Eric Auerbach, Jonathan Auerbach, Sidonia McKenzie
arXiv 1 Jul 2026 · Econometrics
arXiv:2607.00312 · PDF · DOI · OpenAlex · Extracted main text
Researchers often use the density of connections between groups of agents, such as communities, blocs, or markets, to characterize the structure of a social or economic network. In many cases, these groups are selected using the network data, making conventional fixed-group inference procedures potentially invalid. To address this issue, we develop two new confidence intervals that are universally valid post-selection in the sense that they guarantee simultaneous coverage asymptotically over all pairs of groups whose relative sizes do not vanish. Our first interval builds on a strategy of \cite{berk2013valid}. Our second interval is based on a Talagrand-type concentration inequality for empirical processes. Both intervals are simple to compute and scalable to large networks, but a key technical contribution of our paper is show that only the second interval achieves the best-possible width asymptotically up to a constant factor. Three empirical illustrations show that accounting for selection can matter in practice. Some evidence for homophily in a social network and a hub-and-spoke structure in a trade network survives our correction, while evidence for disjoint market segments in a worker transition network does not.
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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 | Berk, Brown, Buja, Zhang and Zhao (2013) Valid post-selection inference | 1.000 | 9 | 4 | 100% |
| 2 | Elliott, Golub and Jackson (2014) Financial networks and contagion | 1.000 | 9 | 3 | 100% |
| 3 | Jarosch, Nimczik and Sorkin (2024) Granular search, market structure, and wages | 1.000 | 7 | 4 | 100% |
| 4 | Alon and Naor (2006) Approximating the cut-norm via Grothendieck's inequality | 0.928 | 5 | 3 | 80% |
| 5 | Gittens and Tropp (2009) Error bounds for random matrix approximation schemes | 0.874 | 6 | 3 | 67% |
| 6 | Schmutte (2014) Free to move? A network analytic approach for learning the limits to job mobility | 0.874 | 5 | 2 | 100% |
| 7 | Carvalho (2014) From micro to macro via production networks | 0.843 | 3 | 3 | 100% |
| 8 | Lehmann and Romano (2006) | 0.843 | 3 | 3 | 100% |
| 9 | Soramäki, Bech, Arnold, Glass and Beyeler (2007) The topology of interbank payment flows | 0.843 | 3 | 3 | 100% |
| 10 | Klein and Rio (2005) Concentration around the mean for maxima of empirical processes | 0.830 | 7 | 3 | 57% |
Showing the top 10 of 137 scored citations.