arXiv 14 Apr 2026 · Econometrics
arXiv:2604.12611 · PDF · DOI · OpenAlex · Extracted main text
Empirical analyses of ordinal outcomes using repeated cross-sectional data rely on marginal distributions, leaving the joint distribution unobserved and the sources of distributional change unidentified. This paper develops a framework to measure and interpret such changes under limited information. The $L_1$ distance between cumulative distribution functions admits an optimal transport representation as the minimal reallocation of probability mass across ordered categories, which provides a foundation for the analysis. This yields both a scalar measure of discrepancy and a structured characterization of how distributional change must occur, which I term minimal-mobility configurations. To address missing data, I adopt a partial identification approach that delivers sharp bounds on the marginal distributions and, in turn, on both the discrepancy measure and its associated configurations. The resulting framework supports inference using standard resampling methods and provides a transparent basis for assessing sensitivity to nonresponse. An application to Arab Barometer data illustrates the approach.
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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 | Fréchet, M (1935) Généralisations du théorème des probabilités totales | 0.644 | 2 | 2 | 100% |
| 2 | Fréchet, M (1951) Sur les tableaux de corrélation dont les marges sont données | 0.644 | 2 | 2 | 100% |
| 3 | Horowitz, J. L. and C. F. Manski (2000) Nonparametric analysis of randomized experiments with missing covariate and outcome data | 0.644 | 2 | 2 | 100% |
| 4 | Vallender, S. S (1974) Calculation of the Wasserstein distance between probability distributions on the line | 0.511 | 2 | 2 | 50% |
| 5 | Chernozhukov, V., H. Hong, and E. Tamer (2007) Estimation and confidence regions for parameter sets in econometric models | 0.405 | 1 | 1 | 100% |
| 6 | Daljord, O. y., G. Pouliot, J. Xiao, and M. Hu (2026) The black market for beijing license plates | 0.405 | 1 | 1 | 100% |
| 7 | Galichon, A (2016) Optimal Transport Methods in Economics | 0.405 | 1 | 1 | 100% |
| 8 | Dupuy, A., A. Galichon, and Y. Sun (2019, 12) (2019) Estimating matching affinity matrices under low-rank constraints | 0.405 | 1 | 1 | 100% |
| 9 | Galichon, A. and M. Henry (2011, 04) (2011) Set Identification in Models with Multiple Equilibria | 0.405 | 1 | 1 | 100% |
| 10 | Galichon, A. and M. Henry (2026) An econometrician's guide to optimal transport | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 22 scored citations.