Random Effects and Fixed Effects Value-Added Equivalence
Observational StudyReview
Researchers and school districts often debate whether to estimate teacher value-added using teacher fixed-effects models or random-effects residual-averaging models, fearing that specification choices could distort teacher rankings.
Picture this
Calculating an athlete's average score by either taking a simple average of their individual race deviations or fitting a complex model that holds all racers constant yields virtually the same performance rank, because most score variation occurs between individual runners rather than between whole race events.
What the evidence says
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.
- Who was studied
- Multi-district administrative panel data across 6 urban public school districts.
- How
- Comparative empirical specification analysis contrasting two-step residual-averaging random-effects models (controlling for section-average baseline scores per Mundlak, 1978) against teacher fixed-effects models.
What to do
Deploy two-step residual-averaging random-effects value-added models with classroom-mean controls as a computationally efficient and statistically equivalent alternative to teacher fixed-effects models.
From the source
"In unpublished work, we have found such a specification yielded value-added estimates that are highly correlated to those from a teacher fixed effects specification, since the lion's share of the variation in student characteristics is within classroom as opposed to between classrooms (Ehlert et al., under review, report similar results with data in Missouri)."
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