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This paper provides estimation and inference methods for a conditionalaverage treatment effects (CATE) characterized by a high-dimensional parameterin both homogeneous cross-sectional and unit-heterogeneous dynamic panel datasettings. In our leading example, we model CATE by interacting the basetreatment variable with explanatory variables. The first step of our procedureis orthogonalization, where we partial out the controls and unit effects fromthe outcome and the base treatment and take the cross-fitted residuals. Thisstep uses a novel generic cross-fitting method we design for weakly dependenttime series and panel data. This method "leaves out the neighbors" when fittingnuisance components, and we theoretically power it by using Strassen'scoupling. As a result, we can rely on any modern machine learning method in thefirst step, provided it learns the residuals well enough. Second, we constructan orthogonal (or residual) learner of CATE -- the Lasso CATE -- that regressesthe outcome residual on the vector of interactions of the residualizedtreatment with explanatory variables. If the complexity of CATE function issimpler than that of the first-stage regression, the orthogonal learnerconverges faster than the single-stage regression-based learner. Third, weperform simultaneous inference on parameters of the CATE function usingdebiasing. We also can use ordinary least squares in the last two steps whenCATE is low-dimensional. In heterogeneous panel data settings, we model theunobserved unit heterogeneity as a weakly sparse deviation from Mundlak(1978)'s model of correlated unit effects as a linear function oftime-invariant covariates and make use of L1-penalization to estimate thesemodels. We demonstrate our methods by estimating price elasticities ofgroceries based on scanner data. We note that our results are new even for thecross-sectional (i.i.d) case.

Estimation and Inference on Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels under Weak Dependence