Investing in Children’s Skills: An Equilibrium Analysis of SocialInteractions and Parental InvestmentsFrancesco Agostinelli *JOB MARKET PAPER(Click here for the most recent version)12th January 2018* Department of Economics, W. P. Carey School of Business, Arizona State University.E-mail: [email protected] Version: September 15, 2014 as part of my written comprehensive exam. Acknowledgements: I am deeplyindebted to my advisor Matthew Wiswall for his constant guidance and support. I owe special thanks to EstebanAucejo, Kevin Reffett, and Daniel Silverman for many suggestions that greatly improved the paper. This project haslargely benefited from many discussions I had with Domenico Ferraro and Greg Veramendi. I also thank AlexanderBick, Adam Blandin, Kelly Bishop, Manjira Datta, Daniela Del Boca, Chris Flinn, Chao Fu, Jorge Luis Garcia, JamesHeckman, Nick Kuminoff, Alvin Murphy, Juan Pantano, Chris Taber, Kegon Tan, Gustavo Ventura, Basit Zafar andall the seminar and workshop participants at the Center for the Economics of Human Development (Universityof Chicago), the Junior Scholar Conference (Federal Reserve Bank of Minneapolis), the ASU General EconomicsWorkshop, the ASU PhD Reunion Conference and the ASU PhD Seminar for their comments and feedback. I amresponsible for all errors, interpretations, and omissions.
AbstractThis paper studies the effects of social interactions on the dynamics of children’s skills.I build a dynamic equilibrium model of child development with two key ingredients: peergroups forming endogenously and parental investments responding to the child’s social interactions. I estimate the model via simulated method of moments using a dataset of U.S.adolescents. Exploiting within school / across cohort variations in potential peers’ compositions, I identify the degree of complementarity between parents and peers in skill formation. I find that the environment where children grow up permanently shapes their developmental trajectories through the effects of social interactions. Moving a child at age12 to an environment where children have 1 percentile higher skills at age 16, on average,improves her skills rank at age 16 by 0.63 percentiles. The effects are in proportion to theexposure time throughout childhood, with an average effect of 0.48 percentiles if the childis moved at age 15. As model validation, I show that these results track the estimates ofthe exposure effects of neighborhoods in Chetty and Hendren (2016a). Decomposing theexposure effects, I find that peers alone account for more than half of the overall findings,while the school and the neighborhood quality account for the remainder. Finally, I evaluatethe effects on child development of a policy that integrates a sizable fraction of low-skilledchildren into a high-income environment. I find: (i) the effects depend on the endogenous formation of new peer groups; (ii) the policy generates dynamic equilibrium effects onparental investments and social interactions, which, if ignored, would lead to policy predictions for children’s skills of approximately seven times smaller.JEL Classification: C51, J13, J24Keywords: Skill Formation, Social Interactions, Child Development, Model Validation, Outof-sample Prediction, Equilibrium Treatment Effects, Heterogeneous Treatment Effects
1 IntroductionThis paper analyzes the effect of social interactions on skill formation in children. In particular,I build and estimate a model of child development, where children grow up in different environments, which are defined by: peers’ composition, neighborhood quality and school quality. Thedynamics of skills is governed by a technology of skill formation, which depends upon parentalinvestments, the current child’s skills and the environment-specific inputs. In this framework,I shed light on the importance of the dynamic effects of children’s endogenous social interactions and the parental investment decisions in explaining developmental differences betweendifferent environments. A growing consensus in the literature emphasizes the importance ofneighborhoods in shaping children’s opportunities later in life (Chetty and Hendren, 2016a,b;Chetty et al., 2016a,b). However, despite extensive research, the mechanisms behind these results remain unexplained. This paper reconciles the previous findings of childhood exposure toneighborhood with the role of children’s social interactions in child development.This project advances the current literature of child development by building and estimating a dynamic equilibrium model of children’s skill formation with two innovative empirically grounded features. First, within different environments, children endogenously select theirpeer groups based on their preferences for their peers’ characteristics. Social interactions canexhibit the tendency of children to become friends with others who share similar characteristics: a phenomenon called homophily bias. Second, parental investments respond to changesin peer groups. Decisions regarding parental investments depend upon a child’s current peers,as well as on expectations about future peer groups. Equilibrium effects arise from the sociallydetermined aspects of parental investments. In this framework, parental investments not onlydirectly affect a child’s skills, but also affect the development of the child’s peers through social interactions. Consequently, the individual return on investing in children is affected by theequilibrium parental engagement within each environment.Skills are formed dynamically through a technology of skill formation, which defines thecomplementarities between parental investments and the other inputs of child development inproducing a child’s skills: the current endowment of skills, the skills of peers, the school qualityand the neighborhood quality. In this framework, there are two main channels through whichpeers affect parental behavior. First, contemporaneous changes in current peers and parentalinvestments are related to the static complementarity between the two inputs. Second, permanent changes in peer composition affect parental behavior through the dynamic complementarity in skill formation. In other words, a permanent change in peer composition affect1
