WPS7384
Policy Research Working Paper 7384
The Impact of Secondary Schooling
in Kenya
A Regression Discontinuity Analysis
Owen Ozier
Development Research Group
Human Development and Public Services Team
August 2015
Policy Research Working Paper 7384
Abstract
This paper estimates the impacts of secondary school on to estimate these impacts. The results show that secondary
human capital, occupational choice, and fertility for young schooling increases human capital, as measured by perfor-
adults in Kenya. The probability of admission to government mance on cognitive tests included in the survey. For men,
secondary school rises sharply at a score close to the national there is a drop in the probability of low-skill self-employment,
mean on a standardized 8th grade examination, permitting as well as suggestive evidence of a rise in the probability of
the estimation of causal effects of schooling in a regression formal employment. The opportunity to attend second-
discontinuity framework. The analysis combines adminis- ary school also reduces teen pregnancy among women.
trative test score data with a recent survey of young adults
This paper is a product of the Human Development and Public Services Team, Development Research Group. 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
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The author may be contacted at oozier@worldbank.org.
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The Impact of Secondary Schooling in Kenya:
A Regression Discontinuity Analysis∗
Owen Ozier†
Development Research Group
The World Bank
∗
I am indebted to Lori Beaman, Blastus Bwire, Pascaline Dupas, Esther Duflo, Steve
Fazzari, Frederico Finan, Sebastian Galiani, Justin Gallagher, Francois Gerard, Erick
Gong, Joan Hamory Hicks, Guido Imbens, Gerald Ipapa, Pamela Jakiela, Seema Jay-
achandran, Pat Kline, Michael Kremer, Ashley Langer, Karen Levy, Isaac Mbiti, Jamie
McCasland, Justin McCrary, Edward Miguel, Salvador Navarro, Carol Nekesa, Rohini
Pande, Bruce Petersen, Robert Pollak, Jon Robinson, Alex Rothenberg, and Kevin Stange,
as well as conference and seminar participants, for their helpful comments. All errors are
my own.
†
Please direct correspondence to oozier@worldbank.org.
1 Introduction
The expansion of schooling in Sub-Saharan Africa over the last 50 years
has made basic education more accessible to many of the world’s poorest:
between 1970 and 2005, average schooling attained by young Africans rose
from 2.6 years to 6.1 years, and continues to grow.1 Increases in educational
participation and attainment have coincided with rising literacy and formal
sector employment across the continent, though the direction of causality is
not clear. Wage returns to education have been shown in other developing
country contexts (Duflo 2001), but similar patterns have not been demon-
strated as convincingly in Africa. One complicating factor is that rates of
employment are quite low. In 2008, for example, only 38 percent of Kenyan
men were employed by someone outside their family.2 In this context, the
effects of education on human capital accumulation, occupational choice,
and fertility decisions may in fact be more socially relevant measures of the
returns to schooling than wage effects.
Most empirical studies find little evidence that African schools have pos-
itive effects on outcomes. Two recent papers find no positive academic ef-
fects at all: Lucas and Mbiti (2014) show that admission to higher quality
secondary schools in Kenya neither raises the probability of completing sec-
ondary school, nor increases 12th grade test scores; de Hoop (2010) estimates
that admission to a higher quality secondary school in Malawi increases the
probability of remaining enrolled in an assigned school, but has no effect on
test scores. These studies, however, only measure the change in academic per-
1
Source: Barro and Lee (2010), tabulation based on 33 countries in sub-Saharan Africa.
2
Source: DHS (2009). This includes all age groups and covers both rural areas and
urban centers.
2
formance brought about by increases in secondary school quality. One might
reasonably expect the effect of attending any secondary school to differ from
the effect of increased school quality. The rise in primary school comple-
tion associated with the achievement of the Millennium Development Goals
means that a large cohort is about to reach the age of secondary schooling,
which until now has been rationed in much of Sub-Saharan Africa. Despite
the policy urgency of this issue, few studies to date have identified the ef-
fect of relaxing this constraint: the impact of secondary schooling on the
marginal student in low-income country contexts.3 A rare exception, Filmer
and Schady (2014), found that scholarship-driven attendance of lower sec-
ondary school in Cambodia had no effect on either test scores or fertility
choices.
In this paper, I use a regression discontinuity approach to estimate the
impacts of secondary schooling in Kenya. The discontinuity I use is based
on a standardized 8th grade test, the Kenya Certificate of Primary Educa-
tion (KCPE). Probability of admission to government secondary school rises
sharply at a cutoff score close to the national mean on the examination. I col-
lect an administrative KCPE dataset, and combine it with a recent, detailed
survey of young adults in Kenya that includes educational attainment, along
with a number of other outcomes. With these two datasets, I use a technique
from time series econometrics to identify the structural breaks in patterns
of secondary school completion, thereby locating the test score cutoffs in
Kenya’s secondary school admission policy. I am able to confirm that the
3
Lucas and Mbiti (2012) find that the increased school participation in Kenya brought
about by the abolition of primary school fees actually reduces average test scores, with
composition effects explaining less than half the decline. This, however, is a very different
population from those who are on the margin of attending secondary school.
3
KCPE score popularly perceived to constitute “passing” the examination is
empirically the most important for boys, while a slightly lower cutoff is more
relevant for girls. This is consistent with a recent survey of local secondary
school administrators, who report lower admissions criteria for girls.
At the admissions cutoff, I find a 15 percent jump in the probability of
completing high school. This is a large effect compared to many commonly
used instruments for education. I perform relevant specification tests, and
find that this effect is significant and stable across a range of specifications,
bandwidths, controls, and sample restrictions.
Students on either side of the admissions cutoff are very similar demo-
graphically, and in a neighborhood of the test score cutoff, admission to
secondary school is “as good as randomized” (Lee 2008). This allows me
to treat the rise in schooling at the admissions cutoff as a source of exoge-
nous variation for estimating the impact of secondary school. I find that
completing secondary school has a substantial impact on human capital ac-
cumulation, as measured by performance on vocabulary and reasoning tests
in adulthood. I estimate a performance improvement of 0.6 standard devi-
ations attributable to the completion of secondary school. This is the first
paper to show such positive effects of secondary schooling in Africa.
For labor market outcomes, I consider rates of employment and low-
skill self-employment. I find clear causal effects: for men in their mid-
twenties, completing secondary school decreases the probability of low-skill
self-employment by roughly 50 percent. There is also suggestive evidence
of a 30 percentage point increase in the probability of formal employment,
though this is not significant in all specifications. It is important to note that
4
most self-employment in this context is not innovative entrepreneurship. In-
stead, it is what Lewis (1954) refers to as “casual labour” or “petty trade;”
it is the transition away from this sector that marks economic development
(Lewis 1954, p.189).
I also find that secondary schooling causes a sharp drop in the probability
of teen pregnancy. Studies of the correlation between education and fertility
have emphasized on a number of possible ramifications: human capital accu-
mulation in the next generation, rates of population growth, and household
bargaining, for example (Strauss and Thomas 1995). I establish a strong
causal effect of secondary schooling on early fertility, opening an avenue for
further study as this population grows older. While my estimates of the ef-
fect are relatively large, this sort of reduction is in accord with the findings of
e (2009) and Duflo, Dupas, and Kremer (forthcoming) in Kenya, as well
Ferr´
¨
as Baird, Chirwa, McIntosh, and Ozler (2010) in Malawi. This contrasts with
the recent work of McCrary and Royer (2011), who find that increases in ed-
ucational attainment in the US induced by age-at-school-entry rules have no
such impact; their instrument acts through a different channel on a different
subpopulation, however, partially explaining the difference in findings.
Thus, I show large effects of secondary schooling on a number of impor-
tant outcomes. A feature of this work, as compared to other recent studies
on secondary schooling in Africa, is that I estimate impacts on the marginal
student who attends secondary school. As a result, these estimates are di-
rectly interpretable as consequences of potential policy changes that would
make secondary school rationing less restrictive. The magnitude of these ef-
fects in a population of this age suggests that permanent differences may be
5
revealed as this cohort grows older, opening a clear avenue for further study.
An additional contribution of this paper is to show whether cross-sectional
analysis, controlling for available covariates, delivers estimates comparable to
the causal effects estimated in the regression discontinuity design. Follow-
ing the general approach of Altonji, Elder, and Taber (2005), I specifically
explore the stability of cross-sectional results in the framework suggested by
Oster (2015), with implications for other settings in which quasi-experimental
variation may not be available.
The remainder of the paper is organized as follows: Section 2 provides a
description of relevant facets of the Kenyan educational system, and the data
I use for estimation.4 Section 3 explains the estimation strategies employed
for different types of analysis. Section 4 presents the detailed specification
checks I carry out and the results of my analysis, Section 5 discusses the
robustness of cross-sectional analysis of the same questions, and Section 6
concludes.
2 Context and Data
Since 1985, the Kenyan education system has included eight years of primary
e 2009). At the end of
schooling and four of secondary (Eshiwani 1990, Ferr´
primary school, students take a national leaving examination, the KCPE. A
score of 50% or higher—currently 250 points out of 500—is considered to be
a passing grade. This examination is the chief determinant of admission to
secondary schools (Glewwe, Kremer, and Moulin 2009).
4
The data appendix provides additional details on the assembly of these datasets.
6
Those who are not admitted to any government school may choose to
re-take the examination the following year, or may consider schooling in
Uganda, vocational education, or private schools with different standards.
Though an official letter of admission to a government secondary school is
rare below this cutoff, it is still not guaranteed for those above it because
the number of candidates passing the KCPE may exceed the number of
spaces available in public schools (Aduda 2008, Akolo 2008). Among those
who are admitted to secondary school, however, many are still unable to
afford tuition and assorted fees: while primary school has been inexpensive
for many years, and was made nominally “free” in 2003, even the lowest-tier
district secondary schools cost hundreds of dollars per year during the period
observed in this study.5
2.1 Data: KLPS2 surveys
This admission rule suggests a fuzzy regression discontinuity design for es-
timating the impacts of secondary schooling. The primary dataset used in
this study is the Kenyan Life Panel Survey (KLPS), an ongoing survey of re-
spondents originally from Funyula and Budalangi Divisions of Busia District,
Kenya (Baird, Hamory, and Miguel 2008). The respondents were sampled
from the population attending grades 2 through 7 at rural primary schools
in 1998. The first round of surveying (KLPS1) was carried out from 2003 to
2005, while the second (KLPS2) ran from 2007 to 2009, both times track-
ing respondents across provincial and even national boundaries. Because the
5
Policy changes after 2008 made low-tier secondary schools considerably less expensive
in Kenya.
7
outcomes of interest occur only for adult respondents, I mainly use the more
recent round of survey data (KLPS2), treating it as cross-sectional data for
5,084 individuals.
The KLPS2 survey is comprehensive, including questions on education,
employment, and fertility, as well as cognitive tests. The education section
includes yearly school participation, from which secondary school completion,
grade repetition, and other measures can be constructed; it also includes
self-reported KCPE scores for students who complete primary school. The
cognitive tests administered as part of the survey assess English vocabulary
and non-verbal reasoning; the labor market section includes employment and
self-employment history, including the dates and sectors of employment, as
well as wages.6
In order to use a regression discontinuity design, I restrict analysis to
respondents reporting a KCPE score in the survey, which reduces sample
size from N=5,084 to N=3,305, including only pupils who complete primary
school and take the KCPE. Table 1 shows summary statistics for the re-
stricted KLPS2 sample. The 3,305 respondents reporting test scores have
higher educational attainment, more educated parents, and lower teen preg-
nancy rates than the full sample; this is to be expected, since these are the
respondents who did not drop out during primary school.
