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«Douglas Harris Tim R. Sass Dept. of Educational Leadership & Policy Studies Dept. of Economics Florida State University Florida State University ...»

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C. Differing Controls for Student Characteristics Table 6A presents estimates of the restricted value-added model with three alternative measures of student heterogeneity: time-invariant student characteristics24, student fixed effects and student random effects. Similar to the results for time-invariant teacher characteristics, we find the use of covariates rather than fixed effects to capture student heterogeneity greatly alters the estimated impacts of time-varying teacher characteristics. Just as when teacher covariates are employed, using student covariates rather than fixed effects suggests that teacher experience significantly influences student outcomes whereas the impact of experience vanishes when student fixed effects are included in the model. This suggests that unmeasured student ability is correlated with both measured teacher characteristics (eg. experience, professional development) and unmeasured teacher attributes (eg. pre-service ability and training), as one would expect if students are not randomly assigned to teachers. Similarly, Aaronson, Barrow, and Sander (2003) easily reject student covariates as a substitute for individual (fixed) student effects.

The third column of Table 6A presents estimates of the gain-score model when student random effects are used to capture student heterogeneity. The results are strikingly similar to those from the model with student covariates and quite different from those from the studentfixed effects model. The fourth column presents the difference between the coefficients from the fixed and random effects models. A Hausman test on the model parameters (other than the student/teacher/school effects) yields a chi-squared value of 189.76 with 29 degrees of freedom.

Thus we can clearly reject the null hypothesis that random effects are uncorrelated with the explanatory variables in the model at better than a 99 percent confidence level. Thus our findings indicate that the random effects estimator produces inconsistent parameter estimates in The measured student characteristics are race/ethnicity, foreign/native born, language parents speak at home and free lunch status.

the context of a gain-score model. This is a significant finding given the extensive use of hierarchical linear modeling (HLM) which use random effects for both students and teachers.

Our results suggest that these models may suffer from considerable bias.

The differences between the fixed and random effects estimators are mirrored in the correlation matrices presented in Table 6B. The estimated teacher fixed effects vary substantially with how student heterogeneity is modeled. The correlation between the estimated teacher effects from the two models is only 0.39. Given that the student fixed effects estimator is always consistent, the low correlation provides further evidence that the random effects specification produces inconsistent parameter estimates.

D. Data Aggregation Table 7 presents evidence on the effects of data aggregation. Both columns in Table 7 provide estimates of gain-score models that include student fixed effects. The results in the first column are from a model which measures the characteristics of individual teachers and which includes teacher and school fixed effects. The second column presents estimates from a model that uses grade-by-school-by-year average teacher characteristics instead of the characteristics of specific teachers and employs school-by-year and grade-by-school fixed effects (rather than student and school fixed effects), similar to Rivkin, Hanushek and Kain (2005). The estimates from the aggregate and disaggregate models are similar in many respects, though the two models differ in the estimated impacts of teacher professional development. The aggregate model finds contemporaneous total professional development hours to have a positive impact on student achievement and lagged total professional development to have no effect. In contrast, estimates from the disaggregated model indicates that contemporaneous total professional development hours are statistically insignificant and lagged hours have are negatively correlated with student achievement gains. Likewise, twice-lagged content-based professional development for teachers is found to boost test scores in the disaggregated model but not in the aggregate model.

V. Conclusion Past research on value-added modeling has been significantly hampered by data limitations, which, in turn, has forced researchers to estimate mis-specified models. The data we use from Florida avoid these limitations and allow for thorough testing of model assumptions and their impact on estimates.

Our results suggest that student and teacher heterogeneity are the most important issues that value-added models must contend with. We confirm the finding of past studies that covariates are inadequate replacements for individual student and teacher effects. Moreover, random effects models yield inconsistent estimates of model parameters due to correlation between the random effects and explanatory variables in the model. The biases introduced by covariate and random effects models extend both to the estimates of the unobserved teacher quality and the effects of time-varying teacher characteristics (experience and professional development) on student achievement.

We also reject the exclusion of individual school effects. There is a low correlation between individual teacher effects from models with and without school effects, suggesting that estimated teacher effects partly reflect the influence of school-wide inputs when school effects are omitted.





The modeling of students’ peers and other non-teacher classroom-level factors appear to have relatively little impact on the estimated effects of teacher quality. The same is true of the modeling of lagged school inputs. We also find that the assumed persistence of educational inputs makes little difference, suggesting the choice between simple gain-score models and unrestricted value-added models, may not be very important. We also find that prior test scores serve as a sufficient statistic for past educational inputs, indicating one can utilize value-added models rather than the more cumbersome cumulative models of achievement.

These results have significant implications for both educational research and policy.

