Partial Identification of Individual-Level Parameters Using Aggregate Data in a Nonparametric Model

Abstract

I develop a methodology to partially identify linear combinations of conditional mean outcomes when the researcher only has access to aggregate data. Unlike the existing literature, I only allow for marginal, not joint, distributions of covariates in my model of aggregate data. Bounds are obtained by solving an optimization program and can easily accommodate additional polyhedral shape restrictions. I provide a procedure to construct confidence intervals on the identified set and demonstrate performance of my method in a simulation study. In an empirical illustration of the method using Rhode Island standardized exam data, I find that conditional pass rates vary across student subgroups and across counties.