In this note, we offer an approach to estimating structural parameters in the presence of many instruments and controls based on methods for estimating sparse high-dimensional models. We use these high-dimensional methods to select both which instruments and which control variables to use. The...

Here we present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter, α, in the presence of a very high-dimensional nuisance parameter, η, which is estimated using modern selection or regularization methods. Our...

We develop results for the use of LASSO and Post-LASSO methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p, that apply even when p is much larger than the sample size, n. We rigorously develop asymptotic...

Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many...

In this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using ℓ1-penalization and post-ℓ1-penalization methods. Focusing on linear and nonparametric regression frameworks, we discuss various econometric examples, present basic...

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR series framework, covering many regressors as a special...

In this note, we propose the use of sparse methods (e.g. LASSO, Post-LASSO, p LASSO, and Post-p LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in the canonical Gaussian case. The methods apply even when...

In this work we study the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions, such as moment restrictions, on the model, and plays a fundamental role in...

This paper studies the computational complexity of Bayesian and quasi-Bayesian estimation in large samples carried out using a basic Metropolis random walk. The framework covers cases where the underlying likelihood or extremum criterion function is possibly non-concave, discontinuous, and of...

This article looks at the theory and empirics of extremal quantiles in economics, in particular value-at-risk. The theory of extremes has gone through remarkable developments and produced valuable empirical findings in the last 20 years. In the discussion, we put a particular focus on...