  We generalize the proximal g-formula of Miao, Geng, and Tchetgen Tchetgen
(2018) for causal inference under unobserved confounding using proxy variables.
Specifically, we show that the formula holds true for all causal models in a
certain equivalence class, and this class contains models in which the total
number of levels for the set of unobserved confounders can be arbitrarily
larger than the number of levels of each proxy variable. Although
straightforward to obtain, the result can be significant for applications.
Simulations corroborate our formal arguments.
