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Over-Reporting Social Services: Evidence from
School Audits in Chile
Eduardo Fajnzylber∗1and Bernardo Lara†2
1Inter-American Development Bank
2School of Business and Economics, Universidad de Talca
March 4, 2021
Abstract
Public subsidies incentivize private institutions to provide social services; how-
ever, incentives can elicit rent extraction activities. This paper studies such
phenomena in Chile, where private and public schools receive attendance-based
subsidies. Analyzing data from school-reported attendance against unique audit
data, we find that pre-K and K12 institutions over-report attendance by approx-
imately 11% and 2.5%, respectively. We identify for-profit motives and low-SES
student proportion as significant predictors of over-reporting. Achievement and
expenditure data show that low-achievement for-profit institutions over-report
for rent extraction purposes. Our results suggest a problematic link between
profit motives and public subsidies, resulting in inefficiency in social services.
Keywords: Economic incentives, manipulation, institutional heterogeneity.
∗E-mail: efajnzylber@gmail.com.
†Corresponding author. Centro de Investigación en Economía Aplicada. Address: Santa Elena
2222, Santiago, Chile. E-mail: blara@utalca.cl.
1
1 Introduction
In economics, a large literature focuses on the design of incentives and their effec-
tiveness at inducing desired behaviors (Gneezy et al.,2011), such as the provision of
public goods. However, one concern is that monetary incentives may result in ma-
nipulation of targeting variables (Jacob and Levitt,2003;Jacob,2005;Larkin,2014)
instead of the desired behavior. While a large literature studies corruption by state-
run organizations (Rose-Ackerman and Palifka,2016), less attention has been given to
fraud among private institutions that receive government subsidies. One sector with
an increasing participation of private providers is education.1Although there is some
evidence of test score tampering (Jacob and Levitt,2003), little is known about the
potential manipulation of one of the main target variables: attendance.
This paper contributes to the literature by (i) providing evidence about the gaming
of incentives (over-reporting attendance) in a subsidized social service (education); (ii)
characterizing the institutional heterogeneity in detected over-reporting behavior; (iii)
analyzing the relationship between over-reporting and efficiency; and (iv) testing the
effectiveness of accountability in curtailing over-reporting.
The analysis focuses on the behavior of pre-K and K12 educational providers in
Chile, a country with considerable institutional heterogeneity and monetary incentives
for daily student attendance. Specifically, education providers (excluding higher ed-
ucation) receive funding based on student attendance.2However, institutions might
over-report attendance to artificially increase funding. Such behavior might produce
an inefficient allocation of resources, particularly if over-reporting is negatively corre-
lated with the quality of the social service. In addition, over-reporting might crowd
out incentives to prevent low-performing students from dropping out.
To test these hypotheses, we analyze data from the School Attendance Inspection
Program (Programa de Fiscalización de la Asistencia Escolar ) of the Superintendency
1In fact, the former U.S. Secretary of Education Betsy Devos proposed increasing public funding
for private schools since the start of her tenure (see https://nyti.ms/2IG8w71).
2This incentive structure is similar to policies applied in the U.S. states of California, Idaho,
Kentucky, Missouri, and Texas (Ely and Fermanich,2013).
2
of Education of Chile (SE, Superintendencia de Educación de Chile). In this program,
SE inspectors visit pre-K and K12 institutions to, among other tasks, verify that the
registries and submitted reports of student attendance are accurate. Data from this
program allow us to identify differences between real and reported attendance at the
aggregate and institutional levels.
Our estimates, based on event study methodologies, indicate substantial over-
reporting of attendance. Such practices are particularly salient among institutions
with profit motives or with a high proportion of low socioeconomic status (SES) stu-
dents. We also find that institutions with high over-reporting have low educational
achievement and high real estate expenditures, which suggests an inefficient allocation
of resources. Such findings are particularly substantial among for-profit institutions.
In addition, we find little evidence that any of the current accountability tools are
effective at preventing over-reporting. Our results (i) provide a warning about the
combination of incentives and profit motives in the provision of social services and
(ii) confirm the concerns about for-profit education that have emerged at the higher
education level Deming et al. (2012); Cellini et al. (2020).
In the next section, we describe the institutional setting. Sections 3and 4discuss
the related literature and conceptual framework, respectively. Thereafter, section 5
describes the data and methodology, while section 6presents the results and discussion.
Section 7concludes with suggestions for further research.
2 Institutional setting
2.1 Chile’s educational system
Pre-K and K12 education in Chile is provided by 4 types of institutions: public (35.8%
of 2016 enrollment), private subsidized for-profit (46.2%), private subsidized nonprofit
(9.8%), and private non-subsidized (8.1%). In the first three types, institutions receive
a monthly public subsidy that is proportional to average (over the last three months)
3
daily attendance as reported to the Ministry of Education (MINEDUC), where the per-
student payment varies across education levels. This is a universal voucher system and
represents almost 90% of total public funding for pre-K and K12 education. One special
part of the voucher system is the Preferential School Subsidy (PSS, Subvención Escolar
Preferencial), which pays schools an additional voucher subsidy for the attendance of
a low-SES student.3Similar to the main subsidy, the PSS subsidy is proportional to
reported daily attendance. In 2015, total funding from the main voucher was US$4.48
billion while the total funding from the PSS voucher was US$873 million. Consequently,
reported attendance was the key parameter in the allocation of over US$5.3 billion, or
2.19% of Chile’s 2015 GDP.
In principle, school voucher systems hold institutions accountable through compe-
tition.4However, the Chilean system, despite its leading position in Latin America,
tends to underperform most OECD countries and lacks equal access to quality educa-
tion.5This unequal access was one of the main triggers of two massive student protests,
in 2006 and 2011.6Both movements focused on the use and distribution of resources
and the role of for-profit educational institutions. In response to the protests, the gov-
ernment created two new accountability institutions: the Education Quality Agency
and the Superintendency of Education (SE). While the first focuses on measuring and
improving educational achievement, the SE was created to hold institutions account-
able for the use of public funds and safeguard individual rights and equal access to
quality education. In short, the SE regulates educational institutions.
2.2 Regulation of attendance reporting
Because daily attendance is the key parameter for funding, institutions have a strong in-
centive to over-report attendance to increase revenue. In response to this challenge, the
3Other funding sources in the publicly funded system include municipal transfers and tuition fees.
4For a survey on school vouchers, see Epple et al. (2017).
5On the 2012 PISA test, Chile scored 423/441 points in math/language. Latin America scored
397/413, and OECD countries scored 494/496. Chile is among the countries with the strongest link
between educational achievement and socioeconomic status (OECD,2016).
6See Washington Post - Chile’s Student Activists: A Course in Democracy and New York Times
- With Kiss-Ins and Dances, Young Chileans Push for Reform.
4
funding formula includes a variable specifically designed to discourage over-reporting.
The MINEDUC constructs for every government observation of real attendance (in-
cluding SE audits) a “divergence” variable, which measures the difference between the
observed attendance and the preceding month’s reported average while correcting for
potential “weather shocks” in the geographical area (see Appendix B). Then, the gov-
ernment uses the average “divergence” of the last three observations of real attendance
to adjust funding.7Table 1shows the funding discounts according to the “divergence”
and the urban/rural status of the institution.
Table 1: Funding adjustment according to the estimated percentage xof over-reporting
Urban schools Rural schools Discount
x≤2% x≤4% 0%
2% < x ≤6% 4% < x ≤10% x/2%
6% < x ≤10% 10% < x ≤14% x%
10% < x ≤14% 14% < x ≤16% 2x%
14% < x 16% < x 3x%
In economic terms, these discounts are insufficient to prevent fraud. With the dis-
counts, institutions still have incentives to over-report if the probability of detection is
low and, even if detected, until a third audit. If there were no administrative or moral
costs of over-reporting, urban schools would over-report attendance by 10%, and rural
schools would over-report attendance by 14%.
