arXiv 10 Jun 2025 · Econometrics
arXiv:2506.08950 · PDF · DOI · OpenAlex · Extracted main text
This paper studies the identification of the average treatment effect on the treated (ATT) under unconfoundedness when covariate overlap is partial. A formal diagnostic is proposed to characterize empirical support -- the subset of the covariate space where ATT is point-identified due to the presence of comparable untreated units. Where support is absent, standard estimators remain computable but cease to identify meaningful causal parameters. A general sensitivity framework is developed, indexing identified sets by curvature constraints on the selection mechanism. This yields a structural selection frontier tracing the trade-off between assumption strength and inferential precision. Two diagnostic statistics are introduced: the minimum assumption strength for sign identification (MAS-SI), and a fragility index that quantifies the minimal deviation from ignorability required to overturn qualitative conclusions. Applied to the LaLonde (1986) dataset, the framework reveals that nearly half the treated strata lack empirical support, rendering the ATT undefined in those regions. Simulations confirm that ATT estimates may be stable in magnitude yet fragile in epistemic content. These findings reframe overlap not as a regularity condition but as a prerequisite for identification, and recast sensitivity analysis as integral to empirical credibility rather than auxiliary robustness.
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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 | Crump, R. K., V. J. Hotz, G. W. Imbens, and O. A. Mitnik (2009) Dealing with limited overlap in estimation of average treatment effects | 0.644 | 2 | 2 | 100% |
| 2 | Imbens, G. and Y. Xu (2025) Comparing experimental and nonexperimental methods: What lessons have we learned four decades after lalonde (1986)? | 0.644 | 2 | 2 | 100% |
| 3 | Becker, S. O. and M. Caliendo (2007, March) (2007) Sensitivity analysis for average treatment effects | 0.405 | 1 | 1 | 100% |
| 4 | Cinelli, C. and C. Hazlett (2020) Making sense of sensitivity: Extending omitted variable bias | 0.405 | 1 | 1 | 100% |
| 5 | Dahabreh, I. J., S. E. Robertson, J. A. Steingrimsson, M. A. Hernán,… (2020) Extending inferences from a randomized trial to a new target population | 0.405 | 1 | 1 | 100% |
| 6 | Dehejia, R. and S. Wahba (1999) Causal effects in non-experimental studies: Reevaluating the evaluation of training programs | 0.405 | 1 | 1 | 100% |
| 7 | Dehejia, R. and S. Wahba (2002) Propensity score matching methods for non-experimental causal studies | 0.405 | 1 | 1 | 100% |
| 8 | Heckman, J. J. and J. A. Smith (1995) Assessing the case for social experiments | 0.405 | 1 | 1 | 100% |
| 9 | Imbens, G. W (2004) Nonparametric estimation of average treatment effects under exogeneity: A review | 0.405 | 1 | 1 | 100% |
| 10 | King, G. and L. Zeng (2006) The dangers of extreme counterfactuals | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 52 scored citations.