arXiv 17 Apr 2025 · Econometrics
arXiv:2504.13273 · PDF · Extracted main text
In the presence of sufficiently weak overlap, it is known that no regular root-n-consistent estimators exist and standard estimators may fail to be asymptotically normal. This paper shows that a thresholded version of the standard doubly robust estimator is asymptotically normal with well-calibrated Wald confidence intervals even when constructed using nonparametric estimates of the propensity score and conditional mean outcome. The analysis implies a cost of weak overlap in terms of black-box nuisance rates, borne when the semiparametric bound is infinite, and the contribution of outcome smoothness to the outcome regression rate, which is incurred even when the semiparametric bound is finite. As a byproduct of this analysis, I show that under weak overlap, the optimal global regression rate is the same as the optimal pointwise regression rate, without the usual polylogarithmic penalty. The high-level conditions yield new rules of thumb for thresholding in practice. In simulations, thresholded AIPW can exhibit moderate overrejection in small samples, but I am unable to reject a null hypothesis of exact coverage in large samples. In an empirical application, the clipped AIPW estimator that targets the standard average treatment effect yields similar precision to a heuristic 10% fixed-trimming approach that changes the target sample.
appendix boundary found by appendix_command · 34% of the source is main text. Read the extracted text to check this.
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 | Ma, X. and Wang, J (2020) Robust inference using inverse probability weighting | 0.969 | 11 | 5 | 91% |
| 2 | Stone, C. J (1982) Optimal global rates of convergence for nonparametric estimators | 0.928 | 5 | 4 | 80% |
| 3 | Crump, R. K., Hotz, V. J., Imbens, G. W., and Mitnik, O. A (2009) Dealing with limited overlap in estimation of average treatment effects | 0.874 | 10 | 2 | 100% |
| 4 | Heiler, P. and Kazak, E (2021) Valid inference for treatment effect parameters under irregular identification and many extreme propensity scores | 0.874 | 5 | 2 | 100% |
| 5 | Ma, Y., Sant'Anna, P. H. C., Sasaki, Y., and Ura, T (2023) Doubly robust estimators with weak overlap | 0.843 | 3 | 3 | 100% |
| 6 | Armstrong, T. B. and Kolesár, M (2017) A simple adjustment for bandwidth snooping | 0.737 | 3 | 2 | 100% |
| 7 | Khan, S. and Tamer, E (2010) Irregular identification, support conditions, and inverse weight estimation | 0.644 | 3 | 2 | 67% |
| 8 | Connors, Alfred F., J., Speroff, T., Dawson, N. V., Thomas, C., Harr… (1996) The effectiveness of right heart catheterization in the initial care of critically ill patients | 0.644 | 2 | 2 | 100% |
| 9 | Sasaki, Y. and Ura, T (2022) Estimation and inference for moments of ratios with robustness against large trimming bias | 0.644 | 2 | 2 | 100% |
| 10 | Semenova, V (2024) Aggregated intersection bounds and aggregated minimax values | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 39 scored citations.