Prospering through prospera: A dynamic model of CCT impacts on educational attainment and achievement in Mexico

Behrman, Jere R.; Parker, Susan; Todd, Petra; Zhang, Weilong Article Prospering through prospera: A dynamic model of CCT impacts on educational attainment and achievement in Mexico Quantitative Economics Provided in Cooperation with: The Econometric Society Suggested Citation: Behrman, Jere R.; Parker, Susan; Todd, Petra; Zhang, Weilong (2025) : Prospering through prospera: A dynamic model of CCT impacts on educational attainment and achievement in Mexico, Quantitative Economics, ISSN 1759-7331, The Econometric Society, New Haven, CT, Vol. 16, Iss. 1, pp. 133-183, https://doi.org/10.3982/QE2291 This Version is available at: https://hdl.handle.net/10419/320327 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ Quantitative Economics 16 (2025), 133–183 1759-7331/20250133 Prospering through Prospera: A dynamic model of CCT impacts on educational attainment and achievement in Mexico Jere R. Behrman Department of Economics, University of Pennsylvania Susan W. Parker School of Public Policy, University of Maryland Petra Todd Department of Economics, University of Pennsylvania, NBER, HCEO, and IZA Weilong Zhang Faculty of Economics, University of Cambridge This paper develops and estimates a dynamic model, which integrates valueadded and school-choice models, to evaluate grade-by-grade and cumulative impacts of the Mexican Prospera conditional cash transfer (CCT) program on educational achievement. The empirical application advances the previous literature by estimating policy impacts on learning, accounting for dynamic selective school attendance, and incorporating both observed and unobserved heterogeneity. A dynamic framework is critical for estimating cumulative learning effects because lagged achievements are important determinants of current achievements. The model is estimated using rich nationwide Mexican administrative data on schooling progression and mathematics and Spanish test scores in grades 4–9 along with student and family survey data. The estimates show significant CCT impacts on learning and educational attainment, particularly for students from poorer households. Results show that telesecondary schools (distance learning) play a crucial role in facilitating school attendance and in fostering skill accumulation. Keywords. Conditional cash transfers, dynamic modeling, educational attainment, learning achievement, Mexico. Jere R. Behrman: [email protected] Susan W. Parker: [email protected] Petra Todd: [email protected] Weilong Zhang: [email protected] We are grateful for financial support from NSF award 1948943 and from the University of Pennsylvania School of Arts and Sciences internal grants “Making a Difference in Diverse Communities” and the “Dean’s Global Inquiries Fund.” We also thank Gabrielle Vasey, Rodrigo Deiana, Elizaveta Brover, Pinar Goktas, Mira Potter-Schwartz, and Erika Trevino-Alvarado for research assistance. We thank Hector Robles Vasquez for preparing databases and for assistance in working with these data. We thank Miguel Szekely for conversations about the Mexican educational system. This paper was presented at the University of Cambridge, the University of Arizona, the University of Maryland, McGill University, the University of Pennsylvania, the Stanford Institute for Theoretical Economics, and the University of Glasgow. We thank Eric French, Magne Mogstad, and Christopher Taber for helpful suggestions. ©2025 The Authors. Licensed under the Creative Commons Attribution-NonCommercial License 4.0. Available at http://qeconomics.org.https://doi.org/10.3982/QE2291 134 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) JEL classification. C53, I25, I38, J24. 1. Introduction Conditional cash transfer (CCT) programs aim to alleviate current poverty through transfers to poor families and to reduce future poverty by making these transfers conditional on investments in the human capital of children and youth. In 1998–2000, a large-scale randomized evaluation of the Mexican PROGRESA CCT program demonstrated substantial impacts on schooling enrollment and attainment, child work, and family income (Parker and Todd (2017)). These findings contributed to a large scalingup in Mexico and an impressive adoption of similar programs in more than 60 countries on five continents (Fiszbein and Schady (2009)). This paper analyzes the understudied, substantive question of whether CCTs improve learning by developing and estimating a dynamic model of academic achievement and school progression. Several studies, using various methods including the original experiment, matching and structural dynamic models, have examined the impacts of PROGRESA/Oportunidades/Prospera on school enrollment and, in some cases, on longer-term schooling attainment (e.g., Schultz (2004), Behrman, Sengupta, and Todd (2005), Behrman, Parker, and Todd (2005,2009), Todd and Wolpin (2006), Attanasio, Meghir, and Santiago (2012), Parker and Vogl (2023)). This literature demonstrated positive program impacts on school enrollment and attainment. However, a longstanding concern has been whether and to what extent this increased school enrollment translates into higher academic achievement, a likely determinant of the extent to which CCTs can improve earnings potential and other longer-term outcomes. Most prior studies did not analyze academic achievement impacts, because the original evaluation data did not include achievement test scores.1 With newly available data, we are now able to examine the effects of the Prospera program (the program name during the time of our data collection) not only on school enrollment and attainment but also on academic achievement in mathematics and Spanish. Nationwide standardized longitudinal administrative test-score data (called the ENLACE data) as well as complete enrollment rosters were merged with administrative information on which students come from Prospera households and on school locations. They were also merged with survey information obtained from students and their parents. These data allow the study of how students’ Prospera beneficiary status affects their school enrollment, school choice, grade progression, and academic achievements over time. Although our longitudinal administrative and survey data are rich and have the advantages of national coverage and large sample sizes, the data were not collected explicitly for the purpose of evaluating the Prospera program. There are at least five significant 1In 2003, Woodcock–Johnson tests in mathematics and Spanish were applied to a single cross-section. Using these data, Behrman, Parker, and Todd (2009) found no impacts of PROGRESA participation on achievement, based on comparing test scores of the original treatment and control groups. However, because the original control group was enrolled in the program 1.5 years after the original treatment group, the schooling differences between them were relatively small, at about 0.2 years of additional schooling. Quantitative Economics 16 (2025) Prospering through Prospera 135 statistical challenges in using observational data of this kind to assess program impacts: (i) selective program participation, largely due to eligibility criteria that restrict access to high-poverty households, (ii) nonrandom school dropout, which mainly occurs after grade 6, (iii) grade retention in any grade, (iv) the availability of multiple school types and school choice, and (v) the presence of a small fraction of students suspected to have cheated on the tests. This paper develops a methodological approach for evaluating the effects of Prospera and illuminating the mechanisms through which program effects operate while accounting for these different features of the data and the context. Some earlier studies consider the selection problem arising from nonrandom dropout in the context of analyzing educational outcome determinants (see, e.g., Cameron and Heckman (1998,2001), Glewwe (2002)). As is common in administrative schooling data, including our data, the test scores are only observed for enrolled children who took the tests at school. The selection problem is dynamic as it occurs at each grade and the students at risk for dropping-out in a particular grade depend on the sample that stayed in school from previous grades. The Prospera CCT program induced students from high-poverty backgrounds who were at high risk for dropping-out to stay in school longer. If the CCT program induces weaker students to remain in school, then average test scores could fall as a result of more marginal students being included in the testing. This kind of selection problem arises whenever tests are administered in school, regardless of whether the data analyzed are experimental or nonexperimental.2 Our goal in this paper is to examine how the Prospera program affects schooling and academic achievement, accounting for the statistical problems noted in (i)–(v) in the penultimate paragraph. To this end, we develop and estimate a dynamic model of students’ school progression that incorporates decision making in each grade (4–9) with regard to enrollment, school choice, and dropping-out as well as gradeand subjectvarying models for academic achievement. Specifically, our modeling framework combines value-added academic achievement models with school-choice models and links equations across ages/grades, allowing for both observed and unobserved heterogeneity. Valued-added models typically specify a relationship among academic achievement, key learning inputs in the current period, and lagged achievement, which is a sufficient statistic for past learning inputs under some assumptions about coefficients of past learning inputs following geometric patterns (Summers and Wolfe (1977), Boardman and Murnane (1979), Hanushek (1979), Todd and Wolpin (2003), Cunha, Heckman, Lochner, and Masterov (2006), Cunha, Heckman, and Schennach (2010)).3Schoolchoice models generally focus on the decision of what type of school to attend (Neal (1997), McEwan (2001), Altonji, Elder, and Taber (2005), Sapelli and Vial (2002), Gallego 2This selection problem also affects cross-country comparisons of standardized tests, such as PISA test scores. The PISA tests are given in schools at age 15 and, in some countries, significant fractions of children have dropped-out by that age. 3There is some debate about whether value-added models with teacher fixed effects should be used to measure teacher effectiveness (see, e.g., Kane and Staiger (2008), Kane, McCaffrey, Miller, and Staiger (2013), Chetty, Friedman, and Rockoff (2014a,b)). Our focus is rather on using these models to capture the cumulative learning process. 