arXiv 27 Feb 2026 · Econometrics
arXiv:2602.24215 · PDF · DOI · OpenAlex · Extracted main text
In the linear-in-means model, endogeneity arises naturally due to the reflection problem. A common solution is to use Instrumental Variables (IVs) based on higher-order network links, such as using friends-of-friends' characteristics. We first show that such instruments are unlikely to work well in many applied settings: in very sparse or very dense networks, friends-of-friends may be similar to the original links. This implies that the IVs may be weak or their first stage estimand may be undefined. For a class of random graphs, we use random graph theory and characterize regimes where such instruments perform well, and when they would not. We prove how weak-IV robust inference can be adapted to this environment, and how scaling the network can help. We provide extensive Monte Carlo simulations and revisit empirical applications, showing the prevalence of such issues in empirical practice, and how our results restore valid inference.
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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 | Bramoulle, Yann and Djebbari, Habiba and Morton, Florian (2009) Identification of peer effects through social networks | 1.000 | 16 | 5 | 100% |
| 2 | Andrews, Isaiah and Stock, James H and Sun, Liyang (2019) Weak instruments in instrumental variables regression: theory and practice | 0.928 | 4 | 4 | 100% |
| 3 | Acemoglu, Daron and García-Jimeno, Camilo and Robinson, James A (2015) State Capacity and Economic Development: A Network Approach | 0.928 | 4 | 3 | 100% |
| 4 | Staiger, Douglas and Stock, James H (1997) Instrumental Variables Regression with Weak Instruments | 0.928 | 4 | 3 | 100% |
| 5 | William W. Wang and Ali Jadbabaie (2025) Weak Identification in Peer Effects Estimation | 0.874 | 9 | 2 | 100% |
| 6 | Moreira, Marcelo J (2003) A conditional likelihood ratio test for structural models | 0.874 | 5 | 2 | 100% |
| 7 | Anderson, Theodore W and Rubin, Herman (1949) Estimation of the parameters of a single equation in a complete system of stochastic equations | 0.843 | 4 | 4 | 75% |
| 8 | Battaglini, Marco and Patacchini, Eleonora (2018) Influencing Connected Legislators | 0.843 | 4 | 3 | 75% |
| 9 | Erdös, P. and Rényi, A (1959) On random graphs I | 0.843 | 3 | 3 | 100% |
| 10 | Manski, Charles F (1993) Identification of endogenous social effects: The reflection problem | 0.843 | 3 | 3 | 100% |
Showing the top 10 of 43 scored citations.