How should researchers conduct causal inference when the outcome of interest is latent and measured imperfectly by multiple indicators? We develop a general nonparametric framework for identifying and estimating average treatment effects on latent outcomes in randomized experiments. We show that latent-outcome estimation faces two distinct noncomparability challenges. First, across studies, different measurement systems may cause estimators to target different empirical quantities even when the underlying latent treatment effect is the same. Second, within a study, different indicators may have different and possibly nonlinear relationships with the same latent outcome, making them not directly comparable. To address these challenges, we propose a design-based approach built around nonparametric bridge functions. We show that these bridge functions can be characterized and identified. Estimation relies on a debiasing procedure that permits valid inference even when the bridge functions are weakly identified. Simulations demonstrate that standard methods, such as principal components analysis and inverse covariance weighting, can generate spurious cross-study differences, whereas our approach recovers comparable latent treatment effects. Overall, the framework provides both a general strategy for causal inference with latent outcomes and practical guidance for designing measurements that support identification, comparability, and efficient estimation.

翻译：当感兴趣的结果是潜变量且通过多个指标不完美测量时，研究者应如何进行因果推断？我们为随机实验中潜变量结果的平均处理效应开发了一个通用的非参数识别与估计框架。研究表明，潜变量结果估计面临两种不同的不可比性挑战。其一，跨研究时，即使底层潜变量处理效应相同，不同的测量系统也可能导致估计量瞄准不同的经验量。其二，在同一研究内，不同指标可能与同一潜变量结果存在不同且可能非线性的关系，使其无法直接比较。为应对这些挑战，我们提出了一种基于非参数桥函数的设计驱动方法。我们证明这些桥函数可以被刻画和识别。估计依赖于一种去偏程序，即使在桥函数弱识别的情况下也能进行有效推断。模拟实验表明，主成分分析和逆协方差加权等标准方法可能产生虚假的跨研究差异，而我们的方法能够恢复可比较的潜变量处理效应。总体而言，该框架既为潜变量结果下的因果推断提供了通用策略，也为设计支持识别、可比性与高效估计的测量方法提供了实用指导。