We develop and estimate a joint model of the education and teacher-expectation production functions that identifies both the distribution of biases in teacher expectations and the impact of those biases on student outcomes via self-fulfilling prophecies. The identification strategy leverages insights from the measurement-error literature and a unique feature of a nationally representative dataset: two teachers provided their educational expectations for each student. We provide novel, arguably causal evidence that teacher expectations affect students' educational attainment. Estimates suggest that the elasticity of the likelihood of college completion with respect to teachers' expectations is about 0.12. On average, teachers are overly optimistic about students' ability to complete a four-year college degree. However, the degree of over-optimism of white teachers is significantly larger for white students than for black students. This highlights a nuance that is frequently overlooked in discussions of biased beliefs: unbiased (i.e., accurate) beliefs can be counterproductive if there are positive returns to optimism or if there are socio-demographic gaps in the degree of teachers' over-optimism, both of which we find evidence of. We use the estimated model to assess the effects of two policies on black students' college completion: hiring more black teachers and "de-biasing" white teachers so that they are similarly optimistic about black and white students.