Debiased Inference of Average Partial Effects in Single-Index Models: Comment on Wooldridge and Zhu

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Notes

1 Our proposed estimator will also use cross-fitting (Chernozhukov et al. 2018), but we suppress this notation here for conciseness.

2 Replication files for all experiments are available at github.com/swager/amlinear, in the folder debiased_single_index_experiments. For convex optimization, we use the R package CVXR (Fu et al. 2017).

3 In fact, as a consequence of the convergence of $\widehat{\gamma }$ to ${\gamma }^{\star }$, which we will establish below, this criterion will imply that $I(\widehat{\gamma };\widehat{\theta })=o_p(n^{-1/2})$.

4 The parts of condition (vi) involving $\widehat{m}-m$ are used only to control the first term in our error expansion, which we treated above using a variation on the argument used in Hirshberg and Wager (2018).