Endogenous Peer Effects in School Participation

Transcription

1 ndogenous Peer ffets in Shool Partiipation Gustavo J. Bobonis and Frederio Finan Otober 006 Abstrat: A remaining obstale in the literature on peer effets has been the inability to distinguish between peer effets that are determined by a person s referene group behavior (endogenous peer effets), and effets that are generated as a result of speifi bakground harateristis of the groups themselves (ontextual peer effets). This paper identifies and estimates endogenous peer effets on hildren s shool partiipation deisions using evidene from the Mexian PROGRSA program, a shool subsidy program targeted at hildren of the rural poor. Beause program eligibility was randomly assigned, we use this exogenous variation in shool partiipation to identify peer effets on the shool enrollment of ineligible hildren residing in the same ommunities. We find that peers have onsiderable influene on the enrollment deision of program-ineligible hildren, and these effets are onentrated among hildren from relatively poorer households. Our findings imply that eduational poliies aimed at enouraging enrollment an produe large soial multiplier effets. A previous version of this paper was entitled 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, and T. Paul Shultz, 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 males. While the use of experimental designs have enabled these studies to properly identify soial. Introdution Reent empirial studies have made important ontributions towards identifying the ausal impat of neighborhood or peer effets on individual behavior. Saerdote (00) and Zimmerman (003), using the random assignment of roommates in U.S. olleges, find evidene of peer effets on the level of aademi effort and membership in soial organizations of ollege students. Kling, Ludwig, and Katz (005) use experimental variation in assignment to different types of vouher reloation programs in five U.S. ities to identify long-term neighborhood effets on youth rime and find differential effets among females and interations, a remaining obstale in the literature has been the inability to distinguish between peer effets that are determined by the behavior of a person s referene group (endogenous peer effets), from those that are generated as a result of speifi bakground harateristis of the groups themselves (ontextual peer effets) (Manski 993). The distintion between these two effets has important poliy impliations beause endogenous peer effets imply potentially large soial multiplier effets and effiieny gains through the feedbak in the behavior of individuals within an existing soial network (e.g., positive student behavior leads to more positive behavior in the network) (Hoxby 000), whereas ontextual peer effets do not have these dynami impliations. This distintion may be of partiular importane for eduation poliy. For instane, understanding whether pupil ahievement is mainly the result of endogenous interations suh as strategi omplementarities in student effort (Kremer, Miguel, and Thornton 004) or negative externalities from students disruption of learning ativities, or whether it results from interating with smarter peers (i.e. peers with greater ognitive development), may have important impliations for the determination of optimal lass sizes (Lazear 00). Moreover, if behavioral peer effets of a speifi sort exist at the neighborhood-level, then understanding whih poliies enourage the internalization of these will make human apital investments more effiient, and will inrease maroeonomi growth (Bénabou 996). In this paper, we identify endogenous peer effets in hildren s shool partiipation deisions using evidene from a human development program in rural Mexio. 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 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. A omplementary literature on lassroom-based peer effets also finds mixed evidene regarding the existene and magnitude of peer effets. Although an exhaustive list of empirial papers in this literature is diffiult to onstrut, reent experimental and non-experimental studies examining peer effets in shool ahievement (in both developed and less developed ountries) inlude Angrist and Lang (004), Boozer and Caiola (00), Ding and Lehrer (005), Graham (005), and Kremer, Miguel, and Thornton (004). Note that ontextual peer effets an lead to potential multiplier effets as a result of sorting into peer groups (pple and Romano 998; Bayer, Ferreira, and MMillan 004).

3 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 the endogenous peer effets in shool enrollment among hildren who were ineligible for the program within the program ommunities. Our main results suggest 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 network enrollment rate, whih represents an inrease of 8.5 perent from baseline. Substantially larger effets of approximately 6.5 perentage points are also found for hildren of relatively poorer households within the ineligibles group - a subgroup of hildren that are more likely to interat with treated hildren in these villages. These estimates indiate that poliy intervention benefited from important soial multipliers, as endogenous soial interations in effet doubled the diret effets of the shool enrollment subsidy in the absene of peer interations. Despite the use of experimental variation, 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 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. We use several approahes to demonstrate that this is not the ase. First, we exploit the rihness of the data to test for other potential program externalities, whih may have affeted the shool enrollment behavior of ineligible households. We do not find any evidene of program-indued improvements in shool quality, or that the program affeted either the onsumption of ineligible households or hildren s health, whih may have led to greater shool enrollment rates. Seondly, 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.