First, the importance of individual fixed effects calls into question the common assumptions made by educational researchers who use HLM analysis. This includes the current accountability systems in Dallas and Tennessee which are also based on an HLM framework.

But perhaps the most significant problems in using value-added models for accountability are that school effects appear to play an important role and that teachers are non-randomly assigned to schools. The first finding implies that, if school effects are excluded from the models, then the teacher effects are biased and capture factors that appear to be outside the control of the teachers.

However, the second fact means that, if the school effects are included in the models, then it is possible only to compare teachers within schools, which may create unproductive competition between teachers. Thus, there appears to be a fundamental trade-off between these two approaches for the purposes of accountability.

The implications of our results for research on teacher quality are somewhat clearer. By testing the assumptions of past models, we have narrowed the range of justifiable models as well as the data requirements that must be met in order to estimate them. Given the coming expansion of standardized testing and improved database capabilities, the importance of understanding value-added modeling will only continue to grow.

–  –  –

Arcidiacono, Peter, Gigi Foster, Natalie Goodpaster and Josh Kinsler (2005). “Estimating Spillovers in the Classroom with Panel Data,” unpublished manuscript.

Andrews, Martyn, Thorsten Schank and Richard Upward, "Practical Estimation Methods for Linked Employer-Employee Data," unpublished manuscript (2004).

Aaronson, Daniel, Lisa Barrow, and William Sander, “Teachers and Student Achievement in the Chicago Public High Schools,” unpublished manuscript (2003).

Arellano, Manuel, and Stephen Bond. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58 (1991), 277-297.

Ballou, Dale, “Rejoinder,” Journal of Educational and Behavioral Statistics, 29:1 (2004), 131Ballou, Dale, William Sanders, and Paul Wright “Controlling for Student Background in ValueAdded Assessment of Teachers,” Journal of Educational and Behavioral Statistics, 29:1

(2004), 37-65.

Boardman, Anthony E., and Richard J. Murnane, “Using Panel Data to Improve Estimates of the Determinants of Educational Achievement,” Sociology of Education, 52 (1979), 113-121.

Bonesr nning, Hans, “The Determinants of Parental Effort in Education Production: Do Parents Respond to Changes in Class Size?,” Economics of Education Review, 23 (2004), 1-9.

Burke, Mary A., and Tim R. Sass, “Classroom Peer Effects and Student Achievement,” unpublished manuscript (2004).

Clotfelter, Charles T., Helen F. Ladd, and Jacob L. Vigdor, “Teacher-Student Matching and the Assessment of Teacher Effectiveness,” unpublished manuscript (2005).

Cooley, Jane, “Desegregation and the Achievement Gap: Do Diverse Peers Help?,” unpublished manuscript (2005).

Dee, Thomas S., “Teachers, Race and Student Achievement in a Randomized Experiment,” Review of Economics and Statistics, 86:1 (2004), 195-210.

Ding, Weili, and Steven F. Lehrer, “Accounting for Unobserved Ability Heterogeneity within Education Production Functions,” unpublished manuscript (2005).

Figlio, David N., “Functional Form and the Estimated Effects of School Resources,” Economics of Education Review, 18 (1999), 241-252.

Goldhaber, Dan, and Emily Anthony, “Can Teacher Quality be Effectively Assessed?,” unpublished manuscript (2004).

Goldhaber, Dan D., and Dominic J. Brewer, “Why Don’t Schools and Teachers Seem to Matter?

Assessing the Impact of Unobservables on Educational Productivity,” Journal of Human Resources, 32:3 (1997), 505-523.

Grunfeld, Yehuda and Zvi Griliches, “Is Aggregation Necessarily a Bad Thing,” Review of Economics and Statistics, 42 (1960), 1-13.

Hanushek, Eric A., “The Trade-off Between Child Quantity and Quality,” Journal of Political Economy, 100:1 (1992), 84-117.

Hanushek, Eric A., Steven G. Rivkin, and Lori L. Taylor, “Aggregation and the Estimated Effects of School Resources,” Review of Economics and Statistics, 78:4 (1996), 611-627.

Harris, Douglas and Tim R. Sass, “The Effects of Teacher Training on Teacher Value Added,” unpublished manuscript (2006).

Houtenville, Andrew J. and Karen S. Conway, “Parental Effort, School Resources and Student Achievement: Why Money May Not 'Matter',” unpublished manuscript (2003).

McCaffrey, Daniel F., J.R. Lockwood, Thomas A. Louis, and Laura Hamilton,. (2004). “Models for Value-Added Modeling of Teacher Effects,” Journal of Educational and Behavioral Statistics, 29:1 (2004), 67-101.

Mendro, Robert L., “Student Achievement and School and Teacher Accountability,” Journal of Personnel Evaluation in Education, 12:3 (1998), 257-267.

