Beyond Levels and Growth

Note: Results are averages across 250 simulations. Standard deviations across the simulations are included in parentheses. True parameter values are included in brackets. is the estimated variation in teacher quality across all grades. Data generation for the Monte Carlos is described in detail in Section IIIC. The three panels of results reflect three different underlying data generating processes. All models include unobserved student ability and unobserved teacher ability in addition to the parameters listed in the table. Across all three models, the average, median, and minimum number of student observations per teacher are approximately 31, 20, and 9. Estimation follows the procedures discussed in Section IIIB.

Note: Sample is constructed using cohorts of North Carolina third grade students who enter between 1998 and 2005. Sample selection is discussed in Section IV. Overall, close to three-quarters of the entire universe of students who ever attend third through fifth grade between 1998 and 2007 are included. Math and reading end-of-grade exams are available at the end of third, fourth, and fifth grade. In addition, a pretest score is available from the beginning of third grade. Scores are normalized using the means and standard deviations of test scores in standard setting years as suggested by the North Carolina Department of Instruction. Observations per Teacher indicate the number of student test scores associated with a particular teacher. Graduate degree is an indicator that a teacher received any advanced degree. Repeat is an indicator that a student is repeating the current grade. Transfers indicate that the student is new to the current school.

Note: Sample is constructed using cohorts of North Carolina third grade students who enter between 1998 and 2005. Sample selection is discussed in Section IV. Overall, close to three-quarters of the entire universe of students who ever attend third through fifth grade between 1998 and 2007 are included. Math and reading end-of-grade exams are available at the end of third, fourth, and fifth grade. In addition, a pretest score is available from the beginning of third grade. Scores are normalized using the means and standard deviations of test scores in standard setting years as suggested by the North Carolina Department of Instruction. The standard deviations within each section are taken with respect to the group identified in the heading. Note that the population standard deviation of the third grade score does not equal exactly the population standard deviation of the lag score using the fourth grade assignment. This simply reflects that not every individual observed in third grade is also observed in fourth grade.

Note: Sample is constructed using cohorts of North Carolina third grade students who enter between 1998 and 2005. Sample selection is discussed in Section IV. Overall, close to three-quarters of the entire universe of students who ever attend third through fifth grade between 1998 and 2007 are included. Math and reading end-of-grade exams are available at the end of third, fourth, and fifth grade. In addition a pretest score is available from the beginning of third grade. Scores are normalized using the means and standard deviations of test scores in standard setting years as suggested by the North Carolina Department of Instruction. The dependent variable is the normalized end of grade math or reading test score. The explanatory variables are unobserved student and teacher ability. In the accumulation model the rate at which past teacher inputs persist is estimated. is the estimated variation in teacher value-added across all grades, while , for example, is the estimated variance of teacher value-added among only third grade teachers. Standard errors are obtained through bootstrap.

Note: See previous table notes for sample information and Sections IIIB1 and IIIB2 for model details. is the estimated variation in teacher value-added across all grades. Standard errors obtained by bootstrap.