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This paper investigates the effects of competition between public and private lower-secondary schools in Mexico (2007-2014) through an equilibrium model of school choice. I specifically focus on estimating differences in teacher quality between schools and their correlation with various school and teacher characteristics. The paper contributes to three strands of literature--teacher value-added models, effects of school competition, and equilibrium models of school choice-- and extends prior models by including nationwide data and high-quality estimates of teacher fixed effects. Leveraging data from the Mexican ENLACE exam and other sources, I aim to uncover the effects of school competition on students and household sorting.