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.

本文提出了在部分观察多元健康相关时间使用数据时获取信息参数界限的分析策略以一种特殊而普遍的方式。一个熟悉的背景是，在 N>1 个时间段内观察到 M>1 个结果各自的总数，但感兴趣的问题涉及它们在 N 个时间段中的每一个未观察到的联合分布的特征——概率、时刻等。例如，人们可能希望了解一个月内经历的任何类型的不健康天数的分布，但只能访问所经历的身体不健康和心理不健康天数的单独月度总数。在演示了在几个抽样假设下部分识别此类分布和相关参数的方法之后，本文继续推导出涉及外生协变量的部分效应的界限。这些结果应用于三个经验练习。所提议的界限是否被证明足够严格以有效地为决策者提供信息只能在上下文中确定，尽管在本文的实证分析中，一些估计的界限可能出人意料地严格。此外，本文的结论表明，随着数据隐私政策越来越限制分析，本文中考虑的问题可能对分析师来说变得越来越突出。