  We consider the problem of estimating causal effects of interventions from
observational data when well-known back-door and front-door adjustments are not
applicable. We show that when an identifiable causal effect is subject to an
implicit functional constraint that is not deducible from conditional
independence relations, the estimator of the causal effect can exhibit bias in
small samples. This bias is related to variables that we call trapdoor
variables. We use simulated data to study different strategies to account for
trapdoor variables and suggest how the related trapdoor bias might be
minimized. The importance of trapdoor variables in causal effect estimation is
illustrated with real data from the Life Course 1971-2002 study. Using this
dataset, we estimate the causal effect of education on income in the Finnish
context. Bayesian modelling allows us to take the parameter uncertainty into
account and to present the estimated causal effects as posterior distributions.
