0.20)       (0.10)       (0.09)
Boys-only                      0.07      –0.31***       –0.19         0.03         0.15         0.10
                             (0.27)       (0.04)        (0.10)       (0.20)       (0.14)       (0.11)
Primary                       –0.02        0.27*         0.15        0.26*         0.10        0.15*
                             (0.16)       (0.16)        (0.12)       (0.15)       (0.10)       (0.08)
Middle                        –0.12         0.00        –0.05       –0.21**       –0.10       –0.14**
                             (0.10)       (0.08)        (0.06)       (0.10)       (0.07)       (0.06)
Secondary                      0.16        –0.10         0.00         0.12         0.07         0.09
                             (0.11)       (0.08)        (0.07)       (0.11)       (0.08)       (0.07)
Urban                          0.01       –0.12*        –0.07         0.07        –0.05         0.00
                             (0.09)       (0.07)        (0.05)       (0.08)       (0.06)       (0.05)
Rural                         –0.01        0.12*         0.07        –0.07         0.05         0.00
                             (0.09)       (0.07)        (0.05)       (0.08)       (0.06)       (0.05)
Bahawalnagar                  –0.01        –0.07        –0.05         0.09        –0.08        –0.01
                             (0.11)       (0.08)        (0.06)       (0.14)       (0.08)       (0.08)
Bahawalpur                    –0.12         0.01        –0.05        0.18*        –0.02         0.06
                             (0.09)       (0.08)        (0.06)       (0.11)       (0.07)       (0.06)
Jhang                        –0.21*         0.05         0.13         0.06         0.00         0.01
                             (0.13)       (0.11)        (0.09)       (0.14)       (0.08)       (0.07)
Lodhran                        0.07       –0.17*        –0.09         0.00       –0.14**       –0.07
                             (0.20)       (0.09)        (0.09)       (0.14)       (0.07)       (0.07)
Multan                        –0.14         0.11         0.00       –0.18**        0.02        –0.06
                             (0.11)       (0.12)        (0.08)       (0.09)       (0.07)       (0.06)
Muzaffargarh                   0.03         0.11         0.08        –0.18         0.05        –0.05
                             (0.12)       (0.11)        (0.08)      (0.09)**      (0.08)       (0.06)
Rajanpur                       0.07        –0.13        –0.05         0.16         0.14         0.14
                             (0.20)       (0.11)        (0.11)       (0.16)       (0.11)       (0.09)
N                              108          160          268          128          191          319
Notes: * denotes statistical significance at the 10% level; ** at the 5% level; and *** at the 1% level.
Heteroskedasticity-robust standard errors are reported in parentheses.



                                                  47
Table 8. Distribution of schools by selected characteristics at baseline, SLQAT and cutoff
neighborhood samples
                                   SLQAT sample                          Cutoff neighborhood sample
                                     z  0,100                                  z  52,82
   Characteristic           (1)           (2)           (3)             (4)            (5)         (6)
                         Phase 3       Phase 4         Diff.         Phase 3        Phase 4      Diff.
                          Share         Share        (1)–(2)          Share          Share      (4)–(5)
Level
Primary                    0.09          0.12         –0.02            0.07          0.12        –0.05
Middle                     0.63          0.72       –0.09***           0.71          0.70         0.01
Secondary                  0.28          0.16        0.12***           0.22          0.18         0.04

Gender type
Coeducational                0.82            0.87         –0.05***           0.87           0.86             0.01
Girls-only                   0.12            0.08          0.03**            0.10           0.09             0.01
Boys-only                    0.07            0.05           0.02             0.04           0.06            –0.02

Registration status
Registered                   0.88            0.81          0.07***           0.88           0.83           0.05*
Unregistered                 0.12            0.19         –0.07***           0.12           0.17           –0.05*

Location type
Urban                        0.45            0.41           0.04*            0.47           0.41             0.06
Rural                        0.54            0.59          –0.04*            0.53           0.59            –0.06

District
Bahawalnagar                 0.21            0.11          0.10***           0.20           0.09           0.11***
Bahawalpur                   0.24            0.20          0.04**            0.25           0.21             0.04
Jhang                        0.13            0.11            0.02            0.14           0.14             0.00
Lodhran                      0.08            0.12         –0.04***           0.07           0.09            –0.02
Multan                       0.13            0.16          –0.03*            0.13           0.20           –0.07**
Muzaffargarh                 0.14            0.20         –0.05***           0.14           0.17            –0.03
Rajanpur                     0.07            0.10          –0.03*            0.06           0.09            –0.03

N                             747            830              --             268             319             --
Notes: * denotes statistical significance at the 10% level; ** at the 5% level; and *** at the 1% level.




