metadata: authors: 0: author: Moshoeshoe,Ramaele Elias
count: Lesotho
docna: 0: docna: Long-Term Effects of Free Primary Education
            on Educational Achievement : Evidence from Lesotho
docty: Policy Research Working Paper
subtopic: Educational Sciences,Primary Education,Gender and Development,Secondary Education
teratopic: Education,Gender
abstracts: cdata!: Many Sub-Saharan African countries have
            instituted free primary education policies, and this has led
            to a significant increase in the primary school enrollment
            rate. However, many children who are in school are not
            learning. It is not clear whether free primary education
            policies have contributed to the decline in the quality of
            education and whether these learning effects are
            long-lasting. This paper addresses the latter question and
            estimates the long-term effects of free primary education on
            educational achievement in Lesotho where the program was
            phased-in on a grade-by-grade basis, beginning with grade
            one in 2000. The timing of the implementation created
            changes in program coverage across age (and grade) groups
            over time. A semiparametric difference-in-differences
            strategy is employed that exploits these variations to
            identify the long-term effects of the free primary education
            policy on educational achievement, using university
            examinations records data for student cohorts with and
            without free primary education. The results indicate that
            the effect of free primary education on academic performance
            is bounded between 2 and 19 percentage points, implying that
            the program increased enrollment without hurting education quality.
geo_reg_key: 517195,517191
repnme: repnme: Long-Term Effects of Free Primary Education
            on Educational Achievement : Evidence from Lesotho
display_title: Long-Term Effects of Free Primary
            Education on Educational Achievement : Evidence from Lesotho
listing_relative_url: /research/2020/09/32421393/long-term-effects-free-primary-education-educational-achievement-evidence-lesotho
topicv3: Education, Skills Development and Labor
            Market m1326135 1484,Primary Education m1326139 480,Education m1327048 470,Secondary Education m1327058 481,Gender m1327621 615
publishtoextweb_dt: 2020-09-21T00:00:00Z
historic_topic: Education,Gender
origu: Office of the Chief Economist (AFECE)
no_of_pages: 42
author_keys: 0: author_key: 1627253
model_extractions: Policy Research Working Paper 9404 Long-Term Effects of Free Primary Education on Educational Achievement Evidence from Lesotho _Ramaele Moshoeshoe_ Africa Region Office of the Chief Economist September 2020
Policy Research Working Paper 9404

# **Abstract**

Many Sub-Saharan African countries have instituted free primary education policies, and this has led to a significant increase in the primary school enrollment rate. However, many children who are in school are not learning. It is not clear whether free primary education policies have contributed to the decline in the quality of education and whether these learning effects are long-lasting. This paper addresses the latter question and estimates the long-term effects of free primary education on educational achievement in Lesotho where the program was phased-in on a grade-by-grade basis, beginning with grade one in 2000. The timing of the implementation created changes in program coverage across age (and grade) groups over time. A semiparametric difference-in-differences strategy is employed that exploits these variations to identify the long-term effects of the free primary education policy on educational achievement, using university examinations records data for student cohorts with and without free primary education. The results indicate that the effect of free primary education on academic performance is bounded between 2 and 19 percentage points, implying that the program increased enrollment without hurting education quality.

This paper is a product of the Office of the Chief Economist, Africa Region. 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://www.worldbank.org/prwp. The author may be contacted at rmoshoeshoe@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
of Free Education on Long-Term Effects Primary Educational Achievement: Evidence from Lesotho<sup>_∗_</sup>

# Ramaele Moshoeshoe

National University of Lesotho The World Bank _Keywords_ : Free Primary Education, Educational achievement, Long-term effects, Lesotho JEL Classification: H52, I22, I28, 015

> _∗_ I thank Kehinde Ajayi, Moussa Blimpo, Justine Burns, David Evans, Deon Filmer, Markus Goldstein, Abbi Kedir, Germano Mwabu, Patrick Plane, the audiences of the AERC December 2018 and June 2019 bi-annual conferences, and participants at the World Bank and National University of Lesotho seminars for helpful comments and suggestions. Pedro Sant’Anna generously helped me to implement his `DRDID` R code. I am grateful to the World Bank-AERC Visiting Scholars program which financed my stay at the World Bank where parts of this paper were developed. Financial support from African Economic Research Consortium (AERC), through grant No. RT18537, is also gratefully acknowledged. All remaining errors are my own. The views expressed in this paper are entirely mine, and do not necessarily represent those of the World Bank or its Board of Directors. Contact emails: rmoshoeshoe@worldbank.org or rmoshoeshoe@gmail.com
# **1 Introduction**

The Dakar Framework for Action (DFA), adopted by World Education Forum in 2000, called for complete, free, and compulsory quality education, with the aim to redress global educational inequalities (UNESCO, 2000, p.8). Since then, several Sub-Saharan African countries have instituted free primary education (FPE) programs<sup>1</sup> by abolishing all primary school user fees. Several studies have quantified the short-term effects of the FPE programs in Sub-Saharan Africa on school enrollment, drop-out, and grade progression (see Deininger 2003; Al-Samarrai and Zaman 2007; Nishimura _et al._ 2008; Grogan 2009; Lucas and Mbiti 2012; Hoogeveen and Rossi 2013; Moshoeshoe _et al._ 2019). These studies find that FPE increased enrollment, reduced school drop-out, and reduced grade-progression. Therefore, largely owing to FPE programs, the primary school enrollment rate in the developing world has reached 91 percent (UNDP, 2016), with 94 percent and 74 percent of children worldwide completing primary education and lower secondary education, respectively (World Bank, 2016, 2018).

However, school attendance is different from learning. The main problem now is that millions of children finish primary school without acquiring functional literacy and numeracy skills, and this is more pronounced in Sub-Saharan Africa (World Bank, 2018; Filmer _et al._ , 2020). Therefore, achieving inclusive and equitable quality education by 2030 is the fourth most important Sustainable Development Goal (SDG) under the 2030 Agenda.

Since the Millennium Development Goals, the SDGs’ predecessor, focused mainly on increasing access to schooling, it is generally believed that the current learning crisis is partly due to school fees’ elimination programs. However, a few studies that quantify the short-term effects of these FPE programs, and similar fee elimination policies in Africa, on education quality (i.e. test scores) find mixed evidence. Lucas and Mbiti (2012), for example, apply a difference-in-differences (DID) strategy, exploiting the variation in pre-program primary school drop-out rates across districts in Kenya to estimate the effect of FPE on primary school completion rate and test scores. They find marginal negative effects of FPE on test scores, but large and positive effects on primary school completion rate. Blimpo _et al._ (2016), on the other hand, find positive effects of the Gambian Girls’ Scholarship program (a secondary school fee elimination program for girls) on student access and learning, using a DID strategy. In as much as this question remains open, data availability remains a hinderance in answering it, and this paper does not attempt to address it for the same reasons.

All else held constant, the negative (or positive) effects of FPE on learning may still show up later on in a child’s academic life. According to Cunha _et al._ (2006), achievement test scores are determined by skills or abilities (both cognitive and noncognitive)<sup>2</sup> that are malleable to environ-

> 1Including but not limited to Burundi, Cameroon, Eswatini, Ghana, Kenya, Lesotho, Mozambique, Namibia, Rwanda, Tanzania, and Zambia.

> 2Cognitive skills are malleable to environmental factors up to age 10 or so, while noncognitive skills are malleable for a much longer time (Cunha _et al._ , 2006)

1
mental (e.g. family and school) influences. These skills are self-productive and complementary. That is, skills acquired at primary school may augment skills attained at the secondary and university levels, and that skills acquired at primary school may raise the productivity of education investments at the secondary and university levels. Therefore, it is reasonable to assume that FPE, through its influence on school inputs and environments, will have lasting effects of education quality. This paper tests this hypothesis.

Further, the paper examines whether FPE effects differ by gender of the student. Because of gender stereotypes in many cultures, girls’ education is mostly considered of a lesser value, resulting in girls getting less education, at least in terms of access. However, the question of whether, conditional on attendance, boys and girls receive the same quality education still remains unanswered. If we are to build a productive, talented, and diverse labor force, it is essential to know well in time the effects of the implemented policies so that they can either be scaled up (if the effects are positive) and/or changed (if the effects are negative).

Therefore, this paper estimates the long-term effects of FPE on education performance and establishes whether these effects, if any, differ by student’s gender. Apart from the fact that this paper is among the first studies to estimate the long-term effects of FPE policies in Sub-Saharan Africa, it contributes to several strands of literature. First, it contributes to the literature that looks at the long-term impacts of schooling inputs on educational outcomes. For example, Fredriksson _et al._ (2013) look at the long-term effects of class size on human capital development. They find that smaller class sizes improve cognitive and noncognitive abilities at age 13, and improve achievement test scores at age 16. Second, it adds to the literature that looks at the short- term impacts of fee eliminations on educational outcomes in developing countries (Grogan, 2009; Lucas and Mbiti, 2012; Hoogeveen and Rossi, 2013; Chyi and Zhou, 2014; Blimpo _et al._ , 2016; Moshoeshoe _et al._ , 2019). Lastly, it adds to the small, but growing, literature on the long-term effects of schooling subsidy programs (including tuition fee eliminations) on human capital development. For example, Xiao _et al._ (2017) estimate the long-term effects a free compulsory education reform in rural China on educational attainment, cognitive skills and health. They find that the reform had long lasting positive effects on educational attainment and cognitive achievement.

I estimate the long term effects of FPE on education quality in Lesotho mainly for the following two reasons. First, unlike in many Sub-Saharan African countries, the FPE program in Lesotho was phased-in grade by grade, starting with grade one in 2000, until it covered the entire primary schooling system in 2006. This implementation strategy makes it possible to follow two cohorts of children (the FPE treated and the FPE untreated cohorts) from primary school through university level, and hence account for the underlying trends in achievement test scores of the cohorts through a difference-in-differences estimation strategy. Second, Lesotho has only one big (and premier) public university, the National University of Lesotho (NUL), and two smaller (and new) private universities, which only opened in 2007 and 2016, respectively. Therefore, it is possible to get 2
data for a sizeable proportion of the FPE treated and untreated cohorts that have written similar standardized achievement tests.

