arXiv 8 Mar 2026 · Econometrics
arXiv:2603.07722 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Molchanov, Ilya (2005) Theory of Random Sets | 0.811 | 4 | 2 | 100% |
| 2 | Hiriart-Urruty, Jean-Baptiste and Lemaréchal, Claude (2001) Fundamentals of convex analysis | 0.737 | 3 | 2 | 100% |
| 3 | Bertsekas, Dimitri P. and Shreve, Steven E (1978) Stochastic Optimal Control: The Discrete Time Case | 0.644 | 4 | 1 | 100% |
| 4 | Beresteanu, Arie and Molchanov, Ilya and Molinari, Francesca (2011) Sharp Identification Regions in Models With Convex Moment Predictions | 0.644 | 2 | 2 | 100% |
| 5 | Ekeland, Ivar and Galichon, Alfred and Henry, Marc (2010) Optimal Transportation and the Falsifiability of Incompletely Specified Economic Models | 0.644 | 2 | 2 | 100% |
| 6 | Schennach, Susanne M (2014) Entropic Latent Variable Integration Via Simulation | 0.644 | 2 | 2 | 100% |
| 7 | Ciliberto, Federico and Tamer, Elie (2009) Market Structure and Multiple Equilibria in Airline Markets | 0.511 | 2 | 1 | 100% |
| 8 | Gu, Jiaying and Russell, Thomas and Stringham, Thomas (2025) Counterfactual Identification and Latent Space Enumeration in Discrete Outcome Models | 0.511 | 2 | 1 | 100% |
| 9 | Gu, Jiaying and Thomas Russell (2023) A Dual Approach to Wasserstein-Robust Counterfactuals | 0.511 | 2 | 1 | 100% |
| 10 | Ackerberg, Daniel A. and Caves, Kevin and Frazer, Garth (2015) Identification Properties of Recent Production Function Estimators | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 29 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | The Projection Solution to the Incidental Parameter Problem | 0.511 | 2 | 1 |