Comment: Reflections on the Deconfounder

The aim of this comment (set to appear in a formal discussion in JASA) is to draw out some conclusions from an extended back-and-forth I have had with Wang and Blei regarding the deconfounder method proposed in "The Blessings of Multiple Causes" [arXiv:1805.06826]. I will make three points here. First, in my role as the critic in this conversation, I will summarize some arguments about the lack of causal identification in the bulk of settings where the "informal" message of the paper suggests that the deconfounder could be used. This is a point that is discussed at length in D'Amour 2019 [arXiv:1902.10286], which motivated the results concerning causal identification in Theorems 6--8 of "Blessings". Second, I will argue that adding parametric assumptions to the working model in order to obtain identification of causal parameters (a strategy followed in Theorem 6 and in the experimental examples) is a risky strategy, and should only be done when extremely strong prior information is available. Finally, I will consider the implications of the nonparametric identification results provided for a narrow, but non-trivial, set of causal estimands in Theorems 7 and 8. I will highlight that these results may be even more interesting from the perspective of detecting causal identification from observed data, under relatively weak assumptions about confounders.