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.

中文翻译：

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在存在陷门变量的情况下用小数据估计因果效应

当众所周知的后门和前门调整不适用时，我们考虑从观察数据估计干预措施的因果效应的问题。我们表明，当可识别的因果效应受到不能从条件独立关系推导出的隐式函数约束时，因果效应的估计量可能会在小样本中表现出偏差。这种偏差与我们称之为陷门变量的变量有关. 我们使用模拟数据来研究不同的策略来解释陷门变量，并建议如何最小化相关的陷门偏差。1971-2002 年生命历程研究的真实数据说明了陷门变量在因果效应估计中的重要性。使用这个数据集，我们估计了芬兰背景下教育对收入的因果影响。贝叶斯建模使我们能够将参数不确定性考虑在内，并将估计的因果效应呈现为后验分布。