arXiv 13 Jan 2023 · Econometrics
arXiv:2301.05703 · PDF · DOI · OpenAlex · Extracted main text
In this paper, I try to tame "Basu's elephants" (data with extreme selection on observables). I propose new practical large-sample and finite-sample methods for estimating and inferring heterogeneous causal effects (under unconfoundedness) in the empirically relevant context of limited overlap. I develop a general principle called "Stable Probability Weighting" (SPW) that can be used as an alternative to the widely used Inverse Probability Weighting (IPW) technique, which relies on strong overlap. I show that IPW (or its augmented version), when valid, is a special case of the more general SPW (or its doubly robust version), which adjusts for the extremeness of the conditional probabilities of the treatment states. The SPW principle can be implemented using several existing large-sample parametric, semiparametric, and nonparametric procedures for conditional moment models. In addition, I provide new finite-sample results that apply when unconfoundedness is plausible within fine strata. Since IPW estimation relies on the problematic reciprocal of the estimated propensity score, I develop a "Finite-Sample Stable Probability Weighting" (FPW) set-estimator that is unbiased in a sense. I also propose new finite-sample inference methods for testing a general class of weak null hypotheses. The associated computationally convenient methods, which can be used to construct valid confidence sets and to bound the finite-sample confidence distribution, are of independent interest. My large-sample and finite-sample frameworks extend to the setting of multivalued treatments.
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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 | Kennedy, E. H (2022) Towards optimal doubly robust estimation of heterogeneous causal effects | 1.000 | 13 | 4 | 100% |
| 2 | Hirano, K., G. W. Imbens, and G. Ridder (2003) Efficient estimation of average treatment effects using the estimated propensity score | 1.000 | 8 | 3 | 100% |
| 3 | Kennedy, E. H., S. Balakrishnan, and L. Wasserman (2022) Minimax rates for heterogeneous causal effect estimation | 1.000 | 8 | 3 | 100% |
| 4 | Khan, S. and E. Tamer (2010) Irregular identification, support conditions, and inverse weight estimation | 1.000 | 5 | 3 | 100% |
| 5 | Kitagawa, T. and A. Tetenov (2018) Who should be treated? Empirical welfare maximization methods for treatment choice | 1.000 | 5 | 3 | 100% |
| 6 | Ai, C., O. Linton, K. Motegi, and Z. Zhang (2021) A unified framework for efficient estimation of general treatment models | 0.928 | 4 | 3 | 100% |
| 7 | Rothe, C (2017) Robust confidence intervals for average treatment effects under limited overlap | 0.874 | 13 | 2 | 100% |
| 8 | Heiler, P. and E. Kazak (2021) Valid inference for treatment effect parameters under irregular identification and many extreme propensity scores | 0.874 | 6 | 2 | 100% |
| 9 | Ma, X. and J. Wang (2020) Robust inference using inverse probability weighting | 0.874 | 5 | 2 | 100% |
| 10 | Li, F., K. L. Morgan, and A. M. Zaslavsky (2018) Balancing covariates via propensity score weighting | 0.843 | 3 | 3 | 100% |
Showing the top 10 of 173 scored citations.