Neighborhood Peer Effects in Secondary School Enrollment Decisions. Gustavo J. Bobonis and Frederico Finan. Current Version: February 2008

Transcription

1 Neighborhood Peer ffets in Seondary Shool nrollment Deisions Gustavo J. Bobonis and Frederio Finan Current Version: February 008 First Version: September 003 Abstrat: This paper identifies neighborhood peer effets on hildren s shool enrollment deisions using experimental evidene from the Mexian PROGRSA program. We use exogenously variation in the shool enrollment of program eligible hildren to identify peer effets on the shooling deisions of ineligible hildren residing in treatment ommunities. We find that peers have onsiderable influene on the enrollment deisions of program-ineligible hildren, and these effets are onentrated among hildren from poorer households. These findings imply that poliies aimed at enouraging enrollment an produe large soial multiplier effets. Previous versions of this paper were entitled ndogenous Peer ffets in Shool Partiipation and Do Transfers to the Poor Inrease the Shooling of the Non-Poor: The Case of Mexio s PROGRSA Program. We are grateful to Josh Angrist, David Card, Ken Chay, Alain de Janvry, Weili Ding, Chris Ferrall, John Hoddinott, Caroline Hoxby, Asim Khwaja, David S. Lee, Steve Lehrer, Craig MIntosh, Rob MMillan, Ted Miguel, lisabeth Sadoulet, Aloysius Siow, T. Paul Shultz, Dunan Thomas, the editor, and two anonymous referees, whose suggestions greatly improved the paper. We also thank seminar partiipants at Berkeley, Queen s, Toronto, CIRPÉ, and NUDC 003 and 005 Conferenes for helpful omments. We thank Caridad Araujo, Paul Gertler, Sebastián Martínez, Iliana Yashine, and the staff at Oportunidades for providing administrative data and for their general support throughout. Bobonis aknowledges finanial support from the Institute of Business and onomis Researh at UC Berkeley and NICHD Training Grant (T3 HD0775). Finan aknowledges finanial support from the Soial Siene Researh Counil. Contats: G. Bobonis, Department of onomis, University of Toronto, Sidney Smith Hall, 00 Saint George Street Room 4057, Toronto, Ontario, M5S 3G3, Canada. Tel: mail: gustavo.bobonis@utoronto.a. F. Finan, Department of onomis, UCLA, Bunhe Hall, Box 95477, Los Angeles, CA , USA. Tel: Fax: mail: ffinan@eon.ula.edu.

2 . Introdution Low seondary shool enrollment rates remain an important onern for muh of the developing world. Despite signifiant improvements over the last 40 years, seondary shool enrollment rates in 000 were only 54 perent among low inome ountries (Glewwe and Kremer 005). Given that eduation fosters growth and improves welfare, promoting seondary shool enrollment represents an important poliy issue. To design appropriate and effetive poliies as a redress for low enrollment rates, it is neessary to understand individuals deisions to enroll into seondary shool. Although many fators affet the deision to enroll into seondary shool, there is an inreasing reognition that individuals neighborhoods or ommunities influene their eduational attainment. Residents of poor neighborhoods tend to attain lower eduational levels and fare substantially worse on a wide range of soioeonomi outomes than individuals living in more affluent ones, in both developed and developing ountry settings (e.g. Case and Katz 99; Kling, Liebman, and Katz 007; Gray-Molina et al. 003; Sanhez-Peña 007). Several existing theories attempt to explain why residential loation may affet individual s shooling outomes. For instane, a hild s deision to enroll into shool may be influened by a desire to onform with others in their referene group due to either peer pressure or soial norms (Bernheim 994; Akerlof 997; Akerlof and Kranton 000; Glaeser and Sheinkman 003). Additionally, there may be informational externalities as individuals learn about the benefits of shooling from the ations of their peers (Bikhhandani, Hirshleifer, and Welh 99). Finally, soial interations may generate important strategi omplementarities in student learning and teahers effort (Kremer, Miguel, and Thornton 004; Lazear 00), whih may attrat students to shool. 3 Thus, neighborhood-level soial interations ould play an important role in an individual s shooling deision proess. Understanding these effets an lead to poliies that enourage the internalization of these interations, making human apital investments more effiient (Bénabou 993; 996). However, to our knowledge, existing empirial researh has not opened the blak-box of neighborhood interations to understand how partiular behaviors of neighbors influene individuals shooling deisions. 4 In this paper, we use evidene from a human development program in rural Mexio to examine the role of neighborhood-level behavioral soial interations on a hild s deision to enroll into seondary Shool enrollment is perhaps a neessary but not a suffiient ondition for improving eduation attainment. Low shool quality remains an important obstale for eduation attainment in developing ountries (Banerjee et al 007). On the other hand, Oreopoulos (003) uses quasi-experimental variation in assignment to different types of publi housing units in Toronto and finds no long-term neighborhood effets on individuals labor market outomes. 3 Also, resoures for loal publi goods, suh as shools, may be limited by the resoures available to ommunity residents, or the apaity of residents to attrat and diret government funding towards these (Benabou, 993). 4 There are various ontributions to the literature on soial learning and soial interations in tehnology adoption whih have been suessful in opening this blak box. xamples are Kremer and Miguel (006), Munshi and Myaux (005), Duflo and Saez (003).

