Xiaohong Chen, Haitian Xie
arXiv 19 Oct 2025 · Econometrics
arXiv:2510.16683 · PDF · DOI · OpenAlex · Extracted main text
This paper studies nonparametric local (over-)identification and the semiparametric efficiency in modern causal frameworks. We develop a unified approach that begins by translating structural models with latent variables into their induced statistical models of observables and then analyzes local overidentification through conditional moment restrictions. We apply this approach to three popular classes of causal models: (1) the general treatment model under unconfoundedness; (2) the negative control model, and (3) the long-term causal inference model under unobserved confounding. The first model yields a locally just-identified statistical model, implying that all regular asymptotically linear estimators of the treatment effect have the same asymptotic variance, which equals the (trivial) semiparametric efficient variance bound. In contrast, the latter two models involve nonparametric endogeneity and are naturally locally overidentified; consequently, some doubly robust orthogonal moment estimators of the average treatment effect are inefficient. Whereas existing work typically imposes strong conditions to restore local just-identification to justify the efficiency of their doubly robust orthogonal moment estimators, we characterize the semiparametric efficient variance bounds, along with efficient estimators, for the (locally) overidentified models (2) and (3). A small real data application, along with a simulation study, illustrates the semiparametric efficiency gains in model (3).
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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 | Imbens, Guido and Kallus, Nathan and Mao, Xiaojie and Wang, Yuhao (2024) Long-term causal inference under persistent confounding via data combination | 0.941 | 18 | 4 | 83% |
| 2 | Chen, Xiaohong and Santos, Andres (2018) Overidentification in regular models self | 0.909 | 8 | 4 | 75% |
| 3 | Chunrong Ai and Xiaohong Chen (2012) The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions self | 0.843 | 10 | 4 | 60% |
| 4 | Chen, Xiaohong and Hong, Han and Tarozzi, Alessandro (2004) Semiparametric Efficiency in GMM Models of Nonclassical Measurement Error, Missing Data and Treatment Effects self | 0.843 | 3 | 3 | 100% |
| 5 | Ai, Chunrong and Linton, Oliver and Motegi, Kaiji and Zhang, Zheng (2021) A unified framework for efficient estimation of general treatment models | 0.811 | 4 | 2 | 100% |
| 6 | Cui, Yifan and Pu, Hongming and Shi, Xu and Miao, Wang and Tchetgen… (2024) Semiparametric proximal causal inference | 0.737 | 4 | 2 | 75% |
| 7 | Hirano, Keisuke and Imbens, Guido W and Ridder, Geert (2003) Efficient estimation of average treatment effects using the estimated propensity score | 0.737 | 3 | 2 | 100% |
| 8 | Ai, Chunrong and Chen, Xiaohong (2003) Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions self | 0.644 | 2 | 2 | 100% |
| 9 | Chunrong Ai and Xiaohong Chen (2007) Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables self | 0.644 | 2 | 2 | 100% |
| 10 | Xiaohong Chen and Han Hong and Alessandro Tarozzi (2008) Semiparametric efficiency in GMM models with auxiliary data self | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 34 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Higher-Order Debiased Estimators for General Treatment Models | 0.511 | 2 | 2 |
| 2 | Semiparametric Efficiency in Policy Learning with General Treatments | 0.405 | 1 | 1 |