Introducing Capybara: Fast and Memory Efficient Fitting of Linear Models With High-Dimensional Fixed Effects

R

Statistics

Linear models

C++

Short demonstration.

Author

Mauricio “Pachá” Vargas S.

Published

January 19, 2024

About

Capybara is a fast and small footprint software that provides efficient functions for demeaning variables before conducting a GLM estimation via Iteratively Weighted Least Squares (IWLS). This technique is particularly useful when estimating linear models with multiple group fixed effects.

The software can estimate GLMs from the Exponential Family and also Negative Binomial models but the focus will be the Poisson estimator because it is the one used for structural counterfactual analysis in International Trade. It is relevant to add that the IWLS estimator is equivalent with the PPML estimator from Santos-Silva et al. 2006

Traditional QR estimation can be unfeasible due to additional memory requirements. The method, which is based on Halperin 1962 article on vector projections offers important time and memory savings without compromising numerical stability in the estimation process.

The software heavily borrows from Gaure 20213 and Stammann 2018 works on the OLS and IWLS estimator with large k-way fixed effects (i.e., the Lfe and Alpaca packages). The differences are that Capybara uses an elementary approach and uses a minimal C++ code without parallelization, which achieves very good results considering its simplicity. I hope it is east to maintain.

The summary tables are nothing like R’s default and borrow from the Broom package and Stata outputs. The default summary from this package is a Markdown table that you can insert in RMarkdown/Quarto or copy and paste to Jupyter.

Demo

Estimating the coefficients of a gravity model with importer-time and exporter-time fixed effects.