3 shool. The PROGRSA program, initiated by the Mexian government in 997, provides ash transfers to marginalized households in rural areas. The transfer is paid to mothers ontingent on their hildren s primary and seondary shool attendane and family visits to health servies. Five hundred and six ommunities were seleted to partiipate in an experimental evaluation of the program; the ommunities were randomly divided into two groups, with the treatment group being phased-in to the program in Marh-April 998 and the ontrol group in November-Deember 999. Within these seleted ommunities, a poverty indiator was onstruted at baseline to lassify eligible and ineligible households. While household eligibility was determined within all (treatment and omparison group) ommunities, only households below a welfare threshold and within the treatment villages beame program benefiiaries during the evaluation period. Using experimental variation in the indued shool partiipation of the subset of eligible hildren in these ommunities, we an identify neighborhood peer effets in seondary shool enrollment deisions among hildren who were ineligible for the program within the program ommunities. The use of this experimental design enables us to overome many of the identifiation problems that plagued previous literature on soial interations (Manski 993). Our first set of results suggest that hildren from ineligible households residing in the PROGRSA villages inreased their seondary shool enrollment rate by 5.0 perentage points relative to ineligible households in ontrol villages. Moreover, there were signifiant differential effets on shool enrollment by household s welfare index level and grade level. For instane, among ineligible households with a value of the welfare index below the median for ineligible households, PROGRSA inreased seondary shool enrollment by 5.5 perentage points, but had no effet for hildren among the upper welfare-index group. Overall, these findings indiate that there was a signifiant spillover effet on the seondary shool enrollment rates of non-eligible households residing in the treatment villages. In the seond stage of the study, we exploit the fat that PROGRSA reated an exogenous shok to seondary shool partiipation of hildren residing in the same villages, to examine the extent to whih soial interations affet hildren s deisions to enroll into seondary shool. We find that hildren have an inreased likelihood of attending seondary shool of approximately 5 perentage points as a result of a 0 perentage-point inrease in the village network enrollment rate. Substantially larger effets of approximately 6.5 perentage points are also found for ineligible hildren of relatively poorer households a subgroup of hildren more likely to interat with treated hildren in these villages. These estimates indiate that the poliy intervention benefited from important soial multipliers, as behavioral soial interations in effet doubled the diret effets of the shool enrollment subsidy. A potential onern with our identifiation strategy is that the program may have affeted ineligible hildren through other mehanisms. The fous of PROGRSA was not limited stritly to

4 eduation, but also enouraged investments in health and nutrition while providing eligible households with substantial monthly payments. With the program induing behavioral hanges among eligible households along several dimensions, it is oneivable that the inrease in enrollment among ineligible households was not neessarily due to peer effets, but rather a response to some other hange in the behavior of eligible households. Our results are onsistent with three alternative explanations. First, although we do not find any evidene that the program had a diret effet on shool quality, we annot definitively rejet the hypothesis that PROGRSA did not improve teaher quality or effort indiretly, as teahers ould have responded to hildren beoming more interested in shool, leading to an inreased shool enrollment of ineligible hildren (Kremer, Miguel, and Thornton 004; Duflo, Dupas, and Kremer 007). Seond, we also annot rejet the hypothesis that non-eligible hildren enrolled into seondary shool with the expetation that this would affet their future program partiipation. A final alternative interpretation for our findings is that ineligible households may have simply responded to information regarding the benefits of shooling and attaining an eduation (Jensen 007). If PROGRSA led parents and students to update their priors on the value of enrollment, then the program may have affeted the enrollment deisions of non-eligible households diretly. The data are however inonsistent with several other hypotheses. We do not find any evidene that the program affeted either the onsumption of ineligible households or hildren s health, whih may have led to greater shool enrollment rates. Also, we ondition on a large number of predetermined mean village-level ontextual and environmental harateristis that may be orrelated with the impats of the intervention, and show that the effets are robust to these speifiations. Lastly, we present evidene inonsistent with a relative redution in transportation osts faed by program village hildren, and with potential ontamination bias onerns. This sensitivity analysis onfirms the validity of the identifying assumptions of the model. Our study ontributes to the growing literature on neighborhood-based peer effets in shooling deisions. The seminal paper by Case and Katz (99) identifies neighborhood-based peer effets in idleness among youth in high-poverty areas in Boston using an instrumental variables strategy to address the refletion problem. Two reent ontributions also use instrumental variable strategies to estimate behavioral peer effets in shooling deisions in various ontexts. Cipollone and Rosolia (007) use plausibly exogenous variation in the shool attainment of men as a result of a poliy following an earthquake in Southern Italy to identify the effet on the shool attainment of women in these regions. Lalive and Cattaneo (006) extend our analysis to test whether soial interations affeted shooling deisions of both primary and seondary shool hildren. They also use subjetive information on 3

