EconBase
← All papers

Linear programming approach to partially identified econometric models

Andrei Voronin

arXiv 19 Mar 2025 · Econometrics

arXiv:2503.14940 · PDF · Extracted main text

Abstract

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.

Citation extraction

51
references
146
in-text mentions
52
distinct cited
0
self-citations
21,921
main-text words

appendix boundary found by appendix_command · 46% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Manski, C. F. and J. V. Pepper (2000) Monotone Instrumental Variables: With an Application to the Returns to Schooling1.000114100%
2Chetverikov, D (2019) Testing Regression Monotonicity in Econometric Models1.00073100%
3De Haan, M (2017) The Effect of Additional Funds for Low-ability Pupils: A Non-parametric Bounds Analysis1.00064100%
4Blundell, R., A. Gosling, H. Ichimura, and C. Meghir (2007) Changes in the distribution of male and female wages accounting for employment composition using bounds1.00063100%
5Gafarov, B (2024) Simple subvector inference on sharp identified set in affine models0.94613485%
6Kreider, 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 misreported0.92843100%
7Siddique, Z (2013) Partially Identified Treatment Effects Under Imperfect Compliance: The Case of Domestic Violence0.92843100%
8Cho, J. and T. M. Russell (2023) Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments0.87472100%
9Mogstad, M., A. Santos, and A. Torgovitsky (2018) Using instrumental variables for inference about policy relevant treatment parameters0.87452100%
10Manski, C. F. and J. V. Pepper (2009) More on monotone instrumental variables0.84333100%

Showing the top 10 of 52 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Generalized Optimal Transport1.00053
2Testing Inequalities Linear in Nuisance Parameters0.73733
3Bounds for within-household encouragement designs with interference0.40511
4Testing the Solvability of Systems of Linear Inequalities0.40511
5Partial Identification of Policy-Relevant Treatment Effects with Instrumental Variables via Optimal Transport0.40511
6Inference for Linear Systems with Unknown Coefficients0.40511