arXiv 26 Oct 2018 · Econometrics · publishedJournal of the American Statistical Association (2019) · 88 citations (OpenAlex)
arXiv:1810.11397 · PDF · DOI · OpenAlex · Extracted main text
Inverse Probability Weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of "small denominators," trimming is routinely employed as a regularization strategy. However, ad hoc trimming of the observations renders usual inference procedures invalid for the target estimand, even in large samples. In this paper, we first show that the IPW estimator can have different (Gaussian or non-Gaussian) asymptotic distributions, depending on how "close to zero" the probability weights are and on how large the trimming threshold is. As a remedy, we propose an inference procedure that is robust not only to small probability weights entering the IPW estimator but also to a wide range of trimming threshold choices, by adapting to these different asymptotic distributions. This robustness is achieved by employing resampling techniques and by correcting a non-negligible trimming bias. We also propose an easy-to-implement method for choosing the trimming threshold by minimizing an empirical analogue of the asymptotic mean squared error. In addition, we show that our inference procedure remains valid with the use of a data-driven trimming threshold. We illustrate our method by revisiting a dataset from the National Supported Work program.
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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 | Fan and Gijbels (1996) Local Polynomial Modelling and Its Applications, New York: Chapman and Hall | 0.644 | 2 | 2 | 100% |
| 2 | Politis and Romano (1994) Large Sample Confidence Regions Based on Subsamples Under Minimal Assumptions | 0.644 | 2 | 2 | 100% |
| 3 | Dehejia and Wahba (1999) Causal Effects in Nonexperimental Studies: Reevaluating the Evaluations of Training Programs | 0.511 | 2 | 1 | 100% |
| 4 | Logan, Mallows, Rice and Shepp (1973) Limit Distributions of Self-normalized Sums | 0.511 | 2 | 1 | 100% |
| 5 | Romano and Wolf (1999) Subsampling Inference for the Mean in the Heavy-tailed Case | 0.511 | 2 | 1 | 100% |
| 6 | Abadie (2003) Semiparametric Instrumental Variable Estimation of Treatment Response Models | 0.405 | 1 | 1 | 100% |
| 7 | Abadie (2005) Semiparametric Difference-in-Differences Estimators | 0.405 | 1 | 1 | 100% |
| 8 | Abadie and Cattaneo (2018) Econometric Methods for Program Evaluation | 0.405 | 1 | 1 | 100% |
| 9 | Arcones and Giné (1991) Additions and Correction to `The Bootstrap of the Mean with Arbitrary Bootstrap Sample Size' | 0.405 | 1 | 1 | 100% |
| 10 | Athey, Imbens and Wager (2018) Approximate Residual Balancing: Debiased Inference of Average Treatment Effects in High Dimensions | 0.405 | 1 | 1 | 100% |
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