TY - JOUR

T1 - Oracle inequalities, variable selection and uniform inference in high-dimensional correlated random effects panel data models

AU - Kock, Anders Bredahl

PY - 2016/11

Y1 - 2016/11

N2 - In this paper we study high-dimensional correlated random effects panel data models. Our setting is useful as it allows including time invariant covariates as under random effects yet allows for correlation between covariates and unobserved heterogeneity as under fixed effects. We use the Mundlak-Chamberlain device to model this correlation. Allowing for a flexible correlation structure naturally leads to a high dimensional model in which least squares estimation easily becomes infeasible with even a moderate number of explanatory variables.Imposing a combination of sparsity and weak sparsity on the parameters of the model we first establish an oracle inequality for the Lasso. This is valid even when the error terms are-heteroskedastic and no structure is imposed on the time series dependence of the error terms.Next, we provide upper bounds on the sup-norm estimation error of the Lasso. As opposed to the classical l(1)- and l(2)-bounds the sup-norm bounds do not directly depend on the unknown degree of sparsity and are thus well suited for thresholding the Lasso for variable selection. We provide sufficient conditions under which thresholding results in consistent model selection. Pointwise valid asymptotic inference is established for a post-thresholding estimator. Finally, we show how the Lasso can be desparsified in the correlated random effects setting and how this leads to uniformly valid inference even in the presence of heteroskedasticity and autocorrelated error terms. (C) 2016 Elsevier B.V. All rights reserved.

AB - In this paper we study high-dimensional correlated random effects panel data models. Our setting is useful as it allows including time invariant covariates as under random effects yet allows for correlation between covariates and unobserved heterogeneity as under fixed effects. We use the Mundlak-Chamberlain device to model this correlation. Allowing for a flexible correlation structure naturally leads to a high dimensional model in which least squares estimation easily becomes infeasible with even a moderate number of explanatory variables.Imposing a combination of sparsity and weak sparsity on the parameters of the model we first establish an oracle inequality for the Lasso. This is valid even when the error terms are-heteroskedastic and no structure is imposed on the time series dependence of the error terms.Next, we provide upper bounds on the sup-norm estimation error of the Lasso. As opposed to the classical l(1)- and l(2)-bounds the sup-norm bounds do not directly depend on the unknown degree of sparsity and are thus well suited for thresholding the Lasso for variable selection. We provide sufficient conditions under which thresholding results in consistent model selection. Pointwise valid asymptotic inference is established for a post-thresholding estimator. Finally, we show how the Lasso can be desparsified in the correlated random effects setting and how this leads to uniformly valid inference even in the presence of heteroskedasticity and autocorrelated error terms. (C) 2016 Elsevier B.V. All rights reserved.

KW - Panel data

KW - Lasso

KW - Oracle inequality

KW - Sup-norm bounds

KW - High-dimensional models

KW - Weak sparsity

KW - Correlated random effects

KW - Mundlak-Chamberlain

KW - Variable selection

KW - Uniform inference

KW - PENALIZED LIKELIHOOD

KW - QUANTILE REGRESSION

KW - DANTZIG SELECTOR

KW - LASSO

KW - ESTIMATORS

KW - SHRINKAGE

U2 - 10.1016/j.jeconom.2016.06.001

DO - 10.1016/j.jeconom.2016.06.001

M3 - Journal article

VL - 195

SP - 71

EP - 85

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 1

ER -