136 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) and Hernando (2009)).4Value-added models and school-choice models are usually estimated in isolation, although there are a few papers that combine them (e.g., Hastings, Neilson, and Zimmerman (2012), Allende et al. (2019), Schellenberg and Walters (2020)). Our model also incorporates dropout decisions and grade retention. The model begins when students finish 4th grade and continues through the 9th grade.5Students in our sample differ in terms of their family backgrounds and their 4th-grade knowledge in mathematics and Spanish as measured by standardized test scores. The vast majority of children attend general primary schools close to home, but some families living in areas with high indigenous populations can choose betweengeneral and bilingual indigenous schools. At the end of each grade, students can progress to the next grade, repeat the same grade or (after grade 6), drop out. Conditional on progressing to lower-secondary school (at the end of grade 6), students/parents make a one-time choice of a lower-secondary school type, from up to three public school options—general, telesecondary, or technical schools—all of which are academically oriented.6 In each period, we model skill accumulation in mathematics and Spanish using value-added production functions, with coefficients that vary by grade, school types, and grade-retention status. The dynamic-panel specification captures the notion that skill accumulation at one stage affects skill attainment at other stages, which has been shown to be essential to characterizing human-capital-skill formation processes (e.g., Cunha et al. (2006), Cunha, Heckman, and Schennach (2010)). When students/parents choose from among different school types, they essentially choose a learning technology. The same inputs (including Prospera participation) may generate substantially different outcome trajectories depending on the school types that are available and are selected. As previously noted, the model we estimate controls for selection arising from school-enrollment, dropout, grade-retention, and school-type choices, all of which potentially affect students’ grade progression and academic achievements. It also accounts for selective program participation arising from the fact that only high-poverty households are eligible to participate in Prospera. In particular, we limit our analysis sub4Some studies use school-choice models to estimate school-voucher effects (Rouse (1998), Figlio and Elena Rouse (2006), Hsieh and Urquiola (2006), Bravo, Mukhopadhyay, and Todd (2010), Angrist, Bettinger, Bloom, King, and Kremer (2002), Angrist, Bettinger, and Kremer (2006)), to study parents’ preferences for school quality, and to analyze the welfare effects of school policies (Epple, Jha, and Sieg (2018), Hastings, Kane, and Staiger (2009), Allende et al. (2019)). 5The Prospera cash transfers for attending school actually start in grade 3. We start our model at grade 4, because the data were collected over a 6-year time frame and we want to follow students through grade 9, which is the last grade of lower-secondary school. There are no nationwide standardized tests in the 10th and 11th grades. By starting the model at grade 4, we do not capture potential program impacts in prior grades and potentially understate program benefits. 6Technical schools differ from general schools by including vocational/technical educational curricular components. Telesecondary schools are distance-learning schools that largely serve rural communities and that enroll almost 20% of lower-secondary school students. Prospera-beneficiary family children attend telesecondary schools in greater proportions than average. We exclude private schools from the choice set as almost no Progresa beneficiaries attend private school. Section two provides more detail on how the school types differ. Quantitative Economics 16 (2025) Prospering through Prospera 137 sample to households that are estimated to have positive probability of being a program beneficiary and, in addition, control for observed heterogeneity between Prospera and non-Prospera students using a rich set of family demographics. Our data set contains information on most of the variables used to determine Prospera eligibility, but we also allow for the possibility of selection on some unobserved factors.7The unobserved heterogeneity is modeled as discrete latent multinomial types, as in Heckman and Singer (1984), Cameron and Heckman (1998). These types enter multiple model equations and, in doing so, allow for across-equation correlated error structures. We allow the unobserved-type distribution to vary by Prospera beneficiary status and an index measure of local poverty. The data we analyze also contain information on small percentages of students in each grade that are suspected to have copied answers on the multiple-choice standardized tests. In the context of a value-added test-score model, copying induces one-sided measurement errors in the dependent variables, the lagged dependent variables, or both, which we explicitly take into account in our maximum likelihood estimation procedure. The outcomes at different ages/grades are school enrollment, school choices, mathematics, and Spanish test scores, dropping-out, and grade retention. We do not know of previous research that estimates value-added models accounting for possible cheating, although cheating on standardized tests is a ubiquitous problem. We use our estimated model framework to evaluate how Prospera-beneficiary status affects schooling progression and academic achievements in different grades. In particular, we simulate school-choice decisions, school-enrollment decisions, and academic achievements with and without the Prospera program, for children from different family backgrounds. There are multiple channels through which Prospera participation can affect these outcomes. First, past participation may increase lagged achievement, which can facilitate present learning. For example, greater comprehension of 6th-grade mathematics can facilitate learning and comprehension of the 7th-grade curriculum.8Second, contemporaneous program participation can directly affect learning if the program encourages regular school attendance, student engagement, and study efforts. There are two reasons why we might expect the Prospera program to influence students in this way. Prospera program rules stipulated that children must attend school at least 85% of days and can only fail a grade once to receive the cash transfers. Additionally, Prospera transfers may reduce the pressure on children/youth to work in labor markets while in school and thereby allow for greater focus on schoolwork (Skoufias and Parker (2001)). Our analysis yields a number of findings regarding Prospera-program effects and the effectiveness of different school types. First, we find that Prospera participation reduces lower-secondary school dropout rates by 0.06–0.09 percentage points. This effect is most 7As discussed in Todd and Wolpin (2003), Rivkin, Hanushek, and Kain (2005) for value-added models and in numerous other studies of schooling (e.g., Behrman, Hrubec, Taubman, and Wales (1980), Behrman and Rosenzweig (1999), Altonji, Elder, and Taber (2005), Rothstein (2009)), it is important to control for unobserved inherent student abilities, personality traits, or motivation, that matter for children’s achievement growth. 8Cunha et al. (2006) term this feature of cognitive achievement production functions “self-productivity.” 138 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) pronounced during the transition from 6th to 7th grade and appears similar for both girls and boys.9In primary-school grades (grades 5 and 6), our findings do not show any significant impact of the program on test scores. However, in lower-secondary grades (grades 7 to 9), we observe positive and statistically significant improvements in test scores. The effects are more substantial in mathematics, with a cumulative effect of 0.21 standard deviations by the 9th grade, compared to 0.04 in Spanish. Girls tend to have higher gains in mathematics, whereas boys show greater gains in Spanish. Therefore, the Prospera program narrows existing gender test score gaps that favor boys in mathematics and girls in Spanish. Additionally, and as expected, the effects of program participation accumulate over time and intensify with prolonged exposure. Intriguingly, children from more disadvantaged backgrounds exhibit significantly larger improvements in test scores. Our results contribute to the understudied yet substantive question of whether CCTs improve learning. Fiszbein and Schady (2009), Baird, Ferreira, Özler, and Woolcock (2014) systematically reviewed a range of CCT programs worldwide and concluded that the effects of CCTs on achievement tests were disappointingly “small, at best.” One caveat is that these conclusions are mostly drawn from relatively short evaluation periods and based on relatively small sample sizes.10 When evaluating CCT programs over longer horizons, some studies report statistically significant effects on academic achievement. For example, Barham, Macours, and Maluccio (2013)usedtherandomized phase-in of the Red de Proteccion Social CCT program in Nicaragua