Testing for Peer Effects in Heteroskedastic Fixed-Effects Panels
Abstract
We study testing for peer effects in linear panel models with individual and time fixed effects when the interaction network is unspecified. We propose a quadratic-form test based on the Gram matrix of residualized peer covariates. A key difficulty is that fixed-effects removal and nuisance estimation destroy the centering of a conventional leave-diagonal-out quadratic form under conditional heteroskedasticity. We introduce a leverage adjustment that restores exact conditional centering and combine it with a residual-based variance estimator. The resulting studentized statistic is asymptotically standard normal as both panel dimensions diverge, without imposing any restriction on their relative growth rates. Under additional conditions, we establish consistency against alternatives. The null theory is further extended to covariates that are weakly dependent over time; the same studentization remains valid without an additional long-run variance estimator. Monte Carlo experiments evaluate the finite-sample size and power of the proposed test across different settings and demonstrate its favorable performance relative to the existing benchmark test. Applications to state tax competition and growth spillovers among OECD countries illustrate the practical relevance in testing for peer effects without specifying the interaction network.
Related
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BibTeX
@misc{cai2026testing,
title = {{Testing for Peer Effects in Heteroskedastic Fixed-Effects Panels}},
author = {Leheng Cai and Weijia Li and Xu Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20045},
eprint = {2610.20045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20045},
}
RIS
TY - UNPB
TI - Testing for Peer Effects in Heteroskedastic Fixed-Effects Panels
AU - Leheng Cai
AU - Weijia Li
AU - Xu Guo
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20045
UR - https://arxiv.org/abs/2610.20045
AB - We study testing for peer effects in linear panel models with individual and time fixed effects when the interaction network is unspecified. We propose a quadratic-form test based on the Gram matrix of residualized peer covariates. A key difficulty is that fixed-effects removal and nuisance estimation destroy the centering of a conventional leave-diagonal-out quadratic form under conditional heteroskedasticity. We introduce a leverage adjustment that restores exact conditional centering and combine it with a residual-based variance estimator. The resulting studentized statistic is asymptotically standard normal as both panel dimensions diverge, without imposing any restriction on their relative growth rates. Under additional conditions, we establish consistency against alternatives. The null theory is further extended to covariates that are weakly dependent over time; the same studentization remains valid without an additional long-run variance estimator. Monte Carlo experiments evaluate the finite-sample size and power of the proposed test across different settings and demonstrate its favorable performance relative to the existing benchmark test. Applications to state tax competition and growth spillovers among OECD countries illustrate the practical relevance in testing for peer effects without specifying the interaction network.
ER -