Semiparametric estimation of peer effects

The first two chapters of this dissertation propose a semiparametric methodology to estimate an education production function with peer effects and use the methodology to estimate peer effects among students in Brazil. The proposed methodology identifies and estimates peer effects under weak assumptions, without imposing a functional form for the production function. Student achievement is modeled as a function of student quality and peer quality. Student quality is defined as a linear combination of student characteristics, and peer quality is the average of this single index in each classroom. Peer effects are identified as the marginal derivative of the production function in relation to peer quality. A three step procedure is proposed to estimate the objects of interest. In the first step, a generalized version of the rank regression proposed by Abrevaya (2000) is used to estimate the parameters of the student quality index. These parameters are estimated using within classroom variation. The second and third steps utilize the control function approach proposed by Newey, Powell and Vella (1999). This methodology is then applied to estimate peer effects in the last year of elementary school in Brazil. Using the rules by which students were allocated to classrooms as a vector of instruments, we find evidence that peer effects are positive for all the students, except for the ones at the bottom of the quality distribution. The results also show that student achievement increases monotonically with student quality. The last chapter of this dissertation outlines a new minimum empirical discrepancy estimator that overcomes missing data and sample combination problems. This inverse probability tilting (IPT) estimator can be used to estimate the average treatment effect (ATE), the average treatment effect on the treated (ATT) and the two sampled instrumental variables (TSIV) model. The proposed estimator attains the semiparametric efficient bound under two auxiliary parametric restrictions, but is consistent if one of these restrictions holds. An original feature of this estimator is its "exact balancing" property: after reweighting, sample moments of always-observed covariates in the complete-case subsample equal their corresponding (unweighted) full sample means. The small sample properties of IPT in a small Monte Carlo study are also explored.