arXiv 9 Apr 2026 · Statistics — Methodology
arXiv:2604.08681 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fu, Jiawei and Green, Donald P (2025) Causal Inference for Experiments with Latent Outcomes: Key Results and Their Implications for Design and Analysis self | 1.000 | 8 | 5 | 100% |
| 2 | Bennett, Andrew and Kallus, Nathan and Mao, Xiaojie and Newey, Whitn… (2025) Inference on strongly identified functionals of weakly identified functions | 0.894 | 7 | 3 | 71% |
| 3 | Miao, Wang and Geng, Zhi and Tchetgen Tchetgen, Eric J (2018) Identifying causal effects with proxy variables of an unmeasured confounder | 0.737 | 3 | 3 | 67% |
| 4 | Newey, Whitney K and Powell, James L (2003) Instrumental variable estimation of nonparametric models | 0.737 | 3 | 3 | 67% |
| 5 | Stoetzer, Lukas F and Zhou, Xiang and Steenbergen, Marco (2025) Causal inference with latent outcomes | 0.737 | 3 | 2 | 100% |
| 6 | Darolles, Serge and Fan, Yanqin and Florens, Jean-Pierre and Renault… (2011) Nonparametric instrumental regression | 0.644 | 2 | 2 | 100% |
| 7 | Horowitz, Joel L (2011) Applied nonparametric instrumental variables estimation | 0.644 | 2 | 2 | 100% |
| 8 | Miao, Wang and Shi, Xu and Li, Yilin and Tchetgen Tchetgen, Eric J (2024) A confounding bridge approach for double negative control inference on causal effects | 0.644 | 2 | 2 | 100% |
| 9 | Santos, Andres (2011) Instrumental variable methods for recovering continuous linear functionals | 0.644 | 2 | 2 | 100% |
| 10 | Severini, Thomas A and Tripathi, Gautam (2012) Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 68 scored citations.