reghdfe: Estimating linear models with multi-way fixed effects

In this presentation, I describe a novel estimator for linear models with multiple levels of fixed effects. I first show that solving the two-way fixed effects model is equivalent to solving a linear system on a graph, and exploit recent advances in graph theory (Kelner et al, 2013) to propose a nearly-linear time estimator. Second, I embed the estimator into an improved version of the one by Guimarães and Portugal (2010) and Gaure (2013). This new estimator performs particularly well with large datasets and high-dimensional fixed effects, and can be also used as a building block of multiple nonlinear models. Finally, I introduce the reghdfe package, which applies this estimator and extends it to instrumental-variable and linear GMM regressions.