William W. Wang, Ali Jadbabaie
arXiv 6 Aug 2025 · Mathematics — Statistics Theory
arXiv:2508.04897 · PDF · Extracted main text
It is commonly accepted that some phenomena are social: for example, individuals' smoking habits often correlate with those of their peers. Such correlations can have a variety of explanations, such as direct contagion or shared socioeconomic circumstances. The network linear-in-means model is a workhorse statistical model which incorporates these peer effects by including average neighborhood characteristics as regressors. Although the model's parameters are identifiable under mild structural conditions on the network, it remains unclear whether identification ensures reliable estimation in the "infill" asymptotic setting, where a single network grows in size. We show that when covariates are i.i.d. and the average network degree of nodes increases with the population size, standard estimators suffer from bias or slow convergence rates due to asymptotic collinearity induced by network averaging. As an alternative, we demonstrate that linear-in-sums models, which are based on aggregate rather than average neighborhood characteristics, do not exhibit such issues as long as the network degrees have some nontrivial variation, a condition satisfied by most network models.
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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 | Y. Bramoullé, H. Djebbari, and B. Fortin (2009) Identification of peer effects through social networks | 1.000 | 8 | 5 | 100% |
| 2 | D. O. Staiger and J. H. Stock (1994) Instrumental variables regression with weak instruments, 1994 | 0.928 | 4 | 3 | 100% |
| 3 | L.-F. Lee (2002) Consistency and efficiency of least squares estimation for mixed regressive, spatial autoregressive models | 0.894 | 7 | 5 | 71% |
| 4 | J. Cai, A. D. Janvry, and E. Sadoulet (2015) Social networks and the decision to insure | 0.843 | 3 | 3 | 100% |
| 5 | A. Hayes and K. Levin (2024) Peer effects in the linear-in-means model may be inestimable even when identified | 0.843 | 3 | 3 | 100% |
| 6 | M. Avella-Medina, F. Parise, M. T. Schaub, and S. Segarra (2018) Centrality measures for graphons: Accounting for uncertainty in networks | 0.644 | 4 | 1 | 100% |
| 7 | D. Acemoglu, V. M. Carvalho, A. Ozdaglar, and A. Tahbaz-Salehi (2012) The network origins of aggregate fluctuations | 0.644 | 2 | 2 | 100% |
| 8 | L. Anselin (2022) Spatial econometrics | 0.644 | 2 | 2 | 100% |
| 9 | A. Banerjee, A. G. Chandrasekhar, E. Duflo, and M. O. Jackson (2013) The diffusion of microfinance | 0.644 | 2 | 2 | 100% |
| 10 | A. Frieze and M. Karoński (2015) Introduction to random graphs | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 46 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Empirical Challenges with Peers-of-Peers Instruments in the Linear-In-Means Model | 0.874 | 9 | 2 |
| 2 | Peer effect analysis with latent processes | 0.405 | 1 | 1 |