Matthew A. Masten, Alexandre Poirier
arXiv 12 May 2017 · Statistics — Methodology · publishedQuantitative Economics (2020) · 39 citations (OpenAlex)
arXiv:1705.04765 · PDF · DOI · OpenAlex · Extracted main text
Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the proportion of units who benefit from treatment is at least a specific value (e.g., at least 50%). For these conclusions, we derive the breakdown frontier for two kinds of assumptions: one which indexes relaxations of the baseline random assignment of treatment assumption, and one which indexes relaxations of the baseline rank invariance assumption. These classes of assumptions nest both the point identifying assumptions of random assignment and rank invariance and the opposite end of no constraints on treatment selection or the dependence structure between potential outcomes. This frontier provides a quantitative measure of robustness of conclusions to relaxations of the baseline point identifying assumptions. We derive $\sqrt{N}$-consistent sample analog estimators for these frontiers. We then provide two asymptotically valid bootstrap procedures for constructing lower uniform confidence bands for the breakdown frontier. As a measure of robustness, estimated breakdown frontiers and their corresponding confidence bands can be presented alongside traditional point estimates and confidence intervals obtained under point identifying assumptions. We illustrate this approach in an empirical application to the effect of child soldiering on wages. We find that sufficiently weak conclusions are robust to simultaneous failures of rank invariance and random assignment, while some stronger conclusions are fairly robust to failures of rank invariance but not necessarily to relaxations of random assignment.
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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 | Dümbgen, L (1993) On nondifferentiable functions and the bootstrap | 0.928 | 5 | 3 | 80% |
| 2 | Masten, M. A. and A. Poirier (2018) a): Identification of treatment effects under conditional partial independence self | 0.909 | 8 | 6 | 75% |
| 3 | Hong, H. and J. Li (2018) The numerical delta method | 0.894 | 7 | 4 | 71% |
| 4 | Imbens, G. W (2003) Sensitivity to exogeneity assumptions in program evaluation | 0.894 | 7 | 3 | 71% |
| 5 | Blattman, C. and J. Annan (2010) The consequences of child soldiering | 0.874 | 6 | 2 | 100% |
| 6 | Fang, Z. and A. Santos (2019) Inference on directionally differentiable functions | 0.860 | 11 | 4 | 64% |
| 7 | Horowitz, J. L. and C. F. Manski (1995) Identification and robustness with contaminated and corrupted data | 0.754 | 7 | 3 | 43% |
| 8 | Kline, P. and A. Santos (2013) Sensitivity to missing data assumptions: Theory and an evaluation of the U.S.\ wage structure | 0.737 | 4 | 3 | 50% |
| 9 | Stoye, J (2005) Essays on partial identification and statistical decisions, Ph.D | 0.737 | 4 | 3 | 50% |
| 10 | Heckman, J. J., J. Smith, and N. Clements (1997) Making the most out of programme evaluations and social experiments: Accounting for heterogeneity in programme impacts | 0.737 | 3 | 3 | 67% |
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