Victor Chernozhukov

This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a number of unknown parameters that is not vanishingly small relative to the sample size.

We give a general construction of debiased/locally robust/orthogonal (LR) moment functions for GMM, where the derivative with respect to first step nonparametric estimation is zero and equivalently first step estimation has no effect on the influence function.

This paper provides a method to construct simultaneous condfience bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two-way effects, strictly exogenous covariates, and possibly discrete outcome variables.

We provide adaptive inference methods for linear functionals of L1-regularized linear approximations to the conditional expectation function.

We extend conformal inference to general settings that allow for time series data.

We propose strategies to estimate and make inference on key features of heterogeneous effects in randomized experiments.

The R package Counterfactual implements the estimation and inference methods of Chernozhukov et al. (2013) for counterfactual analysis.

Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants of low infant birth weights, and auction models.

This paper introduces new inference methods for counterfactual and synthetic control methods for evaluating policy effects.

High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature.

The understanding of co-movements, dependence, and influence between variables of interest is key in many applications. Broadly speaking such understanding can lead to better predictions and decision making in many settings.

This paper introduces two classes of semiparametric triangular systems with nonadditively separable unobserved heterogeneity. They are based on distribution and quantile regression modeling of the reduced-form conditional distributions of the endogenous variables.

Multinomial choice models are fundamental for empirical modeling of economic choices among discrete alternatives. We analyze identifcation of binary and multinomial choice models when the choice utilities are nonseparable in observed attributes and multidimen- sional unobserved heterogeneity with cross-section and panel data.

The R package quantreg.nonpar implements nonparametric quantile regression methods to estimate and make inference on partially linear quantile models. quantreg.nonpar obtains point estimates of the conditional quantile function and its derivatives based on series approximations to the nonparametric part of the model. It also provides pointwise and uniform confidence intervals over a region of covariate values and/or quantile indices for the same functions using analytical and resampling methods. This paper serves as an introduction to the package and displays basic functionality of the functions contained within.

We revisit the classic semiparametric problem of inference on a low dimensional parameter θ0 in the presence of high-dimensional nuisance parameters η0.

This paper provides a method to construct simultaneous confidence bands for quantile and quantile effect functions for possibly discrete or mixed discrete-continuous random variables. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparamet-ric, and nonparametric modeling strategies and does not depend on the sampling schemes. It is based upon projection of simultaneous confidence bands for distribution functions. We apply our method to analyze the distributional impact of insurance coverage on health care utilization and to provide a distributional decomposition of the racial test score gap. Our analysis generates new interesting findings, and com-plements previous analyses that focused on mean effects only. In both applications, the outcomes of interest are discrete rendering standard inference methods invalid for obtaining uniform confidence bands for quantile and quantile effects functions.

We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to avoid non-vanishing biases in addition to handle the high dimensionality of the parameters. A recent growing literature has proposed various estimators that achieve good rates of convergence. Our main contribution complements this literature with the construction of simultaneous confidence regions for the parameters of interest in such high-dimensional linear models with error-in-variables. These confidence regions are based on the construction of moment conditions that have an additional orthogonality property with respect to nuisance parameters. We provide a construction that requires us to estimate an auxiliary high-dimensional linear model with error-in-variables for each component of interest. We use a multiplier bootstrap to compute critical values for simultaneous confidence intervals for a target subset of the components. We show its validity despite of possible (moderate) model selection mistakes, and allowing the number of target coefficients to be larger than the sample size. We apply and discuss the implications of our results to two examples and conduct Monte Carlo simulations to illustrate the performance of the proposed procedure for each variable whose coefficient is the target of inference.

Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well.

We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high-dimensional setting.

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 case, for performing inference on the entire conditional quantile function and its linear functionals.