to study effects on schooling attainment and learning for boys 10 years later. They found a halfgrade increase in schooling and substantial gains (approximately 0.25 standard deviations) in mathematics and language achievement scores. Comparing two cohorts (2007 and 2013), Hadna and Kartika (2017) found statistically significant effects of a CCT program called Program Keluarga Harapanin in Indonesia on three subjects (Bahasa Indonesia, mathematics, and English) as well as national mathematics examinations for junior/high-school students. Our results can reconcile some of the mixed findings in the literature by highlighting the accumulative feature of the CCT program effects. Our study sheds light on the efficacy of various types of Mexican schools in enhancing test scores. This includes telesecondary schools, which predominantly utilize videobased teaching methods and are often the only accessible option for students in rural areas. Our findings indicate that telesecondary schools are, in many instances, as effective or even more so than regular public schools for their attendees. When we use the estimated model to analyze the effect of removing the telesecondary option from the choice set, we find that the dropout rate would be substantially higher and average schooling attainment lower without these schools. Model simulations also show that telesecondary schools are also important determinants of Prospera program impacts. Our finding that these schools play an important role in fostering education in 9Some studies have suggested a greater impact of PROGRESA on secondary-school enrollment for girls (Schultz (2004), Parker and Vogl (2023)), but other research finds similar effects for both genders in lowersecondary education (Behrman, Sengupta, and Todd (2005), Todd and Wolpin (2006)). 10Due to data limitations, there are many fewer studies of achievement than there are of enrollment. For instance, Snilstveit et al. (2017) reviewed 38 studies of the effects of transfers on enrollment; only 11 of the programs analyzed effects on achievement. Quantitative Economics 16 (2025) Prospering through Prospera 139 Mexico is consistent with the difference-in-difference analysis of Fabregas and NavarroSola (2023) that found that the expansion of telesecondary schools led to substantial increases in schooling attainments for local students.11 Lastly, we also explore how inferences based on our model depend on specification assumptions. As a benchmark, we estimate a simpler value-added model grade-bygrade, without controlling for selection from multiple sources (dropout, school choice, grade retention). Comparing the results to those derived from our richer model, the cumulative program impacts are noticeably smaller. Thus, failing to control for dynamic selection would lead to underestimation of Prospera’s impact. We identify three potential reasons for downward biases. First, the program causes students at the margin of dropping-out to stay in school longer and failure to control for this changing composition of students would lead to a downward bias in the impact estimates. Second, the simpler model does not allow heterogeneous impacts across different types of schools and, therefore, does not capture that telesecondary schools are particularly effective for Prospera beneficiaries. Lastly, the simpler model ignores the negative selection of unobserved types, which also leads to an underestimation of program impacts. We find that a richer modeling framework is required to capture heterogeneous program impacts and to control for multiple sources of selection bias. The paper develops as follows. Section 2briefly describes the Mexican school system and the data sets used in this study. Section 3describes the model and Section 4the estimation approach. Section 5presents the empirical results. Section 6presents the estimated cumulative Prospera program effects. It also performs model simulations where the telesecondary schooling option is removed, examines the robustness of program impact estimates to alternative modeling assumptions and explores longer-term program impacts (up to grade 12). Section 7concludes. The Supplemental Appendix (Behrman, Parker, Todd, and Zhang (2024)) provides additional details on data sources and complete model estimates. The Supplemental Appendix will be referred to throughout the paper as SA. 2. Background 2.1 Mexican educational system and child-labor laws The Mexican educational system consists of three levels: primary, secondary, and tertiary education. Formal basic education includes preschool, primary school (grades 1– 6), and lower-secondary school (grades 7–9), all of which are compulsory. However, compulsory schooling laws are not well enforced. Many children dropout before completing grade 9, particularly children from lower-SES families, indigenous backgrounds, and rural areas. Our analysis focuses on public schools. Although Prospera beneficiaries may choose which school to attend, in practice, almost all attend public schools (in our data only 11A recent paper by Borghesan and Vasey (2024) also studies the effectiveness of Mexican telesecondary schools using a marginal treatment effects (MTE) estimation approach applied to a Roy model and using the same data we analyze but focusing on 7th graders. 140 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) 0.28% of beneficiaries in 6th grade are enrolled in private schools). Public primary and lower secondary schools, as part of “educacion basica,” are free of charge. The Secretariat of Public Education (SEP) standardizes curriculum content, which includes Spanish, mathematics, natural sciences, history, geography, art, and physical education.12 Secondary school is divided into lower-secondary school (grades 7–9) and uppersecondary school (grades 10–12). Lower-secondary school is free and students may follow either a general academic track or a technical track, which has more of a vocational focus. Both tracks are designed to prepare students for further education. There are fewer lower-secondary schools than primary schools and attending lower-secondary schools often requires traveling some distance from home, particularly for children living in more remote areas. Public schools do not generally provide transportation. Upper-secondary education (grades 10–12) did not become compulsory until 2012. Some upper-secondary schools are affiliated with large public universities, while others are SEP or state-controlled. At the tertiary level, the Mexican educational system has many different programs and degree options. The Mexican Constitution prohibits child labor for minors under 14 years of age. However, the child-labor laws are not well enforced. 8% of children age 12 report working for pay in the 2010 Mexican census data.13 2.2 ENLACE test-score data and additional survey data From 2006 to 2013, the SEP applied the Evaluación Nacional de Logro Académico en Centros Escolares, called the ENLACE (SEP (2018a)). The test evaluated student performance in mathematics, Spanish, and a rotating subject for all 3rd-to-9th graders at the end of each academic year. The test is directly based on the curriculum (see SEP (2010)) and intended to be an assessment that is informative about learning outcomes to SEP and to parents. In primary school and in lower-secondary school, the grades studied in this paper, the test has no bearing on students’ GPA or grade progression, so it can be considered to be low stakes. Beginning in 2008, ENLACE was also given to students in their final year of upper-secondary school (grade 12).14 The exams were designed to have a mean of 500 and a standard deviation of 100 in their first year of implementation, and subsequent test years were calibrated to allow measurement of changes in learning over time (see SEP (2010)). The test-completion rate is close to 90%. As described by De Hoyos, Estrada, and Vargas (2018), 15.1 million students in 136,000 schools took the examination in 2013, the last year the test was applied. In addition to test scores, the ENLACE data (merged with school roster data) also contain information on the age, gender, Prospera beneficiary status, whether the child attended the day of the test, school ID, and school type for each student. We examine a cohort of students who were in grade 4 in 12The National Institute for Assessment of Education (INEE) monitored standards during our period of study. 13Based on the authors’ tabulations. 14The ENLACE exams have been used as a means of evaluating educational interventions by several papers (Avitabile and De Hoyos (2018), De Hoyos Navarro, Attanasio, and Meghir (2019), De Hoyos, GarciaMoreno, and Patrinos (2017)). Scores on these exams have been shown to have predictive power on important life outcomes including university enrollment and wages (De Hoyos, Estrada, and Vargas (2018)). Quantitative Economics 16 (2025) Prospering through Prospera 147 Figure 2. Mathematics and Spanish test scores distributions by grade and lower-secondary school types. prevalent among the Prospera students. Moreover, cheating is generally associated with less test score inflation among non-Prospera than Prospera students. 148 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) Table 5. Average test scores and proportion cheating, by Prospera status. Grades Non-Prospera Prospera No cheating Cheating No cheating Cheating Grade 4 Fraction 93.8% 6.2% 90.1% 9.9% Math 529 554 480 519 Spanish 521 538 468 496 Grade 5 Fraction 96.6% 3.4% 94.6% 5.4% Math 533 585 494 557 Spanish 534 568 488 533 Grade 6 Fraction 96.9% 3.1% 95.1% 4.9% Math 560 616 525 594 Spanish 557 590 515 561 Grade 7 Fraction 98.2% 1.8% 96.5% 3.5% Math 500 578 492 602 Spanish 490 542 465 534 Grade 8 Fraction 96.2% 3.8% 92.7% 7.3% Math 524 627 526 683 Spanish 497 567 476 579 Grade 9 Fraction 97.2% 2.8% 95.1% 4.9% Math 548 636 562 654 Spanish 501 541 481 532 Note: This table shows average mathematics and Spanish test scores, along with the proportion of students flagged for cheating, disaggregated by Prospera status and grade. “Cheating” refers to students flagged by a copying behavior indicator. 