This dissertation is composed of two related parts. Chapter 1 studies identification of a pre-specified α-th quantile of a distribution of potential outcomes under weaker and more credible assumptions than those usually maintained in analogous settings of treatment-response, and obtains results of partial identification. On the theoretical side, the paper adds to the existing results on non-parametric bounds on quantiles with no prior information and under monotone treatment response, by introducing and studying the identifying properties of α-quantile monotone treatment selection, α-quantile monotone instrumental variables, and their combinations. On the empirical side, theoretical results are illustrated through an application to the Italian education returns.

The second part collects new data to aid identification of family members' preferences, expectations, and interactions in high school curriculum choice with curricular tracking, conceptualized as a choice made under uncertainty and with heterogeneous family decision protocols. In particular, chapter 2 uses these data within a random subjective expected utility framework to answer the following set of questions: (1) What are the most important determinants of curriculum choice among those aspects that are uncertain at the moment of the choice? (2) Conditional on the observed decision protocols, to what extent are parents' beliefs transmitted to children in the choice and do parents' preferences affect it? (3) Is it important to account for multiple decision makers and heterogeneous family decision protocols for this choice?

Chapter 3 proposes that family decision protocol in curriculum choice be interpreted and analyzed as the outcome of a parenting problem, which could be formalized either as a straight parental choice or as a game between the parent and the child. As first steps towards this goal, the paper reviews existing empirical evidence and modeling approaches in analyses of parenting and child outcomes across fields. And it provides new evidence on family decision making in curriculum choice. The chapter concludes by clarifying how the parenting problem generating decision protocol heterogeneity can be inserted in the curriculum choice framework of chapter 2 and which structural channels may produce an association between decision protocol selection and curriculum choice.