Research on modelling peer effects has predominantly relied on linear-in-means models. However, averaging peer responses prevents these models from capturing the effects of extreme peer behavior. To address this limitation, we propose a quantile social autoregressive model based on a novel quantile social norm, which uses empirical quantiles of peer responses. By treating the quantile level as an unknown parameter estimated directly from the data, our approach identifies which segment of the peer response distribution most strongly influences individual behavior. To estimate the model, we introduce new moment conditions using pseudo-response instruments. Because the quantile social norm is nonsmooth, we apply kernel smoothing to the instruments and residuals, ensuring valid statistical inference. Additionally, we establish equilibrium existence and uniqueness and derive the identification conditions. Furthermore, we prove the consistency and asymptotic normality of our proposed estimator. Finally, Monte Carlo experiments examine the finite-sample performance of the estimator, and an empirical application illustrates the interpretation of the estimated quantile levels and their corresponding peer effects.

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