2.5 Local school supply and quality As previously noted, Mexican families can choose among different types of schools, but their options depend on the local supplies. We next examine the supplies of different types of schools and also their quality characteristics. Table 6provides information on the supplies of local schools of different types at the individual level. In Mexico, multiple school sessions are often held in the same building, such as a morning and afternoon session. The different sessions may have different principals and teachers; so, in the data set they are considered to be different schools.17 Primary schools tend to be small, with an average enrollment of less than 200 and, consequently, there are a large number of primary schools. Their small size partly reflects that the school systems do not usually provide transportation and students typically walk to school. Also, 77% of children do not have access to indigenous schools, which are typically located in areas with significant indigenous populations. At the lower-secondary level, there are fewer schools and they are larger. Table 7compares the different school types in terms of some average school quality characteristics, including pupil–teacher ratios and teacher educational levels. The 17In SA Figure B1, we show one illustrative example of local primary school sessions in Aguascalientes, a city in central Mexico. It has 316 school sessions distributed in 250 unique coordinates within 10 kilometers. Quantitative Economics 16 (2025) Prospering through Prospera 149 Table 6. Number of local schools of different types. Mean Std p10 p50 p75 Not available Primary school (within 5 km) General 63 78 9 25 100 3.4% Indigenous 5 6 1 3 6 77.2% Secondary school (within 10 km) General 46 67 4 17 60 14.9% Telesecondary 13 11 4 10 19 8.5% Technical 10 11 2 6 15 16.1% Note: Columns 3–5 report selected percentiles. The last column gives the percentages of individuals for whom a given school type are not locally available. first two columns show characteristics for general and indigenous primary schools. Indigenous primary schools have on average 94 students in comparison to 174 students in general primary schools. The percentages of students who are disabled ranges from 1–2%. Despite having overall fewer students, the student–teacher ratio in indigenous schools is higher—33 in comparison to 24. Another difference is that teachers in indigenous schools are more likely to have only upper-secondary school degrees (17% in comparison to 3%). At the same time, the fraction of teachers with an undergraduate or higher degree is 7 percentage points higher. Thus, teacher schooling attainment exhibits higher variance in indigenous schools. The last three columns of Table 7compare the average school characteristics for general, technical, and telesecondary schools. Technical schools tend to be larger, with an average enrollment of 395 in comparison to 296 for general schools and 75 for telesecondary. Again, the proportion of disabled students across all types of schools is 1–2%. The student–teacher ratio is 14 in general schools, 19 in technical schools, and 24 in telesecondary schools.18 Thus, we see a general pattern of the smaller schools in rural areas having higher student–teacher ratios, which could either reflect that video learning is less teacher-intensive or that teacher or resource shortages are more common in rural areas. Comparing teacher educational profiles across the different kinds of secondary schools, we see that average characteristics are fairly similar. The main difference is that general school teachers are more likely to have undergraduate degrees rather than teaching-college degrees, compared to teachers in technical and telesecondary schools. 3. Model Our modeling framework combines a school-choice model of attendance decisions at different types of schools with models of academic achievement in mathematics and Spanish that are linked across ages/grades. In particular, we specify test-score gains from year-to-year using a value-added framework that relates current achievement to 18These tabulations are based on regular teachers and exclude art and music teachers who often teach at multiple schools. 150 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) Table 7. Mean primary and lower-secondary school characteristics by school types (with standard deviations in parentheses). Characteristic Primary Lower Secondary General Indigenous General Telesecondary Technical Number of students 174 94 296 75 395 (175) (95) (244) (64) (247) Proportion disabled 0.02 0.01 0.01 0.01 0.02 (0.06) (0.07) (0.04) (0.03) (0.05) Student–teacher ratio 24 33 14 24 19 (18) (12) (7) (9) (8) Teachers with HS degree 0.03 0.17 0.03 0.03 0.02 (0.09) (0.30) (0.07) (0.16) (0.06) Teachers with teacher college 0.47 0.26 0.34 0.41 0.42 (0.35) (0.34) (0.34) (0.42) (0.32) Teachers with undergraduate degree 0.47 0.56 0.54 0.44 0.47 (0.34) (0.39) (0.34) (0.42) (0.32) Teachers with post-grad degree 0.03 0.01 0.07 0.11 0.08 (0.10) (0.07) (0.12) (0.23) (0.11) Note: Tabulations based on a school census data set called the 911 data. lagged achievement, family and school inputs into the learning process, and student unobserved heterogeneity (e.g., arising from ability or preferences). Our framework also allows technology for producing test-score gains to vary by type of school. In addition, it incorporates drop-out decisions and allows for grade retention, as described below. Our modeling framework can be considered quasistructural. The educational production function has a structural interpretation as a technology relating inputs to outputs. However, the school-choice model is reduced form, likely reflecting the decisions of students, parents, and school administrators. As discussed below, the outside option in the school-choice model is to drop out. 3.1 General environment and sequential outcomes Individuals are indexed by i,i=1, ,nand each model period corresponds to one school year. In the initial period (af, corresponding to the age at grade 4), students/parents can choose to attend one of two types of primary schools: general (j=1) or indigenous (bilingual) (j=4), depending on the types locally available (within 5 km). At the end of grade 6, students simultaneously make school-enrollment decisions (with j=0 indicating nonenrollment) and school-type choices from up to three options: general (j=1), telesecondary (j=2), or technical (j=3), depending on the types locally Quantitative Economics 16 (2025) Prospering through Prospera 151 Figure 3. Potential sequential outcomes from grades 4 to 9. available (within 10 km). We can summarize the choice set Jg ia at different grades as jia ∈Jg ia =⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ {1, 4}∩M1 i,Ga=4&a=af, {0, 1, 2, 3}∩M2 i,Ga−1=6&IPass i,a−1=1, {0, ji,a−1},Ga−1≥7, (1) where afis the age when the student enters into the sample at grade 4. M1 idenotes the available local primary school types and M2 idenotes the available local lower-secondary school types.19 Let Dija =1 if the individual iis enrolled in school type j(j∈{1, 2, 3, 4})atagea,else Dija =0. Let Di0a=1 if the individual does not enroll in school at age a,elseDi0a=0. Let IPass ia =1 if the individual passes the grade in which she is enrolled at age a,elseIPass ia =0. We assume the passing outcome IPass ia is realized at the end of the school year, prior to the other decisions being made. The potential sequential outcomes from grade 4 to grade 9 are illustrated in Figure 3. As seen in Figure 3, until grade 6 the possible outcomes are whether a student is retained in the current grade (IPass ia =0) or progresses to the next grade (IPass ia =1), conditioning on their primary school types when entering into the model at grade 4, their family background, and their Prospera-beneficiary status. Upon passing grade 6 (IPass ia =1), students simultaneously make enrollment decisions Di0aand school choices Dij a ,depending on locally available school types.20 Once enrolled in a secondary school, students decide in each period whether to drop out or to stay in school. In each grade, there is a probability of passing or having to repeat the grade. Let Gia denote the grade 19In particular, M1 i∈{{1},{4},{1, 4}} and M2 i∈{{1, 2, 3},{1, 2},{1, 3},{2, 3},{1},{2},{3}}. 20Because school enrollment is very high during primary school, we assume students do not drop-out during primary grades. Therefore, they do not make choices about continuing in school until the end of grade 6. 152 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) that the individual is eligible to attend at age a, which increases by one if the student passes the current grade: Gi,a+1=Gia +IPass ia . 