Christian Hansen

We study a panel data model with general heterogeneous effects, where slopes are allowed to be varying across both individuals and times. The key assumption for dimension reduction is that the heterogeneous slopes can be expressed as a factor structure so that the high-dimensional slope matrix is of low-rank, so can be estimated using low-rank regularized regression.

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.

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

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

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.

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

In this article the package High-dimensional Metrics (hdm) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence intervals and significance testing for (possibly many) low-dimensional subcomponents of the high-dimensional parameter vector. Efficient estimators and uniformly valid confidence intervals for regression coefficients on target variables (e.g., treatment or policy variable) in a high-dimensional approximately sparse regression model, for average treatment effect (ATE) and average treatment effect for the treated (ATET), as well for extensions of these parameters to the endogenous setting are provided. Theory grounded, data-driven methods for selecting the penalization parameter in Lasso regressions under heteroscedastic and non-Gaussian errors are implemented. Moreover, joint/ simultaneous confidence intervals for regression coefficients of a high-dimensional sparse regression are implemented. Data sets which have been used in the literature and might be useful for classroom demonstration and for testing new estimators are included.

In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data-rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function-valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces ecient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for post-regularization and post-selection inference that are uniformly valid (honest) across a wide-range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reduced form functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment condition framework, which arises from structural equation models in econometrics. Here too the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function-valued) parameters within this general framework where any high-quality, modern machine learning methods can be used to learn the nonparametric/high-dimensional components of the model. These include a number of supporting auxilliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) oer a uniformly valid functional delta method, and (3) provide results for sparsity-based estimation of regression functions for function-valued outcomes.

In this paper, the authors provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data-rich environments.

Common high-dimensional methods for prediction rely on having either a sparse signal model, a model in which most parameters are zero and there are a small number of non-zero parameters that are large in magnitude, or a dense signal model, a model with no large parameters and very many small non-zero parameters. The authors consider here a generalisation of these two basic models, termed here a “sparse + dense” model, in which the signal is given by the sum of a sparse signal and a dense signal.

We present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter in the presence of a very high-dimensional nuisance parameter that is estimated using selection or regularization methods.

We consider estimation of and inference about coefficients on endogenous variables in a linear instrumental variables model where the number of instruments and exogenous control variables are each allowed to be larger than the sample size.

Common high-dimensional methods for prediction rely on having either a sparse signal model, a model in which most parameters are zero and there are a small number of non-zero parameters that are large in magnitude, or a dense signal model, a model with no large parameters and very many small non-zero parameters. The authors consider a generalization of these two basic models, termed here a “sparse+dense” model, in which the signal is given by the sum of a sparse signal and a dense signal.

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

In this paper, the authors consider estimation of general modern moment-condition problems in econometrics in a data-rich environment where there may be many more control variables available than there are observations.

This paper provides an overview of how innovations in "data mining" can be adapted and modified to provide high-quality inference about model parameters.

In the first part of the paper, we consider estimation and inference on policy relevant treatment effects, such as local average and local quantile treatment effects, in a data-rich environment where there may be many more control variables available than there are observations.

This paper provides an overview of how innovations in "data mining" can be adapted and modified to provide high-quality inference about model parameters.