We show, using three empirical applications, that linear regression estimates which rely on the assumption of sparsity are fragile in two ways. First, we document that different choices of the regressor matrix that do not impact ordinary least squares (OLS) estimates, such as the choice of baseline category with categorical controls, can move sparsity-based estimates two standard errors or more. Second, we develop two tests of the sparsity assumption based on comparing sparsity-based estimators with OLS. The tests tend to reject the sparsity assumption in all three applications. Unless the number of regressors is comparable to or exceeds the sample size, OLS yields more robust results at little efficiency cost.

翻译：我们通过三个实证应用表明，依赖稀疏性假设的线性回归估计在两个方面具有脆弱性。首先，我们证明回归矩阵的不同选择（这些选择不会影响普通最小二乘法（OLS）估计，例如分类控制变量中基线类别的选择）可能使基于稀疏性的估计产生两个标准误或更大的偏差。其次，我们开发了两种基于比较稀疏性估计与OLS估计的稀疏性假设检验方法。在所有三个应用中，这些检验均倾向于拒绝稀疏性假设。除非回归变量数量与样本量相当或超过样本量，否则OLS在几乎没有效率损失的情况下能提供更稳健的结果。