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.

We propose a method for constructing upper and lower bounds on the standard error of a parameter estimated from moment conditions obtained across different samples. Both bounds are derived by exploiting sharp distributional bounds. While this distributional characterization is conceptually appealing, the resulting optimization problem is often numerically challenging due to its non-convex nature. To address this practical difficulty, we complement the distributional characterization with two tractable approaches: (1) explicit sharp bounds when no information about correlations is available, and (2) computationally feasible sharp bounds in more general settings with no or partial correlational information. The latter can be obtained by solving a simple semi-definite program. Finally, we demonstrate the usefulness of our method through three empirical applications in macroeconomics and microeconomics.