To counter fraud, the new SE introduced regulations on the daily registry and
reporting of attendance. The main SE regulations are as follows: (i) every hour,
teachers must record (in permanent ink) individual and total classroom attendance;8
and (ii) schools must upload daily the attendance of the second class (8:45 a.m. to
9:30 a.m.), which directly determines funding.
In addition, the SE created the School Attendance Inspection Program (Programa
de Fiscalización de la Asistencia Escolar), whereby SE inspectors visit institutions
to verify that (i) reported attendance matches actual attendance; (ii) registries fol-
low existing regulations; and (iii) registries are consistent with information from other
7If there have not yet been observations of real attendance, the nonexistent observations are as-
sumed to have zero “divergence”.
8Appendix Tables A.1 and A.2 show SE attendance sheets.
5
databases (e.g., inspectors have used healthcare databases for cross-checking). In addi-
tion, other on-site SE audit programs, such as the Comprehensive Inspection Program,9
also include an inspection of attendance registries.
If an SE inspector detects an irregularity with a registry, the SE can demand the
return of excess funding and impose a fine of between 51 UTM (US$3,621)10 and 500
UTM (US$35,500). In cases of repeat offending and/or detection of other irregulari-
ties, additional available penalties include suspension of funding and the cancellation
of official government accreditation as an educational institution (diplomas are not
recognized).
As reporting irregularities have negative consequences, some institutions have ob-
structed audits by delaying physical access to registries and/or classrooms while al-
tering attendance sheets by replacing false attendance originally recorded in pencil
against regulations with real attendance in permanent ink immediately before audits.
In cases where alteration was not physically observed, institutions explained lower at-
tendance on an audit day versus the preceding days by claiming that the audit day
“happened to be” a low attendance day. Such obstructive behavior implies challenges
in quantifying over-reporting, and in such cases, the SE must provide further proof
of over-reporting to impose penalties. Despite these challenges, 14.6% of attendance
audits in the 2014-2016 period resulted in the SE imposing penalties.11
3 Literature review
The two sets of literature related to this paper study (i) the presence of corrupt prac-
tices in education services and (ii) the impact of monitoring practices on corruption.
The corruption in education services literature investigates high-stakes exam cheat-
ing and misappropriation of education funds. The seminal paper Jacob and Levitt
(2003) studies the interaction between accountability policies and teacher cheating by
9This program includes audits of revenue, expenses, and enrollment policies, among other areas.
10Monthly Tax Unit (Unidad Tributaria Mensual).
11Institutions can appeal SE penalties, including in the courts.
6
analyzing answers to standardized tests in the Chicago Public Schools and finds ev-
idence of teacher cheating that emerges under high accountability pressure. Cullen
and Reback (2006); González et al. (2017) and Dee et al. (2019) confirm this rela-
tionship between corruption and high-stakes scenarios. While Borcan et al. (2017)
also examines cheating on high-stakes exams, it is the sole paper within the corrup-
tion in education services literature that studies explicit corruption or, to the best of
our knowledge, a monitoring system to decrease corruption. The authors analyze a
corruption-fighting policy (based on video monitoring of exams) in Romania and find
that the policy was effective at curtailing bribes intended to facilitate cheating. An-
other significant form of corruption in education services is the misappropriation of
education funds. In investigating the use of funds from an education grant program
in Uganda, Reinikka and Svensson (2004,2011) find that local authorities divert a
significant share of education funding to political campaigns, that public information
campaigns reduce corruption, and that decreases in corruption result in improvements
in school enrollment and educational achievement. This negative correlation between
corruption and achievement is confirmed by Ferraz et al. (2012), which analyzes the
relationship between the Brazilian Comptroller General’s municipal audit results and
education quality across municipalities. While this latter subset of literature sounds
the alarm about the relationship between corruption and inefficiencies in the public
sector, it does not provide much information about corruption among private providers,
which this paper studies.
The second body of literature related to our research studies the effectiveness of
monitoring policies at reducing corruption. Olken (2007) analyzes the effects of ran-
domized audits on the expenditures of government-funded projects in Indonesian vil-
lages and finds that increasing the audit rate from 4% to 100% reduces missing expen-
ditures from 27.7% to 19.2%. Similarly, Avis et al. (2018) studies randomized audits of
municipal usage of Brazilian federal funds and finds that audits reduce detected future
municipal corruption by 8% in the same municipality and 7.5% in municipalities that
neighbor an audited municipality. In contrast, Engel et al. (2015) implement a ran-
7
domized municipal audit letter program in Chile but find little impact. Their results
cast doubt on the usefulness of top-down monitoring in societies with high institutional
quality, such as Chile.
4 Conceptual framework
In our case, the problem facing social service providers (pre-K/K12 institutions) of
how much provision (attendance) to report is similar to that of taxpayers deciding
how much income to report. A classic model in the latter literature is based on the
deterrence framework introduced by Allingham and Sandmo (1972), who adapt the
Becker (1968) model of criminal behavior to tax evasion. We modify the Slemrod
(2019) deterrence model to include a proportional subsidy rather than a proportional
tax. As we are particularly interested in heterogeneity across institutions, we include a
moral/administrative cost parameter θassociated with over-reporting. In making their
reporting decision, we assume that institutions solve the following expected utility12
maximization problem:
max
e≥0υ(e) = (1 −p)·u(ys +e(s−θ)) + p·u(ys −eθ −f(e)) (1)
which depends on the “revenue” without an audit (ys +e(s−θ)) and with an audit
(ys −eθ −f(e)). The variable e=y−yis the level of over-reporting given by the
difference between the reported (y) and actual (y) attendance. The probability of being
audited is p.13 Meanwhile, u(·)is a standard convex utility function (u0>0, u00 ≤0)
that captures the benefit of income or, alternatively, the reputational benefit from
higher expenditure. The penalty f(e)is an increasing function of the detected amount
of over-reporting and includes fines, reputational harm, and legal costs (we assume
that f(0) = 0). Regarding the moral/administrative cost θ, we may think that, for a
strictly short-term profit-oriented institution, θ= 0, while for schools with long-term
12The expected utility can also be interpreted as an expected (generic) profit.
13We assume pto be exogenous. This analysis is similar to an endogenous audit probability p(e).
8
objectives and brand awareness, θ > 0.
On the intensive margin of over-reporting, the first-order condition corresponds to
the following ratio between the marginal utilities under no audit (N) and under audit
(A):
1−p
p·u0
N
u0
A
=1−p
p·u0(ys +e∗(s−θ))
u0(ys −e∗θ−f(e∗)) =θ+f0(e∗)
s−θ(2)
Figure 1shows the graphical analysis of the fraud decision model, assuming a penalty
function f(e > 0) = F−ke that includes a lump-sum fine Fplus a penalty rate
k.14 The subfigures show on the horizontal axis the input level under no audit and
on the vertical axis the input level under audit. The 45°dotted line represents the
allocations with no over-reporting, where point H (honest) is the honest allocation of a
particular institution under analysis. Point H has an isoutility curve υH. The subfigures
also show the schedule of available allocations for over-reporting, which start at point
(ys, ys −F). The slope of the schedule is the right-hand term of equation (2): the
ratio between the unit cost of over-reporting in the case of detection (θ+f0(e)) and
the additional revenue generated by each unit of over-reporting (s−θ). Regarding the
extensive margin, Subfigure 1(a) assumes an isoutility curve υHof point H that crosses
the schedule; thus, the institution will over-report because there is at least one ˜e > 0
such that υ(0) < υ(˜e).15 Moreover, honest behavior is more likely with a higher initial
penalty fee F(moving the schedule down), a higher probability of detection p(flatter
isoutility curves), and a higher moral/administrative cost θ. The latter follows since θ
decreases the expected utility of dishonest behavior.
Next, Subfigure 1(b) shows the interior solution, where the isoutility curve is tan-
gent to the available schedule (equation (2)). Increases in the marginal penalty (f0(e))
or higher probabilities of detection (p) result in lower over-reporting (e∗). With regard
to the moral/administrative cost θ, we can see that the right side of equation (2) in-
creases with θ, since the schedule that the institution faces becomes steeper. On the
left, we have that the ratio of marginal utilities: (i) decreases with θif the coefficient
14Assuming a nonlinear penalty does not fundamentally change the analysis.