4 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, and Setion 6 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. 00 for a more detailed desription of the targeting proess). 3 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 3 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. 3

5 randomly assigned are ritial design aspets for the identifiation of the endogenous 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. 4 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 ). Sine primary shool enrollment is almost universal in rural Mexio, we restrit our interest to the enrollment 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 5, and also the grade levels where PROGRSA has had its greatest impat among eligible households (Shultz 004). In our sample, this onerns approximately,738 hildren 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 shool behavior and ontextual variables that may affet it. 4 There was a round of data olletion in Marh of 998 just prior to the start of the intervention. 5 In 997, primary shool enrollment was lose to 96.5%, ompared to 65% enrollment into seondary shool. 4

6 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 are 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, as the mean number of household members 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 in most dimensions. 6 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 shows that eligible households in treatment villages reeived 70 pesos per month (on average) during the April 998-Deember 999 period (Table, Panel B). Average transfers for ontrol households are nonzero 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. 7 6 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. 7 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. 5

7 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. 8 This administrative data allow us to rule out alternative hypotheses and to test our identifying assumptions (see disussion in Setion 5). Means of harateristis of shools attended by the hildren in the sample are reported in Table, and 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 lead to bias in the oeffiient estimates. Sample attrition rates through the two posttreatment 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 ndogenous Peer ffets In this setion, we disuss the eonometri models used to estimate endogenous peer effets and the assumptions needed for identifiation. The standard approah used to estimate endogenous peer effets assumes that individuals shool enrollment deisions follow a simple linear-in-means model: y = α βx γx λz θy u () i i where y is an indiator variable for the shool enrollment behavior of hild i in village ; X are i i i exogenous harateristis of the individual; X are the mean exogenous harateristis of the referene group; Z are harateristis of the environment (e.g., village) that may influene individuals shool enrollment deisions; and y is the enrollment rate of the referene group. 9 This linear-in-means model provides a formal expression to three hypotheses often advaned to explain the ommon observation that individuals belonging to the same group tend to behave similarly. The first, orrelated effets, proposes 8 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. 9 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. 6

8 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 endogenous peer effets proposes that the behavior of the group influenes individual behavior; the parameter θ in the model aptures this effet. 0 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. 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 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 : i i i T i y = α βx γx λz θy δt u ( ) In addition, there are individuals within the same referene group (denoted with supersript N) who do not reeive treatment: i 0 There are several theories as to why the shool enrollment deisions of one peer s may affet one own enrollment status. For instane, strategi omplementarities in either the eduation prodution funtion, hildren s soial preferenes (e.g., onformist preferenes, or information transmission regarding the payoffs to shooling may lead to soial interations (Akerlof, 997; Cooper and John, 988). Unfortunately, we annot distinguish among these ompeting hypotheses in this eonometri framework. 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. To see this, take the expetation of equation () onditional on X 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 = βx i X 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. 7

9 y = α βx γx λz θy u ( ) N i N i 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 () X = m X ( m ) X N 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: y α β γ = X θ θ λ Z θ δ m 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 y i = βx i X Z m T u θ θ θ θ The partial-population treatment terms in the two redued-form equations have intuitive interpretations. In equation (3), the ( θ ))m T δ ( 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 ( δm ), and (ii) the indiret effet as a result of endogenous 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 endogenous soial interations. Also note that one ould use oeffiient estimates from equations (3) and (4) to identify the diret treatment and endogenous peer effets parameters. Speifially, note that the ratio of the N i (3) (4) m T reduedform oeffiients from equations (3) and (4) is equal to θ, the endogenous 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 = βx i γx λz θy i, N i, i (3 ) N i = ~ ~ ~ ~ ~ α β X β X λz δt ε 8

10 where T ~ θβ γ β = θ m, T is the PROGRSA treatment village indiator variable and omposite oeffiients ~ α α =, θ ~ λ ~ δm λ =, andδ =. Note that equation (3 ) uses T rather than the interation term θ θ 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 unobservable harateristis of the households or villages. However, estimates whih use IV provide quantitatively similar estimates to those reported in the results setions below. m T as the 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 ( X ) and environmental ( ) 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. Z 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. 9

11 Finally, note that we also assume endogenous 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 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; Hoxby 000; Gaviria and Raphael 00). 4. stimates of Spillovers and ndogenous Soial Interation 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. 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. 3 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. As doumented by Shultz (004) and Behrman, Sengupta and Todd (005), hildren in eligible households inreased their shool enrollment by 7.6 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 The onditional means are estimated by taking the mean enrollment within a bandwidth of 0.5. The figure is robust to perturbations to the bandwidth size. 0

