标题： 因果界限与工具变量 显示英文标题

标题： Causal Bounds and Instruments

摘要： 工具变量已被证明是有用的，特别是在社会科学和经济学领域，用于在存在未观测混杂因素的情况下推断一个随机变量 B 对另一个随机变量 C 的因果效应。 在关系为线性的情况下，可以通过研究 C 对 A 的回归以及 B 对 A 的回归来精确识别因果效应，其中 A 是工具变量。 在更一般的情况下，文献中已经开发出在给定 C、B 和 A 联合分布的观测数据时，关于 B 对 C 的因果效应的界限。 通过基于凸多面体分析的方法，我们仅在 (C, A) 和 (B, A) 数据的情况下开发了相同的因果效应的界限。 因此，这些界限与计量经济学中工具变量的标准使用直接类比，但我们并未假设线性关系。 界限的应用通过部分依从性的实验进行了说明。 例如，在遗传流行病学中，'孟德尔工具' S 表示基因型，并且可能很少能够获得 C、B 和 A 的所有联合数据，但涉及这些变量对的研究所可能非常丰富。 还考虑了其他因果效应界限的例子，以表明该方法适用于一般的有向无环图（DAG），但需满足某些条件。 显示英文摘要

摘要： Instrumental variables have proven useful, in particular within the social sciences and economics, for making inference about the causal effect of a random variable, B, on another random variable, C, in the presence of unobserved confounders. In the case where relationships are linear, causal effects can be identified exactly from studying the regression of C on A and the regression of B on A, where A is the instrument. In the more general case, bounds have been developed in the literature for the causal effect of B on C, given observational data on the joint distribution of C, B and A. Using an approach based on the analysis of convex polytopes, we develop bounds for the same causal effect when given data on (C,A) and (B,A) only. The bounds developed are thus in direct analogy to the standard use of instruments in econometrics, but we make no assumption of linearity. Use of the bounds is illustrated for experiments with partial compliance. The bounds are, for example, relevant in genetic epidemiology, where the 'Mendelian instrument' S represents a genotype, and where joint data on all of C, B and A may rarely be available but studies involving pairs of these may be abundant. Other examples of bounding causal effects are considered to show that the method applies to DAGs in general, subject to certain conditions.