We study causal inference in experiments and quasi-experiments, where the economic outcome is imperfectly measured by a remotely sensed variable. The remotely sensed variable is low-cost, scalable, and predictive of the economic outcome in observational data; examples include satellite imagery and mobile phone activity. We model the remotely sensed variable as post-outcome: variation in the economic outcome causes variation in the remotely sensed variable. For example, changes in environmental quality cause changes in satellite imagery, not vice versa. Under this assumption, we propose a formula to nonparametrically identify the causal parameter by combining experimental and observational data. We develop a method for n^{-1/2} inference that is robust to misspecification and that does not restrict the algorithms used to process remotely sensed variables.

翻译：我们研究实验和准实验中因果推断的问题，其中经济结果由遥感变量不完美地测量。该遥感变量成本低廉、可扩展，在观测数据中对经济结果具有预测能力；例如卫星影像和移动电话活动。我们将遥感变量建模为结果后变量：经济结果的变化会导致遥感变量的变化。例如，环境质量的变化引起卫星影像的变化，而非相反。在此假设下，我们提出一个公式，通过结合实验数据和观测数据来非参数识别因果参数。我们开发了一种适用于n^{-1/2}推断的方法，该方法对错误设定具有鲁棒性，且不限制用于处理遥感变量的算法。