                                                         48
Table 9. Summary statistics of outcome measures at baseline, SLQAT and cutoff neighborhood samples
                                                        SLQAT sample                                 Cutoff neighborhood sample
                                                          z  0,100                                         z  52,82
         Outcome measure                     (1)               (2)             (3)              (4)                (5)            (6)
                                         Phase 3            Phase 4         (2)–(1)          Phase 3           Phase 4         (5)–(4)
                                           Mean              Mean         Difference          Mean               Mean        Difference
                                            (SD)              (SD)            (SE)             (SD)               (SD)           (SE)
Number of students                        252.85            222.63        –30.22***          240.82             232.27          –8.56
                                         (155.70)          (106.68)          (6.79)         (134.67)           (108.05)        (10.21)
Number of teachers                         10.22              9.00         –1.22***            9.82               9.32          –0.50
                                           (5.03)            (3.69)          (0.22)           (4.30)             (3.77)         (0.34)
Number of classrooms                        9.56              8.43         –1.13***            8.90               8.59          –0.31
                                           (4.71)            (3.82)          (0.22)           (3.78)             (3.76)         (0.31)
Number of blackboards                       9.93              9.03         –0.90***            9.39               9.27          –0.11
                                           (5.03)            (4.00)          (0.23)           (4.11)             (3.93)         (0.33)
Number of toilets                           3.23              2.95         –0.28***            3.09               2.97          –0.12
                                           (1.80)            (1.94)          (0.09)           (1.59)             (1.75)         (0.14)
Student-teacher ratio                      25.06             25.67            0.60            24.98              25.59           0.60
                                           (9.27)            (9.51)          (0.47)           (9.59)             (8.26)         (0.75)
Student-classroom ratio                    27.51             28.13            0.62            28.30              28.35           0.05
                                          (12.63)           (12.13)          (0.63)          (13.99)            (11.47)         (1.07)
Notes: * denotes statistical significance at the 10% level; ** at the 5% level; and *** at the 1% level. SD denotes standard deviation; SE standard error; and z
the treatment assignment variable, the SLQAT pass rate.




                                                                               49
                                                                         Phase 3
                               1
                              .8
   Probability of treatment




                              .6
                              .4
                              .2
                               0




                                   50   55               60               65                  70                75                  80

                                                               SLQAT student pass rate

                                        School observations                                   LLR smoother for SLQAT failers
                                        LLR smoother for SLQAT passers




                                                                         Phase 4
                               1
                              .8
   Probability of treatment




                              .6
                              .4
                              .2
                               0




                                   50   55              60               65              70                75                  80

                                                               SLQAT student pass rate

                                        School observations                                   LLR smoother for SLQAT failers
                                        LLR smoother for SLQAT passers




Figure 3. Probability of treatment, cutoff neighborhood sample, by phase




                                                                   50
                                                              Phase 3                                                                                                Phase 4




                                                                                                                           100
                    100




                                                                                                                             90
                      90




                                                                                                                             80
                      80




                                                                                                                             70
                      70
Number of schools




                                                                                                  Number of schools




                                                                                                                             60
                      60




                                                                                                                             50
                      50




                                                                                                                             40
                      40




                                                                                                                             30
                      30




                                                                                                                             20
                      20




                                                                                                                             10
                      10
                          0




                                                                                                                                 0
                                   7   17   27        37       47        57   67   77        87   97                                      7   17   27        37       47        57   67   77        87   97
                                                           SLQAT pass rate                                                                                        SLQAT pass rate




                                   Figure 4. Frequency histogram of SLQAT pass rates, SLQAT sample, by phase


                                                              Phase 3                                                                                                Phase 4
                      20




                                                                                                                             20
                      15




                                                                                                                             15
Number of schools




                                                                                                  Number of schools
                      10




                                                                                                                             10
                          5




                                                                                                                                 5
                          0




                                                                                                                                 0




                              52       57        62                 67        72        77                      82                   52       57        62                 67        72        77         82
                                                           SLQAT pass rate                                                                                        SLQAT pass rate




                    Figure 5. Frequency histogram of SLQAT pass rates, cutoff neighborhood sample, by phase




