A Novel Grouped-Gram-Based Algorithm for Fast and Memory-Efficient Fixed Effects Estimation
Keywords:
- Fixed effects,
- Panel data,
- Grouped Gram matrix,
- Within transformation,
- Computational econometrics,
- Memory-efficient algorithms,
- Estimation in high-dimensional models
Abstract
Fixed effects models often rely on the within transformation, which constructs demeaned arrays prior to forming cross-products. This paper develops an estimator that avoids the formation of demeaned arrays by exploiting grouped summaries built from per-unit sufficient statistics. A complete derivation shows that the grouped Gram representation reproduces the classical estimator exactly. The difference lies in memory access patterns and byte movement. The grouped estimator concentrates operations into unit-level accumulations, avoiding the writes associated with array centering. Gains arise once the panel reaches a scale where memory traffic governs run time. Simulations examine coefficient accuracy, bootstrap dispersion, run time and memory use.
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References
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