6
Non-verbal reasoning is measured using Raven’s Matrices, one of the more reliable
measures of general intelligence (Cattell 1971); the vocabulary instrument is based on the
Mill Hill test, originally designed by J. C. Raven to complement the Matrices.
8
2.2 Data: Test scores
While most KLPS variables are quite stable over survey rounds, self-reported
KCPE scores are not. Grade in school in 1999, for example, has a correlation
of 0.95 between responses given in KLPS1 and four years later in KLPS2,
while self-reported test score has a correlation closer to 0.7. The noise in test
scores could pose several problems, since I use KCPE score as the regression
discontinuity running variable.7 Noise in the form of classical measurement
error for only a random subset of the data would simply reduce the power
of the regression discontinuity design. Classical measurement error in all of
the data could eliminate the discontinuity entirely.8 On the other hand, non-
classical error could invalidate the regression discontinuity design, if either
mis-reporting or test repetition were driven by unobservables correlated with
outcomes.9 A histogram of the self-reported scores, in the upper left panel
of Figure 1, shows that the distribution of scores shows signs of non-classical
error, in the form of manipulation of the reported scores around the “passing”
point; a test for density smoothness proposed by McCrary (2008), shown in
the lower left panel, rejects at this point.
This feature of the distribution could arise simply from repeated test-
taking: if many of those who fail the test try again until they pass, the
distribution of most recent test scores could include more mass just to the
right of the cutoff than to the left.10 To see whether this phenomenon is
solely responsible for the shape of the distribution, I consider a slice of the
7
Some authors, such as Imbens and Lemieux (2008), refer to this as a “forcing variable.”
8
More detailed discussion of these points is provided in Appendix A.2.
9
See Martorell (2004) for discussion of multiple potential effects of test repetition.
10
See Appendix A.2 for a concrete example.
9
data, available in KLPS1, in which respondents provided every test score for
as many times as they had taken the KCPE. Even if the most recent test
score is endogenous with respect to the respondent’s type and the location
of the cutoff, the first test score should not be. Appendix Figure A2 shows
that although the problem is less severe in this restricted sample, even these
first scores do not have a smooth density at the discontinuity. However,
administrative data on scores in the region display no such irregularity at the
cutoff score, so I conclude that the self-reports are, in many cases, incorrect,
and administrative data must be matched to the KLPS2 dataset in order to
use a regression discontinuity design.11
To complement the KLPS data, I gathered an auxiliary dataset of 17,384
official KCPE scores from District Education Offices and, when the district-
level offices did not have the records, directly from primary schools. The
official records I was able to collect in 2009 and 2010 include roughly 88
percent of the KLPS schools during the years of interest in this study.12
Based on name, year, and school, I am able to cross-check KCPE scores for
roughly 77 percent of the KLPS respondents who report taking the KCPE.
While many self-reported scores are in accordance with the official records,
there is substantial misreporting.13
Using the 88 percent coverage of the administrative data I could collect, a
11
I show the distribution of regional 2008 test scores in Appendix A.3.
12
Every KLPS source school with missing records was visited at least once by me or
another member of the data collection team; recent re-districting and political upheaval in
Kenya, combined with local problems with record storage over the last 12 years, prevented
the collection of the last 12 percent.
13
I discuss the matching process and characterize misreporting in Appendix section
A.1.5.
10
matching algorithm14 is used to identify corresponding administrative records
for more than 2,500 of the 3,305 respondents reporting a score. For 2,273
respondents, I find exactly one test score; for 263 more, I find two scores in
different (typically consecutive) years. Using the KLPS2 survey to determine
whether matched scores are first or second attempts, I am able to clearly
identify 2,167 first test scores.15 Their distribution is plotted in the upper
right panel of Figure 1 and is tested for a density break in the lower right
panel. I find no evidence of manipulation of administratively reported first
test scores.
2.3 Gender-specific discontinuities
The KCPE cutoff for secondary school admission is well-known in Kenya;
national media recently reported that “Out of the over 695,000 candidates
who sat the KCPE examination, 350,000 candidates attained over 250 marks,
making them eligible to join secondary school.”16 However, a survey of sec-
ondary schools in the area suggests that, though 250 is the modal 2009 cutoff
score reported by school administrators, many competitive schools use higher
cutoffs.17 Further, many schools report different cutoffs for boys and girls:
seven out of eighteen reporting cutoff scores for girls report a value below
250. As such, 250 may not be the cutoff where the largest fraction of girls are
14
The procedure is described in Appendix A.1.5.
15
For some cases where I observer only one test score, it either appears to be a second
score, or it is unclear whether it is a first or second score. I exclude these when using only
first test score.
16
Excerpted from Akolo (2008).
17
Edward Miguel and Matthew Jukes, unpublished data (2009).
11
exogenously induced to attend secondary schools.18 To address these, I apply
a technique from the structural break literature, following Card, Mas, and
Rothstein (2008): I first restrict attention to a window of scores between 150
and 350 points on the KCPE exam; I then regress the outcome (completing
secondary school) on indicators for hypothetical discontinuities from 200 to
300 points and a piecewise linear control for KCPE score, one potential dis-
continuity at a time, separately for men and women. For each sex, I consider
the discontinuity whose regression produces the highest value of R2 to be the
“true” cutoff. Results are shown in Figure 2. For men, the R2 -maximizing
cutoff is 251 points rather than 250 (a close second place). For women, the
best cutoff in this sense is 234 points. Considering these to be the “true”
discontinuities, I use these values for the cutoff, c, in the specification checks
for the first stage and in the estimation that follows.19
18
Because the recent survey only included 2009 cutoffs, I re-visited secondary schools
to find out their history of admissions rules, but current school administrations were not
able to provide records of admissions rules covering the period of study in this paper.
19
Several features of this process are worth noting. Prior to Card, Mas, and Rothstein
(2008), this technique was also used in the context of schooling by both Kane (2003) and
Chay, McEwan, and Urquiola (2005). Estimation of the location of the discontinuity,
in the presence of a discontinuity, is super-consistent (Hansen 2000), and the error is
not asymptotically normally distributed; this is also evident in Monte Carlo simulations
using a data generating process designed to mimic the one I estimate here. Sampling
error in the location of the discontinuity can be ignored in estimation of the magnitude
of the discontinuity, so standard errors in subsequent estimation need not be adjusted
(Card, Mas, and Rothstein 2008). I use the same data for estimating the location of the
discontinuity as for estimating the impact on outcomes; Card, Mas, and Rothstein (2008)
have a much larger sample, and are able to use half the data to locate the discontinuity,
and the other half to estimate the rest of their model. Since my use of the data could
create an endogeneity concern, I carry out robustness checks (selected checks shown in the
Appendix) with the highest discontinuity for women below 250 reported by any surveyed
secondary school in the region—240 rather than 234—and the ex ante cutoff of 250 rather
than 251 for men. I obtain similar empirical results, though the first stage loses power
substantially for women.
12
3 Empirical Strategy
Consider an equation characterizing the causal relationship between whether
an individual completes secondary school, Seci , and outcome Yi :
Yi = π0 + π1 Seci + π2 KCP Ei + π3 Xi + εi (1)
Equation 1 controls for academic ability, proxied by KCPE score, KCP Ei ;
other observable individual characteristics, Xi ; and both a constant term
π0 and idiosyncratic error εi . Direct application of OLS to equation 1 may
lead to biased estimates of π1 for the usual reasons: measurement error in
educational attainment could bias coefficients downwards, while any positive
correlation between εi and Seci , perhaps due to unobserved ability, could
bias estimates upwards (Griliches 1977, Card 2001).
Instead, I use a regression discontinuity approach to identify the effect of
secondary school on outcomes. As described in Section 2, Kenyan students
who take the primary school leaving examination (KCPE) face an admission
rule: below a cutoff score, ci , it is more difficult to gain admission to sec-
ondary school. The identifying assumptions in my analysis are that all other
outcome-determining characteristics except for the probability of secondary
school attendance vary smoothly near the cutoff, and that outcomes change
at the cutoff only because of the induced change in schooling. Because the
probability of attendance does not jump from zero to one, this is a “fuzzy”
regression discontinuity (Imbens and Lemieux 2008), so the causal effect of
13
secondary school on outcomes is:
limk↓ci E [Y |KCP E = k ] − limk↑ci E [Y |KCP E = k ]
τF RD = (2)
limk↓ci E [Sec|KCP E = k ] − limk↑ci E [Sec|KCP E = k ]
As long as the order of polynomial in the running variable and the data
window are the same for the first and second stage outcomes, estimation
of τF RD in equation 2 is equivalent to an instrumental variables approach,
where the first and second stages are:
Seci = α0 + α1 Abovei + α2 Ki + α3 Ki · Abovei + α4 Xi + ζi (2a)
Yi = β0 + βF RD Seci + β2 Ki + β3 Ki · Abovei + β4 Xi + ξi (2b)
In equations 2a and 2b, I use normalized KCPE scores, Ki = KCP Ei − ci ,
shifted so that the discontinuity occurs at Ki = 0; the variable Abovei is equal
to 1 if Ki ≥ 0, and 0 otherwise; the parameter of interest is βF RD ; I allow the
relationship between Yi and Ki to have different slopes on either side of the
discontinuity. This is an estimation based on compliers, the population who
would not complete secondary school if they had scored below the cutoff,
but who would if they score above it. The estimated effect is a local average
treatment effect at the point in the test score distribution where the cutoff
falls. By definition, it is the policy-relevant cutoff for a policy change that
would consider moving the cutoff slightly and changing the number of avail-
able slots in secondary schools. In this case, however, the cutoff also falls very
near the median (and mean) of the test score distribution, which suggests
that the effects I measure are relevant for the median Kenyan KCPE-taker,
14
rather than for outliers in the education or skill distribution.20
3.1 Other estimation approaches
In the case of binary outcome variables, such as whether a respondent is
pregnant by age 18, a nonlinear instrumental variables approach may be
appropriate. In particular, I consider the IV probit, with the same first stage
given in equation 2a, but with second stage:
Pr [P reg 18i = 1] = Φ γ0 + γF RD Seci + γ2 Ki + γ3 Ki · Abovei + γ4 Xi (3)
The IV probit estimation procedure is only correctly specified when the first
stage residuals are asymptotically normally distributed, and when the first
stage is linear.21 An alternative, when the first stage outcome is binary, is
the bivariate probit (Maddala 1983):22
Seci = 1 (δ0 + δ1 Abovei + δ2 Ki + δ3 Ki · Abovei + δ4 Xi + τi > 0) (4)
Yi = 1 (φ0 + φ1 Seci + φ2 Ki + φ3 Ki · Abovei + φ4 Xi + ωi > 0) (5)
This approach uses Seci rather than Seci in the second stage, because it
explicitly models endogeneity through the correlation, ρ, between τi and ωi .
20
By contrast, many US studies relying on date-of-birth identification strategies are
focused on relatively low-achieving students; studies such as the work of Saavedra (2008)
in Colombia estimate the returns only to the highest-quality universities. Neither class of
coefficient is necessarily relevant for the bulk of the population.
21
A binary endogenous regressor would typically not yield asymptotically normal resid-
uals.
22
Maddala (1983) presents the model on pp. 122-3; Greene (2007) discusses the model
further on pp.823-6; Wooldridge (2002) also discusses it on p.478.
