arXiv 20 Mar 2024 · Econometrics · 1 citations (OpenAlex)
arXiv:2403.13738 · PDF · DOI · OpenAlex · Extracted main text
This paper provides a unified framework for bounding policy relevant treatment effects using instrumental variables. In this framework, the treatment selection may depend on multidimensional unobserved heterogeneity. We derive bilinear constraints on the target parameter by extracting information from identifiable estimands. We apply a convex relaxation method to these bilinear constraints and provide conservative yet computationally simple bounds. Our convex-relaxation bounds extend and robustify the bounds by Mogstad, Santos, and Torgovitsky (2018) which require the threshold-crossing structure for the treatment: if this condition holds, our bounds are simplified to theirs for a large class of target parameters; even if it does not, our bounds include the true parameter value whereas theirs may not and are sometimes empty. Linear shape restrictions can be easily incorporated to narrow the proposed bounds. Numerical and simulation results illustrate the informativeness of our convex-relaxation bounds.
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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 | Gafarov, B (2025) Simple subvector inference on sharp identified set in affine models | 1.000 | 15 | 4 | 100% |
| 2 | Mogstad, M., A. Santos, and A. Torgovitsky (2018) Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters | 0.979 | 16 | 7 | 94% |
| 3 | Manski, C. F (1990) Nonparametric bounds on treatment effects | 0.928 | 4 | 3 | 100% |
| 4 | Heckman, J. J. and E. J. Vytlacil (2005) Structural Equations, Treatment Effects, and Econometric Policy Evaluation | 0.811 | 4 | 2 | 100% |
| 5 | Heckman, J. J. and E. J. Vytlacil (2001) a): Instrumental variables, selection models, and tight bounds on the average treatment effect, in | 0.763 | 6 | 2 | 67% |
| 6 | DiNardo, J. and D. S. Lee (2011) Program Evaluation and Research Designs, in | 0.737 | 3 | 2 | 100% |
| 7 | Lee, S. and B. Salanié (2018) Identifying effects of multivalued treatments | 0.737 | 3 | 2 | 100% |
| 8 | Manski, C. F. and J. V. Pepper (2000) Monotone instrumental variables: With an application to the returns to schooling | 0.737 | 3 | 2 | 100% |
| 9 | McCormick, G. P (1976) Computability of global solutions to factorable nonconvex programs: Part I—Convex underestimating problems | 0.737 | 3 | 2 | 100% |
| 10 | Small, D. S., Z. Tan, R. R. Ramsahai, S. A. Lorch, and M. A. Brookhart (2017) Instrumental variable estimation with a stochastic monotonicity assumption | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 46 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Policy Learning under Endogeneity Using Instrumental Variables | 0.405 | 1 | 1 |
| 2 | Evaluating Counterfactual Policies Using Instruments | 0.405 | 1 | 1 |