Nye, Barbara, Spyros Konstantopoulos, and Larry V. Hedges, “How Large are Teacher Effects?,” Educational Evaluation and Policy Analysis, 26:3 (2004), 237-257.

Raundenbush, Stephen W., “What are Value-Added Models Estimating and What Does This

Imply for Statistical Practice?,” Journal of Educational and Behavioral Statistics, 29:1

(2004), 121-129.

Rivkin, Steven G., Eric A. Hanushek, and John F. Kain, “Teachers, Schools and Academic Achievement,” Econometrica, 73:2 (2005), 417-458.

Rockoff, Jonah E., “The Impact of Individual Teachers on Student Achievement: Evidence from Panel Data,” American Economic Review, 94:2 (2004), 247-252.

Rowan, Brian, Richard Correnti, and Robert J. Miller, “What Large-Scale, Survey Results tell us About Teacher Effects on Student Achievement: Insights from the Prospects Study of Elementary schools,” Teachers College Record, 104:8 (2002), 1525-1567.

Sanders, William L., and Sandra P. Horn, “Research Findings From the Tennessee Value-Added Assessment System (TVAAS) Database: Implications for Educational Evaluation and Research,” Journal of Personnel Evaluation in Education, 12:3 (1998), 247-256.

Sass, Tim R., “Charter Schools and Student Achievement in Florida,” Education Finance and Policy, 1:1 (2006), 91-122.

Todd, Petra E. and Kenneth I. Wolpin, “On the Specification and Estimation of the Production Function for Cognitive Achievement,” The Economic Journal, 113 (2003), F3-F33.

Todd, Petra E., and Kenneth I. Wolpin, “The Production of Cognitive Achievement in Children:

Home, School and Racial Test Score Gaps,” unpublished manuscript (2005).

Verbeke, Geert, and Emmanuel Lesaffre, “A Linear Mixed-Effects Model with Heterogeneity in the Random-Effects Population,” Journal of the American Statistical Association, 91:433 (1996), 217-221.

Wright, S. Paul, Sandra P. Horn, and William L. Sanders, “Teacher and Classroom Context Effects on Student Achievement: Implications for Teacher Evaluation,” Journal of Personnel Evaluation in Education, 11 (1997), 57-67.

–  –  –

Number of Students (after first differencing) 7,816 7,816 Number of Observations (after first differencing) 10,329 10,329  Models are estimated using the Arellano and Bond dynamic panel data estimator. Models include the following time varying student/class characteristics: number of schools attended by the student in the current year, “structural” move by student, “non-structural” move by student, indicator of a student repeating a grade, class size, fraction of classroom peers who are female, fraction of classroom peers who are black, average age (in months) of classroom peers, fraction of classroom peers who changed schools, fraction of classroom peers who made a “structural move.” All models also include year, grade level, and repeater-by-grade dummies. Absolute values of t-statistics appear in parentheses. * indicates statistical significance at the.10 level and ** indicates significance at the.05 level and *** indicates significance at the.01 level in a two-tailed test.

–  –  –

age (in months) of classroom peers, fraction of classroom peers who changed schools, fraction of classroom peers who made a “structural move.” All models also include year, grade level, and repeater-by-grade dummies.

Absolute values of t-statistics appear in parentheses. * indicates statistical significance at the.10 level and ** indicates significance at the.05 level and *** indicates significance at the.01 level in a two-tailed test.

–  –  –

Absolute values of t-statistics appear in parentheses. * indicates statistical significance at the.10 level and ** indicates significance at the.05 level and *** indicates significance at the.01 level in a two-tailed test.

–  –  –

Models include the following time varying student/class characteristics: number of schools attended by the student in the current year, “structural” move by student, “non-structural” move by student, indicator of a student repeating a grade.” All models also include year, grade level, and repeater-by-grade dummies. Absolute values of t-statistics appear in parentheses. * indicates statistical significance at the.10 level and ** indicates significance at the.05 level and *** indicates significance at the.01 level in a two-tailed test.

–  –  –

a grade, class size, fraction of classroom peers who are female, fraction of classroom peers who are black, average age (in months) of classroom peers, fraction of classroom peers who changed schools, fraction of classroom peers who made a “structural move.” All models also include year, grade level, and repeater-by-grade dummies.

Absolute values of t-statistics appear in parentheses. * indicates statistical significance at the.10 level and ** indicates significance at the.05 level and *** indicates significance at the.01 level in a two-tailed test.

–  –  –

a grade, class size, fraction of classroom peers who are female, fraction of classroom peers who are black, average age (in months) of classroom peers, fraction of classroom peers who changed schools, fraction of classroom peers who made a “structural move.” All models also include repeater-by-grade dummies. Absolute values of t-statistics appear in parentheses. * indicates statistical significance at the.10 level and ** indicates significance at the.05

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