Identification and Counterfactual Analysis in Incomplete Models with Support and Moment Restrictions

Fuente: arXiv
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Main Author: Li, Lixiong
Format: Preprint
Published: 2026
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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
id 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