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Comprehensive Private School Model for Low-Income Urban Children in Mexico

In low-income countries, private schools are perceived as superior alternatives to the public sector, often improving achievement at a fraction of the cost. It is unclear whether private schools are as effective in middle-income countries where the public sector has relatively more resources. To address this gap, this paper takes advantage of lottery-based admissions in first grade for a Mexico City private school that targets and subsidizes attendance for low-income children. Over three years, selected students via lottery scored 0.21 standard deviation higher than those not selected in literacy tests, corresponding to a normalized gain of one-half of a grade level every two years. Lottery winners also statistically outperformed those not selected in math, but the gains were more modest. Relative to the control group, parents of selected students were more satisfied with their school and had higher educational expectations for their children. Unlike findings from low-income countries, these gains came at increased cost-twice as much on a per pupil basis relative to public schools. Additional analyses indicate gains made by the lowest income students in the sample help explain the school's impact. This suggests private schools could bring down persistent achievement gaps in these countries, but puts into question the validity of implementation at scale.


Policy Research Working Paper 8669
In low-income countries, private schools are perceived as superior alternatives to the public sector, often improving achievement at a fraction of the cost. It is unclear whether private schools are as effective in middle-income countries where the public sector has relatively more resources. To address this gap, this paper takes advantage of lottery-based admissions in first grade for a Mexico City private school that targets and subsidizes attendance for low-income children. Over three years, selected students via lottery scored 0.21 standard deviation higher than those not selected in literacy tests, corresponding to a normalized gain of onehalf of a grade level every two years. Lottery winners also statistically outperformed those not selected in math, but the gains were more modest. Relative to the control group, parents of selected students were more satisfied with their school and had higher educational expectations for their children. Unlike findings from low-income countries, these gains came at increased cost-twice as much on a per pupil basis relative to public schools. Additional analyses indicate gains made by the lowest income students in the sample help explain the school's impact. This suggests private schools could bring down persistent achievement gaps in these countries, but puts into question the validity of implementation at scale. This paper is a product of the Education Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at hpatrinos@worldbank.org.