3.2 Accounting for selective program participation Our aim is to use our estimated model to assess the impacts of Prospera participation on schooling progression and academic achievement, where we treat Prospera beneficiary status as a family characteristic. Pi=1 denotes that a child/youth comes from a Prospera-beneficiary family, else Pi=0. Although the survey data we use were not collected for the purpose of ascertaining Prospera eligibility, the data are rich and contain information on most of the eligibility determinants.21 Program eligibility is not means-tested by income, because income can be difficult to measure in a country with a significant informal sector and where many low-income individuals are engaged in agricultural work. The program-eligibility criteria rather depend mainly on households’ assets (such as car ownership), on characteristics of the household’s residence (such as whether it has dirt floors, piped water, and how many rooms there are per person living in the house) and on household demographics, such as number of children and numbers of dependents per worker.22 The vast majority of eligible households opt to participate, reflecting that the cash transfers are substantial.23 Our empirical strategy in evaluating the impact of Prospera on student test scores and educational progression is to first limit the comparison group subsample to children whose families meet at least a subset of the eligibility criteria. We do so by first estimating a probit model for the probability that each family is eligible for and participates in the Prospera program given the available information. That is, we use information on housing characteristics and demographics that were gathered through the student and parent surveys to estimate a household’s probability of being eligible and participating in the program (a propensity score). The estimated coefficients from this probit regression are shown in SA Table A.3. The percentage correctly classified as being beneficiaries or not under the estimated model is high (90%). Figure 4plots the propensity-score distributions for children from Prospera-beneficiary households (in red) and nonbeneficiary households (in green). As seen in the figure, a large fraction of nonbeneficiaries fall in the first histogram bin, meaning that they have extremely low probabilities of participating in Prospera, generally because their characteristics make them ineligible. To increase comparability between the Prospera and the comparison-group subsamples, we impose a common support restriction and exclude in our impact analysis Prospera beneficiaries and the nonbeneficiaries with 21The precise eligibility criteria are not made public, but some of the authors of this paper were involved in the design of the criteria. 22Families who apply to the program typically fill out a questionnaire to determine their eligibility and their answers on the questionnaire may be checked through home visits. 23As discussed in Parker and Todd (2017), they represent on average about a 20% increase in household income. Quantitative Economics 16 (2025) Prospering through Prospera 153 Figure 4. The propensity score distribution by Prospera status (P). Note: The red histogram represents the propensity score distribution for Prospera children/youth and the green histogram for non-Prospera children/youth. propensity scores below the 1% quantile (the lowest bin of the histogram).This threshold excludes 383 children from Prospera families and 50,798 nonbeneficiary children.24 In addition, our school-choice/dropout and value-added models also include observed covariates to further control for differences between Prospera and non-Prospera households (such as parents’ schooling attainment). We also allow for the possibility that children/youth from Prospera beneficiary families may differ in unobserved ways by including latent unobserved heterogeneity, specified as four discrete multinomial types that enter into all the model equations.25 Let μil =1 denote that individual iis of type l, =0else,wherel∈{1, ,L}and L=4. Ideally, one could allow for the unobserved types to be arbitrarily correlated with the observed variables. However, identifying such a model poses challenges, as it can be difficult to distinguish the direct effects of these observed variables from their indirect effects operating through the unobserved type distribution. For this reason, we restrict the type probability distribution to depend only on a child’s Prospera status (P∈{0, 1}) and a binary marginality indicator (M∈{0, 1}), which is a measure of the poverty level in the locality where the household lives. We denote the conditional type probability as ρl(P,M)≡Pr(μil =1|P,M); it represents the fraction of type lamong students with Prospera status Pand marginality index M.Notethatlρl(P,M)=1, P∈{0, 1},M∈ {0, 1}. 24This type of trimming is common in the application of matching estimators as a way of imposing “common support.” Heckman, Ichimura, and Todd (1997) showed, in the context of evaluating a job-training program, that having a highly comparable comparison group is important to producing reliable nonexperimental impact estimates that replicate experimental estimates. 25See, for example, Heckman and Singer (1984), Cunha and Heckman (2008). Alternatively, we could impose a continuous distribution for the unobserved heterogeneity, for example, a mixture of normal distributions. Mroz (1999) shows the discrete-type assumption performs as well as the normal assumption when the true distribution is normal. When the true distribution is not normal, however, he finds that the discrete-type method performs better. 154 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) 3.3 The model As described in Section 2.4, our modeling and estimation approach is designed to address several statistical challenges that arise in evaluating the Prospera program academic achievement impacts. First, we address the problem of selective program participation by restricting our analysis sample to children estimated to have a positive probability of participating in the program.26 Second, our school-attendance and schoolchoice framework, which models the sequential choices shown in Figure 3,explicitlyaddresses dynamic selection in school choices and dropout decisions. These decisions are permitted to depend both on observed family background characteristics as well as on unobserved factors that are assumed to follow a multinomial distribution (i.e., discrete types). We also incorporate exogenous variables, such as imputed local hourly wages, distances to the nearest school of each type, and the number of local schools of each type, as exclusion restrictions that affect school-type choices and dropout decisions but do not enter the test score outcome equations directly. Third, our model explicitly accounts for grade retention to capture that children may be observed multiple times in the same grade. Fourth, as described later in Section 4.1, we address potential test-score distortions caused by a small fraction of students suspected of cheating (copying). We next describe our multiequation model of academic achievement over multiple grade levels, which includes the following components: value-added models in each grade, the school-choice/dropout models in primary school and at the start of secondary school, and the grade-repetition process. Value-added model: Achievements in mathematics and Spanish evolve over time with school attendance. Let m=1 denote mathematics, m=2 Spanish, and gdenotes the grade level. The value-added model is grade-specific and school-type (j) specific. The coefficients also vary depending on whether the student passed the previous grade IPass i,a−1=1 or is repeating the grade IPass i,a−1=0.27 Let ZA ia denote the vector of observed characteristics of the youth and of the family that enter the achievement production function: Am ia =δmgI 0jl +Ai,a−1δgI 1j+δmgI 2jPi+ZA iaδmgI 3j+ωmgI ija .(2) In this equation, δmgI 0jl is the type-specific intercept that allows for unobserved heterogeneity (ldenotes the type). Ai,a−1={A1 i,a−1,A2 i,a−1}is a 2 ×1 vector including both the mathematics score and the Spanish score from the previous period a−1. The lagged test-score terms are assumed to be sufficient statistics for the impacts of past inputs in the learning process. This specification allows for cross-effects between Spanish and mathematics. For example, better Spanish skills may enhance student’s understanding in their mathematics classes, implying a positive effect of past Spanish scores on current mathematics scores. The impact of the Prospera program is captured by δmgI 2j.We 26The value of imposing common support on the propensity score distribution in the context of social program evaluation is emphasized in Heckman, Ichimura, and Todd (1997). 27If a student repeats a grade, then the lagged test score pertains to the same grade as in the current time period and would therefore have a different associated coefficient from the case where the lag pertains to the previous grade. Quantitative Economics 16 (2025) Prospering through Prospera 155 assume that the error terms ωmgI ija , conditional on the unobserved types, are i.i.d. and normally distributed. Most of the literature considers learning technology to be exogenous. By combining a school-choice model with value-added models that vary by school type, we allow students/parents to select from different available learning technologies. School-choice model: We next specify how individuals make their schooling choice Dij a from the available options, Jg ia (depending on his/her grade and geographic location, as defined in equation (1)). Assuming a random-utility model with Type I extreme-value errors (taste heterogeneity) yields a multinomial logistic model for the probability of choosing option jia: PrDija =1|˜ (a),μl =⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ expμg 0jl +Aia−1φg 1j+Piφg 2j+fjZD ia,wia,Sdistance ija ,Snumber ija   j∈Jg a expμg 0jl+Aia−1φg 1j+Piφg 2j+fjZD ia,wia,Sdistance ija,Snumber ija if jia ∈Jg a, 0ifjia /∈Jg a, (3) where μg 0jl is a type-specific intercept (ldenotes the type). The parameter φg 1jcaptures the effect of test scores on schooling choices, and φg 2jcaptures the impact of Prospera on schooling choices. ZD ia ∈˜ (a)includes demographic and family-background characteristics. There are three additional variables that enter the school-choice equations but not other parts of the model: (i) the imputed hourly wage wia; (ii) the distance to the closest school of each type Sdistance ija ; and (iii) the local supply of schools of each type Snumber ija . As previously noted, the outside option in our school-choice model is to drop out of school, which could be a more attractive option in areas that pay higher wages to child labor. Due to the absence of wage information in our test-score databases, we rely on data from the 2010 Mexican census to impute wages for individuals based on characteristics such as their age, gender, schooling level, and geographical region of residence. Additionally, our imputation procedure incorporates a selection correction mechanism to account for selective labor-force participation.28 The imputed wage, denoted as wia, represents the opportunity costs associated with being enrolled in school. Two other important variables in the school-choice model are the distance to the nearest school (Sdistance ija ) and the log number of local schools of various types (Snumber ija ). These variables are included to capture the effect of local school availability on individuals’ schooling decisions. We assume that the three exogenous variables {wia,Sdistance ija ,Snumber ija }affect schoolchoice decisions but do not directly enter the test-score equations (i.e., exclusion restrictions). These variables are helpful to identify separately the parameters in the value28For a more detailed explanation, please refer to the SA Table A.2. 