5 parents pereption on hildren s ability and shool efforts to understand the reasons for endogenous soial interations in shooling deisions. Their results are omplementary and onfirm many of ours. The paper is strutured as follows. Setion provides a brief disussion of the PROGRSA program and its evaluation omponent, as well as the data used in the analysis. In Setion 3, we present an empirial model of soial interation effets and disuss its identifiation problems. We then desribe our researh design, and how it avoids these identifiation pitfalls. The main estimates are reported in Setion 4, followed by sensitivity tests of the identifying assumption in Setion 5, a disussion of alternative interpretations in Setion 6 and Setion 7 onludes.. PROGRSA Program, valuation, and Data. Bakground on the PROGRSA Program valuation In 997, the Mexian government initiated a large-sale eduation, health, and nutrition program (the PROGRSA Program) aimed at improving human development among hildren in rural Mexio. The program targets the poor in marginal ommunities, where 40 perent of the hildren from poor households drop out of shool after the primary level. The program provides ash transfers to the mothers of over.6 million hildren onditional on shool attendane, health heks and health linis partiipation, at an annual ost of approximately one billion dollars, or 0. perent of Mexio s GDP in 000. The eduation omponent of PROGRSA onsists of providing subsidies, ranging from $70 to $55 pesos per month (depending on the hild s gender and grade level), to hildren attending shool in grades three to nine of primary and lower seondary shool. Overall, the program transfers are sizeable, representing 0 perent of the average expenditures of benefiiary families in the sample. A distinguishing harateristi of PROGRSA is that it inluded a program evaluation omponent from its ineption. PROGRSA was implemented following an experimental design in a subset of 506 ommunities loated aross seven states: Guerrero, Hidalgo, Mihoaán, Puebla, Querétaro, San Luis Potosí, and Veraruz. Among these ommunities, 30 were randomly assigned into a treatment group, with the remaining 86 ommunities serving as a ontrol group, thus providing an opportunity to apply experimental design methods to measure its impat on various outomes. In addition, within these seleted ommunities, a poverty indiator was onstruted using the household inome data olleted from the baseline survey in 997. A disriminant analysis was then separately applied in eah of the seven regions in order to identify the household harateristis that best lassified poor and non-poor households. These harateristis, whih were unknown to the households, were then used to develop an equation for omputing a welfare index that determined eligibility into the program (see Skoufias et al. 4

6 00 for a more detailed desription of the targeting proess). 5 While household eligibility was determined within all (treatment and omparison group) ommunities, only households lassified as eligible and within the treatment villages beame program benefiiaries during the evaluation period. That the eligibility lassifiation exists for both treatment and ontrol ommunities and treatment was randomly assigned are ritial design aspets for the identifiation of the neighborhood peer effets, as will be disussed in Setion 3. An issue in the initial implementation (during the first-year) of the program involved an inrease (by the program administrators) in the number of eligible households, after it was disovered that households with ertain harateristis namely, the elderly poor who no longer lived with their hildren were exluded from the initial eligibility riteria. Beause of this oversight, a new disriminant analysis was onduted, and households were relassified as either eligible (poor) or non-eligible (non-poor) households. Households that were originally lassified as non-poor but inluded in this seond set of eligible households - alled the densifiado group beame program benefiiaries approximately 8 months after the start of the program (Skoufias, Davis, and de la Vega 999). As a result of this hange in program implementation, there are eligible households above and below the initial region-speifi eligibility thresholds. For our analysis we lassify these densifiado households as eligible, sine these are eligible for treatment at some point during the evaluation period.. Data and Measurement Sine the baseline ensus in Otober 997, extensive biannual interviews were onduted during Otober 998, May/June 999, and November 999, on approximately 4,000 households of the 506 ommunities. 6 ah survey is a ommunity-wide ensus ontaining detailed information on household demographis, inome, expenditures and onsumption, and individual soio-eonomi status, health and shool behavior. More speifially, the surveys in Otober 997, Otober 998, May/June 999, and November 999 olleted information on the shool enrollment and grade ompleted of eah hild in the household between 6 and 6 years old. We thus have information on enrollment during three onseutive shool years (997-98, , and ) and grade promotion during two onseutive shool years. Sine primary shool enrollment is almost universal in rural Mexio, we restrit our interest to the enrollment and promotion deisions of hildren who have attained at least a primary eduation but have not ompleted seondary shool at baseline. Seondary shool enrollment is the most problemati deision for shool attainment 7, and also the grade levels where PROGRSA has had its greatest impat among eligible households (Shultz 004). In our sample, this onerns approximately,0 hildren 5 In addition to apturing the multidimensionality of poverty, another advantage of a welfare index is that it permits the lassifiation of new households aording to their soio-eonomi harateristis, other than inome. 6 There was a round of data olletion in Marh of 998 just prior to the start of the intervention. 7 In 997, primary shool enrollment was lose to 96.5%, ompared to 65% enrollment into seondary shool. 5

