Behrooz Moosavi Ramezanzadeh, Arie Beresteanu
arXiv 23 Jul 2026 · Econometrics
arXiv:2607.21807 · PDF · Extracted main text
Partial identification is often set aside in practice because the identification regions it delivers are too wide to be useful, pushing researchers toward strong assumptions that buy point identification at the cost of credibility. We show that a source of information already sitting in most interval-valued datasets can fix this without adding any assumption at all. When an outcome is reported only as an interval---because a data custodian bracketed, top-coded, or formally privatized it to protect respondents---the same custodian typically continues to publish accurate population aggregates of that outcome, precisely because doing so does not compromise any individual record. We develop a framework for exploiting exactly this information: restricting the set of admissible completions of the data to those consistent with a known aggregate, rather than restricting the interval itself, and characterizing the sharp identification region that results for the best linear predictor. The restrictions we study behave in strikingly different ways---some collapse the region by a full dimension, others narrow it while leaving its shape intact. We characterize the geometric effect of each restriction and derive closed-form directional measures of identifying value for the mean and conditional-mean cases. An illustration using interval-valued wages from the Current Population Survey shows that the effect is far from marginal: modest auxiliary information recovers a substantial share of the identifying power usually thought to be lost once an outcome is coarsened.
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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 | Beresteanu, A. and F. Molinari (2008) Asymptotic Properties for a Class of Partially Identified Models self | 0.747 | 12 | 3 | 42% |
| 2 | Beresteanu, A., I. Molchanov, and F. Molinari (2011) Sharp Identification Regions in Models with Convex Moment Predictions self | 0.644 | 2 | 2 | 100% |
| 3 | Chandrasekhar, A. G., V. Chernozhukov, F. Molinari, and P. Schrimpf (2019) Best Linear Approximations to Set Identified Functions: With an Application to the Gender Wage Gap, NBER Working Paper 25593, Na… | 0.511 | 2 | 2 | 50% |
| 4 | Magnac, T. and E. Maurin (2008) Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data | 0.511 | 2 | 2 | 50% |
| 5 | Molchanov, I (2005) Theory of Random Sets | 0.511 | 2 | 2 | 50% |
| 6 | Cross, P. J. and C. F. Manski (2002) Regressions, Short and Long | 0.511 | 2 | 1 | 100% |
| 7 | Molchanov, I. and F. Molinari (2014) Random Sets in Econometrics | 0.511 | 2 | 1 | 100% |
| 8 | Beresteanu, A. and Y. Sasaki (2021) Quantile Regression with Interval Data self | 0.511 | 2 | 1 | 100% |
| 9 | Abowd, J. M., R. Ashmead, R. Cumings-Menon, S. Garfinkel, M. Heineck… (2022) The 2020 Census Disclosure Avoidance System TopDown Algorithm | 0.405 | 1 | 1 | 100% |
| 10 | Chernozhukov, V., H. Hong, and E. Tamer (2007) Estimation and Confidence Regions for Parameter Sets in Econometric Models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 22 scored citations.