                                                                                                                      51
Table 10. Differences in mean outcomes at baseline between SLQAT marginal passers and marginal failers
                                     Phase-3 cutoff neighborhood sample                     Phase-4 cutoff neighborhood sample
                                         z  52,82                      z  62,72                      z  52,82                      z  62,72
                                      (1)             (2)              (3)              (4)             (5)            (6)             (7)              (8)
     Outcome measure              Marginal         Marginal        Marginal         Marginal        Marginal        Marginal        Marginal         Marginal
                                    failers        passers           failers        passers          failers        passers          failers         passers
                                    Mean             Diff.           Mean             Diff.          Mean             Diff.          Mean              Diff.
                                     (SD)            (SE)             (SD)            (SE)            (SD)            (SE)            (SD)             (SE)
Number of students                 242.32           –2.52           268.50           –48.17          229.68           4.33           254.83           –28.01
                                  (138.80)         (16.78)         (188.03)         (34.82)         (99.26)         (12.36)         (114.57)         (20.60)
Number of teachers                   9.91           –0.15             9.82            –0.79            9.23           0.14            9.80             –0.63
                                    (4.22)          (0.54)           (5.41)          (1.08)          (3.36)          (0.43)          (4.03)           (0.71)
Number of classrooms                 8.88            0.04             8.41             0.01            8.53           0.10            9.61            –1.22*
                                    (3.83)          (0.47)           (4.10)          (0.80)          (3.83)          (0.43)          (4.12)           (0.68)
Number of blackboards                9.29            0.16             8.74            –0.02            9.17           0.18           10.22             –1.16
                                    (4.10)          (0.51)           (4.59)          (0.93)          (3.72)          (0.45)          (4.34)           (0.73)
Number of toilets                    3.08            0.01             2.74             0.23            2.98          –0.03            3.37             –0.32
                                    (1.66)          (0.20)           (1.83)          (0.36)          (1.74)          (0.20)          (2.44)           (0.43)
Student-teacher ratio               24.67            0.53            25.95            –0.53           25.48           0.18           26.57             –1.10
                                    (9.28)          (1.19)           (8.10)          (2.33)          (7.90)          (0.94)          (7.32)           (1.52)
Student-classroom ratio             28.69           –0.66            31.97            –4.87           28.18           0.28           27.44             1.55
                                   (13.58)          (1.74)          (15.61)          (3.26)         (10.69)          (1.32)          (8.77)           (2.32)
Notes: * denotes statistical significance at the 10% level; ** at the 5% level; and *** at the 1% level. z denotes the treatment assignment variable, the SLQAT
pass rate; SD standard deviation; and SE standard error.




                                                                               52
Table 11. Local smoothness in conditional mean outcomes at baseline
Local linear regression with triangular kernel and bandwidth h
                                          Phase-3 cutoff neighborhood sample                                  Phase-4 cutoff neighborhood sample
      Outcome measure                  (1)                (2)               (3)                            (4)                (5)               (6)
                                   h  4% pts         h  6% pts        h  8% pts                     h  3% pts        h  4.5% pts       h  6% pts
Number of students                       –97.05                14.32                 –39.12               –78.43             –132.88**             –107.76**
                                        (140.67)              (88.06)                (60.96)             (92.74)              (65.79)               (51.50)
Number of teachers                        –0.72                 1.35                  –0.59                4.37*               –1.41                 –1.78
                                          (3.56)               (2.57)                 (1.75)              (2.51)               (3.26)                (2.08)
Number of classrooms                       0.31                 1.78                   0.61                 2.43               –2.17                 –2.44
                                          (3.24)               (2.23)                 (1.57)              (2.04)               (2.72)                (1.77)
Number of blackboards                     –0.74                 1.71                   0.69                 0.67               –2.98                –2.95*
                                          (3.24)               (2.13)                 (1.56)              (1.73)               (2.30)                (1.73)
Number of toilets                          1.36                1.45*                   0.93                –1.32               –2.13                –2.19*
                                          (1.24)               (0.74)                 (0.61)              (1.65)               (1.56)                (1.25)
Student-teacher ratio                     –8.53                –1.37                  –0.15              –22.37*              –11.91                 –8.70
                                          (8.52)               (4.15)                 (3.39)             (11.98)               (8.20)                (5.46)
Student-classroom ratio                  –14.37                –3.80                  –4.19               –12.26               –5.73                 –3.12
                                         (12.67)               (7.14)                 (5.69)              (9.49)               (7.28)                (5.85)
Notes: * denotes statistical significance at the 10% level; ** at the 5% level; and *** at the 1% level. Bootstrapped standard errors based on 500 replications are
reported in parentheses.