7 who are eligible at baseline to enter any of three lower seondary shool grade levels. By seleting the sample based on grade ompleted at baseline rather than inluding hildren who start ompleting their primary shooling during the post-treatment evaluation period, we avoid issues of dynami seletion into seondary shool (Cameron and Hekman 998). Also, with village-level ensuses, we an reliably onstrut village-level means of household and individual harateristis - inluding shooling deisions and ontextual variables that may affet it. Table presents the mean of various individual and household-level harateristis for both eligible and non-eligible hildren and their differenes between treatment and ontrol villages. The first row in the table demonstrates the hurdle that seondary shool represents for hildren in rural Mexio, and highlights a lear objetive of the program (Table, Panel A). In 997, the enrollment rate of eligible hildren in seondary shool is 66 perent, on average. Although enrollment rates are on average 4 perentage points higher among ineligible hildren, only 70 perent of these were enrolled in seondary shool. As one would expet from the random assignment, the pre-program differene in enrollment rates between treatment and ontrol villages among both eligible and ineligible households is small and statistially insignifiant. In addition, the simple differene in 998 and 999 enrollment rates between treatment and ontrol ommunities provides a straightforward measure of the program s impat on shool partiipation. In both years, enrollment rates in treatment villages were roughly 6 perentage points higher than in ontrol villages among the benefiiary households. Table also shows our first indiation of a possible spillover effet. Although the differene is statistially insignifiant (in the seond year), seondary shool enrollment in the treatment villages is approximately 6 and 4 perentage points higher than in ontrol villages among hildren of ineligible families in 998 and 999, respetively. Given these low enrollment rates, it is perhaps not too surprising that the mean eduational level of heads of households is also quite low, as heads of eligible and ineligible households have only ompleted.6 and 3. years of shooling, respetively (Panel B). These hildren also tend to ome from large households; the average household size in these villages is 7.3 for eligible households and 6.8 for ineligible ones. We also ompare mean attributes at baseline (Otober 997) aross treatment and ontrol villages to evaluate the randomization of our sample (Table, olumns -4, 6-8). As one would hope from the random assignment, there are no statistially signifiant differenes in the observed harateristis of these individuals on most dimensions. 8 In addition to the village-ensus data, we use administrative data on the amount of PROGRSA transfers reeived by the households per survey-round. As expeted, the administrative transfers data on transfers show that eligible households in treatment villages reeived 70 pesos per month (on average) 8 Behrman and Todd (998) ondut an exhaustive analysis of the degree of suess of the random assignment of villages in the PROGRSA Program, and onlude that the randomization was suessful. 6

8 during the April 998-Deember 999 period (Table, Panel B). Average transfers for ontrol households are non-zero beause they begin to reeive program transfers by Deember 999. The differene in transfers between the two groups is large and substantial. More importantly, the administrative data shows no evidene of program leakage, i.e., ineligible households reeiving ash transfers. 9 Finally, we also make use of administrative data on seondary shools in the evaluation regions (whih ontain information on number of pupils by grade, teahers, number of lassrooms, and other infrastruture harateristis of the shools). Without information on whih shool eah hild attends, we math using GPS data hildren from the same village to the seondary shool losest in distane to the village. 0 This administrative data allow us to rule out alternative hypotheses and to test our identifying assumptions (see disussion in Setion 5). Means of baseline harateristis of shools attended by the hildren in the sample are reported in Table ; there are no systemati differenes between treatment and ontrol villages as expeted. Given our panel data struture, an important issue in the empirial analysis is the extent of sample attrition. If being out-of-sample is orrelated with the likelihood of being in the program (treatment) group, then this ould bias the oeffiient estimates. Sample attrition rates through the two post-treatment survey rounds are approximately 0 perent for the sample of hildren in seondary shool, both in eligible and ineligible households (Table A, olumns and 4), and the likelihood of attrition is highly orrelated with individuals observable harateristis (olumns and 5). Fortunately, aross program and omparison groups, attrition rates are balaned and the observables orrelates of attrition are not signifiantly different (olumns 3 and 6). We use baseline individual, household, and ommunity harateristis to ontrol for any potential attrition bias in all our estimations. 3. Identifiation of Neighborhood Peer ffets In this setion, we disuss the eonometri model used to estimate neighborhood peer effets and the assumptions needed for identifiation. We base our empirial model on a simple deision problem of shool enrollment in the presene of soial interations. This will allow us to postulate various mehanisms through whih peers an play a role in shool enrollment deisions. An individuals seondary shool enrollment deision (y i ) an be modeled as a funtion of (i) the hild s expeted learning (whih is in turn determined by the hild s learning (i.e. ognitive) ability, the 9 Although this does not prove that leakage was not an issue in the program s implementation, there is no evidene of it at the entral level. 0 ven though there maybe some measurement error assoiated with mathing hildren to their geographially losest shool, there are at least two reasons why the mislassifiation should be minimal: (i) households in these villages have a very limited hoie of shools, due to the sare number of seondary shools in these marginal areas (only 0 perent of households have aess to a seondary shools in their village); (ii) based on fieldwork onduted by the authors in 003, we were able to perfetly math the villages visited to the seondary shools reported as attended in informal interviews with village members. 7

