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

Abstract: It is well known that the relationship between variables at the individual level can be different from the relationship between those same variables aggregated over individuals. In this paper, I develop a methodology to partially identify linear combinations of conditional mean outcomes for individual-level outcomes of interest without imposing parametric assumptions when the researcher only has access to aggregate data. I construct identified sets using an optimization program that allows for researchers to impose additional shape and data restrictions. I also provide consistency results and construct an inference procedure that is valid with data that only provides marginal information about each variable. I apply the methodology to simulated and real-world data sets and find that the estimated identified sets are too wide to be useful, but become narrower as more assumptions are imposed and data aggregated at a finer level is available.