15
I follow Greene (2007) and others in imposing a bivariate normal distribution
on the error terms. Though in practice, IV probit and bivariate probit yield
marginal effects estimates that are often quite similar to those given by 2SLS,
they have the advantage that, when correctly specified, they can provide
greater statistical power when the probability of an outcome variable is very
close to either zero or one.23 The cost of this power is additional distributional
assumptions, however, so I present results from each of these estimation
techniques, when appropriate.
4 Results
4.1 Specification: bandwidth and polynomial order
For the first stage, I consider a window of data symmetric about the dis-
continuity, and regress completion of secondary school on an indicator for
scoring above the discontinuity and piecewise linear controls in test score. I
plot the resulting estimates of the discontinuity magnitude in the left panel
of Figure 3, as a function of the width of the data window; here, I scale down
scores by a factor of 100 so that coefficient estimates in subsequent tables are
read more easily. The discontinuity estimate fluctuates slightly, but remains
significant and of similar magnitude no matter which bandwidth I use.24 At
each bandwidth, I carry out a specification test in which in addition to the
discontinuity dummy and the piecewise linear controls, I include indicators
23
This can be shown in Monte Carlo simulations, for example.
24
Here I use the term bandwidth in the sense of Imbens and Lemieux (2008), Lee and
Lemieux (2010), and others in the regression discontinuity literature to mean the window
of data used for estimation; this is not a non-parametric regression; I do not weight data
differently according to distance from the discontinuity.
16
for narrow-width bins of KCPE scores: 251-260, 261-270, et cetera.25 I test
these indicators for joint significance; if they are significant, I consider the
piecewise linear first stage to be mis-specified. This test rejects for widths
of 90 points and higher on either side of the discontinuity. The same is true
when I include a piecewise quadratic control in test score. Thus, for the rest
of this paper, I use a bandwidth of 80 points on either side of the discon-
tinuity.26 Finally, I use Akaike’s information criterion to confirm that the
first-order polynomial control is sufficient: piecewise linear (as opposed to
constant, quadratic, cubic, or quartic) is the “best” specification according
to AIC for both the 80-point bandwidth and nearly all other bandwidths
under consideration. I use the same bandwidth and order of polynomial (lin-
ear) in both the first and second stage estimation, so that I can simply use
2SLS both for estimation and standard errors.27
I carry out validity tests of the smoothness assumption using observables,
four of which are depicted graphically in Figure 4. Gender, age, and mother’s
and father’s education vary smoothly at the boundary, with differences that
are neither large enough to be important nor statistically significant. This
contrasts with Urquiola and Verhoogen (2009), who show that schools’ re-
sponses to a class-size policy discontinuity in Chile can invalidate a regression
discontinuity research design. While they find large and significant differences
in parents’ education levels at the discontinuity (as well as sharp changes in
25
For this test, I follow Lee and Lemieux (2010) and Lee and McCrary (2009). The
results are similar when I vary bin width, for example using a width selected by a leave-
one-out cross-validation procedure.
26
Alternatively, I can use the procedure suggested by Imbens and Kalyanaraman (2012);
this yields similar “optimal” bandwidths for most outcomes, though smaller bandwidths
for a few. Results are largely unchanged.
27
See, in particular, Lee and Lemieux (2010) Section 4.3.3.
17
the class size histogram near cutoffs), I find no such patterns here.28
4.2 First stage: Discontinuity
The first stage discontinuity is shown in the upper-left pane of Figure 5,
and in a regression framework in Table 2.29 In Table 2, the discontinuity
is estimated first with genders pooled (columns 1-3), then separately among
men (columns 4-6) and women (columns 7-9). I show the results with and
without a piecewise quadratic control and controls for other covariates: age,
gender, parents’ education levels, and cohort dummies. I cannot reject that
the discontinuities for men and women are of the same magnitude, though
the smaller point estimate for women is consistent with the lower overall level
of secondary schooling for women in this setting. My preferred specifications
are given in columns (2), (5), and (8), in which the discontinuity is measured
as a 16-percentage-point change in the probability of completing secondary
school for men; a 13 percent change for women, and a 15 percent change when
28
See Section A.1.5 and the right panels of Figure 1. In particular, while I cannot rule
out all types of cheating on the KCPE, as in the Texas testing context investigated by
Martorell (2004), none of the known mechanisms for cheating on the exam would permit
endogenous sorting around the discontinuity.
29
In this case, because the data window constrains predictions to within the unit interval,
a logit or probit specification yields marginal effects that are almost identical in magnitude
and significance to the discontinuity estimated here in a linear probability model.
18
pooled.30 31
That controls do not substantially change the point estimate is
unsurprising, given that they do not change significantly at the discontinuity.
When the estimation is carried out separately by gender, the discontinuity
is significant for both men and women, but the F-statistic is now below the
rule of thumb for weak instruments for the subsample of women (Stock and
Yogo 2002)—though I cannot reject the equality of the discontinuities for
men and women. However, because the model is just-identified, the weak-
instruments bias towards OLS is not present (Angrist and Pischke 2009),
though tests may not be correctly sized.
In the right panel of Figure 3, I show the estimated difference between
the cumulative distribution functions for education of the populations on
either side of the discontinuity. For each point in the right panel, I esti-
mate a separate regression of the probability that respondents attain more
than x years of education on a piecewise linear control and an indicator for
the discontinuity; the plot shows the coefficients and confidence intervals
on the discontinuity for each of these outcomes. The KCPE discontinuity
30
Decomposition as suggested by Gelbach (forthcoming) shows that the change in co-
efficient magnitude from column (7) to column (9) is mostly due to the inclusion of the
covariate controls; the slightly larger standard error is brought about because of the in-
clusion of the piecewise quadratic in the running variable. A separate issue is that small
fraction of the sample is still in school; this fraction varies slightly at the discontinuity, and
as such, the completion of secondary schooling may be viewed as a censored outcome in
the first stage, which could be the source of some bias. In practice, restricting the sample
to respondents who are surveyed at least five years after they take the KCPE does not
substantially alter the results.
31
Also note that while I find a larger discontinuity for men than women, Uwaifo Oyelere
(2010) found that variation in free primary education in Nigeria predicts years of education
equally well for men and women. This could be because free primary school induces
additional schooling at too young an age for womens’ early marriage and fertility decisions
to be relevant, and would have been especially true in the period when Nigeria’s primary
education system was first coming into existence, included in Uwaifo Oyelere’s (2010)
analysis.
19
as an instrument clearly predicts secondary schooling, and moreover, sec-
ondary school completion. The estimates, however, drop to insignificance
when estimating the probability of attaining more than 12 years of school-
ing: the KCPE score that induces a marginal student to attend and complete
seondary school does not induce the student to attend college.
4.3 Estimation of outcomes
4.3.1 Human capital
I begin with analysis of the impact of schooling on human capital. The
KLPS2 survey includes a commonly used test of cognitive ability—a subset
of Raven’s Progressive Matrices—and an English-language vocabulary test
based on the Mill Hill synonyms test. Adaptations of both measures have
been used internationally for several decades, and each captures different
aspects of intelligence.32 I standardize both outcomes so that they are mea-
sured in terms of standard deviations in the KLPS2 population, and show
both OLS and 2SLS results for a combined Z-score33 and separately by test
in Panel A of Table 3: completing secondary school improves performance
on these tests by 0.6 standard deviations, with very similar estimates given
32
Though standardized to have mean zero and standard deviation one in the population,
in Table 1 these two cognitive measures have positive mean and standard deviations slightly
less than one, because these summary statistics are only shown for the sample with a
restricted range of first KCPE scores. The “Matrices” are often considered to measure
something akin to “fluid” intelligence, while the vocabulary test measures something more
related to what specialists in the field call “crystallized” intelligence (Cattell 1971). The
relationship of the two measures appears similar here to in other settings: in these data,
as elsewhere (Raven 1989), their correlation is near 0.5.
33
The combined Z-score is equivalent to the “mean effect” of Kling, Liebman, and Katz
(2007) when no data are unevenly missing and the estimation procedure is the same for
both.
20
by 2SLS and (potentially biased) OLS.34 This estimate is robust to the in-
clusion of controls (column 4), and when decomposed, is driven by the larger
and more precisely estimated effect in vocabulary. The reduced form effect,
roughly 0.1 standard deviations at the discontinuity, is shown in the upper
right panel of Figure 5. To the extent that subsequent outcomes depend
on a mixture of human capital and signaling, this is evidence that secondary
schooling in Kenya does not play a purely signaling role: students measurably
gain skills from schooling.35
These results contrast with the recent work of Filmer and Schady (2014)
in Cambodia, who show that increased secondary schooling has no impact
on subsequent test scores, as well as the work of Lucas and Mbiti (2014),
who show that increased quality of secondary schooling in Kenya (at higher
discontinuities in KCPE score) has no impact on subsequent academic out-
comes. This appears to be true even when the marginal student admitted
into the school is not the worst student in the higher-quality school. A clue to
reconciling Lucas and Mbiti’s findings with mine may lie in the recent work of
Urquiola and Pop-Eleches (2010). Using a similar multiple-discontinuity de-
sign to estimate the returns to secondary school quality in Romania, they find
34
Note that this is an ideal OLS specification: it includes the KCPE score as a control,
and restricts the sample substantially; more discussion of OLS and 2SLS agreement is
provided in Section 5.
35
A pessimistic interpretation might hypothesize that the longer respondents have been
out of school, the worse they perform on tests; since secondary schooling delays exit from
school, the apparent positive effect is simply a delayed deterioration of human capital.
The data do not support such an interpretation: the longer respondents have been out of
school (and thus the older they are), the better they do on the tests administered during
KLPS2; the coefficient is too small (around 0.02 standard deviations per additional year
out of school) to explain an effect more than an order of magnitude larger; and the effect
remains significant and of the same magnitude in both OLS and 2SLS after controlling for
duration out of school.
21
very modest positive effects, around .04 standard deviations on an academic
test. These effects are simply too small to be detectable in the Lucas and
Mbiti (2014) study, and when compared with the results I show in Table 3, it
is clear that attending any secondary school could simply have a much larger
effect than increasing the quality of the secondary school. de Hoop (2010)
also finds no positive effects of secondary school quality on a standardized
test outcome in Malawi, but this is in keeping with the aforementioned stud-
ies. On the other hand, the Lucas and Mbiti (2012) finding that increased
primary schooling actually reduced average performance on the KCPE exam
is driven by the setting: the universal primary education policy they study
couples an increase in years of schooling with increased enrollment. While
test scores might have risen for some students who received more schooling,
Lucas and Mbiti (2012) note that the class size and compositional changes
overwhelm any positive effect on test scores. Reconciling the results here
with those of Filmer and Schady is more difficult; similarly to their setting,
additional completed grades are associated with between 0.2 and 0.3 stan-
dard deviations on the tests in the KLPS instrument. The LATE that Filmer
and Schady estimate in Cambodia may be for lower-ability students, less able
to benefit from additional schooling, but I cannot rule out that any other dif-
ference between the Cambodian and Kenyan contexts is responsible for the
difference in findings.