12 perentage points, or 4 perent (Panel B, regression ). Overall, 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 ); however, the effet is impreisely measured (signifiant at 89 perent onfidene) and not robust to individual, household, and village-level ontrols (Panel B, regression ). 4 There are signifiant differential effets on shool enrollment by household s welfare index level (regressions 3 and 4). Among ineligible households with a below-median welfare index, PROGRSA inreased seondary shool enrollment by 5.5 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). 5 Also, 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). 4. stimates of Diret and ndogenous Peer ffets Table 4 reports the estimates of endogenous peer effets (θ) from OLS and IV estimation of equations ( ) and (3 ). The OLS estimate of the overall endogenous 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 a 0.7 perentage point inrease in a hild s probability of enrollment as a result of a perentage point inrease in the referene group s enrollment rate (signifiant at 99 perent onfidene, Table 4, Panel A, regression ). In ontrast, IV estimates of the overall endogenous effet imply an effet of 0.65 without any ontrol-adjustment (regression ), but an effet of a 0.49 inrease in the probability of enrollment in seondary shool one household and villagelevel ontrols are inluded in the model (regression 3). The latter estimate, while signifiant at only 89 perent onfidene, does suggest that endogenous 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. Note that we inlude individual and household-level ontrols, and village-level predetermined ontextual variables: 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. 6 4 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. 5 The differene in effets is statistially signifiant at 90 perent onfidene. 6 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).

13 Substantially larger peer effets are found among the relatively poorer hildren within the ineligible group. The point estimate on the effet for hildren in the below-median welfare-index group is 0.67 (regression 5). The orrelation of own and soial network enrollment rate for this subgroup in ontrol villages implies an effet of (regression 4). Again, the experimental evidene suggests that the OLS estimates are biased upwards, although we annot rejet that the oeffiients are equal. 7 Note that we annot identify the effet on hildren with a high household welfare index, sine the first-stage orrelation is weak for this subgroup (Panel B, regression 6). The average enrollment rate effet is small and indistinguishable from zero in these villages. Therefore, no inferenes an be made on the peer effets for hildren in the wealthier households; the point estimate for this high welfare index group is -5. (not statistially signifiant). That there exists a differential effet by the household welfare index is onsistent with at least two 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. 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). 8 Comparing ineligible hildren from households below median welfare-index to those above median welfare-index, 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 7 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 perturbations in the welfare utoff. Moreover, none of these speifiations suffer from weak-iv problems (results available from the authors upon request). 8 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.

14 links is 48 perent higher among households lassified in below the median welfare-index. 9 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 (006), using experimental variation in the poverty rates of neighborhoods in whih individuals reside in the U.S., find no evidene of non-linear poverty effets. For omparability reasons, we assess whether there are non-linearities in endogenous peer effets by allowing the parameter estimates to vary aording to (i) hildren s baseline enrollment deision, and (ii) baseline village-level enrollment rates. Although point estimates suggests that effets are greater among hildren in ommunities with low baseline enrollment (results not shown), we annot rejet the linearity assumption. 0 Weak instruments are not a main onern in the estimation. There is a robust partial orrelation between the program village treatment indiator and the potentially endogenous regressor, the villagelevel enrollment rate. The F-test statistis refleting the signifiane of the IV in the first stage equations exluding and inluding ontrols are 8.74 and 7.60 in the overall effet model (Panel B, regressions and 3), and the F-statisti for the poorer ineligible group is 3.9 (the first-stage oeffiient is signifiant at 99 perent onfidene) (regression 5). In summary, this evidene is onsistent with the hypothesis that hanges in referene groups shool enrollment behavior affets hildren s own enrollment behavior, and that these effets differ depending on hildren and their family s inherent opportunity osts, as well as by the types of peers they interat with. As will be shown in Setion 5, these results are robust to speifiations, alternative measures of peer behavior, and identifying assumptions. 5. Sensitivity Analyses and Tests of Identifying Assumptions It has been well doumented that the impat of PROGRSA was not restrited to shooling. That the program may have affeted ineligible hildren in ways other than an inrease in the enrollment rates of their referene groups remains a potential onern for our identifiation strategy. Suh a situation would invalidate our exlusion restrition and we would be mistakenly attributing the effets of other 9 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). 0 stimates are available from authors upon request. The LIML estimates of equations ( ) and (3 ), whih are robust to the weak instruments problem (under ertain onditions, see Hayashi 000) give endogenous interation effets very similar to the IV results reported in the text. Results are available upon request. 3

