Simple subvector inference on sharp identified set in affine models

Bulat Gafarov

Journal of Econometrics, 2025, vol. 249, issue PB

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-regular case. These properties are used to construct uniformly valid confidence sets for an element θ1 of a parameter vector θ∈Rd 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 θ, 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.

Keywords: Affine-moment inequalities; Asymptotic linear representation; Higher-order analysis; Delta method; Interval data; Intersection bounds; Partial identification; Regularization; Strong approximation; Stochastic programming; Subvector inference; Uniform inference (search for similar items in EconPapers)
Date: 2025
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:249:y:2025:i:pb:s0304407625000065

DOI: 10.1016/j.jeconom.2025.105952

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