4.3.2 Self-employment and employment
Next, I examine the impact of education on labor market outcomes. Because
many of the younger respondents are still in school, and because men are
22
typically primary earners in Kenya, I consider only the oldest two cohorts of
men for this analysis, so that the incapacitation effect of continued schooling
does not dominate the patterns of interest.36 According to 2008 Demographic
and Health Survey (DHS) data, young men in Kenya without secondary
school have a higher employment rate at age 20 than do men who complete
secondary school, since the latter group has had less time to look for jobs. At
roughly age 25 (the mean age of the older two male KLPS2 cohorts), DHS
data show roughly equal employment rates in these two groups; as they grow
older still, the better educated are more likely to be employed. I confirm
exactly this pattern in KLPS2, shown in Panel A of Table 4, columns 1
and 2. OLS shows a fairly precise zero effect of secondary schooling on
employment at this age. However, the regression discontinuity approach gives
very different results: the coefficient on schooling is positive and significant
depending on controls, shown in IV probit and bivariate probit specifications
in columns 3-6. While 2SLS is positively signed, it is insignificant; this is in
part because 2SLS is less efficient than estimation via IV probit and bivariate
probit when the true model is nonlinear and the mean of the response variable
is close to zero or one, as in this case.37 Depending on the specification, I find
a rise in employment of between 24 and 43 percent in response to secondary
schooling.
Besides being employed by someone outside their family, many respon-
36
As shown in Panel C of Table 1, only 13 percent of the men in the oldest two cohorts
are still in school, as compared to 44 percent in the younger four cohorts. Human capital
effects of secondary school remain broadly similar when limiting the sample to respondents
who were in standards 6 and 7 in 1998, though standard errors widen (predictably) with
the lower sample size; results shown in Panel B of Table 3.
37
As a diagnostic, predicted values from 2SLS clearly lie outside the unit interval.
23
dents are self-employed. Of these, 88 percent have no employees: common
self-employment occupations in KLPS2 include fishing, hawking assorted
wares, and working as a “boda-boda” bicycle taxi driver. On the other hand,
among the employed respondents, the degree of skill varies among unskilled
(loader of goods onto vehicles), semi-skilled (factory worker, carpenter, me-
chanic), and high-skill professional occupations (electronics repair, teachers,
and other government and NGO employees).
As in other labor market studies of relatively young men (Griliches 1977,
Zimmerman 1992), I use sector of employment rather than wage to estimate
the impact of secondary schooling. Clear patterns emerge when I measure
the effect of education on (implicitly low-skill) self-employment, shown as
a reduced form graph in the lower left panel of Figure 5, and presented in
the second row of Table 4. While secondary education and self-employment
are negatively associated in the cross-section (columns 1 and 2), the causal
impact of secondary schooling on low-skill self-employment is much larger;
marginal effects from IV probit and bivariate probit estimation are in broad
agreement with the 2SLS coefficients: a 40-50 percent lower probability of
being self-employed among those who go to secondary school because they
pass the KCPE cutoff.
4.3.3 Fertility
While labor market outcomes are of interest for the men in this sample,
fertility and health outcomes are of more importance for the women: women
are less than half as likely to be employed as men in each of the six KLPS2
24
cohorts.38
In a reduced form graph, shown in in the lower right panel of Figure 5,
and in Panel B of Table 4, I look at the probability of pregnancy by age
18 among female KLPS2 respondents. The association between secondary
schooling and decreased early fertility is strong: in the last two columns,
OLS shows a roughly twelve percentage point drop in teen pregnancy among
secondary school finishers. While these are only cross-sectional associations,
their sign agrees with associations seen in Colombia; Taiwan, China; and
the United States; summarized by Schultz (1988). Two-stage least squares
predicts outside the unit interval, since again, this is a low-probability out-
come, so I use IV probit and bivariate probit estimation in the first four
columns and find a near elimination of teen pregnancy among compliers at
the discontinuity, robust to the inclusion of the usual controls.
This finding contrasts with the work of McCrary and Royer (2011), who
find no conclusive effect of education on timing of womens’ first births. As
McCrary and Royer (2011) point out, however, their study is based on a
manipulation of the age at school entry rather than the age at school exit,
as is the case here. In effect, when a girl starts school one year earlier than
her counterparts because her birthday falls before a cutoff date, she has one
more year of education by the time she considers dropping out of school at a
particular age, perhaps in relation to the legal minimum. Their date-of-birth
instrument thus predicts educational attainment among those who, for the
most part, do not go on to tertiary schooling and in fact stop schooling al-
38
At the discontinuity, men appear slightly less likely to be married by survey time,
and women appear slightly more likely to be married, but neither effect is significant.
Conditional on marriage, spouse education rises slightly at the discontinuity (as one might
expect), but this effect is also statistically insignificant (results not shown).
25
most as soon as possible. However, if pregnancy in the McCrary and Royer
(2011) population is timed in relation to age rather than schooling, such vari-
ation in educational attainment would have no effect. In my case, however,
young teens are given or denied the opportunity to continue schooling (thus
varying age at exit) at the KCPE discontinuity. The KCPE discontinuity
only has an effect on those who choose to continue beyond primary educa-
tion (delaying school exit), and who must be considering tradeoffs between
continuing their education and raising a family. These may be higher abil-
ity students, relative to the Kenyan distribution, than are the McCrary and
Royer (2011) respondents in relation to the US distribution. Thus, while
they find essentially no impact of education on early fertility using variation
in age at school entry, it may still be sensible that in contrast to their work,
I find large effects. Filmer and Schady find no effect of additional schooling
in Cambodia on pregnancy rates, but the non-effect in their setting may be
due to the fact that the median respondent in their survey was still only 14
years old.
Other studies in Sub-Saharan Africa have found similar (though smaller)
e
effects of schooling on teen pregnancy in relation to those I show here. Ferr´
(2009) finds that a policy shift reclassifying 8th grade from secondary to pri-
mary school increased the fraction of students reaching 8th grade, thereby re-
ducing teen pregnancy by 10 percentage points in Kenya in the 1980s. Duflo,
Dupas, and Kremer (forthcoming) observe a 1.5 percentage point reduction
in teen childbearing in Kenya in response to a school uniform distribution
program that helped girls stay in school; and Baird, Chirwa, McIntosh, and
¨
Ozler (2010) find that a conditional cash transfer to bring dropouts back into
26
school reduces teen pregnancies by 5 percentage points in Malawi.
Since many of the secondary schools are single-sex, one interpretation
could be that teens in secondary school simply see members of the opposite
sex less frequently than they otherwise would, so lower rates of pregnancy
follow. This interpretation is not supported by the data, though: when
I categorize secondary schools as single-sex or mixed, I see no significant
difference in the pregnancy decline across the two types of schools.39
In Kenya, dropping out of school is more common among girls than boys,
and is most pronounced once girls enter their teens (Kremer, Miguel, and
Thornton 2009). This is closely linked to pregnancy: girls in the Kenyan
schools are “required to discontinue their studies for at least a year”40 if they
become pregnant. Schooling and childbearing in Kenya are in practice nearly
mutually exclusive, as is true in many other contexts (Field and Ambrus
2008). Though I am aware of no rule prohibiting teen mothers from returning
to school—though rules of that sort exist in other Sub-Saharan countries
e 2009)—teen mothers still face stigmatization in Kenyan primary and
(Ferr´
secondary schools (Omondi 2008), so even after giving birth, they are unlikely
to continue their schooling. The practical mutual exclusivity of pregnancy
and schooling means that high-ability girls at the discontinuity face a trade-
off between attending secondary school and starting a family immediately;
this policy may also differ from the policy environment in the US.
39
In the cross section, the reductions in teen pregnancy associated with going to the two
types of schools are also similar and statistically indistinguishable: 9 percentage points for
girls at mixed schools, and 10 percentage points for those who attend all-girls’ schools.
40
Excerpted from Ferr´ e (2009), p. 5.
27
4.4 Interpretation of the discontinuity
Though the probability of secondary schooling changes sharply at that point,
covariates do not. If the probability of non-government secondary schooling
changed at the discontinuity, however, it could be interpreted differently.
For example, in order to attend secondary school without attaining the cut-
off score, students may choose to enroll in secondary school in Uganda, rather
than Kenya. Less than five percent of the sampled respondents attend sec-
ondary school in Uganda, however, and at the discontinuity, there appears
to be no jump in the probability of attending secondary school in Uganda.41
The discontinuity may also be interpreted as an increase in years of school-
ing rather than an increase in the probability of secondary school completion.
This version of the first stage is shown in Appendix Table A2. This first
stage is evident in all the same specifications as before, and the coefficient
magnitudes are roughly four times larger, since the indicator for completing
secondary school represented four years of schooling. Appendix Tables A3,
A4, and A5 show the results under this first stage, and for the most part, the
coefficients are simply four times smaller. This interpretation is misleading,
however: while compliers at the discontinuity do gain approximately 0.16
standard deviations on the cognitive tests for each additional year of school-
ing (Appendix Table A3, columns 3 and 4), this is true because nearly all
the compliers at the discontinuity gain exactly 4 years of schooling (right
panel of Figure 3), and thus just above 0.6 standard deviations on the tests
(Table 3, columns 3 and 4). The relevant policy experiment is not to extend
41
The lack of a jump at the discontinuity is robust to the controls used throughout this
paper; the point estimate is usually positive and between 0.005 and 0.013, but statistically
indistinguishable from zero; results not shown.
28
secondary school by an additional year, but to change the cutoff so that a
larger fraction of the population attends—and completes—secondary school.
Nevertheless, results are largely robust to the alternative specification.
5 Cross-sectional analysis with key covariates
Though the present analysis turns on a clear source of quasi-experimental
variation, not all contexts offer such opportunities. Without such variation,
any analysis—of the impacts of schooling, in this case—is concerned with
whether omitted variables may complicate the measurement or interpretation
of empirical patterns.
The present study creates at least two opportunities for assessing the level
of omitted variable or selection bias in a cross-sectional analysis. The first
approach is to simply compare the RD estimates to OLS estimates. If they
are in agreement, OLS may not be a bad approach in this setting. While
the cross-sectional approach estimates the average treatment effect (ATE),
and the regression discontinuity estimate instead estimates the local average
treatment effect (LATE) only at the discontinuity, this comparison may still
be informative.
The second approach is to measure whether the OLS estimates vary with
the inclusion of controls. Following Altonji, Elder, and Taber (2005), the
movement of point estimates with the inclusion of controls speaks to selection
on observables; if one assumes an econometric similarity between selection on
observables and selection on unobservables, the stability of estimates under
the inclusion of controls speaks to its stability more generally. In this frame-
29
work, Oster (2015) has pointed out that the movements in R-squared are
as important as movements in point estimates; intuitively, if the observables
explain very little variation, they may simply be the wrong variables for the
question at hand, and may not tell us much about the variation explained
by the unobservables. I follow Oster (2015) and Gonzalez and Miguel (2014)
in assessing the stability of OLS estimates.
In Tables 5, 6, 7, and 8, I show how the cross-sectional (OLS) coefficient
changes over two sample restrictions, and the inclusion of KCPE score as a
control. The first sample restriction is a restriction to KCPE test-takers; the
second is the 80-point bandwidth of test scores near the cutoff.
The estimated relationship between secondary schooling and human cap-
ital (combined vocabulary and Raven’s Matrices score), shown in the first
column of Table 5, is twice as large as the regression discontinuity estimate
(and is statistically distinguishable from it). Restricting the sample in the
second and third columns of the table brings the coefficient much closer to
the regression discontinuity point estimate, and including KCPE score as a
control reduces it even further (though none of columns 2, 3, and 4 is sta-
tistically distinguishable from the estimate in column 5). This pattern is
consistent with OLS being biased by unobserved ability in column 3 as com-
pared to column 4. A regularity across these specifications is that secondary
schooling always appears to have an effect on subsequent test scores in this
context.