Introduction
In low-income countries, private schools are perceived as superior alternatives to the public sector, often improving achievement at a fraction of the cost (e.g., Patrinos, Barrera-Osorio and Guaqueta 2009;Muralidharan and Sundararaman 2015;Andrabi, Das and Khwaja 2008). Many of these countries have weak public school systems, since public sector capacity is strongly correlated with national income (Rauch and Evans 2000;DeJanvry and Dethier 2012). It is unclear whether private schools are as effective in middle-income countries where the public sector has relatively more resources.
This paper analyzes the academic impact and cost of an innovative private schooling model in Mexico. We take advantage of lottery-based admissions in first grade for a Mexico City private school that targets and subsidizes attendance for low-income children. Over three years, students selected via lottery score 0.21 SD higher than students not selected in literacy tests, corresponding to a normalized gain of about onehalf of a grade level every two years. Lottery winners also statistically outperform those not selected in math, but gains are more modest. These gains come at an increased perpupil cost--more than double than traditional public schools. The school we study targets children in poverty. Our findings confirm that this student population benefits the most.
To arrive at this result we re-weight the sample to resemble an average Mexico City household in terms of income and other socio-economic characteristics. Other results suggest parents of children attending the private school are more satisfied and more likely to expect that their children will go to college than parents in traditional public schools.
There are only a handful of rigorous studies exploring the effects of private schooling in middle-income countries. The most well-known school choice program in the region, the Chilean national voucher reform, significantly increased student sorting and stratification by socioeconomic status with mixed results on test scores (see, for a review, Epple, Romano and Urquiola 2017), but positive effects on subsequent labor market outcomes (Bravo, Mukhopadhyay and Todd 2010;Patrinos and Sakellariou 2011). In Colombia, a voucher program which allowed low-income students to attend private secondary schools showed positive effects on high school graduation, college access and the labor market (Angrist, Bettinger and Kremer 2006;Bettinger, Kremer and Saavedra 2010;Bettinger et al. 2018). Most of these studies, however, focus on private school vouchers rather than private schools, and on student outcomes in secondary school.
The majority of students in middle-income countries, however, do not successfully transition from primary into secondary school. In Mexico, for example, only half the students who complete elementary school ever attend high school (Kattan and Szekely 2015). To understand the potential benefits of private schools in these countries, it is important to look at early grades. Establishing a good literacy and numeracy foundation in the early grades will make the transition to secondary school less risky and eventually lead to long-term academic success (Duncan et al. 2007;Hernandez 2011;Cunningham and Stanovich 1997;Watts et al. 2014). To the best of our knowledge, there are no published experimental studies that investigate the academic effects of private schools and costs in middle-income countries in the earlier grades.
Our results meet high evidence standards. Overall and differential sample attrition in the study are low and well within acceptable benchmarks for experimental studies, such as the Institute of Education Sciences' What Works Clearinghouse (Deke, Sama-Miller and Hershey 2015). Our findings are robust to various empirical strategies, including randomization inference and re-weighting for increased external validity. In addition to leveraging the experimental, lottery-based research design to demonstrate academic impacts, we conduct additional observational analyses to understand mediating mechanisms. Using a strategy that matches on baseline covariates, we find that the length of the school day partially mediates the school's effects on achievement.
Our findings are based on the results of a single school and families applying to Christel House de Mexico (CHM) do not resemble the average family in Mexico City. To account for this, we re-estimate all models using a method of entropy weights, which calibrates each observation based on their income and other socio-economic characteristics. Using this information, we generate two re-weighted samples: (1) one that resembles the average Mexico City household and (2) one that resembles a low-income Mexico City household (i.e., those with incomes below the median). This analysis indicates that CHM effects are no longer significant when the population resembles an average family in Mexico City, but are significant when the study sample resembles a low-income family. In other words, re-weighting the units so that study students look more like the average student in Mexico City mitigates our findings and highlights the fact that CHM is a model that is particularly beneficial for the most disadvantaged children.
Our findings are consistent with similar studies conducted in the United States, which suggest private schools are especially favorable for low-income students with poor public schooling alternatives (Chabrier, Cohodes and Oreopoulos 2016;Angrist et al. 2012 for KIPP Schools; Dobbie and Fryer 2011 for Harlem Children's Zone). Our contribution to the debate about the value of private schools in developing countries is to suggest that, at least in the context of middle-income countries like Mexico, expanding private schools could improve outcomes for the most vulnerable children, but will not necessarily save taxpayer money. The results presented in this paper indicate that significantly improving learning outcomes for low-income children in these countries requires substantial additional resources.

Background
Close to 90 percent of elementary and lower secondary students in Mexico attend public schools (OECD 2014). Learning outcomes in public schools are quite poor: close to 60 percent of 15-year old students in the country place below basic proficiency levels in the Math PISA tests (OECD 2015). Results on national standardized tests paint a similar picture: two-thirds of 9th graders test below basic standards in mathematics and one-third test below basic standards in Spanish (INEE 2018). 2 Results for students in rural schools (community schools and "telesecundarias") are particularly dismal: more than 70 percent of students in rural middle schools test below the basic proficiency level in math, and close to 50 percent tests below this level in Spanish.
Most public schools in Mexico meet for half a day (4.5 hours) and follow the Ministry of Education curricula. Most offer some kind of preventive health services, remedial and extracurricular activities. None of these services are required by law. There are no contractual parental commitments, although public school parents in Mexico routinely perform volunteer cleaning and maintenance services (Santibañez, O'Donoghue and Abreu 2014). Teachers are hired centrally by the federal (or state) government and are granted tenure after 2 years on the job. Over 90 percent of national expenditures on education go toward paying staff payroll (OECD 2013). To become a public school teacher, teachers must have a teaching credential, which is granted upon completion of a B.A. teacher education program. Public schools in Mexico can be elementary (grades 1-6), middle (grades 7-9) or high schools (grades 10-12).
In 2007, owing to declining demographic trends in many large cities, the Ministry of Education began converting half-day elementary schools into full day schools. In 2016, there were over 24,000 full-time schools operating across Mexico. About 10 percent of these new full-time schools are located in Mexico City and its metropolitan area. Full time schools operate as 6-hour schools without lunch ("Escuelas de Jornada Ampliada") or 8-hour schools with lunch ("Escuelas de Tiempo Completo"). Research on full-day schools in Latin America finds positive effects on students, particularly those in rural and low-income communities (Cabrera-Hernandez 2016; Padilla-Romo 2016; Holland, Alfaro and Evans 2015).
To enroll in a public school in Mexico City, parents submit an application to the

