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

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 an empirical illustration of the method to Rhode Island standardized exam data.