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UNIFORM INFERENCE IN HIGH-DIMENSIONAL DYNAMIC PANEL DATA MODELS WITH APPROXIMATELY SPARSE FIXED EFFECTS

  • Anders Bredahl Kock (a1) and Haihan Tang (a2)
Abstract

We establish oracle inequalities for a version of the Lasso in high-dimensional fixed effects dynamic panel data models. The inequalities are valid for the coefficients of the dynamic and exogenous regressors. Separate oracle inequalities are derived for the fixed effects. Next, we show how one can conduct uniformly valid inference on the parameters of the model and construct a uniformly valid estimator of the asymptotic covariance matrix which is robust to conditional heteroskedasticity in the error terms. Allowing for conditional heteroskedasticity is important in dynamic models as the conditional error variance may be nonconstant over time and depend on the covariates. Furthermore, our procedure allows for inference on high-dimensional subsets of the parameter vector of an increasing cardinality. We show that the confidence bands resulting from our procedure are asymptotically honest and contract at the optimal rate. This rate is different for the fixed effects than for the remaining parts of the parameter vector.

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Corresponding author
*Address correspondence to Anders Bredahl Kock, Department of Economics, University of Oxford, Aarhus University and CREATES, Manor Road, Oxford OX1 3UQ, UK; e-mail: anders.kock@economics.ox.ac.uk
Haihan Tang, Fanhai International School of Finance and School of Economics, Fudan University, 220 Handan Road, Yangpu District, Shanghai, 200433, China; e-mail: hhtang@fudan.edu.cn.
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Financial support from the Center for Research in the Econometric Analysis of Time Series (grant DNRF78) is gratefully acknowledged.

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Econometric Theory
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