15 mehanisms to peer effets. In this setion, we present a series of robustness heks and tests of our underlying ounterfatual assumption to show that we are in fat providing onsistent estimates of endogenous peer effets. 5. Redued-Form Tests of Alternative Mehanisms In order for the treatment village indiator to serve as a valid instrument, the program annot have indiretly affeted other determinants of an ineligible hild s enrollment deisions. This is a substantive assumption in the ase of PROGRSA, where the program s multidimensionality affeted the livelihoods of benefiiary households through a series of mehanisms. Apart from the inreases in seondary shool enrollment rates among eligible hildren (Shultz 004), researhers have found signifiant inreases in household onsumption levels, food onsumption, and food quality (Hoddinott and Skoufias 004), improvements in health status, and inreases in health are utilization (Gertler 004; Gertler and Boye 00). If any of these program impats reate externalities - in the form of, for example, inter-household resoure transfers, orrelated positive shoks to inome, or positive health externalities that inrease shool enrollment rates for ineligible hildren, then we would be onfounding endogenous peer effets with the positive externalities from these other mehanisms. In additional to other program externalities, hanges in environmental or institutional fators affeting hildren s shool enrollment deisions may also pose onerns. A set of partiularly important hanges affeting shool enrollment deisions were shool supply-side interventions whih aompanied the implementation of the program. Although this was done to mitigate potential ongestion effets due to the expeted inrease in shooling demand, the improvement in shooling failities may have attrated hildren from ineligible households. Consumption xternalities and Relaxation of Credit Constraints To verify whether any of these fators play a role in explaining the shool enrollment spillover effet, we test for the existene of any post-treatment differenes in household onsumption and expenditures, health status of hildren, and ertain shool harateristis whih may have been affeted by the program (Table 5). We do not find any evidene that monthly household expenditures inreased in the two post-treatment periods among ineligible households in program relative to omparison villages (the point estimate reported in Table 5 is -.93, and not statistially signifiant). Sine expenditures do no take into aount onsumption from household prodution, we also estimate household onsumption in the first post-treatment period, and, again, find no signifiant differene in total onsumption among There is also evidene that the program improved women s relative bargaining power within the household (see Adato et al., 000 and Bobonis 004 for a disussion). videne of program impats on other outomes, inluding hildren and adults labor supply (Parker and Skoufias 000), migration patterns (Angelui 004), ability to mitigate shoks (de Janvry et al. 004), and inter-household transfers (Attanasio and Rios-Rull 000) suggest relatively small hanges in these margins. 4

16 these households (point estimate is , not statistially signifiant). 3 Moreover, differential estimates by welfare-index subgroups also results in insignifiant differenes in expenditures and onsumption (rows -, olumns -5). These expenditure and onsumption patterns, as well as the evidene from the transfers data, provide evidene inonsistent with the possibility of inter-household inome transfers from benefiiary to non-benefiiary households, orrelated positive inome shoks at the village-level, or evidene of program leakage (where some ineligible households may have been able to reeive program transfers). Households may be substituting expenditures in different areas as a result of the hildren s shool enrollment. Consistent with the evidene on inreased shool partiipation, estimates suggest an inrease in the share of the household budget spent on eduational expenses (e.g., shool supplies, shool ontributions). The point estimate implies an inrease of 0.5 perentage points (9 perent, or approximately 5 pesos) on eduational expenditures among all ineligible households and 0.4 perentage points (9 perent, approximately 4 pesos) among poorer ineligible households (row 3, olumns and ). However, none of the estimates are signifiant at onventional onfidene levels. It is also possible that the liquidity injetion from the program may have relaxed lending onstraints of eligible households, enabling ineligible households to borrow when hit by negative idiosynrati shoks, and making them less likely to remove their hildren from seondary shool in the event of a shok (Jaoby and Skoufias 997; Angelui and De Giorgi 005). We examine this potential alternative hannel by showing evidene of the expenditure responses of ineligible households to natural shoks in both program and omparison villages for our sub-sample (Table 5, Panel B). 4 If the liquidity onstraint hypothesis was orret, we would expet a relative positive effet on expenditures and shool enrollment among households who suffer a shok in program villages. A potential onern to this test is that natural shok measures may not be very reliable: ineligible households seem to inrease household expenditures in response to natural shoks (Panel B, row ), and we observe a similar pattern using household onsumption data (not reported in the tables). Given this aveat, we do not find evidene that ineligible households in program villages who suffer natural shoks have higher expenditure levels than those in omparison villages (Panel B, row 3). Furthermore, the shool enrollment effet is lower among shok than among no-shok households: the estimated redued form effets are (standard error 0.03, signifiant at 90 perent onfidene) and (standard error 0.09, signifiant at 99 perent 3 We use household expenditures and onsumption as proxies for household inome, sine inome is usually measured with substantial error in agriultural households, and these may better represent permanent inomes of households. Unfortunately, we only have home prodution data for the Otober 998 survey round, and therefore, annot estimate the onsumption models in the seond post-treatment round. 4 We use household survey data to onstrut the shok measure, following Angelui and De Giorgi (005). The survey reorded whether the household has been hit by any of the following natural disasters in the six months preeding the interview: drought, flood, hail, fire, plague, earthquake, and hurriane. We reate a variable whih indiates whether the household has been hit by any natural disaster. 5