                                                                                53
                                                                                                                                                1.                                                   Number of students
                                                                                              Phase 3                                                                                                                                                        Phase 4




                                                                                                                                                                                                             800
                                            800




                                                                                                                                                                                                             600
                                            600
                   Number of students




                                                                                                                                                                            Number of students




                                                                                                                                                                                                             400
                                            400




                                                                                                                                                                                                             200
                                            200
                                                  0




                                                                                                                                                                                                                   0
                                                      50     55              60               65              70                75                  80                                                                 50   55              60               65              70                75                  80

                                                                                    SLQAT student pass rate                                                                                                                                        SLQAT student pass rate

                                                             School observations                                   LLR smoother for SLQAT failers                                                                           School observations                                   LLR smoother for SLQAT failers
                                                             LLR smoother for SLQAT passers                                                                                                                                 LLR smoother for SLQAT passers




                                                                                                                                                2.                                                   Number of teachers
                                                                                              Phase 3                                                                                                                                                        Phase 4
                                              30




                                                                                                                                                                                                               30
                       Number of teachers




                                                                                                                                                                                Number of teachers
                                              20




                                                                                                                                                                                                               20
                                              10




                                                                                                                                                                                                               10
                                                  0




                                                                                                                                                                                                                   0




                                                      50     55              60               65              70                75                  80                                                                 50   55              60               65              70                75                  80

                                                                                    SLQAT student pass rate                                                                                                                                        SLQAT student pass rate

                                                             School observations                                   LLR smoother for SLQAT failers                                                                           School observations                                   LLR smoother for SLQAT failers
                                                             LLR smoother for SLQAT passers                                                                                                                                 LLR smoother for SLQAT passers




                                                                                                                                            3.                             Number of classrooms
                                                                                              Phase 3                                                                                                                                                        Phase 4
                                              30




                                                                                                                                                                                                               30
Number of classrooms




                                                                                                                                                         Number of classrooms
                                              20




                                                                                                                                                                                                               20
                                              10




                                                                                                                                                                                                               10
                                                  0




                                                                                                                                                                                                                   0




                                                      50     55              60               65              70                75                  80                                                                 50   55              60               65              70                75                  80

                                                                                    SLQAT student pass rate                                                                                                                                        SLQAT student pass rate

                                                             School observations                                   LLR smoother for SLQAT failers                                                                           School observations                                   LLR smoother for SLQAT failers
                                                             LLR smoother for SLQAT passers                                                                                                                                 LLR smoother for SLQAT passers




                                                           Figure 6a. Local smoothness in conditional mean outcomes at baseline, by phase




                                                                                                                                                                                                        54
                                                                                                                                        4.                      Number of blackboards
                                                                                              Phase 3                                                                                                                                               Phase 4
                                                30




                                                                                                                                                                                                         30
Number of blackboards




                                                                                                                                                    Number of blackboards
                                                20




                                                                                                                                                                                                         20
                                                10




                                                                                                                                                                                                         10
                                                 0




                                                                                                                                                                                                          0
                                                     50      55              60               65              70                75                  80                                                        50   55              60               65              70                75                  80

                                                                                    SLQAT student pass rate                                                                                                                               SLQAT student pass rate

                                                             School observations                                   LLR smoother for SLQAT failers                                                                  School observations                                   LLR smoother for SLQAT failers
                                                             LLR smoother for SLQAT passers                                                                                                                        LLR smoother for SLQAT passers




                                                                                                                                               5.                                            Number of toilets
                                                                                              Phase 3                                                                                                                                               Phase 4
                                                10




                                                                                                                                                                                                         20
                                                 8




                                                                                                                                                                                                         15
                            Number of toilets




                                                                                                                                                                                Number of toilets
                                                 6




                                                                                                                                                                                                         10
                                                 4




                                                                                                                                                                                                          5
                                                 2
                                                 0




                                                                                                                                                                                                          0




                                                     50      55              60               65              70                75                  80                                                        50   55              60               65              70                75                  80

                                                                                    SLQAT student pass rate                                                                                                                               SLQAT student pass rate

                                                             School observations                                   LLR smoother for SLQAT failers                                                                  School observations                                   LLR smoother for SLQAT failers
                                                             LLR smoother for SLQAT passers                                                                                                                        LLR smoother for SLQAT passers




                                                                                                                                           6.                                   Student-teacher ratio
                                                                                              Phase 3                                                                                                                                               Phase 4
                                                80