9 shool organization and environment, ommon to all hildren, and the ability distribution of peers attending shool); (ii) a desire to onform with the referene group s (i.e. the neighbors ) shool enrollment and partiipation behaviors ((y,, y -i,, y i+,,,y I, ) denoted by y -i, ) due to either peer pressure or soial norms (Bernheim 994); (iii) individual opportunity osts of attending shool whih may vary as a result of a government subsidy for shool partiipation, as well as the pereived safety of ommuting to shool; and (iv) variation in the tastes for shooling. In this theoretial framework, peer effets enter the hild s utility through three main mehanisms. First, it aptures the idea of strategi omplementarities in peer partiipation and effort in the eduation prodution funtion: if the hild enrolls in shool, the time that peers spend in lass as well as their effort levels inside and outside the lassroom an enhane the hild s learning, in addition to an individual s own ability and shool environment. Also, the preferene-based mehanisms for soial interations inorporate the role that the desire to attend shool may be inreasing in the shool enrollment of peers in the referene group (i.e. the proportional omplementarity utility funtion), influened by a desire to onform with others due to either peer pressure or soial norms, resulting in hildren not wanting to deviate from hoies made by others in her referene group (i.e. Akerlof (997) s quadrati onformist utility funtion), or due to hanges in the expeted osts of ommuting to shool due to their peers shool-going (e.g. safety in numbers). Under the assumption that hildren make shool partiipation deisions taking other individuals hoies as given, maximizing utility yields an equation for the hild s optimal shool partiipation level, whih results in the standard linear-in-means empirial model used to estimate neighborhood peer effets: y = α + β + γ + λz + θy + u () i i i where y i is an indiator variable for the shool enrollment behavior of hild i in village ; i are exogenous harateristis of the individual; are the mean exogenous harateristis of the referene group; Z are harateristis of the environment (e.g., village or shool) that may influene individuals shool enrollment deisions; and y is the enrollment rate of the referene group. This linear-in-means model provides a formal expression to various hypotheses often advaned to explain the ommon observation that individuals belonging to the same group or neighborhood tend to behave similarly. The first, orrelated effets, proposes that individuals in the same group tend to behave similarly beause they have similar harateristis or fae similar environments; these are represented in the model by the vetor of parameters β and λ. The seond, ontextual peer effets, proposes that exogenous harateristis of the referene group (e.g., parental involvement in hildren s eduation in the village) influene individual behavior; the vetor of parameters γ aptures these ontextual effets. Finally, the hypothesis of Note that in this speifiation we are assuming that the referene group and the environment are one in the same. This learly need not be the ase. 8

10 endogenous peer effets proposes that the shool enrollment behavior of the group influenes individual behavior; the parameter θ in the model aptures this effet. In the empirial analysis, we annot and do not distinguish from prodution or tastes-based motivations for the soial interation effets; these are aptured in the θ redued-form parameter. As Manski (993) shows, OLS estimation of the linear-in-means model annot separately identify the two types of soial interation effets as a result of the simultaneity of individuals ations. 3 quation () represents individual i s shool enrollment best-response funtion given peers potential shool enrollment deisions and exogenous harateristis. However, the data onsist of equilibrium behavioral hoies of all individuals in a referene group, and therefore the individuals shool enrollment deisions are jointly determined, leading to simultaneity bias (Moffitt 00). Identifiation of parameter θ is possible, however, under a partial-population experiment setting whereby the outome variable of some randomly hosen members of the group is exogenously altered (Moffitt 00). Formally, we an assume that individuals shool enrollment deisions follow model () augmented for the existene of an exogenous treatment T i whih equals unity for a subset of individuals in the referene group and zero otherwise. The individual harateristis of this subgroup are denoted by supersript : y = α + β + γ + λz + θy + δt + u ( ) i i In addition, there are individuals within the same referene group (denoted with supersript N) who do not reeive treatment: N i N i i y = α + β + γ + λz + θy + u ( ) Using equations ( ) and ( ), and realling that group averages are related to within-village treated () and untreated (N) group averages by: N N i y = m y + ( m ) y () = m + ( m ) N i We refer the interested reader to Beker and Murphy (000), Durlauf and Young (00), and Glaeser and Sheinkman (003) for a thorough disussion of the literature on hoie in the presene of soial interations. Duflo and Saez (003) examine redued-form endogenous interation effets with respet to retirement savings deisions in the U.S. using an analogous experimental design. 3 To see this, take the expetation of equation () onditional on and Z, integrating over Z, and solving for y results in the mean equilibrium outome in group, whih, substituted in equation () yields the redued form for individual outomes: α γ + βθ λ y i = + β i + + Z + u. Manski (993) shows that, onditional on θ, this equation has a unique i θ θ θ solution, parameters γ and θ are unidentified, but omposite parameters α, γ + βθ, and λ are identified. Although the θ θ θ identifiation of the omposite parameters does not allow one to distinguish between endogenous and ontextual soial interation effets, it permits one to determine whether some soial effet is present. 9

11 where m is the share of treated individuals in the referene group, we an show, based on Moffitt (00), that the mean equilibrium outome in the referene group satisfies the following ondition: α β + γ λ δ y = + + Z + m T (3) θ θ θ θ Substituting equation (3) in equation ( ), we an solve for the redued-form relationship of the shool enrollment outomes of untreated individuals as a funtion of the partial-population treatment in the referene group, and exogenous individual, referene group, and environmental harateristis: N α N θβ + γ λ θδ N y i = + β i + + Z + m T + u (4) i θ θ θ θ The partial-population treatment terms in the two redued-form equations have intuitive interpretations. In equation (3), the ( δ ( θ))m term an be deomposed into two additive terms: (i) the diret effet of the treatment on the mean enrollment of the referene group, whih is assumed to affet a sub-sample of the referene group ( δ m ), and (ii) the indiret effet as a result of behavioral soial interations ( ( θ ( θ) ) δm ). For the untreated group (equation (4)), the partial-population treatment term aounts for the fat that the untreated group is not diretly affeted by the treatment (by definition), and only inludes the indiret effet: the soial interation effet. Also note that one ould use oeffiient estimates from equations (3) and (4) to identify the diret treatment and peer effets parameters. Speifially, note that the ratio of the m redued-form T oeffiients from equations (3) and (4) is equal to θ, the peer effets parameter. The speifiations that we adopt in this paper are based on equation ( ) and a slight variant of equation (3): y α + u ( ) y N N i = + β i + γ + λz + θy i, N i, i (3 ) N i = ~ ~ ~ ~ ~ α + β + β + λz + δt + ε where T is the PROGRSA treatment village indiator variable and omposite oeffiients ~ α α =, θ ~ θβ + γ β = θ, T ~ λ ~ δm λ =, andδ =. Note that equation (3 ) uses T rather than the interation term θ θ m as the instrumental variable. We allow for this disrepany in the model beause the share of treated individuals in the referene group ( m ), in this ase the share of PROGRSA-eligible hildren in the village, may not be exogenous if there is any sorting of individuals into and out of the village based on 0