Administración Federal de Servicios Educativos del Distrito Federal (AFSEDF), Mexico
City's office of education. Parents must choose schools in their residential or work area.
Charter schools are not legally allowed, and neither are vouchers at any educational level.
Privatization efforts are highly controversial in Mexico due to formidable opposition from powerful teachers' unions (Santibañez and Jarillo 2008;Hecock 2014). This is not unique to Mexico. In low-and middle-income countries public delivery dominates education provision and accounts for over 85 percent of total primary school, and 75 percent of secondary school enrollment (World Bank 2018).

Christel House de Mexico (CHM)
CHM is part of the Christel House International Organization, a philanthropic educational initiative that provides educational services to socioeconomically disadvantaged children. Christel House International operates two schools in India, one in South Africa, four charter schools in the U.S., and one school in Mexico. For this study we collaborated with the school located in Mexico City. During the time of our analysis, the school served grades 1 to 9, but has since expanded to serve grades 1 to 12. The school provides free or heavily subsidized education to over 400 low-income children.
Most children belong to families with disadvantaged circumstances that might include infrequent employment, disability, incarcerated parents, mental illness, homelessness, and single parenthood. In 2013, the last year that Mexico held a national standardized exam testing all students in all grades, CHM 3rd graders scored 661 points in school's operation, including teacher salaries, scholarships, nutrition, extracurricular activities, school uniforms, etc., is funded through local business and individual taxdeductible contributions and charitable donations. The school receives a small amount of public subsidies to pay for school lunches.
Like many charter schools in the U.S., CHM requires strong parental involvement and commitment. Parents sign an agreement at the beginning of the year agreeing to attend 12 sessions of parenting education and donate 40 hours a year to school duties. For the most part, these duties include cleaning and maintenance. Students commit to an attendance rate of at least 95 percent a year. CHM has high levels of compliance with parent-student-school agreements and attendance is very high. Few students have ever been asked to leave for non-compliance reasons.
CHM's educational model targets cognitive (academic) and non-cognitive development. Relative to most public schools in Mexico City, CHM offers a longer school day-9 versus 4.5 hours in most public schools (see Appendix Table A1). Close to six hours per day are spent in academic activities and close to two hours per day are spent on enrichment and other activities (sports, music, art, character development).
CHM follows the curriculum and content standards set by the Ministry of Education in Mexico. They use publicly provided textbooks-which are provided free of charge to all schools (public and private) in Mexico. CHM purchases additional textbooks and resources from commercial curriculum vendors (i.e., Pearson). The school offers a wide range of academic and enrichment activities including sports, arts, English as a second language, a tutoring program for students needing remediation, counseling services for career-and college-readiness, and computer skill development. Consistent with CHM's "holistic" pedagogical approach, students receive preventative health services-mental health services, annual medical and dental check-ups-and a comprehensive nutritional package that includes daily breakfast and lunch following healthy dietary guidelines. All children receive school uniforms and school materials free of charge.
To ensure high-quality teaching, CHM carefully selects teachers and dismisses them if they do not perform up to their standards. Teachers are not unionized and do not have tenure --as they do in public schools. Teachers receive professional development and are monitored and supported by the elementary school coordinator. In addition, the school employs literacy and mathematics coordinators to coach and support teachers in these areas. All students are expected to finish high school and go to college. Table 1 presents a contrast with curricular and program offerings at Mexico City public schools.
CHM offers a much longer school day than traditional public schools, and a slightly longer day than full-time public schools. The school offers more nutrition, enrichment and other services. Overall, teacher seniority is lower than at public schools and teachers can be hired/fired at will. Teacher salaries are also lower at CHM than in public schools.
Class sizes are the same.

Lottery Procedures and Data
Every year CHM has more eligible applicants than open seats for its 1st grade cohort. Before this study began, CHM agreed to hold a public lottery for available first-grade seats. We designed the lottery and carried it out. Figure 1 shows a timeline of the study, including baseline data collection, lottery, and testing.