15If the penalty function is continuous at 0 (no lump-sum F), the institution will over-report if
∂v(e)
∂e |e=0 >0, which will occur whenever 1
p>2 + f0(0)−1
s−θ.
9
Figure 1: Fraud decision model
(a) Honest behavior (b) Optimal decision
of absolute risk aversion (γ=−u00/u0) is decreasing; and (ii) does not change if γis
constant. Therefore, under decreasing or constant absolute risk aversion, we have that
a higher moral/administrative cost decreases over-reporting.16
In sum, heterogeneity in the moral/administrative cost, under standard assump-
tions, implies heterogeneity in over-reporting: institutions with higher reputation or
moral costs (institutions perceived as high-quality or associated with religious motives)
might be less likely to over-report than those with purely short-term profit motives and
little regard for social service reputation. A negative correlation between θand service
quality would imply an inefficient allocation of resources, as low-quality institutions
would receive higher subsidies due to higher over-reporting. In the next sections, we
will examine whether these patterns exist in the data.
16This predicted behavior does not hold in the case of a highly increasing γ, as the lower “revenue”
(due to the higher moral/administrative costs) drives institutions to take more or greater risks.
10
5 Data and methodology
Data
All subsidized educational institutions in Chile report daily attendance to the MINE-
DUC. We use reported daily attendance from each institution from the period 2013-
2016 in addition to observed (audited) attendance and each inspection outcome. To
complement the attendance data, we use public data on other institutional character-
istics, such as location and education levels, among others.17 Table 2shows descriptive
statistics of the main variables over time.
The main data set includes over 1.5 million daily observations per year at approx-
imately 9,000 institutions (pre-K and K12). The average reported daily attendance
is slightly above 280 students. As there is wide variation in attendance (mainly due
to heterogeneity in capacity), we use the logarithm of attendance in the empirical
analysis. There is also significant variation over time in observed attendance, mainly
due to changes in the sample of audited institutions.18 The fifth row shows that over
20% of audited schools had a mismatch between reported and observed attendance.
While the small difference between reported and observed attendance suggests that
over-reporting fraud is an insubstantial problem, the magnitude of the problem might
be concealed by on-the-spot adjustment of daily attendance. It is also worth noting
that the percentage of institutions audited (ninth row) decreases over time, decreasing
from 73.9% in 2013 to 10.4% in 2016, due to the SE’s decision to lessen its focus on
attendance audits in favor of other oversight programs unrelated to attendance.
While the data include all subsidized institutions, most institutions in the data
set are private, and, among these, the vast majority are classified as for-profit insti-
tutions.19 It is also important to note that pre-K institutions comprise approximately
17These public data are available at http://datosabiertos.mineduc.cl/.
18The SE’s audit selection criteria depend on an institution’s history of attendance and inspections
as well as a random component. To protect the secrecy of the SE’s selection criteria, we will not
provide further details.
19While some nonprofit institutions use a for-profit legal designation to avoid the administrative
burdens of a nonprofit designation, the SE provided these classifications to us based on the legal
designation of each institution.
11
Table 2: Means with standard deviations in parentheses of selected variables,
institution-level database, 2013-2016.
Variable Year
2013 2014 2015 2016
mean/sd mean/sd mean/sd mean/sd
Attendance in the day 287.726 289.874 290.371 296.647
(348.0177) (349.7655) (351.8418) (355.0006)
Log of reported attendance 4.738 4.735 4.721 4.751
(1.6556) (1.6776) (1.6956) (1.7010)
Attendance observed by inspector 362.026 411.334 343.714 354.561
(368.5242) (382.0862) (345.4615) (271.5386)
Log of observed attendance 5.377 5.563 5.294 5.514
(1.1185) (1.0675) (1.2130) (0.9943)
Attendance incorrectly reported 0.229 0.231 0.213 0.253
(0.4201) (0.4217) (0.4092) (0.4349)
Diff. logs reported and observed 0.003 0.002 0.004 0.010
(0.0502) (0.0375) (0.0400) (0.1502)
Total enrollment 328.953 330.051 330.117 332.747
(394.4851) (395.3950) (396.2192) (396.8775)
Diff. enrollment and attendance 0.124 0.117 0.117 0.100
(0.2427) (0.2504) (0.2696) (0.2043)
Inspected in the year 0.739 0.445 0.231 0.104
(0.4390) (0.4970) (0.4216) (0.3057)
Private subsidized institution 0.457 0.465 0.473 0.462
(0.4981) (0.4988) (0.4993) (0.4985)
For-profit institution 0.352 0.358 0.365 0.354
(0.4775) (0.4795) (0.4814) (0.4783)
Pre-K institution 0.071 0.072 0.073 0.069
(0.2571) (0.2586) (0.2604) (0.2540)
Institution in rural area 0.393 0.385 0.382 0.382
(0.4885) (0.4865) (0.4859) (0.4859)
Percentage high-priority students 0.677 0.658 0.611 0.616
(0.2265) (0.2173) (0.2121) (0.2127)
Number of institutions 9,061 9,087 9,072 8,981
Observations 1,617,553 1,601,072 1,559,825 1,564,264
7% of the sample. Although attendance is not mandatory, subsidies for pre-K institu-
tions are also proportional to daily attendance. Its voluntary aspect, however, creates
greater scope for over-reporting due to the greater variation in daily attendance, more
difficult detection of discrepancies, and easier justification of absences.
12
Methodology
Given the daily reporting of attendance and unexpected nature of SE inspection visits,
we use an event study methodology popular in the finance literature (MacKinlay,
1997).20 In particular, we focus on the evolution of attendance around the date of the
visit. If there are multiple visits to an institution in a year, we only consider the first
visit to avoid confounding effects. We compare daily reported attendance during the 5
days preceding the visit, the day of the visit, and the 5 days succeeding the visit with
respect to the average attendance of all institutions within the same region each day.
This allows us to both measure potential anticipation effects and observe the evolution
of attendance before and after the visit (Kothari and Warner,2007). The event study
methodology helps us to estimate an average audit effect on the visited institutions for
this 11-day window.
Initially, we assume the following data generation process:
yirt =δ0+
1
X
d=5
δ−dWit+d+δWit +
5
X
d=1
δdWit−d+ηirt (3)
where variable yit is the logarithm of attendance at institution i, located in region r,
on day t.Wit is a dummy variable that indicates that an audit occurred at institution
ion day t. The dummies Wit+dand Wit−dcapture potential changes in the 5 days
preceding and succeeding the visit, respectively. The error term can be decomposed as
ηirt =ψi+φrt +µit , where ψirepresents a school-specific effect, φrt captures any region-
specific time effect (such as a weather shock) in region ron day t, and µit =µit−1+εit
is an idiosyncratic random walk error term.
Given that attendance is a highly autoregressive process,21 we estimate the following
first-difference model (Wooldridge,2003):
∆yirt =α0+
1
X
d=5
β−dWit+d+βWit +
5
X
d=1
βdWit−d+˜
φrt +εirt (4)
20A related method is staggered adoption difference-in-differences (Athey and Imbens,2018).
21Attendance has a 0.9957 correlation with the attendance of the preceding day.
13
where parameter βj(jbetween -5 and 5) captures the change in the logarithm of
attendance between a particular day and the preceding day.22 Because Chilean climate
varies across regions and is a potentially significant predictor of changes in attendance,
it is important to include a region-level time effect ˜
φrt =φrt −φrt−1. Next, βjestimates
the additional change in attendance on day jaround an audit day in comparison to
the change in attendance at unaudited institutions in the region that day.
We estimate this model on several samples. The main identifying assumption is
that the visit day dummies are orthogonal to the institution-level daily idiosyncratic
shock, controlling for region-level time effects. In other words, the attendance trend
should be parallel across institutions in the same region. Moreover, if institutions are
able to anticipate the visit more than 5 days in advance, we should not be able to
detect variations in attendance within the window of analysis.
