Inference in High-Dimensional Regression Models without the Exact or $Lp$ Sparsity

We propose a new inference method in high-dimensional regression models and high-dimensional IV regression models. The method is shown to be valid without requiring the exact sparsity or $Lp$ sparsity conditions. Simulation studies demonstrate superior performance of this proposed method over those based on the LASSO or the random forest, especially under less sparse models. We illustrate an application to production analysis with a panel of Chilean firms.