Figure 1. Timeline of Main Evaluation Events
We collected data on lottery results (including wait list assignments), and enrollment. Each year, we updated the data for both CHM and public schools to account for any sample attrition. Between 2013 and 2015, 242 students participated in the lottery as part of three cohorts. 5 CHM carried out separate lotteries for boys and girls, effectively stratifying by gender, to preserve a balanced gender mix. Through the lottery mechanism, 100 students, belonging to three cohorts, were offered a seat in CHM's 1st-grade cohort and 142 were not offered admission. Of the students offered a spot, 50 percent were girls and 50 percent were boys. In each lottery cohort, CHM also randomly selected 10 students (5 boys, 5 girls) for a wait-list. Children in the random wait list were offered a 5 Applicants with siblings already enrolled in CHM have guaranteed admission and did not participate in the lottery. They are not reflected in these numbers. Two parents/students refused informed consent to participate in this study. While they still participated in the lottery, they are not included in this sample.
spot whenever a lottery winner did not enroll in CHM or dropped out. For the analysis, we classify wait-listed children as treated. Overall, treatment compliance was high. Of those originally offered a 1st grade spot (and not on the waitlist), 94 percent took up the offer and enrolled in CHM. Of those originally on the waitlist and subsequently offered a spot, 9 enrolled in CHM. This represents 6.5 of the control group. However, as previously noted, we count waitlisted children-regardless of subsequent enrollment in CHM-as treated.
Data were collected at baseline (before the lottery) and at the end of each academic year. We followed each cohort from the time of the lottery until the last data collection round in 2015. This means that for the first cohort we have three years of data (i.e. data for 1st, 2nd and 3rd grades), for the second cohort we have two years of data (1st and 2nd grades), and for the third cohort we have one year of data (1st grade). In our tables and discussion, we refer to each of these points as 1st, 2nd, and 3rd follow-ups.
In 2015 the Mexico City office of education (AFSEDF) did not allow test administrators access into control group public schools. During this year control group students were tested in their homes, while CHM students were tested at the school.
Varying testing conditions could by themselves explain some of the differences in test outcomes between treatment and control. To account for this potential source of bias, we run all of our analyses for three samples: (1)  to rent their home, to not have a kitchen, to not be hooked to a public utility source for electricity, and to not have a landline (see Table 2).
After the lottery was conducted, students enrolled in either CHM or a public school. Of the total sample, 43 percent enrolled in CHM, 26 percent enrolled in full-day public schools, and 30 percent enrolled in half-day public schools. An additional two percent enrolled in schools of unknown type (i.e., full-day or half-day).

Balance in Baseline Covariates
Baseline differences between lottery winners (treatment) and losers (control) in baseline demographic and cognitive measures are not significant for any of the variables used in the analysis (see Table 2, Columns 3-4). The F-value for the joint test of balance for all these observable characteristics has a p-value of 0.54. All the differences were less than the WWC standard for baseline equivalence of 0.25 SD of the control group mean (see Table 2, Column 5). Together, these results strongly suggest the study sample was balanced prior to the lottery rendering the experimental design highly internally valid.

