Targeted Undersmoothing

This paper proposes a post-model selection inference procedure, called targeted undersmoothing, designed to construct uniformly valid confidence sets for a broad class of functionals of sparse high-dimensional statistical models. These include dense functionals, which may potentially depend on all elements of an unknown high-dimensional parameter. The proposed confidence sets are based on an initially selected model and two additionally selected models, an upper model and a lower model, which enlarge the initially selected model. We illustrate application of the procedure in two empirical examples. The first example considers estimation of heterogeneous treatment effects using data from the Job Training Partnership Act of 1982, and the second example looks at estimating profitability from a mailing strategy based on estimated heterogeneous treatment effects in a direct mail marketing campaign. We also provide evidence on the finite sample performance of the proposed targeted undersmoothing procedure through a series of simulation experiments

Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels

This paper provides estimation and inference methods for a large number of heterogeneous treatment effects in a panel data setting with many potential controls. We assume that heterogeneous treatment is the result of a low-dimensional base treatment interacting with many heterogeneity-relevant controls, but only a small number of these interactions have a non-zero heterogeneous effect relative to the average. The method has two stages. First, we use modern machine learning techniques to estimate the expectation functions of the outcome and base treatment given controls and take the residuals of each variable. Second, we estimate the treatment effect by l1-regularized regression (i.e., Lasso) of the outcome residuals on the base treatment residuals interacted with the controls. We debias this estimator to conduct pointwise inference about a single coefficient of treatment effect vector and simultaneous inference about the whole vector. To account for the unobserved unit effects inherent in panel data, we use an extension of correlated random effects approach of Mundlak (1978) and Chamberlain (1982) to a high-dimensional setting. As an empirical application, we estimate a large number of heterogeneous demand elasticities based on a novel dataset from a major European food distributor