The results indicate that the FPE program has lasting positive effects on educational quality: it increased university students’ academic performance by between 2 and 19 percentage points. But there are no discernible FPE effect heterogeneities by student gender. This implies that, conditional on university attendance, boys and girls receive the same quality education. The robustness checks results indicate that the increase in educational quality cannot be attributed to some positive time trend, and that these effects are stronger when the sample is narrowed to 18-22 years old, the age range appropriate for the undergraduate level. The results are also robust to model specification errors.

The reminder of the paper proceeds as follows. Section 2 presents the institutional context and policy background. Section 3 briefly provides the theoretical framework while Section 4 discusses the data and presents some descriptive statistics. In Section 5, I explain the identification strategy, and present the main results in Section 6. Section 7 concludes the paper.

# **2 Institutional context and policy background**

## **2.1 Institutional context**

In Lesotho education follows a 7-3-2-4 system, with seven years of primary education, three years of junior secondary education, two years of senior secondary education, and four years of university education (see Figure 1). The official age of entry into primary schooling is six years, such that by age 12, children should be in grade seven. This implies that the official primary school-age is 6 to 12 years old, and that for secondary education is 13 to 17 years old.

At the end of primary school, students take the national exit exam, the Primary School Leaving Exam (PSLE), in order to enter the lower (junior) secondary school. After 3 years of junior secondary education, students take the Junior Certificate (JC) exam to progress to senior secondary, at the end of which they take the Cambridge Overseas School Certificate Exam (COSC).<sup>3</sup> Students can also enroll in different Technical and Vocational Education and Training (TVET) after taking either the PSLE, JC, and/or COSC exams. Given that secondary education is not free in Lesotho, enrollment into TVET is largely dictated by a child’s academic performance (low performance) and/or household wealth.

Unlike many other countries, most primary schools in Lesotho (about 85 percent) are owned and controlled by different churches (see Moshoeshoe _et al._ , 2019), and these churches are represented in the national education advisory board by their appointed education secretaries (Ambrose, 2007). Non-religious private schools constitute about 1 percent of primary schools, and are not covered by

> 3This is now called Lesotho General Certificate of Secondary Education (LGCSE). Through out this paper, COSC and LGCSE are used interchangeably.

3
<!-- Start of picture text --> Age<br>0<br>1<br>2! ecco<br>3/145|3 | Primary FPE<br>61<br>72<br>83<br>94<br>10 5<br>11 6<br>12 7 Secondary TVET<br>14 B Jc 2<br>1 3)5 pee c7 VET 3<br>1 76 |E NUL LCE TVET 21<br>18 1/4!) 14 3<br>20 3.3V 3<br>19 cose | |<br>21 4 4<br>22<br>23<br><!-- End of picture text -->
the FPE policy. The picture is very much similar even at the secondary or high school level because most church-owned primary schools have their secondary schools nearby. However, the share of non-religious private secondary schools is slightly higher than that at primary level. As of 2014, there were about 1.4 percent non-church private high schools (Bureau of Statistics, 2015), and these are concentrated in four districts of the country, namely, Berea, Botha-Bothe, Leribe and Maseru. Notwithstanding this co-ownership structure, and except for non-church private schools, all schools follow the same national curriculum provided by the Ministry of Education and Training (MOET). Further, the government has an overall authority in pronouncing education policies, management and regulation of education, training of teachers, and teachers’ placements, and deployments within government and church-owned schools. But some church-owned schools do at times privately hire contract teachers at their own costs.

With regard to students’ progression within the system, the _de jure_ government policy since 1967 is that of automatic grade promotion at primary school level but, _de facto_ , schools still practice grade retention (Ambrose, 2007).<sup>4</sup> Figure 2 indicates that, between 2000 and 2015, the primary school repetition rate was about 20 percent until 2010, after which it dropped to about 14 percent in 2015. During this period, the primary education repetition rate averaged about 17.3 percent and the PSLE exam failure rate fluctuated between 12 percent and 17 percent. Thus, coupled with delayed school enrollment, the high grade retention rate implies that in any given year (or grade) there are children of different cohorts Moshoeshoe _et al._ (2019).

There is grade retention policy at secondary school level. Figure 2 further shows that, while the transition rate between primary and secondary education is high (about 81 percent), the repetition rate in secondary education is also high, averaging about 12.6 percent between 2000 and 2015. Further, the JC exams failure rate is high; it fluctuated between 24 percent (recorded in 2004) and 32 percent (recorded in 2009 when the first FPE students wrote JC exams) (Bureau of Statistics, 2015). This high failure rate could explain the high dropout rate, of 16 percent at secondary school level. Therefore, those who ultimately get into university are a select group of motivated and high ability students who potentially come from high income households.

Beyond physical and monetary costs, there are no regulatory restrictions on school choice in Lesotho. Thus, school choice is largely determined by school availability, school’s past pass rates, parental wealth, and parental tastes for education. High performing high schools generally attract students from across the country and have stricter entry requirements. Hence, to cope with the high demand, such high schools normally administer entry exams, and often do not re-admit their students whose JC exam’s performance is considered poor (usually second class pass and below). This implies that different schools largely cater for different types of students with regard to performance.

> 4However, since 2010, there has been an increased push for automatic grade promotion at the primary school level. But this latest policy call does not affect the cohorts which this paper studies (i.e. those that were in primary school during the years 2000 to 2006).

5
Figure 2: Primary-to-Secondary education Transition rate, and Repetition rates, 1997-2016 <!-- Start of picture text --> Primary & Secondary education Transition and Repetition Rates<br>80<br>60<br>40<br>20<br>0<br>1995 1997 2000 20052006 2010 2012 2015 2020<br>Year<br>Primary−to−Secondary school Transition rate Primary school repetition Rate<br>Secondary school repetition rate<br><!-- End of picture text --> _Source_ : Own representation using data from UN Institute of Statistics.

As of 2013, there were about 13 higher education institutions, 8 (i.e. 62 percent) of which are public institutions. The National University of Lesotho (NUL) is the main tertiary institution in Lesotho, and remained the only local bachelor’s and master’s degree-awarding institution until 2007. The university admits about 44 percent<sup>5</sup> and 89 percent of Lesotho’s undergraduate and postgraduate students’ population, respectively (Council on Higher Education, 2013).

# **2.2 Policy background**

Lesotho instituted the FPE program in 2000 in order to meet the Millennium Development Goal (MDG) of ensuring that primary education is free and available to all (UNESCO, 2000). As mentioned earlier, Lesotho’s implementation strategy was different from that followed by other African countries. School fees were eliminated sequentially on a grade-by-grade basis starting with grade one in 2000 such that by 2006, all seven primary school grades were under FPE. The main reason for this implementation strategy was to cushion FPE’s financial impact on the public budget (Urwick, 2011).

The FPE policy is an amalgamation of several program components that address both demandand supply-side constraints to schooling. On the demand-side, the policy involves elimination of some private schooling costs such as school fees, stationery and textbooks’ costs. On the supply-

> 5This is as a percent of all those enrolled in local colleges and foreign universities, mainly in South Africa.

6
side, the government recruited more teachers,<sup>6</sup> built additional classrooms in existing schools, and new government schools where none existed before. For example, between 2002 and 2011, the number of primary schools in Lesotho increased by about 10 percent, and the primary school pupil-teacher ratio dropped from 48 to 34 pupils per teacher (MOET, 2011). This increase in infrastructure also helped to reduce the average distance to schools, and hence transportation costs. In addition to school infrastructure, the government provides annual capitation grants, furniture and teaching materials to all schools, including church/private schools (Jopo _et al._ , 2011; Lekhetho, 2013). Except for the differences in years of exposure, the supply-side program components benefited everyone at school while fee eliminations and free stationery and textbooks exclusively benefited those covered by FPE.

Figure 3: Changes in Pupil-Teacher Ratio and enrollment <!-- Start of picture text --> Trends in Secondary School Enrolments Rates Trends in Pupil−Teacher Ratios<br>60 60<br>50 50<br>40 40<br>30 30<br>Gross Enrolment Rate Primary school<br>20 Net Enrolment Rate 20 Secondary school<br>2000 2005 2010 2015 2000 2005 2010 2015<br>Year Year<br>Enrolment Rate<br>Pupil Teacher Ratio (PTR)<br><!-- End of picture text --> _Source_ : Own representation using data from various Education Statistics Reports (MOET, 2010, 2011, 2016).

Figure 3 shows changes in secondary school enrollment (demand for education), on the left panel, and pupil-teacher ratio (supply of education), on the right panel, since the introduction of the FPE program. From the left panel of the figure, we can see that, while the secondary school gross enrollment rate was on the increase between 2001 and 2011, the increase was much faster between 2006 and 2010. The figure further shows that, while the net enrollment rate increased through out the period, the gross enrollment rate plateaued between 2011 and 2015, and then began the upward trend. The year 2007 is when the first cohort of FPE children entered secondary school level.

> 6More young and qualified teachers were recruited. Between 2000 and 2007, the proportion of teachers with tertiary qualifications increase from 6 percent to 14 percent, but teacher quality, as measured by teacher performance on SACMEQ reading test, declined (see Moshoeshoe, 2015).

7
Moshoeshoe _et al._ (2019) find that, within the first three years of the FPE policy implementation, enrollment of primary school-aged children increased by about 29 percent. Therefore, the increase in secondary school enrollment between 2007 and 2011 is partly due to the increased demand for education from the first three FPE cohorts. This first FPE cohort, which potentially had many over-aged children, completed secondary education in 2011. And this partly explains the plateauing of the gross enrollment rate, and the continued increase in net enrollment, between 2011 and 2015.

According to MOET (2011), the government increased the number of secondary schools and recruited more teachers in anticipation of the increased demand. This is evident in the right panel of Figure 3 that shows that secondary schools’ student-teacher ratio was on the increase until 2005, and then began to decline to about 1 teacher per 24 students in 2009. It is clear from this analysis, therefore, that Lesotho’s FPE program had multiple components targeted at primary schools, and it also had a knock-on effect on school resources at the secondary school level. This paper examines the long-term effects of this policy package, not its individual elements.

