Random Effects and Fixed Effects Value-Added Equivalence

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In Simple Words

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.

Research question

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.

Participants

Multi-district administrative panel data across 6 urban public school districts.

Study Design

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.

Results

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.

Takeaway

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.

Source and citation

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Plain-English glossary

Original explanations, informed by the references below. Examples are illustrations, not data from the studies above. The research text stays unchanged.

Baseline

The starting measurements in a study. Researchers use these to compare what participants were like at the start with what happens later.

ExampleBefore a training programme starts, researchers measure workers’ earnings. That first measurement is the baseline.

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