This online appendix provides detailed methods and results for the study "Measuring the Impacts of Teachers I: Evaluating Bias in Teacher Value-added Estimates." The paper evaluates the bias in teacher value-added (VA) estimates, focusing on both forecast bias and teacher-level bias. The methods described here are used to estimate VA, assess bias, and match student data to tax records. The VA estimation process involves three main steps: residualizing test scores, estimating variance components, and constructing VA estimates. Residualization involves removing the effects of student and classroom characteristics from test scores. Variance components are estimated to account for the variability in test scores across students, classrooms, and teachers. VA estimates are then constructed using these variance components and the best linear predictor of teacher quality. The paper also defines and analyzes teacher-level bias, which occurs when VA estimates are systematically biased due to estimation errors. It shows that forecast bias and teacher-level bias are related, and that forecast-unbiased VA estimates can still exhibit teacher-level bias under certain conditions. The matching algorithm used to link school district data to tax records is described, including steps for matching by date of birth, gender, last name, first name, ZIP code, and place of birth. The algorithm is designed to minimize selection bias and ensure accurate matches. The paper also assesses the unconditional sorting of students to teachers based on observable characteristics. It finds that high VA teachers are not systematically assigned to certain types of students, and that the relationship between teacher VA and student characteristics is small. Finally, the paper presents a quasi-experimental estimator of forecast bias, showing that OLS estimation of a specific equation identifies the degree of forecast bias under certain assumptions. The results suggest that teacher quality contributes only a small portion of the achievement gap by family income.This online appendix provides detailed methods and results for the study "Measuring the Impacts of Teachers I: Evaluating Bias in Teacher Value-added Estimates." The paper evaluates the bias in teacher value-added (VA) estimates, focusing on both forecast bias and teacher-level bias. The methods described here are used to estimate VA, assess bias, and match student data to tax records. The VA estimation process involves three main steps: residualizing test scores, estimating variance components, and constructing VA estimates. Residualization involves removing the effects of student and classroom characteristics from test scores. Variance components are estimated to account for the variability in test scores across students, classrooms, and teachers. VA estimates are then constructed using these variance components and the best linear predictor of teacher quality. The paper also defines and analyzes teacher-level bias, which occurs when VA estimates are systematically biased due to estimation errors. It shows that forecast bias and teacher-level bias are related, and that forecast-unbiased VA estimates can still exhibit teacher-level bias under certain conditions. The matching algorithm used to link school district data to tax records is described, including steps for matching by date of birth, gender, last name, first name, ZIP code, and place of birth. The algorithm is designed to minimize selection bias and ensure accurate matches. The paper also assesses the unconditional sorting of students to teachers based on observable characteristics. It finds that high VA teachers are not systematically assigned to certain types of students, and that the relationship between teacher VA and student characteristics is small. Finally, the paper presents a quasi-experimental estimator of forecast bias, showing that OLS estimation of a specific equation identifies the degree of forecast bias under certain assumptions. The results suggest that teacher quality contributes only a small portion of the achievement gap by family income.