Including a measure of earlier ability (KCPE) as a control increases the
R2 appreciably; another way of saying this is that the KCPE control itself has
a T-statistic of 12.8 in this regression: KCPE score before secondary school-
30
ing is strongly predictive of the survey-based test score years later. Using
the criterion suggested by Oster (2015), I test whether additional unobserv-
ables could drive the true cross-sectional effect to zero, and find that under
the assumptions she suggests, unobservables would not change the finding
that secondary schooling in Kenya increases subsequent human capital (test
scores).42 Thus, having a pre-treatment measure of academic capabilities
could be sufficient for (reasonably) unbiased analysis of impacts on learning
outcomes.
When I turn to employment outcomes in Tables 6 and 7, the patterns
are quite different. For both outcomes, the range of values provided by
the cross-sectional point estimates does not include the point estimate from
the regression discontinuity; however, for both outcomes, given the wide
confidence interval in the regression discontinuity design, it is not statistically
distinguishable from the OLS values.
In the case of employment, the cross-sectional relationship is always sta-
tistically indistinguishable from zero, in the case of self-employment, is always
significantly negative. These regressions never have very high R2 values, how-
ever, and the inclusion of the KCPE control does not change this by very
much. As such, the bounding approach of Oster (2015) is very sensitive to
reasonable choices of the maximum R2 that inclusion of unobservables could
yield. For both outcomes, the bounding approach cannot reject null effects or
effects of the opposite sign with Rmax = 0.1. However, with Oster’s suggested
42
I use Oster’s psacalc program in Stata, first with the R2 scale-up factor of Π = 1.3,
then with Rmax = 0.5, following the suggestions in Oster (2015) in light of the discussion
in Gonzalez and Miguel (2014); the Vocabulary + Raven’s outcome in the KLPS survey
is constructed from relatively few items (compared to an hour-long test like the PIAT to
which Oster refers).
31
approach (Π, the ratio of maximum R-squared to the current R-squared, of
1.3), the self-employment pattern appears robust in the cross-section (δ > 1).
It is worth noting that an alternative control, respondent age, is much more
predictive of employment outcomes than KCPE score is, but this control does
not improve R2 for self-employment at all. In sum, this does not lead to any
instructive conclusions for non-experimental estimates of schooling impacts
on the labor market in this setting; OLS and 2SLS are not in close accord,
and R-squared is low, so the potential role of omitted variables still looms
large.
For pregnancy by age 18, the pattern is striking, even if KCPE score is
as unpredictive as for the employment outcomes. In every cross-sectional
regression, secondary schooling and pregnancy by age 18 are almost exactly
mutually exclusive. The low R2 could lead to insignificance in the bounding
approach, but the KCPE control actually makes the pattern s tronger (as
can be seen by comparing the first coefficient in column 3 to that in column
4), so the bounded β from Oster’s approach is even more negative than the
original cross-sectional estimates.
6 Conclusion
Secondary schooling in Kenya has large effects on human capital, reducing
low-skill self-employment and weakly increasing formal employment for older
cohorts of young men by the time of the survey. Teen pregnancy is dramat-
ically reduced by secondary schooling.
The discontinuity occurs at a highly policy-relevant position, near the
32
mean score on the national primary school leaving examination: perhaps as
externally valid as a single “fuzzy” discontinuity could be. An expansion
of secondary schooling that preserved the quality of secondary schools but
reduced the minimum required score would be likely to bring about the effects
I estimate on roughly 15 percent of the population near the discontinuity:
the compliers. As governments (including Kenya’s) consider the expansion of
secondary schooling against other policy options, this study should provide
a useful guidepost for understanding the consequences of such an expansion,
as long as the expansion does not substantially alter the characteristics of
the schools.
The difference between the unambiguously positive human capital find-
ings in this paper and the less cheery conclusions from other studies of educa-
tion in Kenya suggest that increased school enrollment in Sub-Saharan Africa
will have varying consequences, depending on how it is undertaken. The find-
ings in this paper, and in other experimental and quasi-experimental papers,
are contingent on the nature of the exogenous variation: the secondary school
admission instrument I use, at the KCPE discontinuity, induces both a rise
in secondary school completion, and a resulting delay in pregnancy among
female compliers; a date-of-birth instrument in the US that also induces ad-
ditional secondary education has no such effect, however, both because of
the timing of the education effects and because of the underlying skills and
preferences of compliers with the different instruments.
OLS and 2SLS do not always produce similarly signed effects in this
analysis: cross-sectional analysis does not reveal the impact of secondary
schooling on employment on this age, but in a causal framework, the pattern
33
emerges. In the cross-section, controlling for ability is clearly important
for outcomes that are closely linked to ability, such as the human capital
measure in this study. Ability, traditionally linked to academic tests, may
not be nearly as useful a control for other outcomes, at least for the young
Kenyan adults in this study.
This study also highlights a possible avenue for researchers interested in
the consequences of education throughout sub-Saharan Africa: many coun-
tries have examinations much like the KCPE, with analogous cutoff rules for
secondary school admission. An important caveat is that while some ques-
tions in survey data show a very high degree of reliability, this cannot be said
for KCPE scores. Combining administrative test data with a rich follow-up
survey overcomes this obstacle, and may yield novel findings establishing
causal links between education, fertility, and labor markets throughout the
developing world.
34
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39
Figure 1: Self-reported and confirmed KCPE scores with density tests.
800
400
Frequency of self−reported KCPE scores
Frequency of confirmed KCPE scores
600
300
400
200
200
100
40
0
0
50 100 150 200 250 300 350 400 450 50 100 150 200 250 300 350 400 450
KCPE (out of 500) KCPE (out of 500)
KLPS2 data, N=3305 KLPS2 data, N=2167, restricted to confirmed first KCPE scores
.015
.01
.008
.01
.006
.004
.005
.002
0
0
0 100 200 300 400 500 0 100 200 300 400 500
Density discontinuity p<0.001 Density discontinuity p=.949
Left panels: self-reported scores; right panels: confirmed official scores.
Note: KCPE scores prior to 2001 are converted to the current 500-point scale; density graphs generated by the McCrary (2008) Stata program.
Figure 2: Structural break search
251
.116
.114
234
.112
R squared
.11 .108
.106
−.5 −.4 −.3 −.2 −.1 0 .1 .2 .3 .4 .5
Possible discontinuities
Male Female
Estimation based on method used in Card, Mas, and Rothstein (2008).
Figure 3: Discontinuity: a function of bandwidth, and CDF difference
CDF Difference, piecewise linear, small bandwidth, no other controls
.4
.25
Change in P[completing secondary]
.2
.3
.15
.2
.1
.05
.1
0
−.05
0
.2 .4 .6 .8 1 1.2 0 2 4 6 8 10 12 14 16 18 20
Sample restriction: bandwidth about discontinuity Highest level (year/grade) of education
Estimated discontinuity 95 percent C.I. CDF Difference 95% C.I.
Left panel provides estimates and confidence intervals based on piecewise linear specification; right panel
shows the difference in cumulative distribution functions for years of education at the discontinuity.
41
Figure 4: RD Validity: local quadratic regressions of covariates on KCPE scores.
15
15
Mother Education
Father Education
10
10
5
5
0
0
−1 −.5 0 .5 1 −1 −.5 0 .5 1
42
KCPE score KCPE score
Quadratic Regression 10−point bin average Cutoff value Quadratic Regression 10−point bin average Cutoff value
KLPS2 data, N=1853, Discontinuity T=.105 (p=.916) KLPS2 data, N=1907, Discontinuity T=.244 (p=.807)
30
1
.8
25
Percent Female
.6
Age
.4
20
.2
15
0
−1 −.5 0 .5 1 −1 −.5 0 .5 1
KCPE score KCPE score
Quadratic Probability 10−point bin average Cutoff value Quadratic Regression 10−point bin average Cutoff value
KLPS2 data, N=2079, Discontinuity T=.529 (p=.597) KLPS2 data, N=2079, Discontinuity T=.119 (p=.905)
Figure 5: First stage and reduced forms: cognitive performance; self-employment among older men; preg-
nancy by 18 among women. 1
Probability of completing secondary school
1
.8
Combined cognitive score
.5
.4 .6
0
.2
−.5
0
43
−1 −.75 −.5 −.25 0 .25 .5 .75 1 −1 −.75 −.5 −.25 0 .25 .5 .75 1
KCPE score (normalized so that cutoff=0) KCPE score (normalized so that cutoff=0)
Piecewise linear prediction 95% CI Ten−point bins Piecewise linear prediction 95% CI Ten−point bins
KLPS2 data KLPS2 data
.6
.3
Probability of pregnancy by age 18
Probability of self−employment
.4
.2
.2
.1
0
0
−1 −.75 −.5 −.25 0 .25 .5 .75 1 −1 −.75 −.5 −.25 0 .25 .5 .75 1
KCPE score (normalized so that cutoff=0) KCPE score (normalized so that cutoff=0)
Piecewise linear prediction 95% CI Ten−point bins Piecewise linear prediction 95% CI Ten−point bins
KLPS2 data KLPS2 data
Table 1: KLPS2 Summary Statistics
Characteristic Mean Standard Dev. N
Panel A: Respondent characteristics among those with KCPE scores
Age 22.05 (2.57) 3305
Female 0.45 (0.50) 3305
Father’s level of education 10.06 (4.99) 2953
Mother’s level of education 6.61 (4.18) 3049
Panel B: Educational characteristics among those with KCPE scores
Self-reported KCPE Score (out of 500) 254.49 (52.23) 3305
Years of Education 10.14 (2.09) 3305
Still attending school 0.30 (0.46) 3305
Any secondary schooling 0.62 (0.49) 3305
Complete (4y) secondary schooling 0.37 (0.48) 3305
Post-secondary schooling 0.04 (0.18) 3305
Panel C: Outcome variables in subsamples used for estimation
Vocabulary test (standardized) 0.55 (0.69) 1923
Raven’s matrices (standardized) 0.35 (0.91) 1904
Standardized vocabulary + Raven’s 0.51 (0.76) 1904
Attending school | male 0.33 (0.47) 1058
Attending school | male, oldest cohorts 0.13 (0.34) 375
Employed | male 0.21 (0.41) 1058
Employed | male, oldest cohorts 0.34 (0.47) 375
Self-employed | male 0.10 (0.30) 1058
Self-employed | male, oldest cohorts 0.16 (0.37) 375
Pregnant by 18 | female, at least 18 y.o. 0.09 (0.29) 853
Note that this is a subsample of the KLPS2 data; by conditioning on the presence of
a KCPE score, I eliminate all respondents who left school before completing 8th grade
(N=3,305 rather than 5,084). Also note that the average grade in 1998 is between 4 and
5 because the KLPS sample has essentially equal numbers of pupils drawn from each
grade from 2 through 7. Apart from survey non-response, the sample is reduced due to
restrictions for variables with descriptions including “ | female,” and “ | male,” and other
conditions. The variable “Still attending school” is measured in 2007, 2008, or 2009,
depending on when the survey took place; as one would expect, it declines with age and
grade cohorts; likewise, employment rates trend in the opposite direction. KCPE scores
prior to 2001 have been converted to the current 500-point scale.
44
Table 2: Discontinuity (First Stage) Estimation.
