$L_2$Boosting for Economic Applications

Abstract: In the recent years more and more high-dimensional data sets, where the number of parameters $p$ is high compared to the number of observations $n$ or even larger, are available for applied researchers. Boosting algorithms represent one of the major advances in machine learning and statistics in recent years and are suitable for the analysis of such data sets. While Lasso has been applied very successfully for high-dimensional data sets in Economics, boosting has been underutilized in this field, although it has been proven very powerful in fields like Biostatistics and Pattern Recognition. We attribute this to missing theoretical results for boosting. The goal of this paper is to fill this gap and show that boosting is a competitive method for inference of a treatment effect or instrumental variable (IV) estimation in a high-dimensional setting. First, we present the $L_2$Boosting with componentwise least squares algorithm and variants which are tailored for regression problems which are the workhorse for most Econometric problems. Then we show how $L_2$Boosting can be used for estimation of treatment effects and IV estimation. We highlight the methods and illustrate them with simulations and empirical examples. For further results and technical details we refer to Luo and Spindler (2016, 2017) and to the online supplement of the paper.