  Confounding seriously impairs our ability to learn about causal relations
from observational data. Confounding can be defined as a statistical
association between two variables due to inputs from a common source (the
confounder). For example, if $Z\rightarrow Y$ and $Z\rightarrow X$, then $X$
and $Y$ will be statistically dependent, even if there are no causal
connections between the two. There are several approaches available to adjust
for confounding, i.e. to remove, or reduce, the association between two
variables due to the confounder. Common adjustment techniques include
stratifying the analysis on the confounder, and including confounders as
covariates in regression models. Most adjustments rely on the assumption that
the causal effects of confounders, on different variables, do not co-vary. For
example, if the causal effect of $Z$ on $X$ and the causal effect of $Z$ on $Y$
co-vary between observational units, a confounding effect remains after
adjustment for $Z$. This causal-effect covariability and its consequences is
the topic of this paper.
  Causal-effect covariability is first explicated using the framework of
structural causal models. Using this framework it is easy to show that
causal-effect covariability generally leads to confounding that cannot be
adjusted for by standard methods. Evidence from data indicates that the
confounding introduced by causal-effect covariability might be a real concern
in applied work.