Outcome: Completing secondary school
Sample restriction: Pooled Male Female
(1) (2) (3) (4) (5) (6) (7) (8) (9)
KCPE≥cutoff 0.16∗∗∗ 0.15∗∗∗ 0.17∗∗∗ 0.17∗∗∗ 0.16∗∗∗ 0.21∗∗∗ 0.16∗∗∗ 0.13∗∗ 0.12∗
(0.04) (0.03) (0.05) (0.05) (0.05) (0.06) (0.06) (0.05) (0.07)
KCPE centered at cutoff 0.27∗∗∗ 0.27∗∗∗ 0.07 0.3∗∗∗ 0.28∗∗∗ 0.07 0.24∗∗∗ 0.25∗∗∗ 0.06
(0.06) (0.05) (0.18) (0.09) (0.09) (0.31) (0.08) (0.08) (0.26)
(KCPE≥cutoff)×KCPE 0.02 0.006 0.2 -0.02 -0.01 -0.03 -0.006 0.05 0.5
(0.09) (0.08) (0.3) (0.11) (0.11) (0.41) (0.14) (0.13) (0.48)
45
Constant 0.33∗∗∗ 0.44∗∗∗ 0.41∗∗∗ 0.39∗∗∗ 0.41∗∗ 0.37∗∗ 0.27∗∗∗ 0.34∗ 0.32
(0.02) (0.14) (0.14) (0.04) (0.17) (0.18) (0.04) (0.19) (0.19)
Piecewise Quadratic No No Yes No No Yes No No Yes
Controls No Yes Yes No Yes Yes No Yes Yes
Discontinuity F-stat 19.46 21.55 14.87 11.13 12.42 10.94 7.50 5.81 2.71
Observations 1943 1943 1943 1064 1064 1064 879 879 879
2
R 0.14 0.23 0.23 0.14 0.24 0.24 0.12 0.2 0.2
Notes for all regression tables: Standard errors, clustered at the KCPE-score level, are in parentheses. * denotes
significance at the 10% level, ** at the 5% level, and *** at the 1% level. Coefficients on KCPE score and interactions
with it have been scaled up by a factor of 100. KCPE score has been re-centered at the discontinuity (251 for men; 234
for women), so that the coefficient on the discontinuity may be interpreted directly. KCPE scores prior to 2001 have been
converted to the current 500-point scale. Controls, when indicated, include age, parents’ education levels (and an indicator
for survey nonresponse), and indicators for all but one of the six KLPS cohorts.
Table 3: Human capital: all cohorts
Outcome: Mean effect:
Vocabulary and Raven’s Matrices Vocabulary Matrices
(1) (2) (3) (4) (5) (6)
OLS OLS 2SLS 2SLS 2SLS 2SLS
Panel A: Full sample
Completing Std 12 0.612∗∗∗ 0.584∗∗∗ 0.67∗∗ 0.596∗∗ 0.645∗∗ 0.399
(0.032) (0.033) (0.282) (0.3) (0.275) (0.432)
KCPE centered at cutoff 0.663∗∗∗ 0.607∗∗∗ 0.637∗∗∗ 0.602∗∗∗ 0.607∗∗∗ 0.448∗
(0.085) (0.086) (0.168) (0.17) (0.16) (0.232)
(KCPE≥cutoff)×KCPE -0.311∗∗ -0.302∗∗ -0.311∗∗ -0.302∗∗ -0.468∗∗∗ -0.061
46
(0.127) (0.124) (0.127) (0.123) (0.112) (0.175)
Female -0.19∗∗∗ -0.222∗∗∗ -0.183∗∗∗ -0.22∗∗∗ -0.136∗∗∗ -0.25∗∗∗
(0.029) (0.03) (0.042) (0.051) (0.047) (0.073)
Constant 0.361∗∗∗ 1.055∗∗∗ 0.334∗∗ 1.048∗∗∗ 1.580∗∗∗ 0.273
(0.031) (0.204) (0.14) (0.274) (0.219) (0.389)
Controls No Yes No Yes Yes Yes
Discontinuity F-stat . . 20.496 23.070 23.070 23.070
Observations 1923 1923 1923 1923 1923 1923
R2 0.331 0.345 0.33 0.345 0.404 0.153
Panel B: Sample restricted to oldest two cohorts
Completing Std 12 0.689∗∗∗ 0.648∗∗∗ 0.685∗ 0.62 0.958∗∗ 0.129
(0.049) (0.05) (0.385) (0.429) (0.379) (0.569)
Controls No Yes No Yes Yes Yes
Discontinuity F-stat . . 10.783 9.041 9.041 9.041
Observations 693 693 693 693 693 693
2
R 0.42 0.428 0.42 0.428 0.452 0.184
(See Notes for all regression tables below Table 2.) In Panel B, though only the coefficient on
secondary schooling is shown, the specifications are the same as in Panel A, except that the sample is
restricted to the oldest two cohorts.
Table 4: Employment outcomes for men (oldest two cohorts) and fertility outcomes for women
Outcome Estimation
(1) (2) (3) (4) (5) (6) (7) (8)
OLS OLS IVP IVP BVP BVP 2SLS 2SLS
Panel A: Employment outcomes, men
P[Formally employed] -0.036 0.036 0.263 0.427** 0.240 0.359** 0.291 0.549
(0.055) (0.058) (0.253) (0.216) (0.192) (0.171) (0.352) (0.486)
P[Self-employed] -0.104*** -0.12** -0.459*** -0.516*** -0.464*** -0.347** -0.502* -0.601*
(0.040) (0.049) (0.092) (0.103) (0.147) (0.136) (0.273) (0.359)
47
Controls No Yes No Yes No Yes No Yes
Discontinuity F-statistic . . 9.031 5.986 9.031 5.986 9.031 5.986
Observations 378 378 378 378 378 378 378 378
Panel B: Fertility, women
P[Pregnant by 18] -0.119*** -0.138*** -0.454 -0.583*** -0.199** -0.184 -0.333 -0.389
(0.020) (0.022) (0.300) (0.191) (0.086) (0.123) (0.238) (0.286)
Controls No Yes No Yes No Yes No Yes
Discontinuity F-statistic . . 6.993 5.589 6.993 5.589 6.993 5.589
Observations 853 853 853 853 853 853 853 853
(See Notes for all regression tables below Table 2.) Only the coefficient on completed secondary schooling is shown; each
coefficient comes from a separate regression. Abbreviations: BVP and IVP denote bivariate probit and IV probit, respectively;
marginal effects are shown for both. Standard errors for bivariate probit estimates are obtained via bootstrapping with 1,000 draws.
Table 5: Controls and bias: human capital, all cohorts
Outcome: combined vocab/Raven’s score
(1) (2) (3) (4) (5)
OLS OLS OLS OLS 2SLS
∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗
Completing Std 12 1.226 0.821 0.754 0.612 0.67∗∗
(0.022) (0.033) (0.034) (0.032) (0.282)
∗∗∗
Constant -0.196 0.213∗∗∗ 0.26∗∗∗ 0.309∗∗∗ 0.334∗∗
(0.02) (0.03) (0.03) (0.026) (0.14)
Restrict to KCPE takers No Yes Yes Yes Yes
Restrict KCPE bandwidth No No Yes Yes Yes
Control for KCPE No No No Yes Yes
Observations 4885 2149 1923 1923 1923
R2 0.326 0.292 0.271 0.329 0.33
(See Notes for all regression tables below Table 2.) In Tables 5 through 8, Column
(1) uses only robust standard errors, however, because KCPE data are not included in
the first specification. All columns in this table include a control for respondent gender.
48
Table 6: Controls and bias: employment for older two cohorts of men
Outcome: formally employed
(1) (2) (3) (4) (5) (6)
OLS OLS OLS OLS OLS 2SLS
Completing Std 12 -0.014 -0.017 -0.039 -0.035 0.015 0.291
(0.036) (0.047) (0.051) (0.055) (0.058) (0.352)
Constant 0.327∗∗∗ 0.344∗∗∗ 0.362∗∗∗ 0.36∗∗∗ -0.857∗∗∗ 0.223
(0.026) (0.033) (0.036) (0.038) (0.316) (0.197)
Restrict to KCPE takers No Yes Yes Yes Yes Yes
Restrict KCPE bandwidth No No Yes Yes Yes Yes
Control for KCPE No No No Yes Yes Yes
Control for age No No No No Yes No
Observations 664 429 378 378 378 378
R2 0.0002 0.0003 0.002 0.002 0.036 .
See Notes for Table 5.
Table 7: Controls and bias: self-employment, older two cohorts of men
Outcome: self-employed
(1) (2) (3) (4) (5) (6)
OLS OLS OLS OLS OLS 2SLS
Completing Std 12 -0.145∗∗∗ -0.125∗∗∗ -0.127∗∗∗ -0.105∗∗∗ -0.101∗∗ -0.502∗
(0.026) (0.037) (0.04) (0.04) (0.044) (0.273)
Constant 0.246∗∗∗ 0.225 ∗∗∗
0.23 ∗∗∗
0.218 ∗∗∗
0.111 0.403∗∗
(0.02) (0.03) (0.033) (0.032) (0.276) (0.17)
Restrict to KCPE takers No Yes Yes Yes Yes Yes
Restrict KCPE bandwidth No No Yes Yes Yes Yes
Control for KCPE No No No Yes Yes Yes
Control for age No No No No Yes No
Observations 802 429 378 378 378 378
R2 0.034 0.029 0.03 0.034 0.034 .
See Notes for Table 5.
49
Table 8: Controls and bias: fertility outcome, women
Outcome: pregnant by age 18
(1) (2) (3) (4) (5)
OLS OLS OLS OLS 2SLS
Completing Std 12 -0.278∗∗∗ -0.118∗∗∗ -0.117∗∗∗ -0.119∗∗∗ -0.333
(0.012) (0.016) (0.017) (0.02) (0.238)
∗∗∗ ∗∗∗ ∗∗∗
Constant 0.29 0.133 0.134 0.135∗∗∗ 0.214∗∗
(0.011) (0.014) (0.015) (0.016) (0.089)
Restrict to KCPE takers No Yes Yes Yes Yes
Restrict KCPE bandwidth No No Yes Yes Yes
Control for KCPE No No No Yes Yes
Observations 2350 937 853 853 853
R2 0.07 0.04 0.037 0.037 .
See Notes for Table 5.
50
A Online Appendix - not for print publica-
tion
A.1 Data
A.1.1 KCPE logistics
When students take the exam,43 they indicate a list of secondary schools
they would prefer to attend, including one or two from each of three tiers of
secondary schools: national, provincial, and district.44 National schools are
the most competitive and are considered to be of the highest quality; district
schools, the least so.
Initial admission cutoffs are determined centrally by the Ministry of Ed-
ucation. The cufoffs may differ for boys and girls, and vary according to
characteristics of each secondary school.45 After the cutoffs are decided and
test results are available, heads of secondary schools meet in groups to de-
termine matches between schools and students, and make admission offers.
Following this initial selection round, a variety of additional selection mecha-
nisms are employed: students may accept offers; students may contact other
schools which they would prefer to attend, to see whether the admissions
committee is willing to accept them;46 and school leaders may meet again to
carry out a second round of selection if an insufficient number of students
accept offers in the first round. Nevertheless, the odds of secondary school
admission jump up sharply at a KCPE score of 250, and continue to rise
thereafter, as does the quality of the school to which a student is admitted.
A.1.2 KCPE scoring
From 1985 to 2000, the KCPE covered seven subjects, each scored on a 100-
point scale: English, Swahili, math, science, geography, arts, and business;
43
The Kenyan academic year coincides with the calendar year; the KCPE takes place
in early November, and results are announced in the last few days of December.
