  The generalized outcome-adaptive lasso (GOAL) is a variable selection for
high-dimensional causal inference proposed by Bald\'e et al. [2023, {\em
Biometrics} {\bfseries 79(1)}, 514--520]. When the dimension is high, it is now
well established that an ideal variable selection method should have the oracle
property to ensure the optimal large sample performance. However, the oracle
property of GOAL has not been proven. In this paper, we show that the GOAL
estimator enjoys the oracle property. Our simulation shows that the GOAL method
deals with the collinearity problem better than the oracle-like method, the
outcome-adaptive lasso (OAL).