Differential Attrition
Overall sample attrition in the study was low. The sample contains 502 observations over three data collection waves. We are missing data for 18 of these observations (3.5 percent attrition rate). These 502 observations represent 242 students.
We are missing some follow-up data for 16 of these students, or 6.6 percent. Most of these students missed only one test application but have data for the other applications.
This means attrition by wave is lower than the overall reported attrition rate. Student attrition was 1.2 percent of the sample at the first follow-up, 4.9 percent of the sample at the second follow-up, and 6.4 percent of the sample at the third follow-up.
Differential attrition between treatment and control groups can generate bias for the treatment effect estimates if those who leave the treatment group differ from those who leave the control group along dimensions related to the outcome of interest. In such a case, estimated program impact can be biased even if the lottery successfully generates comparable treatment and control groups at baseline.
We follow current practice in the analysis of field experiments (Duflo, Glennerster and Kremer 2006) and use two tests to determine whether attrition is likely to generate bias in program impact estimates. The first examines whether the fraction of applicants with missing outcome data differs between lottery winners and losers. For each applicant cohort, we propose to regress , an indicator random variable for whether outcome data are missing for a given applicant, on lottery status and other previously defined covariates, as follows: (1) The null hypothesis of no difference in the probability of dropping out of the evaluation sample between lottery winners and losers corresponds to : 0. Note that this analysis needs to be conducted for each outcome at each follow-up point since attrition patterns can vary across outcomes and over time.
The second test examines whether the factors that predict attrition are the same between lottery winners and lottery losers. To implement this test, we modify equation (1) to include interactions between and the vector of covariates : (2) and test the null joint hypothesis that all the parameters in the vector are zero: : ⋯ 0, where is the number of baseline characteristics in the vector X.
Rejection of the null hypothesis on these two tests raises concerns about attrition bias. Table 3 shows results of these two tests of differential attrition. The first test (Panel A) finds significant differential attrition of -0.04 for the pooled sample. An analysis of differential attrition by year of the study finds statistically significant differential attrition at the 2nd follow-up (coefficient of -0.06), and no statistically significant differential attrition at the 1st and 3rd follow-ups (coefficients of -0.01, and -0.06). As previously mentioned, during the 2nd year of the study we were denied access into control group schools by the Mexico City educational authorities, which negatively impacted our ability to reach as many control students as we did in the other two years of the study. A second test of differential attrition examines whether factors that jointly predict attrition vary among lottery winners and losers. This test cannot be rejected at conventional levels (see Panel B of Table 3). Together, these results suggest that, if anything, the missing treatment and control group data in the pooled sample and second follow-up appear to be missing at random. These low differential attrition rates are well within the benchmarks issued by the Institute of Education Sciences' What Works  (Barrios, 2014).
EGRA has been used to assess reading skills of children at grades 1-3 in more than 50 countries and 70 languages (Gove and Wetterberg 2011). Prior studies showed it is a valid and reliable tool to measure reading achievement at early grade levels (RTI International 2009). 7 EGRA includes eight subtests, including letter name knowledge, phonemic awareness, letter sound knowledge, listening comprehension, unfamiliar non-6 The WWC sets the maximum acceptable rate of differential attrition at around 7-7.5 percent for studies with overall attrition lower than 10 percent (Deke, Sama-Miller and Hershey 2015). 7 The tests have been criticized on the grounds that they measure a narrow set of skills (e.g. Bartlett et al., 2015). Dubeck and Gove (2015)

Parent Perception Data
A survey was administered to Cohort 2 parents to measure differences in opinions about their child's schooling and expectations. The survey was administered two years after baseline (in 2016). Of 91 parents who consented to respond to the parent survey at baseline, 83 took the survey two years later, a 91 percent response rate.

Research Design and Empirical Strategy
This evaluation follows an experimental design that takes advantage of lotterybased admissions into CHM. To estimate the causal effect of attending CHM on literacy and numeracy test scores, we estimate ANCOVA models that have the form: where are cohort fixed effects; is the number of years applicant i from cohort c has spent in CHM at the time of the post-treatment measurement year t; is the vector of student background characteristics (including baseline cognitive assessment scores); is a residual. We estimate equation (2) using instrumental variables in a two-stage least squares (2SLS) framework in which the randomly assigned lottery outcome serves as an instrument for . Standard errors are clustered at the applicant level.
A possible issue with randomization is that results may be sensitive to just a few outliers or clusters of observations. As described in Young (2018)

Reweighting for External Validity
Families applying to the CHM lottery look very different from the average family in Mexico City. One concern is that our results cannot be easily extrapolated to the average family in Mexico City due to "participation bias" (Andrews and Oster 2018). To account for this, we use the method of "entropy weights" as proposed by Hainmuller (2012) and Hainmueller and Xu (2013) to re-weight the sample to resemble the average Mexico City family. The method resembles propensity score matching. To the extent that most of the potential participation bias is explained by observable characteristics, results will be externally valid (Andrews and Oster 2018).
To estimate the weights, we use Mexican household data from the Encuesta