In addition to measuring the average level of over-reporting in audited institutions,
we are interested in identifying possible differential responses to the incentive struc-
ture, i.e., heterogeneity in over-reporting, for which we need individual institution-level
measures of over-reporting. To obtain this, we repeat the previous estimation sepa-
rately for each region and year and estimate institution-specific coefficients for the day
before the visit (βi,−1), the day of the visit (βi), and the day after the visit (βi,+1).
The time effect ˜
φtcaptures the daily variation common to the region. Thus, the model
that estimates over-reporting at each institution is:
∆yit =α+
2
X
d=5
β−dWit+d+X
i∈A
(βi,−1Wit−d+βiWit +βi,+1Wit+1 ) +
5
X
d=2
βdWit−d+˜
φt+εit (5)
where Ais the set of institutions that were audited in the region that year.
22Coefficient β−5is interpreted as the difference between the logarithm of attendance at the audited
institution and the average logarithm of attendance in the region on the fifth day preceding the visit.
14
6 Results
6.1 Aggregate results
First, we present system-wide estimates of over-reporting based on equation (4). Since
the magnitude of over-reporting might differ across institutional levels, we separate
the analysis between pre-K and K12 institutions.23 For the first set of results, we
use reported attendance for all days. For the second set of results, we use inspectors’
observed attendance on the visit day and reported attendance for the other days. While
we should expect that each set of results provides different estimates of over-reporting,
institutions might adjust the reported attendance of the visit day in response to the
inspector’s visit. They cannot, however, adjust reported attendance for previous days.
Table 3presents estimation results based on reported attendance. The first column
includes all institutions, while the second and third columns include only the subsam-
ples of pre-K institutions and K12 institutions, respectively. Despite the large sample
size, the coefficients for two or more days before the audit day are not statistically or
practically significant. However, an inspector “visit today” event induces a negative
shock in pre-K reported attendance of -0.101 (-9.6%, equivalent to 5.0 students). We
also find a small anticipation effect on the day before the visit, with reported atten-
dance decreasing by 1.3%, although this is explained by the 1.0% of precommunicated
visits that require institutions to prepare materials for other audit dimensions (such as
financial).24 A similar pattern appears in the K12 subsample, although with a smaller
but significant visit-day effect of -0.0229 (-2.3%, equivalent to 6.0 students).
The estimates also show that the decrease in reported attendance is short-lived as
the following two or three days have positive effects. In other words, attendance rapidly
returns to pre-audit levels. To show this, Figure 2presents predicted attendance
during the two-week window surrounding the visit day, where the daily estimates
are the sums of the estimated coefficients. Subfigures 2(a) and 2(b) present estimates
23The pre-K sample comprises institutions that only have pre-K levels while the K12 sample includes
some institutions that also have pre-K levels.
24When restricting the sample to precommunicated visits, the anticipation effect is 2.2%, whereas
excluding precommunicated visits decreases the same effect to 0.2%.
15
Table 3: Aggregate over-reporting, change in log of reported attendance
(1) (2) (3)
All Pre-K K12
∆attend. ∆attend. ∆attend.
VARIABLES reported reported reported
Visit in 5 days 0.00330** 0.000254 0.00348**
(0.00137) (0.00304) (0.00145)
Visit in 4 days 9.22e-06 0.00309 -0.000516
(0.00123) (0.00241) (0.00130)
Visit in 3 days -4.25e-05 -0.00392* 0.000297
(0.00139) (0.00220) (0.00146)
Visit in 2 days 0.00121 -0.00284 0.00165
(0.00178) (0.00248) (0.00190)
Visit tomorrow -0.00236 -0.0124*** -0.00167
(0.00181) (0.00311) (0.00191)
Visit today -0.0283*** -0.101*** -0.0229***
(0.00179) (0.00541) (0.00177)
Visit yesterday 0.0294*** 0.0970*** 0.0243***
(0.00132) (0.00542) (0.00122)
Visit 2 days ago 0.00213* 0.0111*** 0.00128
(0.00121) (0.00300) (0.00127)
Visit 3 days ago 0.00146 0.00511* 0.00128
(0.00133) (0.00261) (0.00140)
Visit 4 days ago 0.00138 -0.000418 0.00161
(0.00169) (0.00241) (0.00181)
Visit 5 days ago 0.00162 0.00264 0.00141
(0.00117) (0.00264) (0.00126)
Constant -0.00113*** 0.000311*** -0.00124***
(5.54e-06) (8.29e-06) (5.03e-06)
Observations 6,283,483 447,930 5,834,434
R-squared 0.057 0.150 0.058
Region-date FE Yes Yes Yes
Clustered standard errors at institution-year level in parentheses
*** p<.01; ** p<.05; * p<.1
based on reported attendance for pre-K and K12 institutions, respectively. Meanwhile,
Subfigures 2(c) and 2(d) present analogous results using observed attendance for the
day of the visit. In all cases, the audit induces a significant decrease in attendance
that disappears after two days. In sum, our results suggest three initial findings: a
nonnegligible level of attendance over-reporting, significant same-day manipulation to
escape detection, and a rapid return to usual reporting practices, implying that audits
do not deter fraud.
Table 4presents results analogous to those in Table 3but uses the attendance
level observed by the inspector on the visit day. Since observed attendance provides a
16
Figure 2: Change in log of attendance around audit day
(a) Reported pre-K (b) Reported K12
(c) Observed pre-K (d) Observed K12
more credible estimation of over-reporting rates than reported attendance, we will use
observed attendance in the rest of the paper. The estimates are very similar to the
previous results, with a same-day over-reporting effect of 0.109 (10.3%, equivalent to
5.4 students) for pre-K institutions and 0.0257 (2.5%, equivalent to 6.7 students) for
K12 institutions. We again observe a rebound effect on the days following the visit.
6.2 Characterizing over-reporting
Thus far, we have presented evidence of over-reporting at the aggregate level. Next, we
study whether there is significant heterogeneity in over-reporting across institutions.
In addition, we identify the variables correlated with over-reporting practices.
Over-reporting heterogeneity is relevant for efficiency considerations. Under homo-
geneous over-reporting, policymakers may reduce the size of the subsidy per student
17
Table 4: Aggregate over-reporting, change in log of observed attendance
(1) (2) (3)
All Pre-K K12
∆attend. ∆attend. ∆attend.
VARIABLES observed observed observed
Visit in 5 days 0.00329** 0.000206 0.00347**
(0.00137) (0.00303) (0.00145)
Visit in 4 days 7.05e-06 0.00308 -0.000517
(0.00123) (0.00240) (0.00130)
Visit in 3 days -5.77e-05 -0.00388* 0.000280
(0.00139) (0.00220) (0.00146)
Visit in 2 days 0.00121 -0.00290 0.00165
(0.00178) (0.00249) (0.00190)
Visit tomorrow -0.00236 -0.0126*** -0.00167
(0.00181) (0.00313) (0.00191)
Visit today -0.0315*** -0.109*** -0.0257***
(0.00187) (0.00576) (0.00184)
Visit yesterday 0.0322*** 0.106*** 0.0267***
(0.00142) (0.00576) (0.00131)
Visit 2 days ago 0.00225* 0.0111*** 0.00140
(0.00122) (0.00301) (0.00127)
Visit 3 days ago 0.00143 0.00524** 0.00125
(0.00133) (0.00260) (0.00140)
Visit 4 days ago 0.00138 -0.000444 0.00161
(0.00169) (0.00241) (0.00181)
Visit 5 days ago 0.00162 0.00263 0.00140
(0.00117) (0.00264) (0.00126)
Constant -0.00113*** 0.000311*** -0.00124***
(5.65e-06) (9.76e-06) (5.12e-06)
Observations 6,283,483 447,930 5,834,434
R-squared 0.057 0.150 0.058
Region-date FE Yes Yes Yes
Clustered standard errors at institution-year level in parentheses
*** p<.01; ** p<.05; * p<.1
and replicate the resource allocation under honest behavior, with no resource misal-
location. In contrast, heterogeneous over-reporting results in a greater allocation of
resources to cheating institutions, which may cause inefficient resource allocation. Con-
sequently, we also analyze the institutional characteristics that predict over-reporting
rates.
