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The incremental component removed by controlling for student demographic characteristics yielded an IV coefficient of -0.025 (SE = 0.521), demonstrating that removing demographic variables does not significantly alter post-randomization outcome predictions, though large standard errors leave the policy trade-off statistically imprecise.
The component removed by peer effect controls predicted student achievement after random assignment with a coefficient of 1.150 (p < 0.01, SE = 0.336), proving it contains causal teacher effectiveness. In contrast, the component removed by individual baseline score controls yielded a coefficient of 0.047 (SE = 0.042), showing baseline score controls successfully remove non-teacher sorting noise.
Prior to randomization, the within-school standard deviation of teacher mean baseline math scores was 0.382 to 0.520. Evaluating instructors using unadjusted end-of-year student test scores yielded a severely biased predictive coefficient of 0.228 (SE = 0.042), significantly overstating true instructor impact.
Averaging student residuals provided an unbiased baseline-adjusted measure of teacher performance that, when combined with shrinkage adjustments, predicted post-randomization achievement gains with an IV slope of 0.955 (SE = 0.123).
Unadjusted end-of-year score ratings yielded a predictive coefficient of 0.228 (p < 0.01, SE = 0.042), significantly overstating true teacher effectiveness differences compared to baseline-adjusted growth models (coefficient = 0.955).
Teacher effect estimates generated from random-effects specifications controlling for classroom section-mean covariates are highly correlated with teacher fixed-effects specifications because the vast majority of student baseline variance exists within classrooms rather than between classrooms.