Cost Data and Analysis
To compare the costs of providing education at CHM compared to traditional public schools attended by control students, we use a version of the ingredients method, a simple yet rigorous procedure to guarantee inclusion of all relevant costs (Dhaliwal et al. 2011;Levin andMcEwan 2001, 2000).
We collected cost data about CHM from school staff using the ingredients method excel worksheet in the fall of 2016. We collected costs only for the elementary school portion of CHM's operations. We pro-rated overlapping or other costs that serve the entire school by elementary school enrollment.
To estimate costs in control schools we used information provided by the Mexico City Office of Education, the Mexican Ministry of Education and other published sources. To fill in gaps and cross-reference the information provided by the Mexico City office of education we collected cost data from a sample of five control group schools.
To estimate the average teacher cost in each of the control schools, we obtained data on the number of teachers and their seniority from the 2016-17 school census ("Forma 911"). Using these data, we identified each of the teachers and other staff working in control group schools by type of position. We used published salary schedules to estimate compensation for each teacher and staff position, taking into account base salary and benefits, as well as any bonuses received by teachers participating in incentive programs such as "Carrera Magisterial." Most public schools in Mexico City received their buildings as donations from private individuals or foundations, and these donations go back many decades. The Mexican office of education was unable to provide information that would allow us to estimate infrastructure costs except in the case of one school, which was being rented at market rates. We pro-rated the rent paid by this one school on the basis of enrollment and applied that rate to other control schools based on enrollment. Utility costs (water, electricity) were obtained using data provided by AFSEDF for 83 public control group schools in our sample.
To estimate the cost of providing breakfast and lunch in schools where this service is available, we use data contained in the school, teacher and student census of 2013 ("CEMABE 2013") as well as budget information for the National Free Breakfast Program. We also use information from CEMABE 2013 to identify control group schools that participate in the national breakfast program. Costs were pro-rated by school enrollment. To estimate the cost of providing lunch in full-day schools, we use data gathered from interviews with five control group schools to calculate per-student lunch costs.
We gathered educational supply costs for textbooks and school supplies.
Textbook costs were obtained using the published cost of producing these textbooks by the National Commission on Free Textbooks ("CONALITEG"). Mexico has a national free textbook program, and all students in public elementary schools receive textbooks free of charge. To estimate school supplies costs, we use published prices from one large supplier in Mexico City. The Mexican Ministry of Education publishes an approved "school supply" list that schools in Mexico City adhere to. This list was used as a benchmark to estimate costs for all control group schools based on their enrollment.
Both CHM and traditional public schools receive donated goods and services. In addition, parents pay out-of-pocket costs. We ask questions in the parent survey about these expenses and report them below. One potentially important cost that we do not include is parental time, which is required at CHM and frequently donated at public schools across the country (Santibañez, O' Donoghue and Abreu 2014). We do not have data to estimate the monetary value of parental time. Given that over 90 percent of the cost of public schools in Mexico covers teaching and non-teaching staff salaries we feel confident our estimation is close to the real cost of providing schooling to students in our sample. Table 4 shows intent-to-treat (ITT) effects of winning the admissions lottery.

Effects on Early-Grade Literacy and Mathematics
Results for the full sample (Table 4, Column 3) show that CHM students who won a seat in the school's first grade cohort via lottery scored about 0.21 SD higher in early grade literacy, and 0.09 SD higher in early grade numeracy than students who did not win the lottery. These results represent an average for lottery Cohort 2013 students observed three times up to third grade; lottery Cohort 2014 students observed two times up to second grade, and lottery Cohort 2015 students observed once in first grade. Column 1 of Results shown in Column 2 of Table 4 show that students who won the lottery for admission into CHM scored 0.19 SD higher than those who did not win the lottery, over the average time spent in CHM without taking into account 2015 -the year where control students were tested in their homes. Unless otherwise noted, all of these effects are statistically significant at the 95 percent confidence level. The magnitude of the effects diminishes only slightly when student controls are included, to 0.17-0.30 SD in literacy, and 0.06-0.10 in mathematics. Figure 2 shows test score growth curves for each grade observed in the study.
Results are pooled for all cohorts. They suggest that CHM improved learning outcomes in literacy in every grade except 2nd grade. In mathematics, CHM improved outcomes every grade, although the absolute levels are lower than they are for literacy. Results are statistically significant at the 95 percent confidence level, except for the 1st grade estimate for math.

