This paper develops a high-dimensional local projections framework for estimating impulse responses in the presence of many potential controls. Other approaches often rely on exact sparsity assumptions, but empirical macroeconomic applications may involve nuisance relationships better described by structured coefficient decay. Building on the orthogonal greedy algorithm with high-dimensional AIC (OGA+HDAIC), I propose a double-selection procedure that separately addresses the shock equation and the outcome equation within local projections. The method allows for nonexact sparsity through polynomially decaying nuisance coefficients, with rates indexed by the decay exponent rather than by an effective sparsity level. Under suitable moment, dependence, and approximation conditions, the estimator achieves asymptotic normality with HAC standard errors. Simulation evidence shows reliable coverage under shock contamination and lower point-estimation error under predictable high-dimensional outcome nuisance. I illustrate the method's practical feasibility in a monetary policy application using the FRED-MD dataset.

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.

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.