Table 4:

Standard deviation of Bayesian shrunken estimated teacher effects

	Grade 4			Grade 5
Model specification:	Height	Math	ELA	Height	Math	ELA
A. 2-level models
RE	0.218	0.286	0.256	0.210	0.253	0.210
FE (shrunk)	0.250	0.344	0.278	0.315	0.258	0.240
RE w/school effects	0.169	0.216	0.184	0.157	0.199	0.155
FE w/school effects (shrunk)	0.166	0.202	0.172	0.160	0.189	0.145
Permutations: FE (mean ${\widehat{\sigma }}_u$ shown)	0.056	0.063	0.065	0.053	0.056	0.068
Permutations within school: FE	0.131	0.083	0.077	0.123	0.084	0.072
B. 3-level models
RE (KRS)	0.000	0.163	0.104	0.000	0.132	0.097
RE w/school effects (KRS)	0.000	0.107	0.077	0.002	0.087	0.062
RE (MLE)	0.000	0.199	0.159	0.000	0.164	0.121
RE w/school effects (MLE)	0.000	0.108	0.070	0.000	0.089	0.056
Chetty et al. drift model (RE)	0.057	0.180	0.128	0.031	0.143	0.123

Notes: For Panel A (2-level models), teacher effects were estimated in four ways: (1) assuming random teacher effects; (2) assuming fixed teacher effects and “shrinking” using the estimated signal-to-noise ratio after estimation; (3) assuming random teacher effects and including school fixed effects; and (4) assuming fixed teacher effects (shrunken after estimation) and including school effects—uses a two-stage method that regresses the outcome on covariates and school fixed effects and then uses the residuals to estimate the teacher fixed effects. For the random permutations we report the mean estimated standard deviation across 499 permutations of students to teachers. For Panel B (3-level models), we used the shrunken residual method from Kane, Rockoff, and Staiger (2008; KRS), or a random effects model with both teacher and classroom variance components (MLE). The last line of Panel B reports the standard deviation in best linear predictors from the teacher effects model with drift used in Chetty et al. (2014a).