  The front-door criterion can be used to identify and compute causal effects
despite the existence of unmeasured confounders between a treatment and
outcome. However, the key assumptions -- (i) the existence of a variable (or
set of variables) that fully mediates the effect of the treatment on the
outcome, and (ii) which simultaneously does not suffer from similar issues of
confounding as the treatment-outcome pair -- are often deemed implausible. This
paper explores the testability of these assumptions. We show that under mild
conditions involving an auxiliary variable, the assumptions encoded in the
front-door model (and simple extensions of it) may be tested via generalized
equality constraints a.k.a Verma constraints. We propose two goodness-of-fit
tests based on this observation, and evaluate the efficacy of our proposal on
real and synthetic data. We also provide theoretical and empirical comparisons
to instrumental variable approaches to handling unmeasured confounding.
