Uniform inference in highdimensional dynamic panel data models with approximately sparse fixed effects

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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.

OriginalsprogEngelsk
TidsskriftEconometric Theory
Vol/bind35
Nummer2
Sider (fra-til)295-359
Antal sider65
ISSN0266-4666
DOI
StatusUdgivet - apr. 2019

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