arXiv:1903.01690v3 [econ.EM] 2 Aug 2019 PPMLHDFE: Fast Poisson Estimation with High-Dimensional Fixed Effects Sergio Correia 1 , Paulo Guimar˜ aes 2 , and Tom Zylkin 3 1 Federal Reserve Board, sergio.a.correia@frb.gov 2 Banco de Portugal, pfguimaraes@bportugal.pt 3 University of Richmond, tzylkin@richmond.edu August 5, 2019 Abstract In this paper we present ppmlhdfe, a new Stata command for estimation of (pseudo) Poisson regression models with multiple high-dimensional fixed effects (HDFE). Estimation is implemented using a modified version of the iteratively reweighted least-squares (IRLS) algorithm that allows for fast estimation in the presence of HDFE. Because the code is built around the reghdfe package, it has similar syntax, supports many of the same functionalities, and benefits from reghdfe’s fast convergence properties for computing high-dimensional least squares problems. Performance is further enhanced by some new techniques we introduce for accelerating HDFE-IRLS estimation specifically. ppmlhdfe also implements a novel and more robust approach to check for the existence of (pseudo) maximum likelihood estimates. Keywords: ppmlhdfe, reghdfe, Poisson regression, high-dimensional fixed-effects 1 Introduction Poisson regression is now well established as the standard approach to model count data. However, it is also gaining popularity as a viable alternative for estimation of multi- plicative models where the dependent variable is nonnegative. Commonly, these models are estimated by linear regression applied to a log-transformed dependent variable. But, as with ordinary least squares (OLS), the only assumption required for consistency of the Poisson regression estimator is the correct specification of the conditional mean of the dependent variable (Gourieroux et al., 1984). In this setting, Poisson regression becomes Poisson pseudo maximum likelihood (PPML) regression. Gourieroux et al.’s results greatly extend the realm of application of Poisson regression because there is no 1