Capybara: Efficient estimation of generalized linear models with high-dimensional fixed effects

Abstract

This paper introduces capybara, an R package implementing computationally efficient algorithms for estimating generalized linear models (GLMs) with high-dimensional fixed effects. Building on Stammann (2018), we combine the Frisch-Waugh-Lovell (FWL) theorem with alternating projections to achieve memory-efficient estimation. Our benchmarks demonstrate that capybara reduces computation time by 95-99% compared to traditional dummy variable approaches while maintaining numerical accuracy to 5 decimal places. For a complex gravity model with 28,000 observations and 3,200 fixed effects, capybara completes estimation in just 6 seconds using 33 MB of memory, compared to 11 minutes and 12 GB with base R. The package is particularly valuable for trade economics, labor economics, and other applications requiring multiple high-dimensional fixed effects to control for unobserved heterogeneity, making previously infeasible models computationally tractable on standard hardware.