12 unobservable harateristis of the households or villages. However, estimates whih use m T as the IV provide quantitatively similar estimates to those reported in the results setions below. Under the onditions of (i) robust partial orrelation between the instrumental variable and the ~ endogenous regressor ( δ 0), and (ii) lak of orrelation between the exluded IV and the disturbane term in equation ( ) ( [ T u N i ] = 0), IV estimation is a onsistent estimator of parameter θ. Condition (i) an be tested in the data, and results will be disussed in Setion 4. Condition (ii), the exlusion restrition, is not diretly testable and is a maintained assumption of the model; the random assignment of the program aross villages is not suffiient to ensure that this ondition holds. The IV exlusion restrition relies on the assumption that an inrease in shool partiipation among ineligible hildren in treatment villages is the effet of the exogenous inrease in shool partiipation among the eligible seondary-shool hildren within the village and not the result of hanges in ontextual variables affeted by the program. Sine it is possible, however, that the program affeted ineligible hildren through other hannels, we follow various strategies to provide evidene that this is not the ase. First, using rih miro data for both eligible and ineligible households, we diretly test whether other potential externalities from program impats or partiular intriaies of the program had an effet on ineligible households. We do not find any evidene of hanges in the onsumption patterns or health status of ineligible households, or in measures of shool quality, for instane. Seondly, we ondition on a large number of predetermined mean village-level ontextual ( ) and environmental ( Z ) harateristis that may be orrelated with the impats of the intervention, and show that the effets are robust to these speifiations. We do not find any evidene of alternative mehanisms, and defer disussion of these results to Setion 5. 4 Finally, note that we also assume neighborhood peer effets to be at the village-level. Although we lak information on the speifi individuals who belong to a hild s referene group, we believe that the assumption of village-level effets may not be problemati for the following reasons. As is ommon in village eonomies in less-developed ountries, there is substantial ethnographi evidene doumenting soial interations at the village level in rural ommunities in Mexio (e.g., Foster 967). Furthermore, rural villages in this sample are quite small, with 47 households per village and only 0 hildren of seondary-shool age per village, on average. Thus in the ontext of Mexio, village peer effets may be 4 We present in the Appendix a more general linear-in-means model of soial interations that allows for diret treatment effets on hildren s ontextual harateristis. To identify endogenous peer effets in this model, we need to assume that the other variables affeted have neither diret nor ontextual soial interation effets on hildren s shool enrollment deisions. If the ondition fails to hold, we an still identify the presene of peer effets, but we annot distinguish between endogenous and ontextual peer effets. We estimated redued-form equations onsistent with this more flexible model, in whih we diretly explore the relationship between shool enrollment and m T. Our results, while less preisely estimated, are onsistent with the estimates reported in Setion 4. These results are available upon request.

13 a more redible assumption than studies that use ity bloks (Case and Katz 99), ensus traks (Topa 00; O Reagan and Quigley 996), or shools (vans, Oates and Shwab 99; Gaviria and Raphael 00), or lassrooms (Hoxby 000) stimates of Spillovers and Neighborhood Peer ffets 4. stimates of Redued-Form Spillover ffets In this setion, we present evidene on the redued-form spillover effets of the program on shool enrollment and grade promotion. We start the disussion with a graphial analysis to shed light on the patterns in the data. Figure presents a series of graphs, based on nonparametri estimates, depiting enrollment rates in seondary shool by the welfare index used to lassify eligible and ineligible households. 6 nrollment rates do not differ at baseline among eligible hildren in program and omparison villages (Figure, Panel A), and the differene is positive but small and insignifiant among ineligible hildren (Panel B). However, for 998 and 999, enrollment rates in program villages among both eligible and ineligible hildren inrease substantially relative to the omparison group (Panels C and D). Within the ineligible group, we observe a striking differene in enrollment rates between treatment and ontrol villages among relatively poorer households. This enrollment differene remains until a household welfare index of approximately 900 units (the median welfare index of ineligible households), at whih point the enrollment rates tend to onverge. This figure suggests that any spillovers of the program may have been onentrated among ineligible households with welfare harateristis relatively similar to the eligible households but lassified above the welfare qualifiation. Parametri linear probability estimates of the redued-form relationship between program and omparison villages enrollment rates mirror the results depited in the Figure. Consistent with Shultz (004) and Behrman, Sengupta and Todd (005), we find that hildren in eligible households inreased their shool enrollment by 6.3 perentage points relative to eligible hildren in ontrol villages (Table 3, Panel A, regression ). The point estimate with household and village-level ontrols implies an effet of 7.0 perentage points, or perent (Panel B, regression ). 7 The point estimate indiates that the program had a slightly greater impat during its first year (although we annot detet any statistially signifiant differenes by year, p-value=0.55) (Panel C, regression ) and among hildren who were to be 5 Although soial interations are assumed to our stritly at the village-level, many of the hildren in the sample are attending shools loated in neighboring villages. If the hildren are interating strongly with hildren in these neighboring villages, a soial network that only omprises own village hildren may be ill defined. However, our instrumental variables strategy allows us to avoid this issue, sine the random assignment of the village to the experimental groups should be unorrelated with both the assignment of neighboring villages to the program and the shooling deisions of hildren in these villages. 6 The onditional means are estimated by taking the mean enrollment within a bandwidth of 0.8. The figure is robust to perturbations to the bandwidth size. 7 When we exlude the densifiados from the sample, a large share of whih did not reeive any benefits during the evaluation period, the effets on eligible hildren are even stronger (Table 3, olumn ). xluding these individuals in the IV speifiations does not affet our results.