44
This mirrors the “rule-of-thumb” tiered system of secondary school choice that Ghana
adopted in 2008, for example (Ajayi 2010).
45
Some school cutoffs are below 250, while others are above. The cutoff governing the
largest fraction of schools in the region, however, is 250.
46
Often the school-imposed KCPE cutoff is higher for these cases, but exceptions are
made at the discretion of the admissions committee for especially meritorious or needy
students.
A1
from 2001 onward, the last two of these—arts and business—were removed
(Orlale 2000, Kremer, Miguel, and Thornton 2009). As a consequence, the
KLPS data include observations in which the maximum score is 700, and
observations where the maximum is 500. Throughout this paper, I normalize
all scores to the 500-point scale.
Those who are not admitted to any government school have several op-
tions if they wish to continue their education: they may repeat eighth grade
and re-take the KCPE; they may still have access to private secondary schools
and vocational schools; or they may travel to Uganda to enroll in school there.
A.1.3 Re-taking the KCPE
One clear pattern both from the survey data and the administrative records is
that students sometimes re-take the test. In the 2003-2005 round of surveying
(KLPS1), the questionnaire asked not only for respondents’ KCPE score, but
also how many times they had taken the KCPE. Of KCPE-takers in the older
cohorts (who had reached eighth grade before being interviewed in KLPS2),
approximately 87 percent said they took it exactly once, 13 percent said that
they had taken the exam twice, and around one tenth of one percent said
they took it three times. The reason such a small fraction re-take such an
important examination, according to my interviews with with both teachers
and pupils, is that it is costly: they have to repeat eighth grade in order to do
it. The survey data are in agreement: more than 98 percent of respondents
who report re-taking the KCPE also report repeating standard 8; conversely,
of those who take the KCPE only once, comparatively few respondents (less
than 3 percent) repeat standard 8 for any reason. While a pupil’s decision to
re-take the test is conditioned on the the pupil’s unobserved ability as well
as the relationship of her first score to the discontinuity—thereby skewing
the second score distribution and any conclusions drawn from it, as in the
case studied by Martorell (2004)—a pupil’s first test score should not show
any sign of manipulation around the discontinuity.
A.1.4 KLPS data
All 73 schools are rural, and together represent 80% of the schools in those
two administrative Divisions. From this population of roughly 22,000 stu-
dents, a representative 7,530 pupils were randomly sampled for two follow-
ups. The survey acts both as a follow-up to the Primary School Deworming
A2
Project (PSDP) (Miguel and Kremer 2004), and as a longitudinal study rep-
resentative of an entire region.
Of 7,530 sampled pupils, 5,084 were surveyed during KLPS2. Though
this is only 67.5 percent of the sample, some of the original sample has
been confirmed deceased, and because some pupils were easier to locate than
others after ten years, each survey wave was carried out in two phases: regular
and intensive. Only a random sample of respondents who were not found
during the regular phase were sought during the intensive phase: 63 percent
of respondents were located in the regular phase, and of the remaining 37
percent, more than half of an intensive sample was located, bringing the
effective tracking rate of KLPS2 to above 80 percent.47
A.1.5 Matching and correcting KCPE scores
If pupils taking KCPE could somehow manipulate their test score to place
themselves just above the secondary school cutoff, it would invalidate the
research design. Administrative data for a recent year across the entire
province, however, depicted in Figure A1, does not show this characteris-
tic. Examination papers from any particular school are graded by separate
teachers for each subject, and are never graded by teachers from the school
where the papers originated, so precise manipulation around the discontinuity
would not be straightforward in any event. To resolve the discrepancy be-
tween the distributions of self-reported and administratively reported KCPE
scores, I gathered an auxilliary dataset of 17,384 official KCPE scores from
the Government of Kenya, via district education offices and school visits.
These official data do not include all schools in all years for several rea-
sons: recent political upheavals made some records inaccessible, re-districting
changed which offices were responsible for maintaining the records in ques-
tion; and record-keeping over the past eleven years at local primary schools
has occasionally been frustated by natural disasters. Nevertheless, the data I
gathered include roughly 88 percent of the KLPS schools48 during the years
47
Discussion of tracking logistics, intensive sampling, and sample attrition in the earlier
2003-2005 round of this survey, KLPS1, may be found in Baird, Hamory, and Miguel
(2008).
48
In the process of visiting many of the schools myself in order to collect this data,
in addition to all the schools in the original Primary School Deworming Project study,
I was also able to visit a number of schools in neighboring districts where some KLPS
respondents had transferred by the time of their KCPE examinations. These records are
included in the 17,384 total.
A3
of interest in this study. I match the KCPE records to the KLPS surveys by
pupil name,49 and by the year(s) and school(s) in which the pupil took the
KCPE. After condensing spelling variations of the same name, I am able to
match KCPE records to KLPS2 surveys whenever there is no better match
in the year and school in which the respondent took KCPE—and at least
two names agree across the two datasets.
Comparing the administrative test scores with the survey data, I am able
to ask what predicts misreporting. A graph of misreporting as a function of
initial test score is shown in Appendix Figure A3: the lower the true score,
the higher the chances of misreporting. In Appendix Table A7, I consider
other predictors in a linear regression framework. Respondents with low
ability as measured by cognitive tests at survey time, those who round their
test scores to a multiple of five, and those who took the test further in the
past are all more likely to misreport the score. None of these, however, is a
very reliable predictor: they do not yield large differences in the probability
of misreporting. The only sharp predictor is whether the respondent took
the KCPE before the KLPS1 survey was administered, and reports the same
score in KLPS1 and KLPS2; in that case, there is an 86 percent chance that
the respondent is reporting the truth, though this is without conditioning on
any other predictors. Nearly all of these cases, of course, are respondents who
scored above 250 on the test. I am able to include these data in robustness
checks that expand the sample slightly, from 2,167 to 2,236 first test scores,
and my results do not change appreciably.
Based on confirmed first test scores, I am also able to chart the proba-
bility of re-taking the test, shown in Appendix Figure A4. As expected, the
probability of re-taking the test is highest for respondents whose first score is
below 250 points. The average test score improvement from the first attempt
to the second is 54 points, just above one standard deviation on the test.
49
Names in Kenya are not as fixed as in the United States: they may be spelled differ-
ently even within the same document (“Winnstone” for “Winston,” for example); order of
names is also typically not fixed (so that “Juma Winston” is likely to be the same person
as “Winston Juma”); and the subset of names reported (“Juma Winston Wandera”) varies
from record to record. I should also note that the distribution of names is skewed more
towards the most common names in western Kenya than in it is in the United States.
“Smith” was the most common surname in the 1990 US census, with just over one percent
of the population; no other surname exceeded one percent. In this region, there are five
names that occur with frequencies above three percent each. Despite this concentration,
unique identification of pupils is made feasible by the typically small exam cohorts from
each school.
A4
A.2 Measurement error and re-taking
Following the notation and discussion of Hahn, Todd, and Van der Klaauw
(2001), consider outcome yi , and a binary indicator for secondary schooling,
xi . Let yi = αi + xi · β . Label KCPE score (centered at the admission cutoff)
zi , so that Pr[xi = 1|zi = z ] is discontinuous at z = 0. Define:
x+ = lim+
E [xi |zi = z ]
z →0
−
x = lim−
E [xi |zi = z ]
z →0
+
y = lim+
E [yi |zi = z ]
z →0
y + = lim−
E [yi |zi = z ]
z →0
Assuming that these limits exist, and that E [αi |zi = z ] is continuous in z at
0:
y+ − y−
β=
x+ − x −
This is true no matter what the correlation between αi and xi is, as long as
the continuity assumption holds. If E [xi |zi = z ] = Pr[xi = 1|zi = z ] has a
discontinuity of x+ − x− = φ at z = 0, then y + − y − = φ · β , and the result
follows; this is the Hahn, Todd, and Van der Klaauw (2001) argument for
identification in the regression discontinuity design.
A.2.1 Continuous classical measurement error in running variable
Let z ˜i = zi + ηi , where ηi is a continuous random variable independent of xi ,
zi , and αi with probability density function fη (·). Suppose we observe yi , xi ,
and z ˜i , but not zi . Define:
˜+ = lim
x +
E [xi |z
˜i = z ]
z →0
˜− = lim
x −
E [xi |z
˜i = z ]
z →0
By iterated expectations:
∞
E [xi |z
˜i = z ] = E [xi |zi = t]fη (z − t)dt
−∞
A5
If fη (·) is differentiable everywhere, application of Leibniz’ rule to the ex-
pression for E [xi |z˜i = z ] above shows that E [xi |z
˜i = z ] is differentiable
everywhere, even if E [xi |zi = z ] = Pr[xi = 1|zi = z ] is not. Thus, in this
setting, x˜+ − x ˜− = 0: there is no discontinuity when the running variable is
measured with this type of error.
A.2.2 Alternative forms of measurement error
Suppose that instead of z˜i = zi + ηi , we observe z ˜i′ = zi + ηi · ζi , where ζi is
binary. Let Pr(ζi = 0) = p, with ζi independent of ηi , xi , zi , and αi . Using
analogously defined limit expressions, x ˜′− = p · φ, and y
˜ ′+ − x ˜′+ − y˜′− = p · φ · β ,
so the regression discontinuity can still be used to consistently estimate β ,
though the discontinuity is made smaller. In neither of these cases (˜ zi or z˜i′ ),
however, should the density of the observed running variable be discontinuous
at z = 0 if the underlying density of zi is smooth at z = 0.
A.2.3 Re-taking
In the presence of test re-taking, a regression discontinuity estimate might
or might not yield the desired local average treatment effect, as discussed by
Martorell (2004). However, it could easily yield an “artificial” discontinuity
in the density of reported test scores, as follows: For this discussion, let k1
and k2 be the first and second test scores a student receives on the KCPE.
Let k1 , k2 ∼ iid N (0, σ 2 ) with mean zero (at the cutoff). The student only
learns the second test score if he does not pass the first time. The student
might then report only the most recent score; the first score if he passes the
first time, the second if he takes the test a second time.
krecent = k1 · 1[k1 ≥ 0] + k2 · 1[k1 < 0]
Though the distributions of k1 , k2 , and even max(k1 , k2 ) are smooth, the
density of krecent is discontinuous at the cutoff. This is because for k + ≥ 0,
of krecent can take the value k + either when k1 < 0 and k2 = k + , or when
k1 = k + . For k − < 0, only the former condition applies. Graphically:
A6
+ +
k1 < 0 and k2 = k k1 = k
k2
k2
0
0
−
k1 < 0 and k2 = k
0 0
k1 k1
Alternatively, the student might follow the same re-taking rule, then report
the best score:
kbest = k1 · 1[k1 ≥ 0] + max(k1 , k2 ) · 1[k1 < 0]
Again, the density of kbest is discontinuous at the cutoff, because for k + ≥ 0,
of kbest can still take the value k + either when k1 < 0 and k2 = k + , or when
k1 = k + . But now, for k − < 0, a modification of the former condition applies:
kbest = k − either when k2 = k − and k2 > k1 , or when k1 = k − and k1 > k2 .
Graphically:
+ +
k1 < 0 and k2 = k k1 = k
k2
k2
0
0
−
k2 > k1 and k2 = k
k1 ≥ k2 and k1 = k
−
0 0
k1 k1
In either case, the density of scores just to the left of the cutoff will be lower
than to the right, and the McCrary (2008) test should reject smoothness at
the cutoff point.