156 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) added models from parameters in the school-choice/dropout model.29 However, the exclusion restriction could be invalid, for example, if higher wages provide incentives for students to work part-time while enrolled in school, which directly affected their testscore performance. Another potential threat to validity is that the travel distance may directly affect the commuting time required to attend schools. Both channels may negatively impact academic performance through fatigue or reduced ability to concentrate on studying. To examine the empirical relevance of such concerns, we also estimated a specification in which the variables {wia,Sdistance ija ,Snumber ija }are added to the valueadded equation (3). We examined (i) whether the coefficients associated with Prosperabeneficiary status change and (ii) whether the estimated coefficients associated with the variables {wia,Sdistance ija ,Snumber ija }are significantly different from 0. We did not find evidence of direct impacts of {wia,Sdistance ija ,Snumber ija }on test scores, conditional on the other model covariates. As we will elucidate in Section 3.5, one way of interpreting our school-choice probability equation is an approximation to a policy function derived from a full dynamic version of our structural model (for related discussion see, e.g., Heckman, Humphries, and Veramendi (2016)). To account for potential nonlinear effects of the state variables on decision making, we adopt a flexible functional form, denoted as f(ZD ia,wia,Sdistance ija ,Snumber ija ).30 Grade retention: Lastly, we specify a probabilistic model for whether a student passes a grade, which depends on the unobserved type μl, the current school type attended jia, academic knowledge as proxied by the achievement scores Aia, the grade level Gia,Prospera beneficiary status Pias well as some demographic and family-background characteristics, ZI ia ∈˜ (a): PrIPass ia =1|˜ (a),μl=γg 0l+Aiaγg 1+γg 2Pi+jiaγg 3+ZI iaγg 4.(4) The coefficients of the passing probability probit model are grade-specific and γg 0lis a unobserved type-specific intercept. 3.4 Treatment-effect heterogeneity Prospera may have heterogeneous impacts for students from different backgrounds. Inspired by the marginal-treatment-effect (MTE) literature, we divide the analysis sample into quartiles based on the Prospera-eligible propensity scores and allow the Prospera impact to vary by quartile.31 Families in the highest quartile, that is, with characteristics 29In a parametric setting, exclusion restrictions are not strictly required. Nonetheless, independent variation in the determinants of dropout and school-choice decisions provides additional sources of identification that do not rely on functional form restrictions. 30In SA Section D, we describe how we use Bayesian Information Criterion (BIC) to determine our final econometric specification. 31We capture potential heterogeneity more parsimoniously than a standard approach in the literature, which is to estimate the treatment effect nonparametrically as a function of the propensity-matching score (e.g., Heckman and Vytlacil (2001,2005,2007)). However, most literature implements MTE in a static setup whereas our model is dynamic. Quantitative Economics 16 (2025) Prospering through Prospera 163 once at the start of primary school and the lower-secondary school type is chosen once at the start of lower-secondary school. Second, we assume that individuals who drop out of school do not afterwards reenroll.43 Third, because the fraction of students who repeat grades is fairly small (see Table 2), we estimate a separate value-added model for retained students but restrict the model coefficients to not vary across grades, separately within primary school and lower-secondary school grades.44 4.4 Evaluating the effects of Prospera-program participation Prospera provides cash transfers for children of beneficiary households who are enrolled in school in grades 3–12. For children in grades 3–9, the transfers typically go to the mothers. Whether a transfer is received for each child depends, however, on whether that child regularly attends school (at least 85% of school days). We consider the family’s Prospera status as a time-invariant characteristic, so it is contained in the initial state space (0). Once families are enrolled in the program, they rarely lose their eligibility. Even if one child is not attending school, the family may still receive transfers for other children and is still considered to be participating. We use the estimated schooling model to simulate school-going and test-score outcomes for Prospera families’ children had they not participated in Prospera. In this way, we are able to assess the grade-specific program impacts as well as the cumulative impacts of participating in Prospera for multiple years. 5. Model estimates We estimate the model parameters by maximum likelihood. The key parameters, specifically those linked to Prospera effects, are shown in SA Section C, whereas the complete set of parameters can be found in SA Section D. In this section, we focus on two aspects: examining score distortion stemming from potential copying behavior, and evaluating the model’s goodness-of-fit based on our adjusted test scores that account for test-score inflation resulting from cheating behavior. 5.1 Test-score measurement equation A unique feature of our data set is that it contains information on which students were flagged by the SEP as potential copiers. Our test-score measurement equation allows the true test score to differ from the measured test score in the event of copying and also allows for heterogeneity in the gains from copying across grades and types of schools (to reflect potential differences in monitoring). In the context of a value-added model, 43In our raw data set, a mere 0.2% (378 individuals) switched schools to a different type during their primary-school years, while 3.2% (6220 individuals) changed school types in lower-secondary school. Additionally, we note that 1.99% (3770 individuals) reenrolled in school after initially leaving. 44That is, we restrict δm4I kj =δm5I kj ,δm6I kj =δm7I kj =δm8I kj ,k={1, 2, 3}in the value-added equation (2) and γ4 k=γ5 k=γ6 k,γ7 k=γ8 k,k={1, 2, 3, 4}in equation (4) in the periods when IPass ia =0.Buttheinterceptterms δmgI 0jl and γg 0lare grade-specific. 164 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) Table 8. Estimated test-score distortion from copying, by grade and school type. Percentages Math Spanish Raw True Diff Raw True Diff Grade 5 General 4.2% 570 525 45 549 521 28 Indigenous 7.0% 540 474 66 515 468 46 Overall 4.4% 568 521 47 546 517 29 Grade 6 General 4.0% 606 554 52 578 545 33 Indigenous 6.3% 566 510 56 536 499 37 Overall 4.1% 603 551 52 575 542 33 Grade 7 General 1.7% 558 499 59 523 489 34 Telesecondary 4.1% 619 525 94 540 486 54 Technical 2.5% 573 498 75 536 489 47 Overall 2.6% 588 510 78 534 488 46 Grade 8 General 3.3% 614 529 85 555 508 47 Telesecondary 9.9% 698 580 118 585 517 68 Technical 4.1% 613 528 85 554 511 43 Overall 5.3% 656 554 102 570 513 57 Grade 9 General 2.6% 631 549 82 531 505 26 Telesecondary 5.7% 667 607 60 529 509 20 Technical 3.8% 621 553 68 536 510 26 Overall 3.8% 642 574 68 532 508 24 Note: The percentages in the second column give the percentages of students suspected of copying in either mathematics or Spanish tests. copying can lead to a one-sided measurement error in either the dependent variable (the test score) or in an independent variable (lagged test scores) or in both variables, but only for students who copied. Table 8shows the percentages of students suspected of copying, which ranges from a low of 1.7% in 7th grade in general schools to a high of 9.9% in 8th grade in telesecondary schools. At the primary-school level, indigenous schools exhibit higher copying rates. We estimate that copying distorts average test scores by 20–118 points for copiers. Our earlier-described estimation approach accounts for this potential distortion. 5.2 Model goodness-of-fit Our model involves a substantial number of parameters, in part due to our deliberate choice not to impose constraints in the value-added model coefficients across various grade levels. These parameters are mostly precisely estimated due to our large sample sizes. Tables 9and 10 provide evidence on the model’s goodness-of-fit. In Table 9, we compare average test scores across grades and by Prospera beneficiary status in the Quantitative Economics 16 (2025) Prospering through Prospera 165 Table 9. Goodness-of-fit for average test scores by Prospera status (P). Prospera Mathematics score Spanish score P=0P=1P=0P=1 Data Sim Data Sim Data Sim Data Sim Grade 5 521 522 495 496 520 519 490 490 Grade 6 550 551 526 527 545 543 515 517 Grade 7 489 489 492 491 477 477 465 465 Grade 8 516 515 529 526 487 487 480 480 Grade 9 540 539 564 563 490 489 481 481 Note: We simulate the test scores 100 times for each individual. In this table, we adjust for any copying in both the simulation and the data. data and based on model simulations. The data averages closely align with the modelsimulated averages, with few exceptions. The estimated model reproduces the observed pattern where Prospera beneficiaries have lower average test scores in primary grades for both subjects. It also captures the trend of test-score disparities between beneficiaries and nonbeneficiaries diminishing in lower-secondary grades, and even reversing in mathematics. Table 10 shows how well our model fits the school-type distribution. The model’s predicted proportions closely match the data, with differences of no more than 0.02. Our model effectively captures two important data features: the higher probability of Prospera-beneficiary children attending telesecondary lower-secondary schools and their higher rates of dropping out. Additionally, it reproduces the observed dropout patterns across different grades. 