Figure 2. Grade Level Growth Curves, All Cohorts
Note: These growth curves represent intent-to-treat with lottery offer as the key explanatory variable, and test outcome as the dependent variable. All regressions include lottery strata fixed effects (gender and cohort) and robust standard errors. Effect sizes are averaged using the meta-analytic technique discussed in the text. See text for more detail.
To account for differences across cohorts in the time spent at CHM, we model the causal effect of attending CHM on outcomes as a function of how much time students spend at the school. To do this we instrument time spent in CHM with lottery offers using a 2SLS approach. Table 5 shows the results. Results change only slightly when demographic and cognitive baseline controls are included.
To put this per-year effect in context, we calculate the average growth of the control group over the period under study. In EGRA, the control group grew an average of 0.45 SD per year in literacy and 0.71 SD per year in math. Relative to the control group, after two years the average student at CHM would be about one-half of a year ahead in literacy, and on par in math.
The results presented above are robust to randomization inference in all samples except the 1st grade only sample in mathematics. Table 6 shows results from randomization inference omnibus tests performed on the joint significance of all pooled test score outcomes. The omnibus tests for randomization inference are significant at the 95 percent confidence level for all samples of the literacy outcomes. The randomized pvalue for the literacy average effect is 0.005, 0.001, and 0.001 for all three samples respectively. For the mathematics outcomes, the values are 0.14 for first grade only, and 0.012 and 0.024 for the comparable testing conditions and all student samples. These results imply that our findings are not sensitive to just a few outliers or clusters of observations as can sometimes be the case with smaller-sample studies.  Table 4. We use the randcmd in STATA to conduct these tests (Young, 2017). For each test, we conduct 1,000 permutations.

Early-grade Gains Accounting for Differences in Length of School Day
CHM's positive impact on early grade literacy and numeracy can be explained by a number of factors: length of the school day, better teachers, more parental involvement, health prevention services, better leadership, etc. We do not have data to unpack everything driving CHM's positive impact, but we do have data on one key factor: length of the school day. Our data allow us to identify whether Mexico City public schools attended by the control group are on a half-day (4-hour) or on a full-day (6 or 8 hour) schedule. With this information we can estimate the effects of CHM relative to other fullday schools and separate out the effect of the longer school day from the overall impact.
One issue with this estimation is that while students enter CHM via lottery, parents do not follow a random process to enroll their students in public schools. Parents could self-select into full-time public schools in ways that could bias an estimation of program effects. To explore this potential bias, we run descriptive statistics on students by whether they attend school full-or half-day. Results are shown in Table 7 and suggest balance on most characteristics, except for two. First, the Raven baseline score is statistically higher in the full-day school sample. This is not the case for the verbal WISC score. The magnitude of the Raven score difference, however, is small: about 0.02 SD.
Second, single parents are more likely to seek out full time schools for their children. All other demographic characteristics show no significant differences among students attending full-and part-time public schools. To account for any bias that may arise from parental self-selection into full-time schools based on observable characteristics, we use propensity score matching. First, we restrict the sample to students who attend CHM and full-time public schools and fall within the common support region. To estimate the common support region and predict the propensity score we estimate a probit model of lottery status on baseline student covariates and lottery strata. We do this for the subset of schools that include CHM and full time public schools only. We then use the min/max method to eliminate observations that fall outside the common support region. Next, we estimate ITT using a matching estimator that accounts for the propensity to be selected for the program for students at CHM or full day public schools. We estimate the LATE using instrumental variables with the propensity score as an independent variable. Results are shown in Table 8.

Re-Weighted Results -External Validity
To explore whether our findings are sensitive to whether or not CHM lottery applicants are observationally similar to the average family in Mexico City, we reestimate all models using entropy weights as described in the methods section. We use two sets of weights: (1) "average weights" based on the entire Mexico City household sample and (2) "low-income weights" using only households below the median income.
Results are shown in Table 9. When the study sample is weighted to resemble the "average student" both the ITT and IV literacy effects of CHM are either negative ("comparable testing conditions" sample) or not statistically significant (full sample). The effects on math are not statistically significant across the board. When the study sample is weighted to resemble a low-income student (see Table 9, Columns 3 and 4), however, the results are once again positive and statistically significant for literacy. Results remain non-significant for math. This result is striking for two reasons. First, even though our results come from a single school, they can be replicated for a larger population of students who are observationally similar (i.e., students below the median income distribution in Mexico City). Second, CHM's model of education is most beneficial to low-income students-their intended targeted population. When we give more weight to slightly better-off students so that the study sample resembles the average Mexico City household, CHM test scores are no longer above the control group test scores (and are even lower under some specifications). However, when we re-weight the study sample so that the lowest income students get a higher weight, the results are once again significant. Other authors have arrived at similar conclusions using charter school evidence from the United States (Chabrier, Cohodes and Oreopoulos 2016).

