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's 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.

Factorial designs are widely used to study multiple treatments in one experiment. While t -tests using a fully-saturated “long” model provide valid inferences, “short” model t -tests (that ignore interactions) yield higher power if interactions are zero, but incorrect inferences otherwise. Of 27 factorial experiments published in top-5 journals (2007–2017), 19 use the short model. After including interactions, over half of their results lose significance. Based on recent econometric advances, we show that power improvements over the long model are possible. We provide practical guidance for the design of new experiments and the analysis of completed experiments.