Abstract
Abstract 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 data set, 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.
Highlights
Understanding causal relations forms the basis of decision-making in society
We find that grade point average (GPA) is a trapdoor variable due to a functional equality constraint on the causal effect of interest
We have shown how it is possible to estimate causal effects when the back-d oor and front-door adjustments are not applicable and highlighted the potential issues related to the application of theoretical identifying formulas to finite data sets
Summary
Understanding causal relations forms the basis of decision-making in society. The role of statistics is to provide tools that allow us to estimate the causal effects of planned interventions. As an example of such a constraint, we show that in the causal graph of Figure 1, a causal effect does not depend on the value of a variable W despite it appearing in the identifying functional of the interventional distribution.
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