# **3 Conceptual Framework**

Understanding the process of a child’s cognitive development has remained the preoccupation of economists since the early works of Leibowitz (1974) and Becker and Tomes (1986). According to Haveman and Wolfe (1995), a child’s development is principally determined by three factors, namely: government choices regarding the amount of resources invested in education; parental investment decisions in the form of quantity and quality of resources devoted; and the child’s own choices (but only past age 13 or 15). In this setting, the government moves first by making direct investment in the child and setting the economic environment, within which parents, and then children, operate. Here the view is that investment in children cannot happen outside government involvement and that this investment takes place only after the child is born.

However, Cunha, Heckman, Lochner and Masterov (2006) argue that skill (or ability) formation is a life cycle process that starts much earlier in life, from the womb, and that abilities, cognitive and non-cognitive, are malleable to environmental influences. They postulate that early and late investments in a child’s development are complementary. Thus, early high quality child investments increase the productivity of later child investments (i.e. skill begets skill), and this effectively places parents as very important first movers under the Haveman-Wolfe sequential framework. But equally important is the role played by the society or government in the second stage of human capital development (after birth) because early investments are only productive if there is follow-up investment.

Indeed Behrman (2010) propounds that, for children aged 6 or 7 to 15, educational achievement is partly determined by formal schooling and its characteristics, including out-of-school experiences such as homework conditional on preschool investments, individual, family, market and 8
Figure 4: The Directed Acyclic Graph (DAG) of causal effect of FPE on academic performance <!-- Start of picture text --> School<br>building SES<br>Fee Elimination Access or PTR Academic Academic<br>enrollment performance t performance t +6<br>Textbooks<br>Teacher<br>recruitment<br><!-- End of picture text --> _Source_ : Own representation. _Notes_ : PTR is the Pupil Teacher Ratio; SES is socioeconomic status. The direction of the arrow (A _→_ B) indicates the direction of the cause from node A to node B.

institutional characteristics. Hence, early quality childhood investment, both at home and at school, manifests itself in the form of high achievement and low grade retention. It is clear that achievement is a function of not only abilities but also school inputs, thereby placing family and government at the center of the child’s development.

Figure 4 is the directed acyclic graph (DAG) of the causal path ways from FPE program components (i.e. fee eliminations, textbooks, teacher-recruitment, and school building) to academic achievement. We can see from this figure that, because elimination of schools fees, building of more schools, and provision of textbooks reduce the costs of schooling, they are expected to affect access to schooling positively. The increase in enrollment will lead to an increase in the pupilteacher ratio (PTR), all else held constant, and this will in turn affect (current or primary school) academic achievement. Recruiting more teachers will reduce PTR and, hence, improve academic achievement.

Further, textbooks availability and teacher recruitment have a direct influence on academic achievement, and students’ socioeconomic status (SES) affects academic achievement directly and through its influence on access and PTR, holding all else constant. There is a positive relationship between SES and achievement. Therefore, fee eliminations will lead to an influx of low SES children into the schooling system and lower achievement. Lastly, (current or primary) academic achievement can also influence current enrollment and academic achievement in the next period, say six years later.

I therefore model knowledge acquisition as a cumulative process that combines a full history of family, community and school inputs with the child’s innate ability to produce child’s achievement 9
as measured by test scores at a point in time (Todd and Wolpin, 2003). Let _Ait_ be student _i_ ’s academic achievement (or test scores), and **S** _it_ and **X** _it_ denote vectors of school-supplied inputs (e.g. student _i_ ’s class size, school infrastructure, quality of teachers, etc) and family-supplied inputs at time _t_ , respectively. Allowing for the idiosyncratic error, which includes all omitted inputs (observed and unobserved) and measurement error, _εit_ , and inherited ability, _ai_ 0, the general achievement production function is given as: In this framework, a student’s performance at the university level is influenced not only by her current individual and household characteristics, but also by current and previous school/universitysupplied inputs. Because skill begets skill, the influence of past school-supplied inputs is partly reflected in the child’s performance in JC and COSC/LGCSE examinations.

# **4 Data and Descriptive Statistics**

This paper uses the National University of Lesotho’s students’ administrative records data for years 2010 up to 2014. It makes use of first-year and second-year students’ data. As the largest and oldest undergraduate degree-awarding university in Lesotho, the NUL admits the largest share of all students who achieve the minimum score for university entry in the senior high school exit examinations. It therefore admits the largest proportion of students who have gone through the FPE system. Given that the first cohort that has gone through the FPE program first entered university level in 2012, the second-year students are a control group, while the first years are a treatment group. I discuss this group categorization in detail in Section 5.

The data contains information on each student’s gender, date of birth, academic year, the senior high school exit (or Cambridge Overseas School Certificate (COSC)) examination pass grade, the NUL Admission Point System (APS) score<sup>7</sup> for each student, the high school attended, faculty, department or program of study, the overall weighted mean or year mean performance, and whether a student is local or international. The overall weighted mean (OWM) is the main outcome variable. It is calculated as the weighted sum of the final scores of core, pre-requisite, and/or elective subject courses that make a maximum of 36 credit hours, where the weights are

> 7 APS score (commonly known as the aggregate score) is the sum of grade points/ranks for 6 COSC subjects, including English language. For example, grade A<sup>*</sup> (or A<sup>+</sup> ) is given point/rank 1, grade A is equivalent to 2 points, grade B is equivalent to 3 points, etc. Therefore, the lower the APS score the higher the performance in COSC exams. The lowest achievable APS score is 6 and indicates the highest level of performance in all six subjects.

10
Table 1: Summary Statistics

||Pre-|FPE (201|0-2011)|Post-|FPE (20|12-2014)<br>lfdif|
|---|---|---|---|---|---|---|
|Variable|N|Mean|Std.Dev|N|mean|_p−_vaue or .<br>Std.Dev|
|OWM|5654|59.88|9.605|7795|59.25|9.094<br>0.0001|
|Standardized OWM|5654|0.0268|1.034|7795|-0.0204|0.970<br>0.0068|
|Female|5776|0.563|0.496|8016|0.601|0.490<br>0.0000|
|Age|5764|21.10|3.915|8004|20.89|3.588<br>0.0016|
|_COSC pass_|||||||
|First class|4765|0.300|0.458|7713|0.314|0.464<br>0.0991|
|Second class|4765|0.551|0.497|7713|0.571|0.495<br>0.0245|
|Third class|4765|0.149|0.356|7713|0.115|0.319<br>0.0000|
|APS|5221|14.92|5.242|7343|15.43|5.413<br>0.0000|
|_Distribution of Students_|_by (S_|_chool) Dist_|_rict (%)_||||
|Berea|5776|0.0734|0.261|8016|0.109|0.312<br>0.0000|
|Botha-Bothe|5776|0.0682|0.252|8016|0.0828|0.276<br>0.0015|
|Leribe|5776|0.199|0.399|8016|0.178|0.382<br>0.0017|
|Mafeteng|5776|0.101|0.301|8016|0.112|0.316<br>0.0321|
|Maseru|5776|0.352|0.478|8016|0.340|0.474<br>0.1401|
|Mohale’s Hoek|5776|0.0829|0.276|8016|0.0639|0.245<br>0.0000|
|Mokhotlong|5776|0.0303|0.171|8016|0.0308|0.173<br>0.8623|
|Qacha’s Nek|5776|0.0156|0.124|8016|0.0147|0.120<br>0.6823|
|Quthing|5776|0.0298|0.170|8016|0.0250|0.156<br>0.0842|
|Thaba-Tseka|5776|0.00606|0.0776|8016|0.0126|0.112<br>0.0001|
|Foreign|5776|0.0424|0.202|8016|0.0314|0.175<br>0.0006|
|_Distribution of Students_|_by Fa_|_culty (%)_|||||
|Agriculture|5776|0.0571|0.232|8016|0.0586|0.235<br>0.7101|
|Education|5776|0.254|0.436|8016|0.246|0.431<br>0.2653|
|Health Sciences|5776|0.0703|0.256|8016|0.0750|0.263<br>0.2969|
|Humanities|5776|0.115|0.319|8016|0.130|0.337<br>0.0052|
|Law|5776|0.0452|0.208|8016|0.0485|0.215<br>0.3610|
|Science & Technology|5776|0.144|0.351|8016|0.124|0.329<br>0.0006|
|Social Sciences|5776|0.315|0.465|8016|0.318|0.466<br>0.7142|

_Source_ : Own calculations using NUL students’ records data for 2010, 2011, 2012, 2013, and 2014. _Notes_ : OWM is the overall weighted mean, calculated as the weighted sum of final scores of core, pre-requisite, and/or elective subject courses that make a maximum of 36 credit hours, where the weights are each course’s credit hours divided by 36. The N for some variables is smaller due to missing values.

11
each course’s credit hours divided by 36.<sup>8</sup> I construct the student’s district information based on the location of the high school attended<sup>9</sup> .

Table 1 gives the summary statistics for the sample, first and second year students not exposed to FPE, 2010 to 2011, and those exposed to FPE, 2012 to 2014. There are 6,613 students who are in the first and second years of their undergraduate studies (diploma and degree programs) pre-FPE, and 9,610 of them post-FPE. If I exclude diploma students, there are 5,776 and 8,016 students from 230 high schools, pre- and post-FPE, respectively.

From Table 1, we can see that the pre-FPE and post-FPE periods, the OWM dropped by about 1 percentage point from 60 percent to 59 percent. The average age dropped slightly from 21.1 years old pre-FPE to 20.9 post-FPE, indicating that more young students were enrolled in the university post-FPE. This decline in average age of students could be the result of early or on-time school entry due to FPE program.

On average, post-FPE students were of poor quality: the APS score increased from 14.9 to 15.4 points, indicating a decline in academic performance. The percentage of students passing the COSC exams with first-class statistically remained constant at about 30 percent, and that of second-class students increased 55 percent to 57 percent between these periods. The proportion of students passing with a third class dropped by about 3 percentage points. Therefore, the decline in academic performance is largely attributed to the increase in the proportion of those attaining the second-class COSC pass from 19.5 percent to 21 percent. Furthermore, this drop in performance potentially implies that, while some students attained the same pass categories pre- and post-FPE, their pass marks were towards the lower end of each pass category.

