Before revision:  In the partially linear model setting popular in causal inference, we use Stein's lemma to show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally distributed  .
After revision:  In the partially linear model setting popular in causal inference, we use Stein's lemma to show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally distributed . Our proof relies on Stein's lemma and may be of independent interest .