For this analysis, we first estimate equation (5) for each region and year to obtain
the visit effect (βi,−1+βi) and rebound effect (βi,+1 ) for each visited institution i. To
avoid outliers, we drop over-reporting estimates beyond three standard deviations from
the over-reporting average at each education level.
18
Table 5presents the fraction of institutions we classify as over-reporters based on
statistical significance (βi<0with 95% confidence interval) and the average estimated
coefficients by education level. The last column of the table represents the estimated
over-reporting (β−1+β), conditional on being classified as an over-reporter. We identify
63.5% of all institutions as over-reporters, with this figure increasing to 77.2% for pre-
K institutions. Among over-reporters, the decrease in the logarithm of attendance
induced by the audit visit is 0.140 (13.1%) for pre-K institutions and 0.055 (5.4%) for
K12 institutions.
Table 5: Fraction over-reporting and average estimated coefficients by education level
Mean combined effect
Level fraction significant day before visit day day after among over-reporters
Pre-K 0.770 -0.010 -0.098 0.093 -0.140
K12 0.628 -0.002 -0.030 0.024 -0.055
All 0.635 -0.007 -0.029 0.030 -0.063
To understand the extent of over-reporting, Figure 3presents the box plots of
βi(visit-day effect) and βi,+1 (day-after effect) by education level.25 Three notable
aspects of these figures are as follows: (i) as expected, most of the same-day coeffi-
cients lie below the zero line, suggesting extensive over-reporting; (ii) the prevalence
of over-reporting and the median value are greater among pre-K institutions than K12
institutions; and (iii) the day-after effect seems to mirror and offset the audit-day
effect.
Figure 4, which presents the scatterplot of βiagainst βi,+1, confirms the drop-
bounce pattern of over-reporting. Most pre-K institutions lie in the upper-left quadrant
and near the 45°line. This finding suggests that the lower reported attendance on the
visit day reverts to previous levels the next day. Although a similar pattern appears
at the K12 level, there is more dispersion around the four quadrants. In sum, the
drop-bounce pattern occurs at the institution level and is not an aggregation result.
25Box plots show the median, the 25th and 75th percentiles, and the upper and lower adjacent
values.
19
Figure 3: Box plots of estimated βcoefficients by institution level
Figure 4: Scatter plot of βpre and βi,+1 coefficients by education level
Predictors of heterogeneity
To identify which factors predict fraud, Table 6presents OLS regression results with
the institution-level visit-day over-reporting measure as a dependent variable. All
20
regressions control for region and year fixed effects. Columns (1) and (3) only include
a private subsidized institution dummy and its interaction with a for-profit dummy
(public institutions are the omitted group). We find that the share of high-priority
students—who carry an additional voucher—increases over-reporting. Specifically, a
10% increase in high-priority students predicts a 0.9% increase in over-reporting at the
pre-K level and 0.4% at the K12 level. More importantly, the results also show that for-
profit motives only predict higher over-reporting than nonprofit private institutions at
the K12 level. However, for-profit institutions over-report more than public institutions
at both levels (the p-value of the Wald test is in the bottom row). As the difference
might arise from differences between institutions in terms of socioeconomic challenges
and incentives, columns (2) and (4) show the results after controlling for enrollment,
composition of students, and a rural dummy variable. These results confirm that for-
profit institutions over-report more than public institutions at both levels and more
than nonprofits at the K12 level. As a result, over-reporting produces a different
funding allocation across different institution types.
Table 6: OLS regression on school-level over-reporting effects
(1) (2) (3) (4)
Pre-K Pre-K K12 K12
VARIABLES ˆ
βiˆ
βiˆ
βiˆ
βi
Private institution -0.00856 -0.0134 0.0168*** 0.00216
(0.0386) (0.0380) (0.00196) (0.00215)
Private for-profit institution -0.0258 -0.0283 -0.0247*** -0.0162***
(0.0363) (0.0369) (0.00220) (0.00215)
Log enrollment 0.000372 0.0126***
(0.00771) (0.00130)
Percentage high-priority students -0.0857*** -0.0414***
(0.0290) (0.00499)
Institution in rural area 0.0355 0.00935***
(0.0453) (0.00259)
Constant -0.0671*** -0.0206 -0.0288*** -0.0699***
(0.0157) (0.0420) (0.00117) (0.00949)
Observations 921 918 12,574 12,574
R-squared 0.054 0.064 0.024 0.052
Region FE Yes Yes Yes Yes
Year FE Yes Yes Yes Yes
P-value (H0: for-profit<public) 0.0240 0.00915 0.000038 0.00000
Clustered standard errors at institution level in parentheses
*** p<.01; ** p<.05; * p<.1
To appreciate the difference in over-reporting across institution types, Figure 5
21
shows box plots for public, private nonprofit, and private for-profit institutions. We
see that over-reporting is greatest among for-profit schools. This result suggests that
for-profit institutions capture more resources by inflating their attendance reports,
while the opposite occurs among private nonprofit institutions.
Figure 5: Box plots of the estimated βcoefficients by institution type and day
6.3 Efficiency analysis
Although over-reporting is subject to legal and moral objections, it is possible that
high-achievement institutions over-report and the result is a more productive allocation
of resources. In addition, institutions might use additional resources for educational
inputs. In these cases, over-reporting might not lead to an inefficient allocation of
resources. To determine whether that is the case, we next estimate the correlation
between achievement and over-reporting.
22
Over-reporting and achievement
To measure achievement, we use the normalized “effectiveness” score from the SNED26
national school evaluation system, which is generated in three steps. First, the SNED
classifies schools according to geographic region, urban/rural location, and education
level. Second, it clusters schools within each classification based on a socioeconomic
vulnerability index, average household income, and average parental education. Third,
the SNED defines the “effectiveness score” as the achievement score on the standardized
national achievement tests (SIMCE) for each education level tested in the school in
comparison to the average score within the cluster of similar schools. Therefore, our
measure of achievement already controls to some extent for student socioeconomic
backgrounds and differences across education levels.
Using our achievement measure, we estimate a simple linear model of achievement
as a function of “over-reporting intensity” dummies and a set of control variables.
Although our coefficients do not have a causal interpretation, they help us understand
whether over-reporting allocates resources to high, average, or low achievement schools.
Table 7shows the results. Column (1) shows the gross differences in achievement across
over-reporting groups, with the base group being schools over-reporting by less than
2% (approximately half of the sample, includes 0%). We observe a negative correlation
between over-reporting and achievement: schools over-reporting by between 5% and
10% (18% of the sample) perform 35.4% of an SD worse than the base group, while the
over-10% group performs 56.5% of an SD worse. Moreover, the results after controlling
for student composition, location, enrollment, institution type, and municipality and
year fixed effects (columns (2) and (3)) still show a significant (although smaller)
negative correlation between over-reporting intensity and achievement. In particular,
the estimates in column (2) show that schools over-reporting by 5%-10% perform worse
by approximately 8.5% of an SD, while schools over-reporting by more than 10%
perform worse by approximately 11% of an SD. In sum, the evidence suggests that
over-reporting drives resources to low-efficiency schools.
26Sistema Nacional de Evaluación del Desempeño de los Establecimientos Educativos Subvenciona-
dos. See Mizala and Urquiola (2013) for further details.