The decline in performance can also be deduced from the faculty student shares. The three faculties of Agriculture, Health Sciences, and Science and Technology have the strictest entry requirements: candidates must score high in mathematics, sciences, and english language, and have low APS score. The share of students in the faculty of Science and Technology (FOST) declined by 2 percentage points between periods. While part of the decline in FOST student share could be due to differences in student career or course tastes, it is also more likely that most students could not meet the admission requirements due to their relatively poor performance at COSC level. To further support this interpretation, data also reveals that the proportion of students admitted into diploma courses at the NUL’s Institute of Extra-Mural Studies (IEMS) increased by 4 percentage points. We know that high performing students would normally go for degree programs. Hence the increase in the proportion of students going for a diploma program

> 8Suppose that a student has registered for 12 courses, each with 3 credit hours (or contact hours per week). These courses make a total of 36 credit hours, and will all be used in the calculation of the OWM. If the student scores 60% in each course, then her OWM is the weighted sum of all the 60s, where the weights are 363<sup>=</sup> 121<sup>,which</sup> equals 60%. If the student has taken courses with more than 36 credit hours, then only courses making at least 36 credit hours, starting with core and pre-requisite (i.e. required) courses, are included in the OWM calculation.

> 9Even though some students attend schools outside their home districts, a large proportion of them do attend schools within their home districts.

12
is indicative of the students’ poor COSC performance post-FPE relative to pre-FPE. In sum, the table shows that there has been a drop in student performance between pre- and post-FPE.

# **5 Identification Strategy**

In this section, I explain the semiparametric difference-in-differences (DID) identification strategy that the paper employs to tease out the long-term treatment effect of the FPE program on academic performance (Abadie, 2005; Chang, 2020). In order to fix ideas, I begin by explaining the standard DID method (Angrist and Pischke, 2009; Blundell and Dias, 2009; Imbens and Wooldridge, 2009), assess the plausibility of its assumptions, and then explain the semiparametric DID strategy.

## **5.1 Standard method**

Here I explain the standard DID strategy when repeated cross-sections data are available. Suppose student _i_ belongs to group _Gi_ = _g ∈{_ 0 _,_ 1 _}_ (where _Gi_ = 1 is the treatment cohort), and is observed in period _Ti_ = _t ∈{_ 0 _,_ 1 _}_ (where _Ti_ = 1 is post-program period). Let _Yi_ (0) and _Yi_ (1) be her potential outcomes (e.g. achievement test score) before and after the program, respectively. Therefore, the DID estimand (or the average treatment effect on the treated (ATT)), _δDID_ , is given by where _E_ [ _Yi|Gi_ = 1 _, Ti_ = 1] = _E_ [ _Yit_ =1 _|Di_ = 1 _, T_ = 1] is the average outcome for the treatment group unit in post-program period. This double differencing procedure removes the bias due to permanent pre-existing differences between the two groups, and that due to common time trends unrelated to the program. Therefore, the DID method requires that the control group should not be influenced by the program, and should be comparable to the treatment group. In practice, the following two-way fixed effects (TWFE) linear regression model is used to estimate the ATT<sup>10</sup>

where _Di_ = _Ti × Gi_ = _d ∈{_ 0 _,_ 1 _}_ is the treatment indicator, _γ_ is the year-specific effect common to both control and treatment cohorts; _λ_ is a cohort-specific, time-invariant coefficient; _δDID_ is the DID effect parameter, **X** _i_ is a vector of controls (current and past school- and family-supplied

> 10 Equation 3 is an estimable version of the production function in Equation 1, where _Yi ≡ Ai_ .

13
inputs), and _εi_ is an unobserved individual error term.<sup>11</sup> Interacting _Di_ with an indicator for gender will identify the gender effects of the program.

As mentioned earlier, the FPE program was progressively implemented from grade 1 in year 2000 such that the first FPE cohort that successfully passed senior high school exit examinations entered the university in 2012. Given the school entry age of 6 years, the age-appropriate cohort for first, and second year(s) of university education are 18, and 19, respectively. Thus, the treatment group is defined in two ways. First, the treatment group is defined by age-group (i.e. the ageappropriate cohort for university year 1). Second, it is defined by grade-group (i.e. whether a university student wrote primary school exit exams in 2006 or after, irrespective whether she ought to have written it earlier and be in the second year of university education). Table A.1 summarizes the composition of the control and treatment groups over time.

Given that the FPE did not have age restrictions, it is inevitable that the control group under the age-appropriate cohort treatment group definition also includes the FPE treated students either because of delayed school enrollment and/or grade repetition. Higher age of school entry increases academic performance and the effect is long-lasting (Black _et al._ , 2011; Ponzo and Scoppa, 2014; C ́aceres-Delpiano and Giolito, 2019). Thus, the control group’s performance is likely inflated. Further, the control group could be contaminated by the potential presence of intra-household spill-over effects, whereby a younger sibling who directly benefited from FPE may have freed up some household resources to pay fees and textbooks for an older sibling in secondary education and help her to concentrate better at school. While Moshoeshoe _et al._ (2019) find no evidence of these intra-household spill over effects at the primary school level, it is possible that these spill-overs might be present at this level. The main advantage of the age-group definition is, however, that it cannot be manipulated for one to fall into any particular group. For these reasons, the DID estimand is likely biased downward, and identifies the lower bound effect of FPE.

With respect to the grade-group (year of study) treatment group definition, the treatment group is much broader as it likely includes those who delayed school enrollment, and those who repeated grades in primary school level, secondary level, and/or at university level. All those who were not covered by the no-fee policy at primary school level, but ended up being in the same grades with the FPE-treated cohort at the secondary school level and at university level are thought to be indirectly FPE-treated due to class peer effects. The control group in this case is largely clean of contamination because students are less likely skip grades. It includes all second year students, including those who are repeating the year and excluding all those who are repeating the first year. The later group, first-year repeaters, contaminate the treatment group and will likely bias upwards the performance of first years. Since the composition of the control group is similar preand post-FPE, there is likely to be an upward bias in FPE effect. Therefore, under this treatment

> 11This TWFE model implicitly imposes further assumptions that treatment effects are homogeneous across subpopulations, and that there are no covariate-specific trends in both the treatment and control groups (Sant’Anna and Zhao, 2020).

14
group definition, the DID method likely identifies the upper bound effect of FPE.

# **5.2 Assessing the plausibility of the parallel trends assumption**

From the previous section, we know that the most important identifying assumption for the DID method is the parallel trends assumption that, in the absence of the FPE policy, the change in academic performance of the treatment group would have been equal to the to the change in academic performance of the control group. I discuss the plausibility of this assumption in this subsection. First, I assess the assumption plausibility when treatment group is defined by year of study, and then discuss it when treatment group is defined age appropriate for years 1 and 2 at university level. Lastly, I look at the compositional differences between the control and treatment groups.

## **5.2.1 Parallel trends in academic performances of first and second year undergraduate students**

Figure 5 shows the trends in students’ academic performance for the period 2010–2014. As we can see from the figure, academic performance of both first- and second-years increased between 2010 and 2011, but plummeted in 2012, the year when the first FPE cohort entered university. Since then, academic performance of first-years has recovered, surpassing the pre-FPE levels in the following years. While the gap in average performance between first- and second-years remained almost constant between 2010 and 2011, the first years’ average performance dropped significantly in 2012 relative to that of the second- years (see also Table A.2 ). Taken together, this analysis points out that the trends in first- and second-years’ academic performances were parallel before treatment (i.e. that is before the FPE cohort entered university level). This, therefore, implies that academic performance of second year students is a credible counterfactual for academic performance of first year students.

## **5.2.2 Parallel trends in academic performances of 16-18 year old and 19-23 year old student groups at the undergraduate level**

I now turn to the assessment of the parallel trends assumption when the treatment group is defined as the age-appropriate cohort for the first year of university. Because of early school entry, some children do reach university before the age of 18 years. In the data, there is a small fraction of students aged below 18 years in their first year of university. While it is possible that age (i.e. date of birth) was captured incorrectly for some students in this category, there is a small fraction of students who enter the schooling system before the age of 6 years. According to MOET (2016), about 7 percent and 17 percent of children aged 16 years and 21 years and older, respectively, were in their last grade of secondary school in 2016. Therefore, I define the treatment cohort as those 15
Figure 5: Trends in Students’ average Academic Performance by Year of Study: 2010–2014 <!-- Start of picture text --> 62<br>60<br>58<br>95% CI<br>First Years<br>95% CI<br>Second Years<br>56<br>2010 2011 2012 2013 2014<br>Academic Year<br>Student Overall Weighted Mean (OWM)<br><!-- End of picture text --> _Source_ : Own calculations using the NUL students records data for the academic years 2010, 2011, 2012, 2013, and 2014. _Notes_ : OWM is the overall weighted mean.

aged 16-18 years because they are of the appropriate age for first year of university, and those aged 19-23 years as the control cohort.

Figure 6 presents trends in students’ academic performance between 2010 and 2014 by treatment cohort. We can see from the figure that the trends in academic performance of the 16-18 year olds and the 19-23 year olds are parallel throughout the period. As mentioned earlier, the control group (i.e. the 19-23 year cohort) possibly includes children directly affected by FPE. Hence, it is more than likely that the observed drop in average performance of this cohort in 2012 is largely driven by the decline in performance of fraction of old but FPE-treated children. This further supports the idea that our DID method under this treatment group definition will only identify the lower-bound effect of FPE on academic performance.