6. Assessing cumulative Prospera-program effects 6.1 The cumulative Prospera-program effects Average treatment effect on treated As previously described, educational production functions typically assume that knowledge acquisition in mathematics and Spanish is Table 10. Goodness-of-fit to school-type distribution. Lower-secondary choice General Telesecondary Technical Dropout Data Sim Data Sim Data Sim Data Sim Nonbeneficiary (P =0) Grade 7 0.49 0.47 0.13 0.13 0.31 0.30 0.08 0.09 Grade 8 0.46 0.44 0.12 0.12 0.29 0.28 0.13 0.15 Grade 9 0.41 0.40 0.11 0.11 0.26 0.26 0.23 0.23 Prospera beneficiary (P =1) Grade 7 0.26 0.24 0.43 0.44 0.21 0.22 0.10 0.10 Grade 8 0.24 0.23 0.41 0.41 0.20 0.20 0.16 0.16 Grade 9 0.21 0.20 0.36 0.36 0.17 0.18 0.26 0.26 Note: We simulate the test scores 100 times for each individual. 166 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) a cumulative process. The value-added model specification allows lagged knowledge to have an effect on contemporaneous knowledge accumulation, so that the history of inputs into the learning process matters. If Prospera participation increases knowledge at a particular grade, then this benefit can have a persistent effect on learning in future grades. That is, program participation can have both direct effects on current test scores as well as indirect effects operating through lagged test scores. In Table 11, we use our estimated model to simulate the effects of being a Prospera beneficiary over multiple grades, starting with grade 4. Our estimation procedure allows for Prospera effects that operate through all of the different channels of our school progression and achievement model and that may differ for girls and boys. Columns labeled P=1 show the outcomes for Prospera-beneficiary children/youth with their participation in the program. Columns labeled ˜ P=0 show the simulated (counterfactual) outcomes were they not to participate in the program.45 It is only possible to assess test-score impacts for children/youth who would attend school both with and without Prospera. Therefore, our reported program impacts on test scores in column “Diff” represent lower bounds, as they do not include potential academic achievement gains for children/youth who in the absence of Prospera would not be attending the grade.46 Our results show positive benefits of being a Prospera beneficiary in lower-secondary grades but essentially no effect for math and Spanish in primary grades. In lower-secondary school, the cumulative Prospera impact in mathematics increases with the grade level and reaches a high of 0.21 standard deviations by grade Table 11. Cumulative program impacts. Mathematics score Spanish score P=1˜ P=0DiffS.E.P=1˜ P=0Diff S.E. Grade 5 495 496 −0.2 0.7 490 491 −0.9 0.7 Grade 6 527 522 4.3 0.8 517 521 −4.1 0.7 Grade 7 492 478 13.7 2.0 465 459 6.3 1.6 Grade 8 527 513 14.2 1.8 481 476 4.8 1.5 Grade 9 562 541 20.8 2.2 482 478 4.0 1.8 Dropout rate Retention rate P=1˜ P=0DiffS.E.P=1˜ P=0Diff S.E. Grade 5 – – – – 0.04 0.04 −0.004 0.002 Grade 6 – – – – 0.02 0.03 −0.003 0.001 Grade 7 0.11 0.17 −0.07 0.01 0.003 0.002 0.000 0.000 Grade 8 0.16 0.23 −0.08 0.01 0.003 0.004 −0.001 0.001 Grade 9 0.25 0.33 −0.08 0.01 0.003 0.004 −0.001 0.001 Note: We report test score impacts for children/youth who would attend school both with andwithout Prospera. The cumulative impacts are obtained through bootstrap simulation with 100 replications. In particular, we first draw the model parameters from their estimated distributions and simulate the cumulative test scores and impacts for each bootstrap iteration. Then we obtain standard errors from the empirical distributions. The columns “Diff” capture the test-score gain of these subgroups. The columns “S.E.” report the standard errors of the test-score gains from the program. 45Our simulation keeps the distribution of unobserved types for Prospera beneficiaries fixed. 46As we show in Figure 6and Figure 7, absent children are disproportionally from most disadvantaged family backgrounds and, therefore, tend to have larger program gains on average. Quantitative Economics 16 (2025) Prospering through Prospera 167 9. In Spanish, the cumulative gains are substantially smaller — about 0.04 standard deviations.47 We might expect the estimated program effects to be larger in lower-secondary school than primary school because the transfer amounts that families receive for school attendance are much larger.48 Also, older children typically have more demands on their time that compete with schoolwork than do younger children, such as taking care of younger siblings, housework, working for family businesses, or working for pay after school. The Prospera cash transfers may reduce these outside time uses, allowing them to focus more on schoolwork. The lower panel of Table 11 reports the Prospera impact on the dropout rate (cumulative) and on the probability of repeating a grade. The results show that Prospera reduces the dropout rate by 0.08 before the start of grade 9, with the most pronounced effect during the primary to lower-secondary school transition. We also find that Prospera primarily reduces the retention probability during primary school but has no significant effect on retention during lower-secondary school. Comparison of program effects for female and male students The Prospera program provides greater subsidies to girls than boys for attending school in post-primary grades. Table 12 examines whether program effects differ by gender. The test-score impacts are significantly positive for both girls and boys in all grades except for grade 5. The largest impacts are observed in lower-secondary school grades and impacts are larger in mathematics than in Spanish. Interestingly, the estimates indicate that participation in Prospera leads to a slight reduction in gender academic achievement gaps. Male students have a 7-point advantage in average mathematics scores over females at grade 6. Participation in the Prospera program through grade 9 boosts female students’ mathematics scores by 21.8 points in comparison to 19.6 for males and reduces the gender gap by 3.0 points (=(564-560)- (542-541)). In terms of Spanish test scores, female students have on average a 29-point advantage over males at grade 6. Prospera participation is also associated with a reduction in the gender gap in Spanish scores by grade 9, albeit by a slightly smaller margin of 2.0 points (=(495-467)-(492-462)). The program also narrows the gender gap in dropout rates. For the current Prospera beneficiaries, the cumulative dropout rate by grade 9 is 23.3 percentage points for females and 27.0 percentage points for males. When we simulate the model taking away the Prospera program, we find that the gender difference increases from 3.7 (=27.0-23.3) percentage points to 6.3 (=36.4-30.1) percentage points. Turning to the bottom panel of the table, we do not find significant gender differences in the Prospera effect on grade retention. In summary, our results show that both females and males benefit from Prospera participation and that the program generally reduces gender disparities in mathematics and Spanish test scores and in dropout rates. 47The average effect on the Spanish score displays substantial heterogeneity among Prospera beneficiaries, as will be shown below. 48In the fall semester of 2008, the transfers ranged from 130 to 265 pesos for primary school and 405 to 495 (385 to 430) for females (males) in lower-secondary school (US1=11 pesos in 2008). 168 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) Table 12. Gender differences in cumulative Prospera effects (by grade 9). Female Male P=1˜ P=0Diff S.E.P=1˜ P=0Diff S.E. Mathematics score Grade 5 500 499 0.7 0.9 491 492 −1.1 1.1 Grade 6 530 525 4.7 1.1 523 519 3.9 1.2 Grade 7 495 481 14.2 2.4 488 475 13.3 2.2 Grade 8 525 511 14.9 2.0 530 516 13.5 2.0 Grade 9 564 542 21.8 2.5 560 541 19.6 2.5 Spanish score Grade 5 503 505 −1.3 0.9 476 476 −0.5 1.0 Grade 6 531 536 −4.5 0.9 502 506 −3.6 1.0 Grade 7 484 480 4.6 1.9 446 437 8.1 1.7 Grade 8 498 494 4.2 1.8 462 456 5.5 1.7 Grade 9 495 492 3.2 1.9 467 462 5.0 2.1 Dropout rate Grade 7 0.10 0.16 −0.06 0.01 0.11 0.18 −0.07 0.012 Grade 8 0.15 0.22 −0.07 0.01 0.16 0.25 −0.09 0.011 Grade 9 0.23 0.30 −0.07 0.009 0.27 0.36 −0.09 0.009 Retention rate Grade 4 0.03 0.03 −0.003 0.002 0.05 0.06 −0.004 0.003 Grade 5 0.01 0.02 −0.002 0.002 0.03 0.04 −0.003 0.002 Grade 6 0.001 0.001 0.000 0.000 0.004 0.004 0.000 0.000 Grade 7 0.001 0.002 −0.001 0.001 0.005 0.006 −0.001 0.002 Grade 8 0.002 0.002 −0.001 0.001 0.005 0.007 −0.002 0.001 Note: Estimates obtained through model simulation. See the note to Table 11. Prospera effects by propensity-scores quartiles We next explore the heterogeneous Prospera impacts for students from different backgrounds in Figures 6and 7. Figure 6shows the effects of Prospera participation on test scores broken down by propensity-scores quartiles. As described in Section 3.4, the propensity score is a summary statistic of students’ family background, with quartile 1 denoting the most advantaged families and quartile 4 denoting the most disadvantaged families. Our estimates show larger impacts in later grades and smaller impacts in earlier grades, regardless of propensity-score quartiles. These patterns are consistent