Investigating health-related time use with partially observed data

This paper suggests analytical strategies for obtaining informative parameter bounds when multivariate health-related time use data are partially observed in a particular yet common manner. One familiar context is where M>1 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 monthly totals of physically unhealthy and mentally unhealthy days that are experienced. After demonstrating methods to 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 tight to usefully inform decisionmakers can only be determined in context, although in this paper’s empirical analysis some of the estimated bounds turn out to be perhaps surprisingly tight. Moreover, it is suggested in the paper’s conclusion that the issues considered in this paper may become increasingly salient for analysts as data privacy policies increasingly constrain analyses.