# **5.2.3 Compositional differences**

Notwithstanding the above evidence establishing the second years and the 19-23 year old university students as the plausible counterfactuals for the respective treatment groups, compositional differences between the control and treatment groups can cause the violation of the parallel trends assumption. That is, the identifying assumption may be implausible if pre-treatment individual characteristics that are correlated with the dynamics of the outcome variable are not balanced 16
Figure 6: Trends in Students’ average Academic Performance by Cohort: 2010–2014 <!-- Start of picture text --> 61<br>60<br>59<br>58<br>16−18 years old cohort<br>19−23 years old cohort<br>57<br>2010 2011 2012 2013 2014<br>Academic Year<br>Student Overall Weighted Mean (OWM)<br><!-- End of picture text --> _Source_ : Own calculations using the NUL students records data for the academic years 2010, 2011, 2012, 2013, and 2014. _Notes_ : OWM is the overall weighted mean.

between the FPE-treated and FPE-untreated groups (Abadie, 2005). In such a case, therefore, the FPE effect identified by the standard DID would be biased. It is, therefore, important to check whether the pre-PFE characteristics are balanced between the control and treatment groups. Table 2 presents the pre-FPE compositional differences between the control and treatment groups. Specifically, the table shows pre-FPE mean differences, by treatment group, in the main outcome variable (OWM) and the individual characteristics (APS, age, gender, and location). Column (3) shows the _p−_ value of the _t−_ test for differences in mean characteristics of the control and treatment groups pre-FPE. Looking at these _p−_ values, we can see that there are statistically significant differences between the control and treatment group with respect to their age, pre-university (i.e. COSC) academic performance, gender and location (e.g. Berea and BothaBothe district).<sup>12</sup> Undoubtedly, these characteristics are associated with the changes in student’s academic performance over time. For example, because early and current investments in human

> 12Column (5) of the table presents the normalized difference in characteristics between groups. The normalized difference between means is a scale-free measure ̄ of the difference in the distribution of characteristics by treatment status, and is given as Norm-diff _≡△_ **X** = _~~√~~_ _<u>XS</u>_ <u>10</u> _−_<sup>2+</sup> _<u>X</u>_<sup> ̄</sup><sup>_S_</sup> <u>01</u><sup>2,where</sup><sup>_S_</sup> _G_<sup>2isthesamplevarianceof</sup><sup>_Xi_insub-samplewith</sup> treatment _Gi_ = _{_ 0 _,_ 1 _}_ . If the normalized difference is less than one quarter in absolute value, the unconfoundedness assumption is likely satisfied and the model is less sensitive to functional form (Imbens and Wooldridge, 2009). Using this indicator, we can see that pre-FPE performance at the COSC exams (pre-university entry exams) is different between groups.

17
Table 2: Pre-FPE Compositional Differences between Control and Treatment groups

|Vibl<br>|Treatment|Control|p-value|Dif (_X_1_−X_0)|Norm-dif|
|---|---|---|---|---|---|
|arae|(1)|(2)|(3)|(4)|(5)|
|OWM|58.5060<br>|61.0930<br>|0.0000|-2.5869|-0.1866|
||(10.9261)|(8.5287)||||
|APS|19.2063<br>|11.2710<br>|0.0000|7.9353|1.5799|
||(3.9627)|(3.0859)||||
|Child Age|21.3088<br>|22.1000<br>|0.0000|-0.7912|-0.1239|
||(4.7751)|(4.2376)||||
|Gender (female)|0.5920<br>|0.5651<br>|0.0270|0.0269|0.0384|
||(0.4915)|(0.4958)||||
|_School or Home District_||||||
|Berea|0.0699<br>|0.0817<br>|0.0694|-0.0118|-0.0315|
||(0.2550)|(0.2740)||||
|Botha-Bothe|0.0717<br>|0.0573<br>|0.0177|0.0144|0.0413|
||(0.2580)|(0.2324)||||
|Leribe|0.1863<br>|0.1963<br>|0.3017|-0.0100|-0.0180|
||(0.3894)|(0.3973)||||
|Mafeteng|0.0991<br>(0.2989)|0.1005<br>(0.3007)|0.8549|-0.0013|-0.0031|
|Maseru|0.3729<br>|0.3579<br>|0.2040|0.0151|0.0221|
||(0.4837)|(0.4794)||||
|Mohale’s Hoek|0.0801<br>|0.0801<br>|0.9988|-0.000|-0.0000|
||(0.2716)|(0.2715)||||
|Mokhotlong|0.0304<br>(0.1718)|0.0288<br>(0.1673)|0.6990|0.0016|0.0067|
|Qacha’s Nek|0.0158<br>(0.1247)|0.0169<br>(0.1289)|0.7214|-0.0011|-0.0062|
|Quthing|0.0298<br>(0.1701)|0.0316<br>(0.1750)|0.6736|-0.0018|-0.0073|
|Thaba-Tseka|0.0088<br>(0.0933)|0.0066<br>(0.0808)|0.3069|0.0022|0.0178|
|_Faculty_||||||
|Agriculture|0.0374|0.0632|0.0000|-0.0258|-0.0836|
||(0.1899)|(0.2434)||||
|Education|0.1778<br>|0.2696<br>|0.0000|-0.0917|-0.1566|
||(0.3824)|(0.4438)||||
|Health Sciences|0.0541<br>(0.2262)|0.0692<br>(0.2538)|0.0107|-0.0151|-0.0444|
|Humanities|0.0758<br>(0.2646)|0.1265<br>(0.3324)|0.0000|-0.0507|-0.1194|
|Law|0.0430|0.0356|0.1275|0.0073|0.0266|
||(0.2029)|(0.1856)||||
|Science & Technology|0.1272<br>(0.3333)|0.1234<br>(0.3289)|0.6346|0.0039|0.0083|
|Social Sciences|0.2401|0.3125|0.0000|-0.0723|-0.1147|
|Observations|(0.4272<br>3419|(0.4636)<br>3194||||

_Source_ : Own calculations using NUL students’ records data for the academic years 2010, 2011, 2012, 2013, and 2014. _Notes_ : OWM is the overall weighted mean. The treatment group is all students in their first year of university studies. Standard deviations are in parentheses. The reported p-values are for tests of equality of means between the treatment and control groups (independent samples). _Diff_ stands for difference in means by treatment status. ̄Norm-diff means normalized differences between treatment and control means computed as _△_ **X** = _~~√~~_ _<u>XS</u>_ <u>10</u> _−_<sup>2+</sup> _<u>X</u>_<sup> ̄</sup><sup>_S_</sup> <u>01</u><sup>2,where</sup><sup>_S_</sup> _G_<sup>2isthesamplevarianceof</sup><sup>_Xi_in</sup> subsample with treatment _Gi_ = _{_ 0 _,_ 1 _}_ . _G_ = 1 if a student is in second year.

18
capital development are complementary, a child’s high school academic performance influences her performance at university level. Given these compositional differences, Abadie (2005) proposes that the treatment effect be estimated by the semiparametric DID strategy, which allows for the distribution of both observed and unobserved characteristics to differ by treatment group. Further, the semiparametric DID method relaxes the implicit assumption in the standard DID specification that treatment effects are not heterogeneous, and it is robust to functional form misspecification as it treats the covariates nonparametrically (Sant’Anna and Zhao, 2020; Chang, 2020). Below I present this strategy as implemented in the paper.

# **5.3 Semiparametric DID strategy**

Under the semiparametric DID strategy, the main identifying assumption is that, conditional on individual pre-FPE characteristics, the average performance of the FPE-treated and FPE-untreated students would have followed parallel trends in the absence of the FPE policy (Assumption 3.1, Abadie (2005)). Therefore, taking the average of the differences in change in academic performance over time between FPE-treated and FPE-untreated with similar pre-FPE characteristics allows us to identify an unbiased estimate of the ATT ( _δSDID_ ) (Abadie, 2005; Houngbedji, 2018; Sant’Anna and Zhao, 2020; Chang, 2020). This estimator requires that individuals first be matched based on their propensity score (i.e. the probability of being under FPE conditional on their pre-FPE characteristics, _π_ 0( **X** _i_ ) _≡ P_ ( _D_ = 1 _|_ **X** _i_ )), before averaging the differences in outcome changes over time. In a repeated cross-sections setting, as in this study, Abadie (2005) shows that the ATT is given by

if _P_ ( _D_ = 1) _>_ 0 and _π_ 0( **X** _i_ ) _<_ 1, where Substituting _φ_ into equation 4 gives where _Y_<sup> ̃</sup> = _λ·T_ (1 _<u>i−−λλ</u>_ )<sup>_·Y_,and</sup><sup>_λ_istheproportionofpost-treatmentindividualsinthesample.13</sup> Therefore, _δSDID_ is an inverse probability weighted average of temporal changes in _Y_<sup> ̃</sup> . It weighs the FPE-untreated individuals by their probability of being under FPE given their characteristics.

> 13Subscript _M_ in the expectation sign indicates that the expectation is taken on data coming from the following mixture distribution _PM_ ( _Y_ = _y, D_ = _d, X_ = _x, T_ = _t_ ) = _λ·t·P_ ( _Y_ (1) = _y, D_ = _d, X_ = _x_ )+(1 _−λ_ ) _·_ (1 _−t_ ) _·P_ ( _Y_ (0) = _y, D_ = _d, X_ = _x_ ), where _λ ∈_ (0 _,_ 1).

19
According to Abadie (2005), if the parallel trends assumption holds unconditionally, and also conditional on the predetermined variables of interest like gender, the conditional identification can still be used to tease out the effect of treatment for different population groups. Given that the object of this paper is also to evaluate the heterogeneous effects of FPE by gender, I use the semiparametric estimator in this paper to examine the FPE policy effects on academic performance.

# **6 Results**

This section presents the estimation results of the long-run effect of FPE on student achievement. First, in Section 6.1, I present results from the non-parametric estimation of ATT ( _δ_<sup>ˆ</sup> _DID_ ) directly from equation 2. These non-parametric results are important because they are based on a framework that (1) does not impose, a priori, any functional form assumptions on the data, and (2) allows us to visualize the effect (without any controls). Second, I present, in Section 6.2, the semiparametric DID results having controlled for observed differences in individual characteristics between the control and treatment groups, and for cohort effects using age fixed effects models.

## **6.1 Non-parametric estimation results**

Table 3 presents the non-parametric results of the long-term effects of FPE on educational achievement. Panel A shows the (lower-bound effect) results when the treatment group is defined by the age appropriate for year one of university, and panel B shows the (upper-bound effect) results when the treatment group is defined by year of study.

Looking at Panel A of Table 3, we can see that, pre-FPE policy, the average academic performance in the control group ( _E_ [ _Yi|Gi_ = 0 _, Ti_ = 0]) and the treatment group ( _E_ [ _Yi|Gi_ = 1 _, Ti_ = 0]) was, respectively, 59.97 percent and 58.94 percent. After the FPE policy implementation, the average academic performance dropped slightly to 59.95 percent in the control group ( _E_ [ _Yi|Gi_ = 0 _, Ti_ = 1]), and 58.57 percent in the treatment group ( _E_ [ _Yi|Gi_ = 1 _, Ti_ = 1]). However, the decline in performance over time, for the two groups respectively, is both economically and statistically insignificant. The non-parametric estimate of the average treatment effect on the treated (ATT: ˆ _δDID_ = _∆G_ =1 _− ∆G_ =0) is equal to 0.34 percentage points drop in academic performance, which is not statistically significant. This, therefore, implies that the non-parametric lower bound effect of FPE on student achievement is statistically equal to zero.

