Simula@BI: High-dimensional CCE: The Cross-Sectionally Averaged Adaptive Lasso

We consider the Common Correlated Effect estimator (CCE) for panels with multifactor error structure and extend the framework under Gaussian designs to the setting where the number of covariates in each cross-section is large and potentially larger than the sample size.

Before using the CCE estimator, we perform regularization directly on the cross-sectionally averaged model, thus designing the Cross-sectionally Averaged aDAptive Lasso estimator (CADA-Lasso). We show that CADA-Lasso is oracle efficient and selection consistent.

The model rewriting favours selection of those variables having in the DGP both a non-negligible effect on the response as well as being driven by the same factors as those that drive the response. De-biasing for post-selection inference is however still necessary and we attain uniformly valid inference for the CADA-Lasso by using a post-double-selection mechanism.

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