Consistent estimation with many moment inequalities
In this paper, we consider estimation of the identified set when the number of moment inequalities is large relative to sample size, possibly infinite. Many applications in the recent literature on partially identified problems have this feature, including dynamic games, set-identified IV models, an...
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| Published in | Journal of econometrics Vol. 182; no. 2; pp. 329 - 350 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.10.2014
Elsevier Sequoia S.A |
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| Abstract | In this paper, we consider estimation of the identified set when the number of moment inequalities is large relative to sample size, possibly infinite. Many applications in the recent literature on partially identified problems have this feature, including dynamic games, set-identified IV models, and parameters defined by a continuum of moment inequalities, in particular conditional moment inequalities. We provide a generic consistency result for criterion-based estimators using an increasing number of unconditional moment inequalities. We then develop more specific results for set estimation subject to conditional moment inequalities: we first derive the fastest possible rate for estimating the sharp identification region under smoothness conditions on the conditional moment functions. We also give rate conditions for inference under local alternatives. |
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| AbstractList | In this paper, we consider estimation of the identified set when the number of moment inequalities is large relative to sample size, possibly infinite. Many applications in the recent literature on partially identified problems have this feature, including dynamic games, set-identified IV models, and parameters defined by a continuum of moment inequalities, in particular conditional moment inequalities. We provide a generic consistency result for criterion-based estimators using an increasing number of unconditional moment inequalities. We then develop more specific results for set estimation subject to conditional moment inequalities: we first derive the fastest possible rate for estimating the sharp identification region under smoothness conditions on the conditional moment functions. We also give rate conditions for inference under local alternatives. All rights reserved, Elsevier In this paper, we consider estimation of the identified set when the number of moment inequalities is large relative to sample size, possibly infinite. Many applications in the recent literature on partially identified problems have this feature, including dynamic games, set-identified IV models, and parameters defined by a continuum of moment inequalities, in particular conditional moment inequalities. We provide a generic consistency result for criterion-based estimators using an increasing number of unconditional moment inequalities. We then develop more specific results for set estimation subject to conditional moment inequalities: we first derive the fastest possible rate for estimating the sharp identification region under smoothness conditions on the conditional moment functions. We also give rate conditions for inference under local alternatives. |
| Author | Menzel, Konrad |
| Author_xml | – sequence: 1 givenname: Konrad surname: Menzel fullname: Menzel, Konrad email: km125@nyu.edu organization: Department of Economics, NYU, United States |
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| Keywords | Many weak moments Partial identification Set estimation C13 C12 C15 C14 Moment inequalities Conditional moment inequalities |
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| Snippet | In this paper, we consider estimation of the identified set when the number of moment inequalities is large relative to sample size, possibly infinite. Many... |
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| SubjectTerms | Conditional moment inequalities econometric models Econometrics economic analysis economic theory Estimating techniques Game theory Identification Inequality Literature Many weak moments Mathematical functions Moment inequalities Parameter estimation Partial identification Samples Set estimation Studies |
| Title | Consistent estimation with many moment inequalities |
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