Now turning to Panel B of Table 3, we can see that, pre-FPE policy, the average academic performance in the control group was 61.09 percent, while in the treatment group it was 58.51 percent. Post-FPE policy introduction, the average academic performance dropped slightly by 0.31 percentage points in the control group to stay at 60.78 percent. In the treatment group, however, student performance increased by 0.41 percentage points to 58.92 percent. While these time changes in performance within each group are both economically and statistically insignificant, the 20
Table 3: Effect of FPE on Student achievement: Non-parametric results by Treatment group definition

||Pre-FPE|Post-FPE|_∆G_=_g_|
|---|---|---|---|
|_A: Group defned by Age-appr_|_opriate cohort_|||
|Control group|59.9683|59.9494|-0.0189|
||(0.1358)|(0.1019)|(0.1667)|
|Treatment group|58.9376|58.5742|-0.3634|
||(0.2943)|(0.2233)|(0.3628)|
|ATT: <sup>ˆ</sup>_δDID_ =_∆G_=1_−∆G_=0|||-0.3445<br>(0.3992)|
|_B: Group defned by year of st_|_udy_|||
|Control group|61.0930|60.7804|-0.3126|
||(0.1527)|(0.1332)|(0.2019)|
|Treatment group|58.5060|58.9179|0.4118|
||(0.1898)|(0.1266)|(0.2197)|
|ATT: <sup>ˆ</sup>_δDID_ =_∆G_=1_−∆G_=0|||0.7244**<br>(0.2984)|

_Source_ : Own calculations. _Notes_ : _∆G_ = _g_ = _E_ [ _Yi|Gi_ = _g, Ti_ = 1] _− E_ [ _Yi|Gi_ = _g, Ti_ = 0] is time change in OWM for group _Gi_ = _g ∈{_ 0 _,_ 1 _}_ . Standard errors in parentheses and significance levels are indicated as follows: *** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1.

non-parametric estimate of the average treatment effect on the treated (ATT: _δ_<sup>ˆ</sup> _DID_ = _∆G_ =1 _−∆G_ =0) is statistically significant. The ATT is equal to 0.72 percentage points, which implies that FPE increased academic performance by 0.72 percentage points. Taken together, these results indicate that the FPE effect is bounded between zero and 0.72 percentage points, at least in this nonparametric setting.

While these non-parametric results are intuitive, they may be biased by the differences in the composition of the treatment and control groups over time. One of the obvious differences between the control and treatment groups is age (see Table 2). Those in the treatment group are significantly younger than those in the control group, implying that they are from different age cohorts. If the younger cohort was in primary school during times of good economic performance, they possibly enjoyed better familial resources during their formative years compared to the older cohort. To the extent that human capital investments are more productive when made at an early stage (see Cunha and Heckman, 2009; Heckman and Mosso, 2014), the observed better performance of the treatment group is potentially due to the differences in investments (family wealth) enjoyed while young. Further, it is possible that the younger cohort was taught by young and motivated teachers in both primary and secondary school, hence their better performance in high school exit or COSC examinations (see Table 2). Therefore, the observed increase in academic performance post-FPE could actually be attributed to these factors, and not FPE. In the next Section, I estimate the FPE effect after controlling for these potential confounders. For example, I control for age fixed 21
effects to approximate the cohort effects on performance (Cabus and De Witte, 2011).<sup>14</sup>

# **6.2 Semiparametric DID estimation results**

In this section, I present the semiparametric estimates of the FPE effect after controlling for compositional differences between groups. The results are shown in Table 4, which shows both the overall and heterogeneous effects of FPE by gender and faculty (or program of study). Columns (1) and (2) show results when the treatment group is those in their first year of university (identifying the upper-bound effect), and columns (3) and (4) show results when the treatment is those aged 16-18 years old (identifying the lower-bound effect). Columns (1) and (3), report the estimates of the average effect of FPE when the treatment group is defined by year of study, and by age appropriate for year one of university studies, respectively. Columns (2) and (4) present results showing how the average effect of FPE varies across different groups of students (i.e. gender and faculty of study groups).

Looking at column (1) of Table 4, we can see that the, having controlled for groups’ compositional imbalances, the upper bound effect the FPE policy on academic achievement is 15.79 percentage points, which is statistically significant at 1 percent level. This implies that the FPE policy increased university academic performance of the beneficiaries by about 15.79 percentage points. Given the pre-FPE average performance of 59.76 percent, this increase represents a 26 percent increase in academic performance at the university level, which is economically significant. If we look at column (3), however, we can see that the lower bound effect of FPE on academic performance is 2.94 percentage points (or 0.5 percent), which is economically and statistically insignificant. Therefore, these results indicate that the FPE effect is effectively bounded between zero and 16 percentage points. It is important to note that, apart from the differences in the effect size, these semiparametric results are consistent with the non-parametric results presented above. This gives us assurance that the FPE policy did not cause a decline, but an increase, in academic performance. The results are consistent with those of Xiao _et al._ (2017) who found long lasting positive effects of a free and compulsory education program in China.

In standard deviations form, the FPE lower bound effect is 0.13 standard deviations, while the FPE upper bound effect is 0.82 standard deviations. To put these results into perspective, the short-run class size effect estimated by Fredriksson _et al._ (2013) is 0.23 standard deviations and the estimated long-run effect of free and compulsory education on math performance by Xiao _et al._ (2017) is 0.101 standard deviations. Therefore, the lower bound effect is comparable to these other estimates in the literature, while the upper bound is almost eight times larger than Xiao _et al._ (2017)’s estimate, for example.

Turning to the columns (2) and (4) on the heterogeneous effects of FPE by gender and faculty

> 14The standard DID results are presented in Table A.3, and are largely consistent with the nonparametric results except that they are not statistically significant (see columns (1) and (2)).

22
Table 4: Long-term Effect of FPE on Educational Achievement

|VARIABLES|Treatmen<br>First year|t group:<br> students.|Treatm<br>16-18|ent group:<br> year olds|
|---|---|---|---|---|
||(1)|(2)|(3)|(4)|
|_Total ATT of FPE_<br>|||||
|ATT (<sup>ˆ</sup>_δSDID_)|15.7940***|19.3648***|2.9394|2.3894|
||(2.3166)|(5.5198)|(3.0303)|(8.4694)|
||[3.4080]|[6.4826]|[7.8675]|[18.5473]|
|_Heterogenieties of FPE efect_|||||
|female||0.9700||4.8939|
|||(4.9266)||(6.7208)|
|||[5.6126]||[11.5040]|
|Agriculture||-6.3270||-56.5824***|
|||(9.3363)||(17.3100)|
|||[11.4092]||[26.0263]|
|Health Sciences||11.5125||-18.5925|
|||(8.6084)||(13.2479)|
|||[9.2857]||[27.0102]|
|Humanities||6.1071||46.2779|
|||(9.8383)||(11.4773)|
|||[10.6054]||[32.7043]|
|Law||-11.2598||7.0008|
|||(9.9782)||(13.1108)|
|||[11.8654]||[21.3546]|
|Science & Technology||-15.1297**||-10.4212|
|||(7.8899)||(10.4535)|
|||[7.4746]||[19.2751]|
|Social Sciences||-9.5815||-4.8977|
|||(5.8828)||(8.4315)|
|||[7.0641]||[16.1814]|
|Observations|9,274|9,274|6,127|6,127|

_Notes_ : The point estimates of the FPE effect on achievement (OWM) and standard errors in parentheses are produced using `asdid` Stata command by Houngbedji (2016). Bootstrapped standard errors, clustered by high school attended, in brackets with 1000 replications, and significance levels are indicated as follows: *** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1. Models (1) and (3) report estimates of the average ATT. Models (2) and (4) show how the ATT varies across different groups of students. All models are estimated using a linear polynomial function of degree 4 to approximate the propensity score. The covariates used in the estimation of the propensity score are APS, gender, district, and age dummies to approximate the cohort effects.

23
(or program of study), we can see from Table 4 that the effect of FPE on student achievement is bounded between zero effect to 19.36 percentage points increase on students achievement. The upper bound slightly increases in this case, but not by a significant margin. More importantly, there are no noticeable heterogeneities by gender. This implies that FPE policy has affected academic performance of females and males equally. However, the effect of FPE varies by program of study. For instance, looking at column (2) results, we notice that, post-FPE, academic performance of students doing science and technology programs is 4 percentage points (i.e. 19 _._ 36 _−_ 15 _._ 13) lower than that of a typical student, this effect is significant at 5 percent. Further, we can see from column (4) results that the program decreased academic performance of those in the faculty of agriculture.

The faculties of agriculture, health sciences, and science and technology have exactly the same entry requirements, the most important being a good COSC pass in mathematics and sciences. Therefore, while these results seem to suggest that FPE-treated students are less prepared on mathematics and science subjects, they likely reflect the effect of discontinuing the bridging program for students into these faculties (or programs), known as the pre-entry science program (PESP), in 2012.<sup>15</sup> In the next section, I test the sensitivity of the results against this potential confounder.

# **6.3 Robustness checks**

In this section, I present a number of robustness checks’ results. First, I show that the results are less likely to have been driven by selection bias. Second, I present the placebo test results, using the pre-FPE data, assuming that FPE was introduced in 1999, such that the first FPE-treated cohort entered university in 2011. Third, I narrow the age window to include only students aged between 18 and 22 years old. Fourth, I present the semiparametric DID results controlling for some confounding factors, particularly the discontinuity of PESP at NUL, which affected all students doing physical science-based programs. Lastly, I present the doubly robust DID estimates that are robust to misspecification in either the propensity score ( _π_ 0( **X** _i_ ) _≡ P_ ( _D_ = 1 _|_ **X** _i_ )) or the outcome regression models for _E_ [ _Yit|D_ = _d, T_ = _t,_ **X** _i_ ],<sup>16</sup> following Sant’Anna and Zhao (2020).

## **6.3.1 Who entered the university post FPE?**

Given that I use university administrative data, which are not representative of the population, one basic concern could be that the students who got admitted into university post FPE program are different from those admitted pre-FPE in a number of ways. First, it could be that post FPE program, the number of those completing secondary school and qualifying for university entrance

> 15I explain the PESP program in detail below.