23
Table 7: Efficiency across over-reporting rates
(1) (2) (3)
VARIABLES Achievement Achievement Achievement
Over-report 2%<x<5% -0.0391 0.0192 0.0216
(0.0331) (0.0238) (0.0235)
Over-report 5%<x<10% -0.354*** -0.0851*** -0.0797***
(0.0333) (0.0265) (0.0262)
Over-report 10%<x -0.565*** -0.112*** -0.109***
(0.0405) (0.0348) (0.0346)
Percent low SES students -4.029*** -3.609***
(0.0866) (0.0988)
Institution in rural area 0.390*** 0.386***
(0.0416) (0.0417)
Log enrollment 0.208*** 0.210***
(0.0189) (0.0190)
Private subsidized institution 0.368***
(0.0376)
For-profit institution -0.145***
(0.0356)
Constant 0.147*** 1.299*** 0.897***
(0.0209) (0.147) (0.154)
Observations 12,246 12,246 12,246
R-squared 0.043 0.511 0.523
Municipality FE No Yes Yes
Year FE No Yes Yes
Clustered standard errors at institution level in parentheses
*** p<0.01; ** p<0.05; * p<0.1
Focusing on the last institutional heterogeneity result, Table 8presents the achieve-
ment analysis by institution type. Among public schools, there is a significant (and
positive) association between a mild level of over-reporting (between 2% and 5%) and
achievement. Among private nonprofit schools, we find weak evidence (significant at
15%) that intermediate levels of over-reporting predict lower achievement by 13.4% of
an SD than the group over-reporting by less than 2%. The negative conditional cor-
relation between over-reporting and achievement is stronger among private for-profit
schools, where intermediate and high over-reporting schools have lower achievement
by approximately 20% of an SD. This finding suggests that, even after controlling for
student composition, over-reporting is driving resources to worse performing for-profit
schools.
In summary, our results suggest that over-reporting does not result in a better
allocation of resources, at least in terms of higher achievement. This implies that
the resulting allocation of resources is inefficient, as over-reporting drives resources to
24
Table 8: Achievement across over-reporting rates by institution type
(1) (2) (3)
Achievement Achievement Achievement
public private private
VARIABLES non-profit for-profit
Over-report 2%<x<5% 0.0626** 0.0588 -0.0480
(0.0318) (0.0605) (0.0437)
Over-report 5%<x<10% 0.0218 -0.134 -0.187***
(0.0322) (0.0928) (0.0503)
Over-report 10%<x -0.0224 0.00432 -0.211***
(0.0422) (0.120) (0.0641)
Percent low SES students -2.854*** -3.958*** -3.496***
(0.203) (0.219) (0.145)
Institution in rural area 0.407*** -0.00604 0.295***
(0.0531) (0.152) (0.0939)
Log enrollment 0.175*** 0.195*** 0.298***
(0.0280) (0.0592) (0.0315)
Constant 0.607** 1.503*** 0.511**
(0.257) (0.435) (0.230)
Observations 6,832 1,540 3,874
R-squared 0.374 0.730 0.603
Municipality FE Yes Yes Yes
Year FE Yes Yes Yes
Clustered standard errors at institution level in parentheses
*** p<0.01; ** p<0.05; * p<0.1
low-achievement institutions. Once again, for-profit institutions drive the bulk of the
effect.
Over-reporting and use of resources
Our results raise a question regarding the use of the “extra” resources that do not result
in higher achievement. One hypothesis is that achievement differentials would be even
larger if these “extra” resources were not available. On the other hand, for-profit schools
might use the additional funding for inputs unrelated to achievement. One concern
regarding for-profit institutions in Chile is that they might extract/accumulate rents by
investing public funding in real estate assets or pay inflated rent prices to school owners.
Moreover, government regulations restricting profit withdrawals would encourage such
behavior.
To test whether over-reporting for-profit schools spend more resources on real es-
tate (purchase, construction, or rent), we use detailed SE data on school expenditures.
We classify these expenditures as human resources (salaries, bonuses, etc.), education
25
(learning materials, student welfare, consulting, training, etc.), operations (utilities,
financial reallocations, etc.), building and maintenance of infrastructure, purchases
of physical assets (real and movable property), and rent of physical assets (real and
movable property). Based on this classification, Table 9presents truncated regression
results for the logarithm of the per-student enrolled expenditure across expenditure
classes as a function of the over-reporting intensity and socioeconomic/geographic fac-
tors.27 The results from column (2) suggest that for-profit schools over-reporting by
more than 5% spend less on education inputs, while columns (5) and (6) show that
the same schools spend more on acquiring and renting physical assets. These results
suggest that for-profit schools use additional resources for real estate investments and
rent extraction and not for achievement inputs. Public and private nonprofit high
over-reporters (results available in Appendix Tables A.3 and A.4) also show higher
expenditures on rent. However, public schools spend more on achievement inputs, and
nonprofit schools spend less on purchasing assets.
Table 9: Expenditure classes across over-reporting rates, for-profit schools
(1) (2) (3) (4) (5) (6)
ln human ln educ ln oper ln build ln purchase ln rent
VARIABLES exp pc exp pc exp pc exp pc exp pc exp pc
Over-report 2%<x<5% 0.00191 0.0665 0.0186 0.0394 -0.158 -0.0787
(0.0214) (0.0606) (0.0491) (0.0566) (0.173) (0.136)
Over-report 5%<x<10% -0.0231 -0.243*** -0.00620 -0.00174 0.514*** 0.128
(0.0282) (0.0709) (0.0539) (0.0621) (0.185) (0.134)
Over-report 10%<x 0.0426 -0.119* -0.0978 -0.0304 0.334* 0.445***
(0.0267) (0.0683) (0.0650) (0.0732) (0.193) (0.140)
Percent low SES students 0.0331 2.807*** 0.0739 -0.209 0.306 -0.915**
(0.0481) (0.150) (0.140) (0.146) (0.403) (0.369)
Institution in rural area 0.251*** -0.00403 0.684*** 0.517*** 0.901*** 0.763***
(0.0318) (0.0952) (0.0795) (0.0919) (0.270) (0.227)
Constant 7.183*** 2.265*** 5.358*** 3.501*** 1.917*** 4.342***
(0.0490) (0.214) (0.158) (0.236) (0.625) (0.515)
Observations 2,074 2,034 2,074 2,034 1,222 1,496
Institution for-profit for-profit for-profit for-profit for-profit for-profit
Region FE Yes Yes Yes Yes Yes Yes
Clustered standard errors at institution level in parentheses
*** p<0.01; ** p<0.05; * p<0.1
In sum, our results show that over-reporting results in an inefficient allocation of
resources. In particular, it drives public subsidies toward low-achievement for-profit
27We use a truncated regression because some expenditure classes (mainly purchases/rent of assets)
have zero expenditure.
26
schools, which use part of the extra resources on real estate expenditures, potentially
as a vehicle for rent extraction.
6.4 Accountability
Thus far, we have established that institutions over-report attendance and that top-
down standard monitoring does not seem to correct this behavior. In this section, we
test whether different exposure to monitoring or penalties results in better reporting
practices.
Although audit visits do not create sustainable corrections during the following
week, it is possible that over-reporting decreases later (after a school meeting, for ex-
ample). Thus, we extend the window of analysis to 5 weeks before and after the audit
and estimate equation 4, but replace daily dummies with weekly dummies. Subfig-
ures 6(a) and 6(b) show the medium-term evolution of attendance for pre-K and K12
institutions, respectively.28 Both subfigures show that one week after the audit visit, in-
stitutions have returned to their previous attendance levels. Therefore, over-reporting
is robust to audit visits, even if we allow for a longer change period.
Another approach to detect long-term audit effects is to measure the over-reporting
rates using a second audit visit. The SE revisits institutions with prior attendance
reporting problems. Although institutions might suspect that a new visit is coming,
they do not know the date of the second visit. An expectation of a second audit is
not a problem if the threat of a second audit deters misbehavior. Subfigures 6(c)
and 6(d) show the results for second visits in an academic year. We see that the
change in behavior is only marginal, as institutions over-report at similar rates and
rapidly return to pre-visit reporting levels.29 Consequently, we do not find evidence of
long-term reductions in over-reporting from second audits.
As mentioned previously, the SE can impose fines on institutions that engage in
misbehavior. To test whether financial penalties can correct misbehavior, we examine
28Regression results are available in Appendix Table A.5.
29Regression results are available in Appendix Table A.6.
