arXiv 7 Jun 2025 · Econometrics
arXiv:2506.06776 · PDF · DOI · OpenAlex · Extracted main text
This paper studies inference on the value of a linear program (LP) when both the objective function and constraints are possibly unknown and must be estimated from data. We show that many inference problems in partially identified models can be reformulated in this way. Building on Shapiro (1991) and Fang and Santos (2019), we develop a pointwise valid inference procedure for the value of an LP. We modify this pointwise inference procedure to construct one-sided inference procedures that are uniformly valid over large classes of data-generating processes. Our results provide alternative testing procedures for problems considered in Andrews et al. (2023), Cox and Shi (2023), and Fang et al. (2023) (in the low-dimensional case), and remain valid when key components--such as the coefficient matrix--are unknown and must be estimated. Moreover, our framework also accommodates inference on the identified set of a subvector, in models defined by linear moment inequalities, and does so under weaker constraint qualifications than those in Gafarov (2025).
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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 | Andrews, I., Roth, J., and Pakes, A (2023) Inference for Linear Conditional Moment Inequalities | 1.000 | 17 | 5 | 100% |
| 2 | Manski, C. F. and Pepper, J. V (2000) Monotone instrumental variables: With an application to the returns to schooling | 1.000 | 11 | 4 | 100% |
| 3 | Dupas, P (2014) Short-Run Subsidies and Long-Run Adoption of New Health Products: Evidence From a Field Experiment | 1.000 | 10 | 3 | 100% |
| 4 | Cox, G. F., Shi, X., and Shimizu, Y (2025) Testing inequalities linear in nuisance parameters | 1.000 | 9 | 3 | 100% |
| 5 | Cox, G. and Shi, X (2023) Simple Adaptive Size-Exact Testing for Full-Vector and Subvector Inference in Moment Inequality Models | 1.000 | 8 | 4 | 100% |
| 6 | Fang, Z., Santos, A., Shaikh, A. M., and Torgovitsky, A (2023) Inference for Large‐Scale Linear Systems With Known Coefficients | 1.000 | 8 | 4 | 100% |
| 7 | Hsieh, Y.-W., Shi, X., and Shum, M (2022) Inference on estimators defined by mathematical programming | 0.874 | 6 | 2 | 100% |
| 8 | Andrews, D. W. K. and Soares, G (2010) Inference for Parameters defined by Moment Inequalities Using Generalized Moment Selection | 0.843 | 3 | 3 | 100% |
| 9 | Mogstad, M., Santos, A., and Torgovitsky, A (2018) Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters | 0.843 | 3 | 3 | 100% |
| 10 | Imbens, G. W. and Angrist, J. D (1994) Identification and Estimation of Local Average Treatment Effects | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 43 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Inference for Linear Systems with Unknown Coefficients | 1.000 | 9 | 4 |
| 2 | Testing Inequalities Linear in Nuisance Parameters | 0.843 | 4 | 3 |
| 3 | Synthetic Parallel Trends | 0.737 | 3 | 2 |
| 4 | Testing Exclusion and Shape Restrictions in Potential Outcomes Models | 0.644 | 2 | 2 |
| 5 | On the falsification of instrumental variable models for heterogeneous treatment effects | 0.405 | 1 | 1 |