> 16Sant’Anna and Zhao (2020) shows that the outcome regression DID estimator is given as _δ_ ˆ _DID_ = _Y_ ̄1 _,_ 1 _−_ ̄ � _Y_ 1 _,_ 0 + _n_<sup>_−_</sup> _treat_<sup>1</sup> � _i|Di_ =1<sup>(ˆ</sup><sup>_μ_0</sup><sup>_,_1(</sup><sup>**X**</sup><sup>_i_)</sup><sup>_−μ_ˆ0</sup><sup>_,_0(</sup><sup>**X**</sup><sup>_i_))</sup> �, where _Y_<sup> ̄</sup> _d,t_ = _n_<sup>_−_</sup> _d,t_<sup>1</sup><sup>_·_�</sup> _i|Di_ = _d,Ti_ = _t_<sup>_Yit_is the sample average outcome for</sup> ˆ treatment group _d_ units in time _t_ , and _μd,t_ ( **X** _i_ ) is the estimator for _md,t_ = _E_ [ _Yit|D_ = _d, T_ = _t,_ **X** _i_ ].

24
Figure 7: School attendance and Secondary School or Higher Education Completion <!-- Start of picture text --> Secondary School Completion School attendance<br>.4 1<br>2008<br>2014<br>95% CI<br>.8<br>.3<br>.6<br>.2<br>.4<br>.1<br>.2<br>2008<br>2014<br>95% CI<br>0 0<br>5 10 15 17 20 24 25 5 10 15 17 20 24 25<br>Age Age<br>Proportion attending school<br>Proportion with secondary or higher education<br><!-- End of picture text --> _Source_ : Own calculations using the 2008 and 2014 Lesotho Demographic Health Survey data. _Notes_ : Household survey weights have been used to get the age-specific proportions.

increased. Therefore, without an increase in its capacity, the university may have admitted the best students from a larger pool of qualifying students compared to the pre-FPE period. This would overstate the real impact of the FPE program on achievement. Second, it could be that the pre- and post-FPE cohorts that got admitted into the university differ by household wealth. Specifically, the post-FPE cohort could be poorer than the pre-FPE cohort, which would likely attenuate the FPE program effect. Therefore, I use a nationally representative data from the 2008 (pre-FPE period) and 2014 (post-FPE period) Lesotho Demographic Health Surveys (LDHS) in order to make sense of who actually got into university pre- and post-FPE.

The left panel of figure 7 shows the proportion of individuals who have completed secondary or higher education by age, pre- and post-FPE, and the right panel of the figure shows the enrollment rates by age, pre- and post-FPE. In 2014, the first age-appropriate FPE cohort to enter the university was aged 20 years old. We can see from the left panel of figure 7 that, pre- and postFPE, the age-specific probability of completing secondary or higher education is statistically equal for those aged 21 and below. The right panel of the figure further shows that the enrollment rates of those aged between 14 and 24 years are statistically equal pre- and post-FPE. Taken together, this implies that the pool of potential university applicants did not increase significantly post-FPE. It is, therefore, less likely that the university could have admitted students from the very top end of the achievement distribution of all qualifying students post-FPE compared to those admitted 25
Table 5: Secondary school completion and Completed years of education

||(1)|(2)|
|---|---|---|
|VARIABLES|Secondary Completion|Years of Education|
|year2014|0.0058|0.4973**|
||(0.0282)|(0.2398)|
|Household-poor (omitted = poorer)|0.0081|1.3286***|
||(0.0083)|(0.1570)|
|Household-middle|0.0469***|2.4016***|
||(0.0101)|(0.1597)|
|Household-rich|0.0808***|3.4853***|
||(0.0125)|(0.1700)|
|Household-richer|0.2359***|5.0930***|
||(0.0208)|(0.1992)|
|Household size|-0.0028**|-0.0305**|
||(0.0014)|(0.0122)|
|female|0.0379***|2.9445***|
||(0.0086)|(0.1397)|
|year2014_×_Household-poor|0.0046|-0.0849|
||(0.0123)|(0.1629)|
|year2014_×_Household-middle|0.0103|-0.3457**|
||(0.0140)|(0.1641)|
|year2014_×_Household-rich|0.0176|-0.6085***|
||(0.0211)|(0.2011)|
|year2014_×_Household-richer|0.0323|-0.5967**|
||(0.0325)|(0.2546)|
|female_×_Household-poor|0.0016|-0.7557***|
||(0.0108)|(0.1621)|
|female_×_Household-middle|0.0122|-1.0507***|
||(0.0126)|(0.1500)|
|female_×_Household-rich|0.0220|-1.4964***|
||(0.0144)|(0.1639)|
|female_×_Household-richer|-0.0035|-2.1604***|
||(0.0215)|(0.1866)|
|year2014_×_female|0.0291***|-0.1402|
||(0.0112)|(0.1038)|
|Constant|-0.0455|3.9527***|
||(0.0407)|(0.3609)|
|Observations|16,259|16,259|
|R-squared|0.193|0.327|

_Notes_ : Linearized (svy) standard errors in parentheses and significance levels are indicated as follows: *** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1. Other included controls are age dummies, location and its interaction with household wealth, gender of household head, marital status, and household relationship structure. The sample is those aged 16 to 24 years.

26
pre-FPE.

Further, I present evidence in table 5 to show that the pre- and post-FPE cohorts do not come from different wealth groups, and even if they do, such differences would attenuate rather than overstate the FPE effect. Column (1) of the table presents the determinants of the probability of completing secondary or higher education, while column (2) presents the determinants of completed years of education. From column (1), we can see that, all else constant, the probability of completing secondary or higher education did not increase post-FPE. And the interaction of year and household wealth dummies indicates that, while household wealth increases the chances of completing secondary or higher education, the influence of household wealth did not change post-FPE. That is, pre- and post-FPE cohorts come from the same wealth groups.

From column (2), we can see that, everything held constant, 16-24 year-old children completed 0.5 more years of schooling post-FPE and those from wealthier households completed more years of schooling. However, the influence of household wealth on completed years of schooling attenuated post-FPE as indicated by the negative coefficients on year-wealth interaction dummies. The gap in completed years of education between those from rich and poor households was reduced. Consequently, if those who completed more years of education are the ones more likely to proceed to acquire higher education, the pool of students admitted into university post FPE is relatively poor compared to that admitted pre-FPE. This may have downward biased the FPE effect. Thus, taken together, the estimated effect could not have been an artefact of pre- and post-FPE differences in student composition.

# **6.3.2 Pre-FPE effect of FPE on student academic performance**

Here I estimate the placebo FPE effect using the pre-FPE data (i.e. 2010-2011), assuming that the FPE-treated first enrolled in university in 2011. Because the FPE-treated students were not at the university in those years, we do not expect to see any positive placebo FPE effect on performance because, if there is, it would imply that the observed increase in academic performance post-FPE presented in Table 4 cannot be attributed to FPE. It would imply that academic performance is simply continuing its upward trend post-FPE. The results are reported in Table 6. Looking at column (1) results, we can see that, pre-FPE, there was no statistically significant increase in academic performance. The results in column (2) indicate that, in fact, academic performance was on the decline pre-FPE, although the decline is statistically insignificant. Taken together, these results, therefore, indicate that the observed significant increase in academic performance post-FPE is indeed attributable to FPE, not some positive time trend.

# **6.3.3 Narrow age range (18-22 years old sample)**

Given the school entry age of 6 years, the 18 to 22 year olds are the age appropriate cohort for undergraduate university level. Further, narrowing the age range of the sample increases the 27
Table 6: Long-term Effect of FPE on Educational Achievement: pre-FPE (placebo) effect

|VARIABLES|(1)<br>Treatment group:<br>First year students|(2)<br>Treatment group:<br>16-18 year olds|
|---|---|---|
|ATT (<sup>ˆ</sup>_δSDID_)|3.3336|-11.5052|
||(3.6820)|(4.6691)|
||[4.6907]|[8.2950]|
|Observations|3,827|2,409|

_Notes_ : The point estimates of the FPE effect on achievement (OWM) and standard errors in parentheses are produced using `asdid` Stata command by Houngbedji (2016). Bootstrapped standard errors, clustered by high school attended, in brackets with 1000 replications, and significance levels are indicated as follows: *** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1. All models are estimated using a linear polynomial function of degree 4 to approximate the propensity score. The covariates used in the estimation of the propensity score are APS, gender, district, and age dummies to approximate the cohort chances that the treatment and control groups were in primary and high school at the same times, though in different grades. This then makes it likely that they have experienced more or less the same teacher and school resource inputs, other than no fee school attendance and free textbooks. We, therefore, can expect the FPE effects to be stronger within this age range. The results are presented in Table 7. Indeed we can see from the table that the FPE effect estimates on academic performance, in columns (1) and (2) are slightly larger than those reported in Table 4 (the main results), although with large bootstrapped standard errors. Nonetheless, these results indicate that the main results are not sensitive to sample restrictions.

# **6.3.4 Discontinuity of the Pre-Entry Science Program (PESP)**

The university began running the Pre-Entry Science program (PESP) in 1996 with the aim of bridging the knowledge gap between high school and university science and mathematics education, and ultimately enhance students’ performance in science programs. During the PESP period, all students admitted into science programs would have to go through PESP, where they would be taught science subjects - biology, chemistry, mathematics, and physics - and English. And all those who would have completed the PESP would now proceed to enroll into what was known as the common first year of science programs.

However, due to financial constraints, PESP was discontinued in 2012. To counter the potential negative effects of this on students’ performance, the Faculty of Science and Technology, which used to run the PESP and the common first year program, employed extra staff and extended the first year program’s academic year by two (2) weeks. These two policy shocks coincided with the entry of the first FPE cohort into the university (i.e. the FPE policy), and will likely bias the 28
Table 7: Long-term Effect of FPE on Educational Achievement: Narrow age range (18-22)

|VARIABLES|(1)<br>|(2)<br>|
|---|---|---|
||Treatment group:<br>First year students|Treatment group:<br>16-18 year olds|
|ATT (<sup>ˆ</sup>_δSDID_)|19.8659|3.7067|
||(3.8932)|(2.1174)|
||[100.3128]|[15.0155]|
|Observations|10,032|3,943|

_Notes_ : The point estimates of the FPE effect on achievement (OWM) and standard errors in parentheses are produced using `asdid` Stata command by Houngbedji (2016). Bootstrapped standard errors, clustered by high school attended, in brackets with 1000 replications, and significance levels are indicated as follows: *** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1. All models are estimated using a linear polynomial function of degree 4 to approximate the propensity score. The covariates used in the estimation of the propensity score are APS, gender, district, and age dummies to approximate the cohort overall FPE on academic achievement.

