Andrei Voronin
arXiv 19 Mar 2025 · Econometrics
arXiv:2503.14940 · PDF · Extracted main text
Sharp bounds on partially identified parameters are often given by the values of linear programs (LPs). This paper introduces a novel estimator of the LP value. Unlike existing procedures, our estimator is root-n-consistent, pointwise in the probability measure, whenever the population LP is feasible and finite. Our estimator is valid under point-identification, over-identifying constraints, and solution multiplicity. Turning to uniformity properties, we prove that the LP value cannot be uniformly consistently estimated without restricting the set of possible distributions. We then show that our estimator achieves uniform consistency under a condition that is minimal for the existence of any such estimator. We obtain computationally efficient, asymptotically normal inference procedure with exact asymptotic coverage at any fixed probability measure. To complement our estimation results, we derive LP sharp bounds in a general identification setting. We apply our findings to estimating returns to education. To that end, we propose the conditionally monotone IV assumption (cMIV) that tightens the classical monotone IV (MIV) bounds and is testable under a mild regularity condition. Under cMIV, university education in Colombia is shown to increase the average wage by at least $5.5%$, whereas classical conditions fail to yield an informative bound.
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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 | Manski, C. F. and J. V. Pepper (2000) Monotone Instrumental Variables: With an Application to the Returns to Schooling | 1.000 | 11 | 4 | 100% |
| 2 | Chetverikov, D (2019) Testing Regression Monotonicity in Econometric Models | 1.000 | 7 | 3 | 100% |
| 3 | De Haan, M (2017) The Effect of Additional Funds for Low-ability Pupils: A Non-parametric Bounds Analysis | 1.000 | 6 | 4 | 100% |
| 4 | Blundell, R., A. Gosling, H. Ichimura, and C. Meghir (2007) Changes in the distribution of male and female wages accounting for employment composition using bounds | 1.000 | 6 | 3 | 100% |
| 5 | Gafarov, B (2024) Simple subvector inference on sharp identified set in affine models | 0.946 | 13 | 4 | 85% |
| 6 | Kreider, B., J. V. Pepper, C. Gundersen, and D. Jolliffe (2012) Identifying the effects of SNAP (food stamps) on child health outcomes when participation is endogenous and misreported | 0.928 | 4 | 3 | 100% |
| 7 | Siddique, Z (2013) Partially Identified Treatment Effects Under Imperfect Compliance: The Case of Domestic Violence | 0.928 | 4 | 3 | 100% |
| 8 | Cho, J. and T. M. Russell (2023) Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments | 0.874 | 7 | 2 | 100% |
| 9 | Mogstad, M., A. Santos, and A. Torgovitsky (2018) Using instrumental variables for inference about policy relevant treatment parameters | 0.874 | 5 | 2 | 100% |
| 10 | Manski, C. F. and J. V. Pepper (2009) More on monotone instrumental variables | 0.843 | 3 | 3 | 100% |
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