We study the finite sample behavior of Lasso-based inference methods such as post double Lasso and debiased Lasso. We show that these methods can exhibit substantial omitted variable biases (OVBs) due to Lasso not selecting relevant controls. This phenomenon can occur even when the coefficients are sparse and the sample size is large and larger than the number of controls. Therefore, relying on the existing asymptotic inference theory can be problematic in empirical applications. We compare the Lasso-based inference methods to modern high-dimensional OLS-based methods and provide practical guidance.

翻译：我们研究了基于激光索的推理方法(如后双激光索和下偏向激光索)的有限抽样行为。我们表明,由于激光索没有选择相关控制,这些方法可以显示大量省略的可变偏差(OVBs ) 。即使系数稀少,抽样大小大于控制数量,这种现象也可能发生。因此,在经验应用中,依赖现有的无反应推理理论可能会产生问题。我们将基于激光索的推理方法与基于现代高维的OSLS的方法进行比较,并提供实用的指导。