the return of parental investments through the dynamic aspect of skill formation.The model is estimated using data on U.S. adolescents from the National Longitudinal Studyof Adolescent Health (Add Health). Add Health provides information about friendships withineach school, which is key for analyzing the formation of peer groups. Moreover, informationabout child achievements and parental investments are available.The identification of the model comes with two main challenges: (i) unobserved heterogeneity in how peer groups are endogenously formed; and (ii) children’s skills and parental investments are unobserved. Ignoring these issues by using correlational relationships would causethe model’s estimates and subsequent quantitative analysis to be biased.The first challenge presents itself from the fact that peer groups may be formed based onadditional unobserved heterogeneity, which can cause correlation between peer groups’ realization and the residual unexplained variation in skill formation. To address this concern, Iimplement a standard instrumental variable (IV) approach in the literature. This identificationstrategy exploits random variations in cohort composition within school / across cohorts. Theidea behind this identification strategy is simple: random changes in cohort compositions affect the opportunities for friendships between children. These shifts in the formation of peergroups affect the return of parental investments and the subsequent parental decisions.1In addressing the second challenge, Cunha et al. (2010) illustrate that even the classicalmeasurement error in measuring a child’s skills can cause important biases in estimating thetechnology of children’s skill formation. Following the approach in Cunha et al. (2010) andAgostinelli and Wiswall (2016), I implement a dynamic latent factor model, which allows meto identify the joint distribution of latent skills and investments by exploiting multiple measurements in the data.I estimate the model via simulated method of moments (SMM). I find that parental investments and peers are substitute inputs in producing children’s skills. At the same time, I finda strong dynamic complementarity between parental investments and future expected peers.As a result of these two findings, a permanent change in peer composition has two opposingeffects on parental investments. On one hand, “better” peers generate contemporaneous substitution effects in investment decisions due to the high substitutability in the production function. On the other hand, higher expected future skills for peers produce an “income” effectthrough the dynamic complementarity of skill formation. Parents have the incentive to invest1For previous use of similar source of identifying variation, see Hoxby (2000); Hanushek et al. (2003); Ammermueller and Pischke (2009); Lavy and Schlosser (2011); Lavy et al. (2012); Bifulco et al. (2011); Burke and Sass (2013);Card and Giuliano (2016); Carrell et al. (2016); Olivetti et al. (2016); Patacchini and Zenou (2016)2
more in their children because a higher-skilled child benefits more from higher-skilled peers inthe future.Furthermore, my estimates suggest that the formation of peer groups displays an extensivedegree of homophily bias. I show evidence of homophily bias with respect to a child’s race andlevel of latent skills. A child who is in the lower quartile of the skill distribution and belongs toa minority group is four times more likely to befriend a same-race child than a different-racechild. In addition, the same child is two times more likely to befriend a same-skill and samerace child than a same-race child in the upper quartile of skill distribution.I first use the estimated model to analyze the extent to which growing up in different environments accounts for the variation in children’s outcomes. I find sizable effects for childrenmoving to better environments. The effects are in proportion to the exposure time. The earlierchildren are moved, the higher the effect. A child who is moved at age 12 to an environmentwhere children have 1 percentile higher skills at age 16 exhibits, on average, an improvement inher skills rank at age 16 by 0.63 percentiles. The average effect is 0.48 percentiles if the child ismoved at age 15. As model validation, I show that my findings track (out-of-sample) the quasiexperimental findings of childhood exposure effects of neighborhoods for the U.S. from Chettyand Hendren (2016a). In addition, my model allows me to decompose these effects. I find thatpeers account for more than half of the exposure effects.The relative importance of peers for the exposure effects underlines the role of policies thatchange peers’ composition and promote socioeconomic integration in environments, as a wayto improve outcomes for disadvantaged children. I find that by moving the most disadvantaged children (in the lower quartile of skill distribution) from a low-income environment to ahigh-income environment generates important dynamic equilibrium effects, with heterogeneous treatment effects for both the moved and receiving children. I first consider a large-scalepolicy, i.e. a policy that moves a sizable fraction of disadvantaged children into a higher-incomeenvironment (approximately 5% of the population of the receiving cohort). I find that the policyincreases the skills of the moved population of 16-year-old children, on average, by approximately 0.40 standard deviations. On average, I do not find any adverse effect for receiving children. On the contrary, when the fraction of moved population increases to 30%, I find that thepolicy generates winners and losers. First, I find that the policy increases the skills of the movedpopulation of 16-year-old children on average by 0.22 standard deviations. In contrast, thereis an adverse effect for receiving children, with the skills of 16-year-old children decreasing, onaverage, by 0.15 standard deviations. Additionally, I find that children who remained in thesending environment benefit from the outflow of the most disadvantaged companions, with an3
average increase in skills at age 16 of 0.17 standard deviations.I find that large-scale changes in peers’ composition generate important equilibrium feedback effects, and as a result amplify the policy effects. Ignoring equilibrium effects would lead tolarge biases in counterfactual policy predictions for children’s final skills. In the case of the larger policy, I find that the policy predictions for the children’s skills in the receiving environmentwould be approximately seven times smaller. Part of the bias is due to the dynamic-equilibriumfeedback effects on parental investments. In fact, in the absence of dynamic-equilibrium feedback effects, the static complementarity between parents and peers dominates the dynamiceffects of the policy.I find that policy effects for receiving and remaining children reduce in magnitude as thefraction of moved children decreases. An increase of inflow of the most disadvantaged childrenfrom the low-income environment to the high-income environment increases the probabilityof the receiving children becoming friends with the new companions. For the same reason, anincrease of the outflow of the moved population benefits children who remain in the sendingenvironment. For children who were moved, the opposite is true. The higher the outflow ofdisadvantaged companions, the higher the chances that the moved children remain friendswith each other in the new environment.My structural model allows me to analyze the distributional policy effects. I find that largescale changes in peers’ composition exhibit heterogeneous treatment effects as a result of theendogenous fo