Federico Crippa, Danil Fedchenko
arXiv 23 Oct 2024 · Econometrics
arXiv:2410.18272 · PDF · DOI · OpenAlex · Extracted main text
This paper considers the problem of ranking objects based on their latent merits using data from pairwise interactions. We allow for incomplete observation of these interactions and study what can be inferred about rankings in such settings. First, we show that identification of the ranking depends on a trade-off between the tournament graph and the interaction function: in parametric models, such as the Bradley-Terry-Luce, rankings are point identified even with sparse graphs, whereas nonparametric models require dense graphs. Second, moving beyond point identification, we characterize the identified set in the nonparametric model under any tournament structure and represent it through moment inequalities. Finally, we propose a likelihood-based statistic to test whether a ranking belongs to the identified set. We study two testing procedures: one is finite-sample valid but computationally intensive; the other is easy to implement and valid asymptotically. We illustrate our results using Brazilian employer-employee data to study how workers rank firms when moving across jobs.
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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 | Corradini, V., L. Lagos, and G. Sharma (2023) Collective Bargaining for Women: How Unions Create Female-Friendly Jobs, Tech | 1.000 | 12 | 5 | 100% |
| 2 | Sorkin, I (2018) Ranking Firms Using Revealed Preference | 1.000 | 9 | 4 | 100% |
| 3 | Lagos, L (2024) Union Bargaining Power and the Amenity-Wage Tradeoff | 1.000 | 5 | 3 | 100% |
| 4 | Shah, N., S. Balakrishnan, A. Guntuboyina, and M. Wainwright (2016) Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues, in | 1.000 | 5 | 3 | 100% |
| 5 | Stigler, S. M (1994) Citation Patterns in the Journals of Statistics and Probability | 0.843 | 3 | 3 | 100% |
| 6 | Chatterjee, S. and S. Mukherjee (2019) Estimation in Tournaments and Graphs under Monotonicity Constraints | 0.811 | 4 | 2 | 100% |
| 7 | Mogstad, M., J. P. Romano, A. M. Shaikh, and D. Wilhelm (2024) Inference for Ranks with Applications to Mobility Across Neighbourhoods and Academic Achievement Across Countries | 0.737 | 3 | 2 | 100% |
| 8 | Strzalecki, T (2024) Stochastic Choice Theory | 0.644 | 2 | 2 | 100% |
| 9 | Blavatskyy, P (2018) Fechner’s Strong Utility Model for Choice among n>2 Alternatives: Risky Lotteries, Savage Acts, and Intertemporal Payoffs | 0.644 | 2 | 2 | 100% |
| 10 | Oliveira, I. F. D., N. Ailon, and O. Davidov (2018) A New and Flexible Approach to the Analysis of Paired Comparison Data | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 44 scored citations.