27
Figure 6: Analysis of over-reporting under different accountability tools, 2013-2016
(a) Pre-K - medium term (b) K12 - medium term
(c) Pre-K - 2nd visit (d) K12 - 2nd visit
(e) Pre-K - SE penalty (f) K12 - SE penalty
(g) Pre-K - MINEDUC adjustment (h) K12 - MINEDUC adjustment
28
the subsample of institutions that were audited and fined for incorrect attendance
reporting. Note that this is the textbook monitoring situation: there is an audit, it
detects a problem, and a penalty ensues. Once again, Subfigures 6(e) and 6(f) do not
show a decline in (relatively large) over-reporting behavior. Institutions substantially
decrease their reported attendance on the audit day, only to return to their previous
behavior on subsequent days.
Finally, the MINEDUC can adjust funding based on consistent evidence that an
institution over-reports attendance. Therefore, institutions might stop fraud after
observing a funding penalty by the MINEDUC, which signals that the MINEDUC
classified them as over-reporters and that over-reporting will cause discounts. To study
the effects of the discounts, we analyze over-reporting in the subsample of institutions
that had funding adjustments in the preceding year. Subfigures 6(g) and 6(h) show
that institutions still over-report the year following the funding penalty.30
In conclusion, we find that attendance fraud is quite robust to the existing ac-
countability tools. This casts doubt on the ability of top-down monitoring to address
incentive manipulation in a heterogeneous and decentralized social service provision
system.
7 Conclusions
In this paper, we present evidence that schools, particularly low-quality for-profit
schools, commit attendance fraud to increase revenue. This implies several challenges
to social services provision. First, the manipulation of monetary incentives introduces
the need for monitoring systems, which is often expensive. Second, the greater fraud
rates among for-profit institutions demonstrate that profit motives also motivate cor-
ruption. These results confirm concerns about the role of for-profit institutions in
education, which (Deming et al.,2012;Cellini et al.,2020) have confirmed for higher
education. Third, the results also suggest that corruption introduces an inefficient dis-
30Regression results are available in Appendix Table A.8.
29
tribution of public funds, as inferior quality institutions can capture more resources.
Hence, the consequences of fraud are not only moral; the quality and efficiency of social
services suffers as a result of fraud.
Our results also have implications for the use of market tools. Although markets
reward positive innovations, our findings show that negative forms of innovation, such
as new forms of “cheating the government,” can also generate rewards. In addition, top-
down monitoring policies of the government may not keep pace with negative forms of
innovation. In that sense, bottom-up policies, such as those in Björkman and Svensson
(2009); Reinikka and Svensson (2011); Björkman Nyqvist et al. (2017), might be more
effective at preventing fraud.
Finally, it is necessary to address the indirect victims of fraud: the “ghost students”
that schools reported as present but in reality were absent. These students might
advance through education levels with little attendance or learning. Correspondingly,
the next goal of our research agenda is to identify the negative consequences for these
ghost students.
30
Acknowledgements
We want to thank Analía Jaimovich, Marcela Ortiz, Mauricio Farías, César Muñoz,
Lucciano Villacorta, Eduardo Engel, Eugenio Giolito, Martin Carnoy, Eric Bettinger,
Claudio Agostini, Andrea Repetto, Evelyn Kim, and the Superintendency of Educa-
tion, which provided us access to audit and expenditure data, under a strict confiden-
tiality agreement. We also thank Fondecyt Iniciación (project 11200352) for financial
support. Preliminary results of this article were included in a report presented to the
Inter-American Development Bank.
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Appendix
Figure A.1: Distribution of inspections across months
35
Appendix Tables
Table A.1: Registry of individual attendance for school voucher funds purposes
Source: Circular N°1, Superintendency of School Education (2014).
Table A.2: Registry of attendance in each class
Source: Circular N°1, Superintendency of School Education (2014).
36
Table A.3: Log of expenditure per student enrolled and over-reporting, public schools
(1) (2) (3) (4) (5) (6)
ln human ln educ ln oper ln build ln purchase ln rent
VARIABLES exp pc exp pc exp pc exp pc exp pc exp pc
Over-report 2%<x<5% 0.0677*** 0.0808** -0.0181 0.0638* 0.0605 0.233
(0.0255) (0.0363) (0.0325) (0.0387) (0.114) (0.178)
Over-report 5%<x<10% 0.0589* 0.0842** 0.00904 0.137*** 0.0653 0.240
(0.0325) (0.0400) (0.0337) (0.0417) (0.116) (0.188)
Over-report 10%<x 0.174*** 0.0523 0.0716* 0.124** 0.202* 0.584***
(0.0337) (0.0471) (0.0413) (0.0518) (0.122) (0.205)
Percent low SES students 0.638*** 1.296*** 0.750*** 0.405*** 1.214*** 0.149
(0.101) (0.135) (0.131) (0.143) (0.383) (0.677)
Institution in rural area 0.0733** -0.103** 0.200*** 0.131*** 0.455*** 0.494*
(0.0359) (0.0427) (0.0384) (0.0422) (0.120) (0.267)
Constant 7.171*** 3.010*** 4.686*** 2.596*** 1.327** -2.617***
(0.0731) (0.158) (0.161) (0.117) (0.520) (0.807)
Observations 3,444 3,459 3,466 3,264 1,073 1,011
Institution public public public public public public
Region FE Yes Yes Yes Yes Yes Yes
Clustered standard errors at institution level in parentheses
*** p<0.01; ** p<0.05; * p<0.1
Table A.4: Log of expenditure per student enrolled and over-reporting, private non-
profit schools
(1) (2) (3) (4) (5) (6)
ln human ln educ ln oper ln build ln purchase ln rent
VARIABLES exp pc exp pc exp pc exp pc exp pc exp pc
Over-report 2%<x<5% -0.0520 0.0343 0.0416 -0.0142 0.00329 -0.406
(0.0328) (0.0744) (0.0599) (0.1000) (0.175) (0.355)
Over-report 5%<x<10% -0.0719 -0.00762 0.120 -0.0118 -0.440* -0.0509
(0.0826) (0.0937) (0.0751) (0.132) (0.266) (0.458)
Over-report 10%<x 0.0357 -0.0997 -0.0785 0.0830 0.166 1.042*
(0.0618) (0.132) (0.105) (0.172) (0.500) (0.562)
Percent low SES students 0.209*** 2.112*** 0.294** -0.654** 0.575 -3.652***
(0.0810) (0.188) (0.149) (0.257) (0.435) (0.937)
Institution in rural area 0.194*** -0.204 0.416*** -0.106 -0.00460 -1.294
(0.0475) (0.137) (0.0925) (0.149) (0.465) (0.788)
Constant 7.236*** 3.801*** 5.117*** 4.944*** 2.033*** 0.995
(0.0704) (0.195) (0.173) (0.479) (0.546) (3.666)
Observations 790 786 791 778 524 503
Institution non-profit non-profit non-profit non-profit non-profit non-profit
Region FE Yes Yes Yes Yes Yes Yes
Clustered standard errors at institution level in parentheses
*** p<0.01; ** p<0.05; * p<0.1
37
Table A.5: Weekly analysis, change in log of attendance, 2013-2016
(1) (2) (3)
∆attend. ∆attend. ∆attend.
VARIABLES observed observed observed
Visit in 5 weeks -9.34e-05 -0.000117 -0.000191
(0.000677) (0.00117) (0.000649)
Visit in 4 weeks 0.000590 -0.00112 0.000627
(0.000848) (0.00119) (0.000890)
Visit in 3 weeks 0.000945 0.00125 0.000654
(0.000598) (0.000867) (0.000652)
Visit in 2 weeks 0.000558 -0.00119* 0.000445
(0.000695) (0.000608) (0.000716)
Visit in week -5.72e-06 -0.00399*** 0.000251
(0.000656) (0.000895) (0.000686)
Visit today -0.0334*** -0.112*** -0.0265***
(0.00210) (0.00591) (0.00209)
Visited within week 0.00766*** 0.0251*** 0.00627***
(0.000436) (0.00149) (0.000416)
Visited 2 weeks ago -0.000881 0.000844 -0.000876
(0.000565) (0.000531) (0.000545)
Visited 3 weeks ago 0.000140 -8.51e-05 0.000360
(0.000664) (0.000472) (0.000661)
Visited 4 weeks ago -0.000169 9.67e-05 1.04e-05
(0.000520) (0.00104) (0.000531)
Visited 5 weeks ago -0.000116 -0.00169*** 6.28e-06
(0.000524) (0.000447) (0.000491)
Constant -0.00109*** 0.000337*** -0.00119***
(1.97e-05) (1.07e-05) (1.70e-05)
Observations 5,858,199 418,340 5,438,784
R-squared 0.059 0.152 0.060
Level All Pre-K K12
Region-date FE Yes Yes Yes
Clustered standard errors at institution-year level in parentheses
*** p<0.01; ** p<0.05; * p<0.1
38
Table A.6: Analysis of 2nd visit, change in log of attendance, 2013-2016
(1) (2) (3)
∆attend. ∆attend. ∆attend.
