Studying peer effects in language is critical because they often reflect behavioral and personality traits that are important determinants of economic outcomes. However, language is unstructured, non-numeric, and high-dimensional. We combine Large Language Model (LLM) embeddings with structural econometric identification to provide a unified framework for identifying peer effects in language. This unified framework is applied to 80,000-120,000 written exchanges among residents of low security correctional facilities. The LLM language profiles predict three-year recidivism 30\% more accurately than pre-entry covariates alone, showing that text representations capture meaningful signals. We analyze peer effects on multidimensional language embeddings while addressing network endogeneity. We develop novel instrumental variable estimators for peer effects that accommodate multivariate outcomes, sparse networks, and multidimensional latent variables. Our methods achieve root-N consistency and asymptotic normality under realistic sparsity conditions, relaxing the dense-network assumption. Results reveal significant peer effects in residents' language profiles.

翻译：研究语言中的同伴效应至关重要，因为这些效应往往反映了作为经济结果重要决定因素的行为与人格特质。然而，语言具有非结构化、非数值化及高维度的特性。本研究将大型语言模型（LLM）嵌入与结构计量识别方法相结合，提出了一个识别语言中同伴效应的统一框架。该框架被应用于低安全级别惩教机构居民之间8万至12万条书面交流记录。LLM语言画像对三年内再犯率的预测准确度比仅使用入狱前协变量高出30%，表明文本表征能够捕捉有意义的信号。我们在处理网络内生性的同时，分析了同伴效应对多维语言嵌入的影响。我们开发了适用于多元结果、稀疏网络及多维潜变量的新型同伴效应工具变量估计量。我们的方法在现实稀疏性条件下实现了根号N一致性与渐近正态性，从而放宽了对稠密网络假设的要求。研究结果揭示了居民语言画像中存在显著的同伴效应。