with the Prospera effects being cumulative with greater exposure associated with greater impact. Among the four quartiles, we observe the largest estimated cumulative impacts for students in the highest quartile, who are the ones from the most disadvantaged backgrounds. Prospera increases their test scores in mathematics by 0.29 standard deviations and their test scores in Spanish by 0.09 standard deviations and both effects are statistically significant. The top propensity score quartile contains the majority (52.7%) of the Prospera beneficiaries. Figure 7displays the cumulative effects of Prospera on three key outcomes: (i) Panel (a) presents grade attainment; (ii) Panel (b) presents the cumulative dropout rate; and (iii) Panel (c) presents the total number of retentions during primary school. The first two outcomes are evaluated at the end of a 6-year period, corresponding to the end Quantitative Economics 16 (2025) Prospering through Prospera 169 Figure 6. Prospera academic achievement effects by propensity-score quartiles. Note: 95% confidence intervals, depicted as bars, are derived using a parametric bootstrap method with 100 replications. of grade 9 (for students who do not experience grade retention or drop out). The third outcome, the cumulative number of retentions, is assessed upon completion of primary school. The estimated impacts are shown conditional on the propensity score quartile. Notably, the most substantial impacts (with the exception of cumulative retentions) are Figure 7. Prospera effects on schooling grade attainment, dropout, and number of retentions by propensity-score quartiles. Note: 95% confidence intervals, depicted as bars, are derived using a parametric bootstrap method with 100 replications. 170 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) observed in the fourth quartile, comprised of the most disadvantaged students. Because students opting to drop out are generally lower performing, disregarding the selection bias associated with dynamic dropouts tends to exaggerate the downward bias when estimating the program effects, particularly for students in the fourth quartile compared to those in other quartiles. Comparing ATT with ATU Next, we compare the average treatment effect on individuals who received treatment, commonly referred to as “ATT,” with the average treatment effect on those who did not receive treatment, commonly referred to as “ATU.” In our analysis, the “untreated” group consists of children/youth who are not beneficiaries of the Prospera program (P=0)but who had a positive probability of being a beneficiary, as determined by their household characteristics. (Recall that we imposed common support as described previously.) The results in Table 13 indicate that the impact of the Prospera program is significantly greater for the treated group compared to the untreated group. For instance, the Prospera program leads to substantial improvements in mathematics and Spanish scores for the treated students, with increases of 20.8 and 4.0. For the untreated group, the program only results in a mathematics score improvement of 12.3 and has little effect on Spanish scores. At the extensive margin, Prospera reduces the dropout rate by 0.08 for the treated group but by only 0.05 for the untreated group. Lastly, Prospera also has a greater impact on reducing retention probabilities for the treated group compared to the untreated group. These differences are in line with our earlier findings, shown in Figure 6.Thosefigures showed that the most substantial impacts are observed among the most disadvantaged groups. Now considering that these highly disadvantaged students are disproportionately more likely to be program beneficiaries, they predominantly fall into the treated group rather than the untreated group. Thus, it is expected that the ATT would be higher than the ATU. 6.2 The importance of the telesecondary-school option As previously described, children/youth from Prospera-beneficiary households often live in rural areas where telesecondary schools are available and they more often attend this school type. We next evaluate the importance of telesecondary school as a determinant of Prospera impacts on school enrollment. In particular, we use our estimated model to simulate what educational outcomes would look like were the telesecondaryschool option not available. The simulation takes into account that students might then have to travel further distances to get to schools or dropout if telesecondary schools had been their only option. Table 14 shows the distribution of local lower-secondary schoolchoice sets in the data (baseline) and after removing the telesecondary option. For 6.9% of students, telesecondary schools are the only option. The upper panel of Table 15 shows the simulated dropout proportion (at grade 9) for current Prospera telesecondary enrollees when the telesecondary schools are removed from their choice sets. The dropout proportion increases dramatically from 0.18 to 0.52. Quantitative Economics 16 (2025) Prospering through Prospera 171 Table 13. Comparing ATT, ATU, and overall treatment effect. ATT ATU Overall Mean S.E. Mean S.E. Mean S.E. Mathematics score Grade 5 −0.2 0.7 0.8 1.1 0.4 0.8 Grade 6 4.3 0.8 5.2 1.1 4.9 0.9 Grade 7 13.7 2.0 9.1 1.8 10.7 1.7 Grade 8 14.2 1.8 7.6 1.9 9.9 1.7 Grade 9 20.8 2.2 12.3 2.4 15.2 2.1 Spanish score Grade 5 −0.9 0.7 0.1 1.0 −0.3 0.8 Grade 6 −4.1 0.7 −2.5 1.0 −3.1 0.8 Grade 7 6.3 1.6 3.5 1.6 4.5 1.5 Grade 8 4.8 1.5 1.6 1.7 2.7 1.5 Grade 9 4.0 1.8 −0.2 1.8 1.2 1.7 Dropout rate Grade 7 0.07 0.01 0.03 0.007 0.05 0.01 Grade 8 0.08 0.01 0.04 0.007 0.06 0.01 Grade 9 0.08 0.01 0.05 0.007 0.06 0.01 Retention rate Grade 4 −0.004 0.002 −0.002 0.002 −0.001 0.001 Grade 5 −0.0025 0.0015 −0.0016 0.0011 −0.0009 0.0006 Grade 6 0.0001 0.0002 −0.0001 0.0002 0.0001 0.0001 Grade 7 −0.0009 0.0011 −0.0006 0.0008 −0.0003 0.0003 Grade 8 −0.0010 0.0008 −0.0005 0.0007 −0.0003 0.0002 Note: “ATT” denotes the average treatment effect on individuals who received the treatment, while “ATU” denotes the average treatment effect on those who did not receive it. The “untreated” group consists of children and youth who are not Prospera beneficiaries (P=0)but had a positive probability of eligibility, based on household characteristics. Estimates are derived from model simulations. Average educational attainment over the 6 years of our observation period (up to grade 9) falls from 8.76 grades to 7.57 grades. Despite using different data sources and evaluation approaches, our results align with evidence on telesecondary schools’ importance reported in Navarro-Sola (2019).49 The lower panel of Table 15 shows simulated academic achievement for current Prospera telesecondary enrollees who continue their education even after telesecondary schools are no longer available. At grade 9, we observe a decrease in average mathematics test scores, from 602 to 535, and a decrease in average Spanish test scores from 492 to 473. This finding is consistent with the test score distributional differences seen in Figure 2, which suggested that telesecondary schools are relatively effective in enhancing students’ test scores, particularly in mathematics, 49Using a difference-in-difference approach and Employment and Occupation National Survey (EONS) data set, she showed that the construction of an additional telesecondary per 50 children would encourage 10 individuals to enroll in lower-secondary education, causing an average increase of one additional grade of education among individuals that could have attended it. 172 Behrman, Parker, Todd, and Zhang Quantitative Economics 16 (2025) Table 14. The school-choice distribution with and without the telesecondary option. Baseline No telesecondary General, technical and telesecondary 0.696 N/A General and telesecondary 0.072 N/A General and technical 0.061 0.757 Telesecondary and technical 0.078 N/A Only general 0.012 0.090 Only telesecondary 0.069 N/A Only technical 0.008 0.080 No local schools 0.004 0.073 6.3 Quantifying the importance of dynamic selection The multiequation modeling framework that we implemented controlled for multiple sources of dynamic selection—due to dropout, school choice, and grade retention—as well as for cheating and missing data. It incorporated unobserved types to control for potential selectivity on unobserved factors. Arguably, in Mexico, selection is an important consideration, given that school enrollment drops significantly in lower-secondary school grades and that parents can select from available schools.50 In the US context, value-added models are often implemented without accounting for selection. To explore the importance of controlling for multiple sources of selection, we compare our baseline results with results obtained from a simpler value-added model that we estimate grade-by-grade without distinguishing school types: Am ia =δmg 0+Ai,a−1δg 1+δmg 2Pi+ZA iaδmg 3+ωmg ia . Compared with equation (3), the contemporaneous Prospera effect δmg 2is homogeneous across school types and we do not model school choice. Also, this model does not include permanent unobserved heterogeneity (types). The cumulative program effect can Table 15. Simulated dropout, educational attainment, and achievement for Prospera telesecondary enrollees when the telesecondary option is removed. With telesecondary Without telesecondary Dropout rate 0.18 0.52 Grades attained 8.76 7.57 Test scores at grade 9 Math score 602 535 Spanish score 492 473 Note: The simulation is based on the Prospera beneficiaries who are currently enrolled in telesecondary school at grade 7. 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Manuscript received 22 November, 2022; final version accepted 19 September, 2024; available online 9 October, 2024. The replication package for this paper is available at https://doi.org/10.5281/zenodo.13771826. The Journal checked the data and codes included in the package for their ability to reproduce the results in the paper and approved online appendices.