Title: The Fragility of Sparsity" (with Ulrich Müller and Sebastian Roelsgaard) There is no paper yet, but the abstract is:

We argue, using three empirical applications, that linear regression estimators which rely on the assumption of sparsity are fragile in two ways. First, we document that different choices of the regressor matrix that don't impact long regression estimates, such as the choice of baseline category with categorical controls, move the post-double-selection estimates by one standard error or more. Second, we develop two tests of the sparsity assumption based on comparing sparsity-based estimators with long regression. Both tests tend to reject the sparsity assumption in all three applications. Unless the number of regressors is comparable to or exceeds the sample size, long regression yields more robust results at little efficiency cost.