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Simple subvector inference on sharp identified set in affine models

Bulat Gafarov

arXiv 29 Mar 2019 · Econometrics · publishedJournal of Econometrics (2025)

arXiv:1904.00111 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper studies a regularized support function estimator for bounds on components of the parameter vector in the case in which the identified set is a polygon. The proposed regularized estimator has three important properties: (i) it has a uniform asymptotic Gaussian limit in the presence of flat faces in the absence of redundant (or overidentifying) constraints (or vice versa); (ii) the bias from regularization does not enter the first-order limiting distribution; (iii) the estimator remains consistent for sharp (non-enlarged) identified set for the individual components even in the non-regualar case. These properties are used to construct uniformly valid confidence sets for an element $\theta_{1}$ of a parameter vector $\theta\in\mathbb{R}^{d}$ that is partially identified by affine moment equality and inequality conditions. The proposed confidence sets can be computed as a solution to a small number of linear and convex quadratic programs, leading to a substantial decrease in computation time and guarantees a global optimum. As a result, the method provides a uniformly valid inference in applications in which the dimension of the parameter space, $d$, and the number of inequalities, $k$, were previously computationally unfeasible ($d,k=100$). The proposed approach can be extended to construct confidence sets for intersection bounds, to construct joint polygon-shaped confidence sets for multiple components of $\theta$, and to find the set of solutions to a linear program. Inference for coefficients in the linear IV regression model with an interval outcome is used as an illustrative example.

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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
1Shapiro, A (1991) Asymptotic analysis of stochastic programs0.87452100%
2Chernozhukov, V., S. Lee, and A. M. Rosen (2013) Intersection Bounds: Estimation and Inference0.8434375%
3Freyberger, J. and J. L. Horowitz (2015) Identification and shape restrictions in nonparametric instrumental variables estimation0.81142100%
4Kaido, H. and A. Santos (2014) Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities0.81142100%
5Trostel, P., I. Walker, and P. Woolley (2002) Estimates of the economic return to schooling for 28 countries0.81142100%
6Andrews, I., J. Roth, and A. Pakes (2019) Inference for linear conditional moment inequalities, Tech0.73732100%
7Beresteanu, A. and F. Molinari (2008) Asymptotic properties for a class of partially identified models0.73732100%
8Chernozhukov, V., H. Hong, and E. Tamer (2007) Estimation and confidence regions for parameter sets in econometric models0.73732100%
9Cho, J. H. and T. M. Russell (2023) Simple inference on functionals of set-identified parameters defined by linear moments0.73732100%
10Kaido, H., F. Molinari, and J. Stoye (2015) Inference for projections of identified sets0.73732100%

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