Aggregate versus Disaggregate Data in Measuring School Quality

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OLS 101.94 62.86 Variance Estimates Dis. Within Sch. 0.560 0.008 Dis. Between Sch. 0.070 0.012 Agg.Within Sch. 0.556 0.444 Agg Between Sch. 0.067 0.015 Note: Results are for 1000 simulations, each including 100 schools. The number of students per school is a lognormal random variable with mean 120 and variance 50000. Mean is the average over all simulations, RMSE is root mean squared error, Top Ten is the average number of schools ranked in the top ten with the estimator, that belong to the true top ten set. Estimators compared are the disaggregate estimator, its standardized version, the aggregate estimator, its standardized version, and the OLS estimator of school effects. Variance estimates are also presented for the disaggregate and aggregate methods. 1
Table 2. Estimates of school quality using aggregate vs. disaggregate data with measurement error. Measure Type of estimator Mean Std.Dev. Spearman Disaggregate 0.8557 0.0321 Std. disaggregate 0.8503 0.0347 Aggregate 0.8581 0.0326 Std. aggregate 0.8544 0.0347 OLS 0.8423 0.0389 RMSE Disaggregate 0.1324 0.0130 Std. disaggregate 0.5283 0.0552 Aggregate 0.1364 0.0164 Std. aggregate 0.5248 0.0567 OLS 0.1667 0.0278 Top Ten Disaggregate 6.50 1.197 Std. disaggregate 6.45 1.188 Aggregate 6.48 1.235 Std. aggregate 6.53 1.185 OLS 6.29 1.188 School Size Avg. Real Group 116.36 64.52 In Top Ten Group Disaggregate 137.19 68.01 Std. disaggregate 116.00 64.28 Aggregate 141.90 73.20 Std. aggregate 117.93 65.74 2
Page 1 and 2: Aggregate versus Disaggregate Data
Page 3 and 4: Aggregate versus Disaggregate Data
Page 5 and 6: Another problem with using aggregat
Page 7 and 8: iefly here. However, little effort
Page 9 and 10: and dividing by the number of stude
Page 11 and 12: 2 4 −1 ' −1 ' −1 (7) Cov( u |
Page 13 and 14: y V a . Following a procedure analo
Page 15 and 16: equation (2). Then measurement erro
Page 17 and 18: is 1 2 2 σ u + σ e / n ) such as
Page 19 and 20: Results show that when many small s
Page 21 and 22: References Clotfelter, C. T., & Lad
Page 23: Table 1. Estimates of school qualit
Page 27 and 28: Table 3. Estimates of school qualit
Page 29 and 30: Table 4. Estimates of school qualit
Page 31 and 32: Appendix Derivation of the aggregat
Page 33: 2 ⎡u⎤ ⎛ ⎡ ⎜ ⎡0 ⎤ σ u

Aggregate versus Disaggregate Data in Measuring School Quality

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