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：我们研究实验与准实验中因果推断的若干问题，其经济结果被遥感变量不完美地测量。这类遥感变量成本低廉、可规模化扩展，且在观测数据中能预测经济结果，例如卫星影像和手机活动数据。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产生变化。以环境质量变化引起卫星影像变化为例，其因果关系不可逆。基于该假设，我们提出一种结合实验数据与观测数据来非参数识别因果参数的公式。我们开发了一种适用于n^{-1/2}推断的方法，该方法对模型设定错误具有稳健性，且不限制处理遥感变量的算法类型。