                                                                                                                                                                                                         80
                                                60




                                                                                                                                                                                                         60
    Student-teacher ratio




                                                                                                                                                        Student-teacher ratio
                                                40




                                                                                                                                                                                                         40
                                                20




                                                                                                                                                                                                         20
                                                 0




                                                                                                                                                                                                          0




                                                     50      55              60               65              70                75                  80                                                        50   55              60               65              70                75                  80

                                                                                    SLQAT student pass rate                                                                                                                               SLQAT student pass rate

                                                             School observations                                   LLR smoother for SLQAT failers                                                                  School observations                                   LLR smoother for SLQAT failers
                                                             LLR smoother for SLQAT passers                                                                                                                        LLR smoother for SLQAT passers




                                                          Figure 6b. Local smoothness in conditional mean outcomes at baseline, by phase




                                                                                                                                                                                                    55
                                                                                                                       7.                               Student-classroom ratio
                                                                             Phase 3                                                                                                                                Phase 4
                          150




                                                                                                                                                                    100
                                                                                                                                                                      80
Student-classroom ratio




                                                                                                                              Student-classroom ratio
                          100




                                                                                                                                                                      60
                                                                                                                                                                      40
                            50




                                                                                                                                                                      20
                                0




                                                                                                                                                                          0




                                    50      55              60               65              70                75                             80                              50   55              60               65              70                75                  80

                                                                   SLQAT student pass rate                                                                                                                SLQAT student pass rate

                                            School observations                                   LLR smoother for SLQAT failers                                                   School observations                                   LLR smoother for SLQAT failers
                                            LLR smoother for SLQAT passers                                                                                                         LLR smoother for SLQAT passers




                                         Figure 6c. Local smoothness in conditional mean outcomes at baseline, by phase




                                                                                                                                                             56
Table 12. Discontinuity estimates of conditional mean outcomes
Local linear regression with triangular kernel and bandwidth h
                                          Phase-3 cutoff neighborhood sample                                  Phase-4 cutoff neighborhood sample
                                             Partially-fuzzy RD estimates                                             Sharp RD estimates
      Outcome measure                  (1)                (2)                (3)                           (4)                (5)               (6)
                                   h  6% pts         h  9% pts        h  12% pts                    h  3% pts        h  4.5% pts       h  6% pts
Number of students                       180.3                –29.03                –28.03              122.66***              85.20**               88.84**
                                      (8.09e+14)            (18002.95)            (6230.31)              (45.75)               (42.77)               (41.32)
Number of teachers                        6.46                  3.34                 3.09                 5.07**                3.39*                 3.46*
                                      (3.96e+13)             (331.89)              (42.19)                (2.35)                (1.92)                (1.82)
Number of classrooms                      2.63                 –0.75                 1.43                 9.85**                4.55*                4.00**
                                      (1.77e+13)             (121.08)              (95.78)                (3.89)                (2.38)                (2.02)
Number of blackboards                      --                    --                   --                  6.56**                3.14*                 2.83*
                                                                                                          (2.71)                (1.85)                (1.72)
Number of toilets                          --                    --                    --                  0.07                 –0.37                 –0.14
                                                                                                          (1.28)                (0.95)                (0.85)
Student-teacher ratio                     0.39                 –6.17                 –5.07                 1.23                 –0.85                 –1.04
                                        (97.98)               (86.51)              (114.35)               (3.97)                (2.77)                (2.54)
Student-classroom ratio                  11.48                  1.45                 –4.77                –29.18               –11.39                 –8.12
                                        (88.45)              (131.10)               (59.86)              (22.29)                (9.89)                (7.24)
Notes: * denotes statistical significance at the 10% level; ** at the 5% level; and *** at the 1% level. Bootstrapped standard errors based on 500 replications are
reported in parentheses.




                                                                                57
                                                                       1.          Number of students                                                                                                                     2.          Number of teachers
                                                                                              Phase 4                                                                                                                                            Phase 4




                                                                                                                                                                                                      40
                                              800




                                                                                                                                                                                                      30
                                              600




                                                                                                                                                                            Number of teachers
                   Number of students




                                                                                                                                                                                                      20
                                              400
                                              200




                                                                                                                                                                                                      10
                                                    0




                                                                                                                                                                                                       0
                                                        50   55              60               65              70                75                  80                                                     50   55              60               65              70                75                  80

                                                                                    SLQAT student pass rate                                                                                                                            SLQAT student pass rate

                                                             School observations                                   LLR smoother for SLQAT failers                                                               School observations                                   LLR smoother for SLQAT failers
                                                             LLR smoother for SLQAT passers                                                                                                                     LLR smoother for SLQAT passers




