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We present the L2Boosting algorithm and two variants, namely post-Boosting and orthogonal Boosting. Building on results in Ye and Spindler (2016), we demonstrate how boosting can be used for estimation and inference of low-dimensional treatment effects. In particular, we consider estimation of a treatment effect in a setting with very many controls and in a setting with very many instruments. We provide simulations and analyze two real applications. We compare the results with Lasso and find that boosting performs quite well. This encourages further use of boosting for estimation of treatment effects in high-dimensional settings.

Survey scientists increasingly face the problem of high-dimensionality in their research as digitization makes it much easier to construct high-dimensional (or "big") data sets through tools such as online surveys and mobile applications. Machine learning methods are able to handle such data, and they have been successfully applied to solve predictive problems. However, in many situations, survey statisticians want to learn about causal relationships to draw conclusions and be able to transfer the findings of one survey to another. Standard machine learning methods provide biased estimates of such relationships. We introduce into survey statistics the double machine learning approach, which gives approximately unbiased estimators of parameters of interest, and show how it can be used to analyze survey nonresponse in a high-dimensional panel setting. The double machine learning approach here assumes unconfoundedness of variables as its identification strategy. In high-dimensional settings, where the number of potential confounders to include in the model is too large, the double machine learning approach secures valid inference by selecting the relevant confounding variables.

We consider estimation of and inference about coefficients on endogenous variables in a linear instrumental variables model where the number of instruments and exogenous control variables are each allowed to be larger than the sample size. We work within an approximately sparse framework that maintains that the signal available in the instruments and control variables may be effectively captured by a small number of the available variables. We provide a LASSO-based method for this setting which provides uniformly valid inference about the coefficients on endogenous variables. We illustrate the method through an application to demand estimation.