$L_2$Boosting for Economic Applications

摘要

In the recent years more and more high-dimensional data sets, where thenumber of parameters $p$ is high compared to the number of observations $n$ oreven larger, are available for applied researchers. Boosting algorithmsrepresent one of the major advances in machine learning and statistics inrecent years and are suitable for the analysis of such data sets. While Lassohas been applied very successfully for high-dimensional data sets in Economics,boosting has been underutilized in this field, although it has been proven verypowerful in fields like Biostatistics and Pattern Recognition. We attributethis to missing theoretical results for boosting. The goal of this paper is tofill this gap and show that boosting is a competitive method for inference of atreatment effect or instrumental variable (IV) estimation in a high-dimensionalsetting. First, we present the $L_2$Boosting with componentwise least squaresalgorithm and variants which are tailored for regression problems which are theworkhorse for most Econometric problems. Then we show how $L_2$Boosting can beused for estimation of treatment effects and IV estimation. We highlight themethods and illustrate them with simulations and empirical examples. Forfurther results and technical details we refer to Luo and Spindler (2016, 2017)and to the online supplement of the paper.