14 enrolled in either sixth or seventh grades in 998, the last year of primary shool and the first of seondary shool (regression ). The results presented in olumns 3-5 suggest that PROGRSA may have also benefited ineligible hildren. On average, hildren from ineligible households residing in the PROGRSA villages inreased their seondary shool enrollment rate by 5.0 perentage points relative to ineligible households in ontrol villages (Panel A, regression 3); however, the effet is impreisely measured (signifiant at 89 perent onfidene) and not robust to individual, household, and village-level ontrols (Panel B, regression 3). 8 There are signifiant differential effets on shool enrollment by household s welfare index level (regression 4). Among ineligible households with a below-median welfare index, PROGRSA inreased seondary shool enrollment by 5.7 perentage points (statistially signifiant at 90 perent onfidene), but had no effet for hildren among the upper welfare-index group (-0.9 perentage points and not statistially signifiant, not reported in the tables). 9 Similar to the differential effets exhibited by treated households, the point estimates indiate that the spillover effets were also larger during the first year of the program (4.0 perentage points). Finally, the spillover effets for those ineligible hildren just entering into seondary shool are large and sustained during the two aademi years at approximately 5.6 perentage points (Panel C, regression 5). 0, In Table 4, we investigate the effets of the program on promotion rates of ineligible hildren. Although the program has small and marginally signifiant grade promotion effets among all eligible seondary shool-ready hildren (Panel B, regressions and 3), the effets are more pronouned among those hildren just entering into seondary shool in both eligible and ineligible households (4.4 perentage points and 5.6 perentage points; Panel B, regressions and 5), and those residing in ineligible households below the median in terms of the welfare index. For instane, among ineligible households with a below-median welfare index, PROGRSA inreased seondary shool promotion rates by 6. perentage points (statistially signifiant at 95 perent onfidene), whih implies an inrease of roughly perent. Both the diret and indiret grade promotion effets are sustained during the aademi year around the perentage points range (8-4 perent), providing us onfidene that the 8 This result is onsistent with Behrman, Sengupta, and Todd (005) s lak of an overall effet among ineligible hildren. That said, we find positive spillover effets among hildren in the 0-3 years age group, onsistent with their finding of a spillover effet for year olds. Our effets are more preisely estimated due to the fat that we onentrate on individuals of seondaryshool age and that we pool observations aross age-speifi groups. 9 The differene in effets is statistially signifiant at 90 perent onfidene. 0 One exeption is the lak of a spillover effet on girls. Despite the fat that PROGRSA had a larger impat on eligible girls (Shultz, 004; Behrman, Sengupta and Todd, 005), we do not find a similar differential spillover effets between boys (the point estimate is 0.033, standard error 0.030, not statistially signifiant) and girls (point estimate of 0.07, standard error 0.03, not statistially signifiant) one we inlude household and village-level ontrols (not reported in the tables). To further hek robustness, we estimate program spillover effets using a speifiation with village ontextual harateristis and find largely similar results: overall effet estimates of.8 perentage points (standard error.5), and larger effets for the subgroup of hildren in households below the welfare index median (5.4 perentage points, standard error.9) and those just entering seondary shool (5.0 perentage points, standard error 3.). These estimates are also robust to the inlusion of muniipality fixed effets and to employing probit speifiations available from the authors upon request. 3