                                                                   3.         Number of classrooms                                                                                                                   4.         Number of blackboards
                                                                                              Phase 4                                                                                                                                            Phase 4
                                                                                                                                                                                                      40
                                                30




                                                                                                                                                                                                      30
                                                                                                                                                    Number of blackboards
Number of classrooms




                                                20




                                                                                                                                                                                                      20
                                                10




                                                                                                                                                                                                      10
                                                    0




                                                                                                                                                                                                       0




                                                        50   55              60               65              70                75                  80                                                     50   55              60               65              70                75                  80

                                                                                    SLQAT student pass rate                                                                                                                            SLQAT student pass rate

                                                             School observations                                   LLR smoother for SLQAT failers                                                               School observations                                   LLR smoother for SLQAT failers
                                                             LLR smoother for SLQAT passers                                                                                                                     LLR smoother for SLQAT passers




                                                                         5.        Number of toilets
                                                                                              Phase 4
                                                15
                                                10
                          Number of toilets




                                                    5
                                                    0




                                                        50   55              60               65              70                75                  80

                                                                                    SLQAT student pass rate

                                                             School observations                                   LLR smoother for SLQAT failers
                                                             LLR smoother for SLQAT passers




                                                                  Figure 7a. Local discontinuities in conditional mean outcomes, phase 4




                                                                                                                                                                                                 58
                                        6.       Student-teacher ratio                                                                                             7.        Student-classroom ratio
                                                                    Phase 4                                                                                                                    Phase 4
                        50




                                                                                                                                                    80
                        40




                                                                                                                                                    60
                                                                                                                Student-classroom ratio
Student-teacher ratio




                        30




                                                                                                                                                    40
                        20




                                                                                                                                                    20
                        10




                                                                                                                                                     0




                             50    55              60               65              70                75                                  80             50   55              60               65              70                75                  80

                                                          SLQAT student pass rate                                                                                                    SLQAT student pass rate

                                   School observations                                   LLR smoother for SLQAT failers                                       School observations                                   LLR smoother for SLQAT failers
                                   LLR smoother for SLQAT passers                                                                                             LLR smoother for SLQAT passers




                                  Figure 7b. Local discontinuities in conditional mean outcomes, phase 4




                                                                                                                                               59
Table 13. Discontinuity estimates of conditional mean outcomes at false cutoffs, phase-4 cutoff neighborhood sample
Local linear regression with triangular kernel and bandwidth h
                                                    Cutoff = 57%                                              Cutoff = 77%
Outcome measure                        (1)               (2)                 (3)                 (4)               (5)                                (6)
                                   h  7% pts       h  10.5% pts       h  14% pts         h  4% pts         h  6% pts                         h  8% pts
Number of students                      –21.38                –18.77                 –18.59               57.99                 8.42                  9.86
                                        (48.84)               (47.11)                (47.28)            (122.09)              (85.87)               (72.00)
Number of teachers                       –1.21                 –1.02                  –0.99                3.80                 2.11                  2.00
                                         (1.79)                (1.65)                 (1.65)             (3.70)                (2.69)                (2.35)
Number of classrooms                     –1.74                 –1.69                  –1.67                2.39                –0.30                 –0.05
                                         (1.84)                (1.61)                 (1.58)             (3.57)                (2.58)                (2.10)
Number of blackboards                     0.95                  0.29                   0.14               –1.81                –2.64                 –2.85
                                         (3.70)                (3.52)                 (3.50)             (3.23)                (2.23)                (1.92)
Number of toilets                         2.91                  2.38                   2.12                0.56                 1.38                  0.78
                                         (4.46)                (4.08)                 (4.00)             (3.73)                (2.65)                (2.38)
Student-teacher ratio                    –2.46                 –2.49                  –2.50                2.21                 0.06                  0.21
                                         (2.28)                (2.13)                 (2.11)             (4.10)                (2.78)                (2.30)
Student-classroom ratio                  –0.21                 –0.32                  –0.36                1.51                –0.40                 –0.64
                                         (0.79)                (0.76)                 (0.76)             (1.76)                (1.40)                (1.14)
Notes: * denotes statistical significance at the 10% level; ** at the 5% level; and *** at the 1% level. Bootstrapped standard errors based on 500 replications are
reported in parentheses. The subsample for the investigation at 57% is schools with pass rates between 52% and 66%. Similarly, the subsample for the
investigation at 77% is schools with pass rates between 67% and 82%.




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