Randomized controlled trials generate experimental variation that can credibly identify causal effects, but often suffer from limited scale, while observational datasets are large, but often violate desired identification assumptions. To improve estimation efficiency, I propose a method that leverages imperfect instruments - pretreatment covariates that satisfy the relevance condition but may violate the exclusion restriction. I show that these imperfect instruments can be used to derive moment restrictions that, in combination with the experimental data, improve estimation efficiency. I outline estimators for implementing this strategy, and show that my methods can reduce variance by up to 50%; therefore, only half of the experimental sample is required to attain the same statistical precision. I apply my method to a search listing dataset from Expedia that studies the causal effect of search rankings on clicks, and show that the method can substantially improve the precision.

翻译：随机对照试验通过实验变异能够可靠识别因果效应，但通常受限于样本规模，而观测数据集虽然规模庞大却常违背理想的识别假设。为提升估计效率，本文提出一种利用不完全工具变量的方法——这些预处理协变量满足相关性条件但可能违反排他性约束。研究表明，这类不完全工具变量可生成矩约束条件，与实验数据相结合能有效提升估计效率。本文概述了实施该策略的估计方法，并证明所提方法可使方差降低高达50%；换言之，仅需一半的实验样本即可达到相同的统计精度。通过对Expedia搜索列表数据集中搜索排名对点击率的因果效应进行实证分析，验证了该方法能显著提升估计精度。