  Factorial experiments are ubiquitous in the social and biomedical sciences,
but when units fail to comply with each assigned factors, identification and
estimation of the average treatment effects become impossible. Leveraging an
instrumental variables approach, previous studies have shown how to identify
and estimate the causal effect of treatment uptake among respondents who comply
with treatment. A major caveat is that these identification results rely on
strong assumptions on the effect of randomization on treatment uptake. This
paper shows how to bound these complier average treatment effects under more
mild assumptions on non-compliance.
