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We study whether reallocating existing teachers across schools within a district can increase student achievement, and what policies would help achieve these gains. Using a model of multi-dimensional value-added, we find meaningful achievement gains from reallocating teachers within a district. Using an estimated equilibrium model of the teacher labor market, we find that achieving most of these gains requires directly affecting teachers' preferences over schools. In contrast, directly affecting principals' selection of teachers can lower student achievement. Our analysis highlights the importance of equilibrium and second-best reasoning in analyzing teacher labor market policies.