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.

Financial-market risk, commonly measured in terms of asset-return volatility, plays a fundamental role in investment decisions, risk management and regulation. In this paper, we investigate a new modeling strategy that helps to better understand the forces that drive market risk. We use componentwise gradient boosting techniques to identify financial and macroeconomic factors influencing volatility and to assess the specific nature of their influence. Componentwise boosting is capable of producing parsimonious models from a, possibly, large number of predictors and—in contrast to other related techniques—allows a straightforward interpretation of the parameter estimates. Considering a wide range of potential risk drivers, we apply boosting to derive monthly volatility predictions for the equity market represented by S&P 500 index. Comparisons with commonly-used GARCH and EGARCH benchmark models show that our approach substantially improves out-of-sample volatility forecasts for short- and longer-run horizons. The results indicate that risk drivers affect future volatility in a nonlinear fashion.

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.