Parent perceptions
High parental involvement and expectations can positively influence academic outcomes for low-income students (Domina 2005;Marschall 2006;Yamamoto and Holloway 2010). Most research in the U.S. finds that charter school parents tend to be more satisfied and more involved in school than public school parents (Gleason et al. 2010;Cheng and Peterson 2017). This is also the case at CHM (see Table 10).
Parents of students who win the lottery of admission at CHM think more highly of their school than control parents, 0.97 points above the control group mean of 2.9 on a Likert-type scale where 1 is "Bad" and 4 is "Excellent" (Table 10, Column 2). CHM parents think their child's school is more demanding academically than parents whose kids attend public schools (coefficient of 0.70). There does not appear to be a different in perception among parents with regard to how strict (discipline-wise) their child's school is--not surprising since public schools in Mexico are notoriously strict when it comes to enforcing order and discipline (Ochoa Cervantes and Diez-Martinez 2013). CHM parents also tend to have higher expectations for their child's education than parents in the control group. On a scale of 1-10, control group parents set the probability of their child completing high school at 9.2. CHM parents set this probability 0.35 points higher, although the difference is statistically significant only at the 10 percent level.
Parents who win the lottery to attend CHM have significantly higher expectations than control group parents that their child will complete college, 1.03 points higher (on a scale of 1-10) over the control group mean of 8.6.   supplies, and nutrition. The only category in which CHM parents spend significantly more money than public school parents is in transportation to and from school.

Conclusion
In low-income countries, private schools are perceived as superior alternatives to the public sector. The evidence suggests private schools can deliver high-quality education, at a fraction of the cost of public schools, in low-income countries (Patrinos, Barrera-Osorio and Guaqueta 2009;Muralidharan and Sundararaman 2015;Andrabi, Das and Khwaja 2008). We know less about the advantages private schools offer in middleincome countries to students who in some cases have a plethora of public school options.
We use a lottery-based admissions process for one comprehensive private school model in Mexico City to test the claim that private schools benefit low-income children.
We find that children living in urban poverty in Mexico City perform better on academic tests of early grade literacy and mathematics when they attend a full-day, This study aims to fill an important gap in the literature examining private school impact on early-grade outcomes. One limitation of the study is that it focuses on earlygrade basic literacy and mathematics skills. Although these foundational skills predict future academic outcomes (Duncan et al. 2007), they may not be able to capture the full range of benefits offered by a comprehensive school like CHM. Efforts to prepare children for college are likely to bear fruition in high school, one of the riskiest transitions for students in Latin America (Busso, Bassi and Muñoz 2013). Following this sample of students over a longer period of time and collecting data on cognitive and noncognitive outcomes, as well as on additional mediating factors that are policy relevant would greatly add to our understanding of whether and how private schools can benefit low-income populations in the region.  Notes: These are responses for the parents of Cohort 2014 students. Survey was administered in June of 2016 (end of the school year). Parents were asked to refer to the study sample child only, when responding questions. Parent responses were coded in the column (CHM or Public School) corresponding to their actual child's enrollment (not lottery-status). This was done in order to get accurate estimates of average costs in CHM vs. public schools. As explained in the text, the vast majority (94%) of students in our sample complied with their assigned lottery status, so the numbers here accurately reflect what parents in treatment/control groups were paying out of pocket. All expenses were converted to US$ using an exchange rate of 20 Mexican Pesos per US$. Monthly expenses such as transportation, lunch, school materials, tuition and fees, were converted to yearly costs using a 10-month academic school year. Other school expenses include: school events and festivities, field trips, school carnival, school pictures, extended day fees, and music lesson fees.