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.