VARIABLES observed observed observed
Visit in 5 days 0.000557 -0.00183 0.000633
(0.00113) (0.00230) (0.00117)
Visit in 4 days -0.00121 0.000474 -0.00156
(0.00111) (0.00336) (0.00115)
Visit in 3 days -0.00152 -0.00341 -0.00135
(0.00123) (0.00314) (0.00128)
Visit in 2 days 0.000558 -0.00317 0.00107
(0.00179) (0.00278) (0.00187)
Visit in 1 day -0.00338** -0.0152*** -0.00265*
(0.00155) (0.00343) (0.00161)
Visit today -0.0336*** -0.103*** -0.0292***
(0.00168) (0.00565) (0.00166)
Visit 1 day ago 0.0320*** 0.102*** 0.0278***
(0.00153) (0.00530) (0.00150)
Visit 2 days ago 0.000524 0.0108*** -0.000216
(0.00115) (0.00262) (0.00119)
Visit 3 days ago -0.000923 0.00342 -0.00107
(0.00124) (0.00254) (0.00128)
Visit 4 days ago 0.000953 0.000310 0.00104
(0.00146) (0.00263) (0.00153)
Visit 5 days ago 0.00152 0.00174 0.00145
(0.00127) (0.00272) (0.00133)
Constant -0.000555*** 0.000256*** -0.000620***
(1.13e-05) (1.52e-05) (1.14e-05)
Observations 6,146,734 456,943 5,689,076
R-squared 0.069 0.159 0.070
Level All Pre-K K12
Region-date FE Yes Yes Yes
Clustered standard errors at institution-year level in parentheses
*** p<0.01; ** p<0.05; * p<0.1
39
Table A.7: Analysis of institutions penalized by SE, change in log of attendance, 2013-
2016
(1) (2) (3)
∆attend. ∆attend. ∆attend.
VARIABLES observed observed observed
Visit in 5 days -0.00404 -0.0298 -0.00180
(0.00445) (0.0185) (0.00467)
Visit in 4 days 0.00742** 0.0188 0.00587
(0.00341) (0.0114) (0.00370)
Visit in 3 days -0.00572 -0.00944 -0.00556
(0.00385) (0.00946) (0.00435)
Visit in 2 days 0.00254 -0.0135 0.00392
(0.0114) (0.0115) (0.0127)
Visit tomorrow 0.00149 -0.0442*** 0.00662
(0.00811) (0.0160) (0.00883)
Visit today -0.0423*** -0.112*** -0.0351***
(0.00582) (0.0339) (0.00548)
Visit yesterday 0.0479*** 0.136*** 0.0385***
(0.00437) (0.0202) (0.00413)
Visit 2 days ago 0.00108 0.0232* -0.00261
(0.00312) (0.0129) (0.00342)
Visit 3 days ago 0.00442 0.0122 0.00351
(0.00446) (0.0113) (0.00498)
Visit 4 days ago -0.00108 -0.00685 -0.000886
(0.00860) (0.0112) (0.00952)
Visit 5 days ago 0.00275 -0.000181 0.00119
(0.00788) (0.0114) (0.00872)
Constant -0.00219*** 0.000693*** -0.00244***
(8.30e-05) (0.000189) (9.10e-05)
Observations 168,181 15,616 150,451
R-squared 0.138 0.311 0.141
Level All Pre-K K12
Region-date FE Yes Yes Yes
Clustered standard errors at institution-year level in parentheses
*** p<0.01; ** p<0.05; * p<0.1
40
Table A.8: Analysis of institutions penalized by MINEDUC, change in log of atten-
dance, 2013-2016
(1) (2) (3)
∆attend. ∆attend. ∆attend.
VARIABLES observed observed observed
Visit in 5 days 0.00321 0.00903 0.00243
(0.00340) (0.0101) (0.00359)
Visit in 4 days 0.00757 -0.00126 0.00831
(0.00516) (0.00525) (0.00594)
Visit in 3 days -0.00451 0.00474 -0.00538
(0.00622) (0.00544) (0.00697)
Visit in 2 days 0.00729 0.00983 0.00710
(0.00468) (0.00601) (0.00526)
Visit tomorrow -0.0103** -0.0342*** -0.00756*
(0.00404) (0.00673) (0.00441)
Visit today -0.0587*** -0.106*** -0.0523***
(0.00655) (0.00977) (0.00716)
Visit yesterday 0.0635*** 0.118*** 0.0567***
(0.00323) (0.0101) (0.00330)
Visit 2 days ago 0.00413* 0.00450 0.00369*
(0.00214) (0.00862) (0.00221)
Visit 3 days ago 0.00232 0.00951 0.00149
(0.00221) (0.00749) (0.00215)
Visit 4 days ago 0.000606 0.00124 0.000323
(0.00317) (0.00412) (0.00354)
Visit 5 days ago 0.000975 0.00321 5.47e-05
(0.00197) (0.00400) (0.00219)
Constant -0.000821*** 0.000302*** -0.00102***
(2.61e-05) (2.60e-05) (2.93e-05)
Observations 598,223 98,264 499,675
R-squared 0.068 0.170 0.078
Level All Pre-K K12
Region-date FE Yes Yes Yes
Clustered standard errors at institution-year level in parentheses
*** p<0.01; ** p<0.05; * p<0.1
41
Appendix B: MINEDUC estimations
Here, we specify how the MINEDUC calculates “divergence” measures (“ divergencias”)
from daily reports. The divergence (for institution i, day d, and month m) is calculated
in the following steps:
1. The MINEDUC estimates the attendance shock in the school as the difference
between the average attendance reported by the institution in the previous month
and the attendance observed by the inspector (ηschool = ¯ymonth −yday).
2. The MINEDUC calculates the average shock in step 1 in all the schools inspected
in the province that day (¯εday ).
3. The MINEDUC calculates the average shock in step 1 in all the institutions
inspected in the province that month (¯εmonth).
4. The MINEDUC separates the daily component of the shocks as the difference
between the averages calculated in steps 2 and 3 (ηday = ¯εday −¯εmonth).
5. Finally, the MINEDUC calculates the divergence at the institution level as the
difference between the estimated shock at the institution and the estimated daily
component of the shock (over-reporting =ηschool −ηday).
Given the complexity of this over-reporting formula, we present a practical exam-
ple in Table B.1. A particular school shows 10% higher attendance during the month
in comparison to the attendance observed in the audit. However, other schools vis-
ited that day also show a difference in attendance (4%), as do other schools visited
that month (1%). The MINEDUC estimates the attendance shock of that particular
day as the 3% difference. Finally, by subtracting 3% from the observed difference in
attendance (10%), the MINEDUC estimates the school’s over-reporting to be 7%.
42
Table B.1: Over-reporting of attendance estimation by MINEDUC
Step Variable Result
(1) Observed difference in the school attendance (ηschool) 10%
(2) Average difference in province on the same day (εday ) 4%
(3) Average difference in province in the same month (εmonth) 1%
(4)=(2)-(3) Estimated attendance shock in province on the day (ηday) 3%
(5)=(1)-(4) Estimated over-reporting at school 7%
43
