Identification and Counterfactual Analysis in Incomplete Models with Support and Moment Restrictions
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| Format: | Preprint |
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2026
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| _version_ | 1866908872971649024 |
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| author | Li, Lixiong |
| author_facet | Li, Lixiong |
| contents | This paper develops a unified identification framework for counterfactual analysis in incomplete models characterized by support and moment restrictions. I demonstrate that identifying structural parameters and conducting counterfactual analyses are isomorphic tasks. By embedding counterfactual restrictions within an augmented structural model specification, this approach bypasses the conventional "estimate-then-simulate" workflow and the need to simulate outcomes from models with set predictions. To make this approach operational, I extend sharp identification results for the support-function approach beyond the integrable boundedness condition that is imposed in sharp random-set characterizations but may be violated in economically relevant counterfactual analyses. Under minimal regularity conditions, I prove that the support-function approach remains sharp for the $moment$ $closure$ of the identified set. Furthermore, I introduce an irreducibility condition requiring all support implications to be made explicit. I show that for irreducible models, the identified set and its moment closure are statistically indistinguishable in finite samples. Together, these results justify using support-function methods in counterfactual settings where traditional sharpness fails and clarify the distinct roles of support and moment restrictions in empirical practice. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_07722 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Identification and Counterfactual Analysis in Incomplete Models with Support and Moment Restrictions Li, Lixiong Econometrics This paper develops a unified identification framework for counterfactual analysis in incomplete models characterized by support and moment restrictions. I demonstrate that identifying structural parameters and conducting counterfactual analyses are isomorphic tasks. By embedding counterfactual restrictions within an augmented structural model specification, this approach bypasses the conventional "estimate-then-simulate" workflow and the need to simulate outcomes from models with set predictions. To make this approach operational, I extend sharp identification results for the support-function approach beyond the integrable boundedness condition that is imposed in sharp random-set characterizations but may be violated in economically relevant counterfactual analyses. Under minimal regularity conditions, I prove that the support-function approach remains sharp for the $moment$ $closure$ of the identified set. Furthermore, I introduce an irreducibility condition requiring all support implications to be made explicit. I show that for irreducible models, the identified set and its moment closure are statistically indistinguishable in finite samples. Together, these results justify using support-function methods in counterfactual settings where traditional sharpness fails and clarify the distinct roles of support and moment restrictions in empirical practice. |
| title | Identification and Counterfactual Analysis in Incomplete Models with Support and Moment Restrictions |
| topic | Econometrics |
| url | https://arxiv.org/abs/2603.07722 |