Chapter one studies peer effects on student achievement among first graders randomly assigned to their classrooms as part of Tennessee's Project STAR. The analysis draws on previously unexploited pre-assignment measures of achievement available for sixty percent of the sample. Data are not missing at random. This makes identification of peer effects challenging. Given random assignment of students to classes, this paper develops a way to point identify peer effects without any other assumptions on the missing peer data. Estimates suggest moderate, positive average effects of mean peer lagged achievement. Allowing heterogeneous effects, some evidence suggests lowerachieving students may benefit more than higher-achieving students do from increases in the peer mean. This paper also analyzes individual-deletion procedures (IDP) in the context of peer effects, whereby researchers delete individuals with missing data and analyze complete-data individuals as if they represent the population. These procedures are widely used but poorly understood. This paper describes the bias and inconsistency of IDP estimates.;Chapter two examines the use of cross-sectional data to estimate implicit prices of attributes using hedonic methods. A large literature uses hedonics to estimate the implicit price of fatal risks from labor market data. Usually enough assumptions are made to point identify people's willingness to pay (WTP) for changes in attribute levels. Instead, this paper proposes a weak set of assumptions about the shape of indifference curves to partially identify WTP. Indifference curves are assumed to be increasing and convex in an attribute-cost space that is finitely bounded above. Shape restrictions provide informative partial identification without assuming perfectly competitive equilibrium. When combined with conventional equilibrium assumptions, tighter bounds are obtained. Estimates from conventional analysis are contrasted with the bounds obtained under this new approach. Data are consistent with a wide range of WTP values even given equilibrium and credible shape restrictions. This suggests that conventional estimates are driven largely by the convenient but questionable conditions imposed on preferences rather than by the data or properties of equilibrium.;Chapter three studies the productivity of various investments for the pre-school development of cognitive skills applying the recently-developed Cunha-Heckman model of skill formation to data from the Infant Health and Development Program (IHDP). The data combine an extremely-useful experimental manipulation of early investment levels with rich measures over an important period of development. The IHDP recruited low birth weight, premature newborns and randomly assigned a package of age-0 to 3 investments (home-visits and high-quality childcare). We focus on the 362 children with the highest birth weights (2001-2500 grams), whose development is most similar to that of children born at normal weight and term. As with other early childhood interventions, treatment produced large cognitive effects, which partially faded-out over time. We develop evidence on four competing hypotheses with very different policy implications that could explain the fade-out.
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