The Fragility of Sparsity

Understand

We show, using three empirical applications, that linear regression estimates predicated on the assumption of sparsity are fragile in two ways.

• First, we document that different choices of the regressor matrix which do not impact ordinary least squares (OLS) estimates, such as the choice of baseline category with categorical controls, can move sparsity-based estimates by two standard errors or more.
• Second, we develop two tests of the sparsity assumption by comparing sparsity-based estimators with OLS.
• The tests tend to reject the sparsity assumption in all three applications.