Simple subvector inference on sharp identified set in affine models
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arXiv
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866909267004489728 |
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| author | Gafarov, Bulat |
| author_facet | Gafarov, Bulat |
| contents | 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 \emph{uniformly valid} confidence sets for an element $θ_{1}$ of a parameter vector $θ\in\mathbb{R}^{d}$ 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 $θ$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1904_00111 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Simple subvector inference on sharp identified set in affine models Gafarov, Bulat Econometrics 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 \emph{uniformly valid} confidence sets for an element $θ_{1}$ of a parameter vector $θ\in\mathbb{R}^{d}$ 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 $θ$, 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. |
| title | Simple subvector inference on sharp identified set in affine models |
| topic | Econometrics |
| url | https://arxiv.org/abs/1904.00111 |