Identification of a Class of Health-Outcome Distributions under a Common Form of Partial Data Observability

This paper suggests analytical strategies for obtaining informative parameter bounds when multivariate health-outcome data are partially observed in a particular yet common manner. One familiar context is where M>1 health outcomes' respective totals across N>1 time periods are observed but where questions of interest involve features—probabilities, moments, etc.—of their unobserved joint distribution at each of the N time periods. For instance, one might wish to understand the distribution of any type of unhealthy day experienced over a month but have access only to the separate totals of physically unhealthy and mentally unhealthy days that are experienced. After demonstrating methods to bound, or partially identify, such distributions and related parameters under several sampling assumptions, the paper proceeds to derive bounds on partial effects involving exogenous covariates. These results are applied in three empirical exercises. Whether the proposed bounds prove to be sufficiently narrow to usefully inform decisionmakers can only be determined in context, although it is suggested in the paper's conclusion that the issues considered in this paper are likely to become increasingly important for analysts.