15 program promoted the shool enrollment and study effort of hildren ontinuing in or re-entering seondary shool onto the seond year of the program. 4. stimates of Neighborhood Peer ffets Table 5 reports neighborhood peer effets (θ) estimates from OLS and IV estimation of equations ( ) and (3 ). The IV estimate of the overall neighborhood peer effet implies that a one perentage point inrease in the referene group s enrollment rate leads to a 0.65 perentage point inrease in a hild s probability of enrollment (signifiant at 99 perent onfidene, Table 5, Panel A, regression ). The magnitude of the peer effet estimate dereases to 0.54 perentage points one individual and householdlevel ontrols as well as state fixed effets are inluded (signifiant at 95 perent onfidene, Panel A, regression ), and redues further to 0.49 perentage points one the following village-level predetermined ontextual variables are inluded: the proportion of seondary shool-age girls and the proportion of indigenous hildren in the village, mean village-level family size and eduational level, age, and gender proportions of heads of households (signifiant at 89 perent onfidene, Panel A, regression 3). In ontrast, the OLS estimate of the overall peer effet for the ontrol villages, whih does not take into aount the problems of self-seletion into referene groups, the refletion problem, and unobserved heterogeneity in the population, implies peer effets in the perentage point range as a result of a one perentage point inrease in the referene group s enrollment rate (signifiant at 99 perent onfidene, Table 4, Panel C, regressions -3). The IV estimates suggest that peer effets are quite large for this population. And, even though we annot neessarily rejet that the OLS and SLS estimates are signifiantly different from eah other, the results do suggest that the OLS estimates are biased upwards. Substantially larger peer effets are found among the relatively poorer hildren within the ineligible group and among those in the lower seondary shool grades. The point estimate on the effet for hildren in the below-median welfare-index group is 0.67 (Panel A, regression 4) and that on the hildren just entering seondary shool is (regression 5). The estimates with and without ontextual ontrols for the aademi year, with point estimates of and perentage points, indiate that these effets are sustained into the seond year of the program (regressions 6-7). The OLS estimates of soial network enrollment rate effets for these subgroups in ontrol villages imply effets of and respetively (Panel C, regressions 4-7). Again, the experimental evidene suggests that 3, 4 the OLS estimates are biased upwards, although we annot rejet that the oeffiients are equal. A speifiation whih uses m T as the exluded instrument gives an estimate of the endogenous peer effets (θ) of 0.48 (standard error = 0.76, signifiant at 9 perent onfidene). 3 A speifiation whih uses m T as the exluded instrument gives an estimate of endogenous peer effets (θ) of (standard error = 0.58, signifiant at 97 perent onfidene). In speifiations that inlude baseline enrollment as an additional regressor (to take into aount potential pre-treatment differenes), the estimated effets vary between (standard error = 0.36; signifiant at 89 perent onfidene) and (standard error = 0.79; signifiant at 97 perent onfidene) given small 4

16 That there exists a differential effet by the household welfare index is onsistent with various explanations. First, this differential effet may simply suggest that households that are relatively poor and more redit onstrained are more responsive to a positive induement of attending shool. Alternatively, these differential effets may reflet differenes in soial ties between ineligible households that are just above the welfare utoff and those that are better off. In partiular, if hildren from ineligible households that are slightly above the utoff are more likely to interat with eligible hildren in the village, then the indued shool partiipation of eligible hildren should have a more pronouned effet on this subgroup of hildren. However, the differential effets may be stritly due to the fat that the instrument is stronger for the subsample of hildren residing in low welfare index households. To test this hypothesis without information on the exat peer network of eah student we onstrut a measure of the number of extended-family members who live in different households and an enroll into seondary shool for eah hild in the village; this measure serves as a proxy for a hild s number of family-related peers in the village (a potential subset of a hild s peer group). 5 Comparing ineligible hildren from households below the median of the welfare index to those above the median, we find that the number of eligible extended-family links at baseline is signifiantly greater for ineligible hildren in the first group (0.97 hildren) relative to the latter group (0.65 hildren), among hildren with some extended-family link in the village. This differene of approximately 0.3 hildren (standard error, 0.09, signifiant at 99 perent onfidene; not reported in the tables), implies that the number of eligible links is 48 perent higher among households lassified in the below median welfare-index group. 6 While we do not expet all interations to our in these villages solely at the extended-family level, this evidene is onsistent with poorer ineligible hildren tending to interat more with eligible hildren. As noted by other researhers (e.g., Graham 005; Hoxby and Weingarth 006), the linear-inmeans model is unable to provide answers to the equity-effiieny tradeoffs that pervade in theoretial disussions of peer effets. Kling, Liebman, and Katz (007) using experimental variation in the poverty rates of neighborhoods in whih individuals reside in the U.S., find no evidene of non-linear poverty perturbations in the welfare utoff. Moreover, none of these speifiations suffer from weak-iv problems (results available from the authors upon request). 4 We annot identify effets on hildren with a high household welfare index, sine the average enrollment rate effet is small and indistinguishable from zero in these villages (point estimate , standard error 0.044) and thus the first-stage orrelation is weak for this subgroup (point estimate 0.05, standard error 0.06). Therefore, no inferenes an be made on the peer effets for hildren in the wealthier households. 5 We onstrut identifiers for extended-families in the villages by grouping hildren aording to unique identifiers of their parents last names. In Latin Ameria, eah individual has two last names, the first being the father s first last name and the seond the mother s first last name. Therefore, we an onstrut the households where individuals are related (within reasonable errors) by using unique numerial identifiers of eah ombination of last names. 6 Assuming that other hildren who are not mathed to an extended-family network atually have no extended-family eligible links, (therefore, we an impute a zero number of extended-family links for all these hildren), we an onstrut measures for all ineligible hildren in the village. We also find a greater number of links for hildren in the below-median welfare index group (0.58 hildren) relative to other ineligible hildren (0.4 hildren); a differene of 0.6 hildren (standard error 0.06, signifiant at 99 perent onfidene). 5