A7
A.3 Additional figures and tables
Figure A1: True administrative distribution from 2008
6000 Official 2008 Western Province Data
Frequency of KCPE Scores
2000 0 4000
50 100 150 200 250 300 350 400 450
KCPE score (out of 500)
KCPE 2008 Western Province data, N=84989
Figure A2: Self-reported KLPS1 first KCPE scores with smoothness test
300
.02
Frequency of self−reported first KCPE scores
.015
200
.01
100
.005
0
0
50 100 150 200 250 300 350 400 450
KCPE (out of 500) 0 100 200 300 400 500
KLPS1 data, N=1414, restricted to self−reported first KCPE scores Density discontinuity p<0.001
Generated using the Stata program developed by McCrary (2008).
A8
Figure A3: Misreporting test score, as a function of true test score: local
linear estimates
1 .8 Local estimates: large misreporting of test score
P[misreport score]
.4 .2
0 .6
−1 −.5 0 .5 1
First KCPE score (rescaled)
Fan regression estimate 95 percent bootstrap C.I. Ten−point bins
quartic kernel width .5 ; restricted to respondents who do not repeat std 8
Graph generated using the algorithm proposed by Fan (1992).
Figure A4: Retaking the test: local linear estimates
Local estimates: repeating std 8 (retaking the test)
.4 .3
P[repeat std 8]
.2 .1
0
−1 −.5 0 .5 1
First KCPE score (rescaled)
Fan regression estimate 95 percent bootstrap C.I. Ten−point bins
quartic kernel width .5
Graph generated using the algorithm proposed by Fan (1992).
A9
Table A1: Cross-section relationship between cognitive performance and
wage
Outcome: Log(Wage), conditional on observation
(1) (2) (3)
Standardized cognitive measure 0.256∗∗∗ 0.199∗∗∗ 0.291∗∗∗
(0.035) (0.039) (0.084)
Constant 7.874∗∗∗ 7.940∗∗∗ 8.052∗∗∗
(0.035) (0.04) (0.082)
Observations 772 592 208
R2 0.066 0.042 0.055
In column 1, wages are regressed on the standardized measure of cog-
nitive ability (standardized sum of vocabulary and Raven’s Matrices
Z-scores). In column 2, the sample is restricted to men; in column 3,
it is restricted to men in the oldest two cohorts (Standards 6 and 7 in
1998). Wages are reported in Kenyan Shillings per month.
A10
Table A2: Robustness: alternative discontinuity (first stage) estimation.
Outcome: Highest grade level of educational attainment
Sample restriction: Pooled Male Female
(1) (2) (3) (4) (5) (6) (7) (8) (9)
∗∗∗ ∗∗∗
KCPE≥cutoff 0.65 0.57 0.83∗∗∗ 0.68 ∗∗∗
0.6∗∗∗ 0.84∗∗∗ 0.64∗∗∗ 0.56∗∗ 0.82∗∗
(0.16) (0.14) (0.22) (0.21) (0.19) (0.29) (0.24) (0.23) (0.34)
∗∗∗ ∗∗∗ ∗∗∗
KCPE centered at cutoff 1.80 1.59 0.92 1.76 1.53∗∗∗ 1.32 1.86∗∗∗ 1.63∗∗∗ 0.4
(0.25) (0.24) (0.78) (0.33) (0.33) (1.14) (0.37) (0.37) (1.22)
A11
(KCPE≥cutoff)×KCPE -0.52 -0.56 -1.39 -0.34 -0.32 -1.86 -1.10∗∗ -0.91 -0.76
(0.41) (0.37) (1.38) (0.53) (0.49) (1.85) (0.56) (0.57) (2.06)
Constant 10.06∗∗∗ 13.04∗∗∗ 12.90∗∗∗ 10.24∗∗∗ 12.70∗∗∗ 12.64∗∗∗ 9.88∗∗∗ 12.76∗∗∗ 12.55∗∗∗
(0.1) (0.59) (0.59) (0.12) (0.74) (0.76) (0.16) (0.87) (0.85)
Piecewise Quadratic No No Yes No No Yes No No Yes
Controls No Yes Yes No Yes Yes No Yes Yes
Discontinuity F-stat 16.63 15.73 13.98 10.22 9.88 8.46 7.25 5.68 5.73
Observations 1943 1943 1943 1064 1064 1064 879 879 879
R2 0.18 0.28 0.28 0.19 0.29 0.29 0.16 0.25 0.25
(See Notes for all regression tables below Table 2.)
Table A3: Robustness: human capital, all cohorts
Outcome: Mean effect:
Vocabulary and Raven’s Matrices Vocabulary Matrices
(1) (2) (3) (4) (5) (6)
OLS OLS 2SLS 2SLS 2SLS 2SLS
Educational attainment 0.162∗∗∗ 0.152∗∗∗ 0.167∗∗ 0.153∗∗ 0.166∗∗ 0.103
(0.009) (0.009) (0.07) (0.077) (0.067) (0.112)
KCPE centered at cutoff 0.53∗∗∗ 0.521∗∗∗ 0.517∗∗ 0.519∗∗∗ 0.518∗∗∗ 0.392
(0.086) (0.086) (0.203) (0.2) (0.184) (0.284)
∗ ∗
(KCPE≥cutoff)×KCPE -0.21 -0.21 -0.207 -0.21 -0.368∗∗∗ 0.0008
A12
(0.125) (0.123) (0.138) (0.136) (0.127) (0.193)
Female -0.181∗∗∗ -0.203∗∗∗ -0.178∗∗∗ -0.202∗∗∗ -0.117∗∗ -0.238∗∗∗
(0.029) (0.03) (0.044) (0.059) (0.051) (0.086)
∗∗∗ ∗∗∗
Constant -1.070 -0.666 -1.125 -0.676 -0.286 -0.882
(0.096) (0.233) (0.744) (1.058) (0.9) (1.560)
Controls No No Yes Yes Yes Yes
Discontinuity F-stat . . 17.290 16.965 16.965 16.965
Observations 1923 1923 1923 1923 1923 1923
R2 0.352 0.358 0.352 0.358 0.443 0.15
(See Notes for all regression tables below Table 2.) Note that this differs from Table 3 in that the
first stage uses highest level of educational attainment rather than an indicator for completing secondary
school.
Table A4: Robustness: employment outcomes, older two cohorts of men
Outcome Estimation
(1) (2) (3) (4) (5) (6)
OLS OLS IVP IVP 2SLS 2SLS
P[Formally employed] -0.022∗∗ -0.009 0.151 0.087∗ 0.062 0.118
(0.01) (0.011) (0.159) (0.046) (0.078) (0.113)
P[Self-employed] -0.019∗∗∗ -0.023∗∗∗ -0.382∗∗∗ -0.12∗∗∗ -0.106∗ -0.129
(0.006) (0.008) (0.075) (0.026) (0.059) (0.08)
Controls No Yes No Yes No Yes
Discontinuity F-stat . . 8.118 5.346 8.118 5.346
Observations 378 378 378 378 378 378
(See Notes for Table 4.) Note that this differs from Panel A of Table 4 in that the first stage uses
highest level of educational attainment rather than an indicator for completing secondary school;
the bivariate probit is not appropriate for a continuous first stage and is omitted.
Table A5: Robustness: fertility outcome (women)
Outcome Estimation
(1) (2) (3) (4) (5) (6)
OLS OLS IVP IVP 2SLS 2SLS
P[Pregnant by 18] -0.038∗∗∗ -0.045∗∗∗ -0.544∗∗∗ -0.134∗∗∗ -0.079 -0.09
(0.006) (0.007) (0.197) (0.048) (0.055) (0.064)
Controls No Yes No Yes No Yes
Discontinuity F-stat . . 6.993 5.624 6.993 5.624
Observations 853 853 853 853 853 853
(See Notes for Table 4.) Note that this differs from Panel B of Table 4 in that the first stage
uses highest level of educational attainment rather than an indicator for completing secondary
school; the bivariate probit is not appropriate for a continuous first stage and is omitted.
A13
Table A6: Robustness: alternative discontinuity location.
Outcome: Highest grade level of educational attainment
Sample restriction: Pooled Male Female
(1) (2) (3) (4) (5) (6) (7) (8) (9)
∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗
KCPE≥cutoff 0.14 0.14 0.15 0.14 0.15∗∗∗ 0.17∗∗∗ 0.13∗∗ 0.13∗∗ 0.14∗
(0.04) (0.04) (0.05) (0.05) (0.05) (0.07) (0.06) (0.05) (0.08)
KCPE centered at cutoff 0.3∗∗∗ 0.28∗∗∗ 0.26 0.32∗∗∗ 0.28∗∗∗ 0.11 0.28∗∗∗ 0.27∗∗∗ 0.4
(0.07) (0.06) (0.23) (0.09) (0.09) (0.32) (0.09) (0.09) (0.34)
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(KCPE≥cutoff)×KCPE 0.02 0.004 -0.05 -0.006 -0.001 0.11 0.009 0.03 -0.29
(0.1) (0.09) (0.33) (0.12) (0.11) (0.43) (0.15) (0.13) (0.51)
Constant 0.35∗∗∗ 0.46∗∗∗ 0.46∗∗∗ 0.4∗∗∗ 0.43∗∗ 0.41∗∗ 0.31∗∗∗ 0.38∗∗ 0.4∗∗
(0.03) (0.13) (0.14) (0.04) (0.17) (0.18) (0.04) (0.19) (0.2)
Piecewise Quadratic No No Yes No No Yes No No Yes
Controls No Yes Yes No Yes Yes No Yes Yes
Discontinuity F-stat 10.66 14.49 7.96 7.16 9.99 6.81 4.94 5.81 3.21
Observations 1935 1935 1935 1059 1059 1059 876 876 876
2
R 0.14 0.23 0.23 0.14 0.24 0.24 0.12 0.21 0.21
(See Notes for all regression tables below Table 2.) Note that this table differs from Table 2 in that the discon-
tinuity is located at KCPE=250 for men and KCPE=240 for women, rather than the locations detected automatically
Table A7: Predictors of (large) misreporting of KCPE score.
(1) (2) (3) (4)
KCPE: self-reported -0.18∗∗∗ -0.01 -0.01 0.06∗
(0.03) (0.03) (0.03) (0.03)
Reporting a multiple of 5 0.16∗∗∗ 0.13∗∗∗ 0.13∗∗∗ 0.09∗∗∗
(0.02) (0.02) (0.02) (0.03)
Reporting exactly 250 0.12∗ 0.08 0.08 0.02
(0.07) (0.07) (0.07) (0.08)
Grade in 1998 0.03∗∗∗ 0.04∗∗∗ 0.04∗∗∗ 0.02∗∗
(0.007) (0.007) (0.007) (0.01)
Raven cognitive test . -0.02∗∗∗ -0.02∗∗∗ -0.01∗∗
(0.005) (0.005) (0.006)
KLPS1 and KLPS2 scores agree . . . -0.6∗∗∗
(0.03)
Female . . 0.008 0.03
(0.02) (0.03)
Constant 0.3∗∗∗ 0.81∗∗∗ 0.76∗∗∗ 0.85∗∗∗
(0.04) (0.05) (0.06) (0.08)
Control for mother education No No Yes No
Observations 1906 1888 1888 935
R2 0.08 0.15 0.15 0.44
Here, “large” misreports are survey responses which differ from the true test score
by more than 5 points.
A15