Therefore, as a robustness check, I control for this potential confounding factor by removing all PESP affected students from the Faculties of Agriculture, Health Sciences, and Science and Technology, and estimate the FPE effect on academic achievement. The results are reported in table 8. We can see from this table that, similar to the main results, the upper bound effect of FPE is positive and the lower bound effect of FPE is negative but are statistically insignificant with large bootstrapped standard errors. It is clear, therefore, that the effect of FPE program is not driven by the PESP discontinuity, and the resulting increase in employment and teaching time.<sup>17</sup>

# **6.3.5 Doubly Robust DID estimates**

If the propensity score is mis-specified, the semiparametric (inverse probability weighted) DID estimates are biased (Sant’Anna and Zhao, 2020). Therefore, to check the sensitivity of the results to potential misspecification of the propensity score, I use the Doubly Robust (DR) DID estimator proposed by Sant’Anna and Zhao (2020). Under repeated cross-section framework, as in the current case, Sant’Anna and Zhao (2020) provide the following two DR DID estimands that are consistent and locally semiparametrically efficient;

> 17The standard DID results presented in table A.3- see columns (3) and (4) - are consistent with the results presented here.

29
Table 8: Long-term Effect of FPE on Educational Achievement: Without PESP-affected students

|VARIABLES|(1)<br>|(2)<br>|
|---|---|---|
||Treatment group:<br>First year students|Treatment group:<br>16-18 year olds|
|ATT (<sup>ˆ</sup>_δSDID_)|16.7749|-3.5147|
||(3.7257)|(3.1510)|
||[10.5722]|[15.3209]|
|Observations|9,946|3,893|

_Notes_ : The point estimates of the FPE effect on achievement (OWM) and standard errors in parentheses are produced using `asdid` Stata command by Houngbedji (2016). Bootstrapped standard errors, clustered by high school attended, in brackets with 1000 replications, and significance levels are indicated as follows: *** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1. All models are estimated using a linear polynomial function of degree 4 to approximate the propensity score. The covariates used in the estimation of the propensity score are APS, gender, district, and age dummies to approximate the cohort and where 1 _{T_ = _t}_ is an indicator function that equals 1 event in the braces is true, _μ_<sup>_rc_</sup> _d,Y_<sup>(</sup><sup>_T,_</sup><sup>**X**</sup><sup>_i_) =</sup> _T · μ_<sup>_rc_</sup> _d,_ 1<sup>(</sup><sup>**X**</sup><sup>_i_) + (1</sup><sup>_−T_)</sup><sup>_· μrc_</sup> _d,_ 0<sup>(</sup><sup>**X**</sup><sup>_i_),and</sup><sup>_μrc_</sup> _d,t_<sup>(</sup><sup>**X**</sup><sup>_i_)istheoutcomeregressioninrepeatedcross-section</sup> settings.

Table 9 presents the results. Panel A reports traditional DR DID estimates that are DR consistent and locally semiparametrically efficient. Panel B reports DR DID estimates that are DR consistent, locally semiparametrically efficient, and DR efficient (i.e. they are efficient under misspecification in either the outcome model, _μ_<sup>_rc_</sup> _d,t_<sup>(</sup><sup>**X**</sup><sup>_i_),orthepropensityscore,</sup><sup>_π_(</sup><sup>**X**</sup><sup>_i_)).</sup> We can see from panel A of the table that DR estimates are positive and statistically significant when the treatment group is defined as the first year students (the upper bound effect). We observe the same in panel B. For example, the results from column (1) of panel A indicate that the FPE program increased students academic performance by between 0.77 percentage points (or 1 percent) and 2.89 percentage points (or 5 percent). In standard deviations, the FPE effect is bounded between 0.03 and 0.15 standard deviations. While these effects are economically smaller than those reported in the main results table, they are consistent in terms of the direction of the 30
Table 9: Long-term Effect of FPE on Educational Achievement: DR DID estimates

|VARIABLES|(1)<br>|(2)<br>|
|---|---|---|
||Treatment group:<br>First year students|Treatment group:<br>16-18 year olds|
|Panel A: Traditio<br>|nal DR DID estimates||
|ATT (<sup>ˆ</sup>_δDRDID_)|2.8628***<br>(0.8439)<br>[1.1369, 4.5888]|0.7666<br>(0.5148)<br>[-0.3085, 1.8416]|
|Observations|14,095|14,095|
|Panel B: Improve|d DR DID estimates||
|ATT (<sup>ˆ</sup>_δDRDID_)|5.7425***<br>(0.8318)<br>[1.4052, 10.0798]||
|Observations|14,095||

_Notes_ : The point estimates of the FPE effect on achievement (OWM) and standard errors in parentheses are produced using `DRDID` R code by Sant’Anna and Zhao (2020). Bootstrapped standard errors with 1000 replications are in parentheses. 95% Confidence intervals in brackets. Significance levels are indicated as follows: *** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1. The covariates used in the estimation of the propensity score are APS, gender, district, and age (age dummies in the first column to approximate the cohort effects, and age and age squared in the second column). Panel A reports traditional DR DID estimates that are DR consistent and locally semiparametrically efficient. Panel B reports DR DID estimates that are DR consistent, locally semiparametrically efficient, and DR efficient (i.e. they are efficient under misspecification in either the outcome model or the propensity score).

# **6.4 Potential mechanisms**

So far, I have not specified any possible channels through which FPE program generates these positive effects. This section attempts to narrow down on the possible causal channels through which the observed positive effects the program could have emerged based on figure 4 and previous research.

It is well documented in the literature that elimination of user-fees leads to an increase in access to schooling and, conditional on teacher recruitment, increases pupil teacher ratio (PTR) (see Grogan, 2009; Chyi and Zhou, 2014; Moshoeshoe _et al._ , 2019). And high PTR, especially due to an influx of poor children coming to school, leads to a decline, or at the most no change, in academic performance, holding all else constant (see Case and Deaton, 1999; Lucas and Mbiti, 2012). Similarly, building more schools, holding teacher recruitment constant, leads to an increase in access and PTR, and hence a decrease in academic achievement.

Furthermore, conditional on enrollment and teacher quality, increasing access to textbooks leads to an increase, at least not a decline, in academic achievement (see Glewwe _et al._ , 2009; 31
Fr ̈olich and Michaelowa, 2011; Kuecken and Valfort, 2013). And the increase in teacher quality (i.e. teacher level of qualification and years of experience) can increase, but not decrease, academic achievement (Glewwe _et al._ , 2011; Harris and Sass, 2011; Chetty _et al._ , 2014).

Following the introduction of the FPE program, there was a decline in PTR, an increase in students’ textbook ownership, and an increase in teacher qualification and years of professional training (Moshoeshoe, 2015). Further, Moshoeshoe (2019) shows that academic achievement of six graders increased between 2000 (pre-FPE) and 2007 (post-FPE), and this increase was partly attributable to the fall in PTR. Therefore, the increase in teacher employment likely contributed to the increase in academic achievement at primary school level.

Taken together, therefore, it is less likely that the positive FPE program effects documented in this paper are due to fee eliminations. The progressive implementation of the fee eliminations allowed the government to plan for the influx by recruiting more teachers and building more schools, which potentially enabled teachers to adjust their teaching strategies, as they learn, to effectively reach low-ability and/or poor students. These additional program components, individually and in complementarity with each other, are the likely drivers of the positive FPE program effect on academic achievement. For instance, while the school building component of the FPE program is less likely to have contributed to the increase in academic achievement individually, it was potentially complemented by teacher recruitment and textbook provision to positively affect achievement. And because skill begets skill, this led to an increase in academic achievement at university level.

# **7 Conclusion**

This paper examines the long-term effect of Free Primary Education policy on educational achievement, and how this varies by gender. The results indicate that the effect of FPE on educational achievement at university level is bounded between 2 percentage (which is statistically insignificant) and 20 percentage points (which is statistically significant at 1 percent). I do not find any FPE effect heterogeneities by student gender, but the effect varies by faculty or program of study.

In countries where the FPE policy was introduced simultaneously for all grades, it was found that education quality declined, at least in the short run (see Lucas and Mbiti, 2012). However, in countries where no user-fees programs have been implemented progressively across the country, like the rural China’s free and compulsory education reform program, there are positive longrun effects on education quality (Xiao _et al._ , 2017). The results suggest that other Sub-Saharan African countries that are yet to implement free education programs can potentially increase their chances of meeting the SDG goal of inclusive and equitable education quality for all if they replicate Lesotho’s FPE implementation approach. Further, these results provide important policy lessons to many countries (e.g. Tanzania) that are implementing (or contemplating to implement) free secondary or lower secondary education programs.

32
This paper is not without limitations. As highlighted earlier, the FPE program in Lesotho is a true package of supply and demand side programs all geared towards achieving quality education for all. Therefore, while these results are interesting, they must be interpreted with caution: they do not show the effects of just fee eliminations. As we have seen in figure 3, maybe in anticipation of the influx into the secondary schooling system, secondary school resources increased from 2005. These results are partly attributable to resource increase at the secondary school level. Second, the study sample is a very select group of smart students who are potentially from rich households. Nonetheless, these results are informative in that they show how the program has affected this group.

Furthermore, I cannot completely rule out the possibility that the FPE treated group worked harder than they would have in order to compensate for the perceived lower education quality they received under FPE. That is, there could have been a Hawthorne effect. In addition to this, it is also possible that secondary school teachers may have doubled their effort when teaching the FPE cohort for the same reasons of perceived primary school education. While these are real threats to the validity of the results, nothing indicates that there has been any of these coordinated responses by students and/or teachers that could have biased the results this way. Further research is still needed to tease out the pathways through which the FPE policy increased students academic performance.

33