In aggregated variables the impact of interventions is typically ill-defined because different micro-realizations of the same macro-intervention can result in different changes of downstream macro-variables. We show that this ill-definedness of causality on aggregated variables can turn unconfounded causal relations into confounded ones and vice versa, depending on the respective micro-realization. We argue that it is practically infeasible to only use aggregated causal systems when we are free from this ill-definedness. Instead, we need to accept that macro causal relations are typically defined only with reference to the micro states. On the positive side, we show that cause-effect relations can be aggregated when the macro interventions are such that the distribution of micro states is the same as in the observational distribution and also discuss generalizations of this observation.

翻译：在聚合变量中，干预的影响通常定义不清，因为相同宏观干预的不同微观实现可能会导致下游宏观变量的不同变化。我们证明，这种聚合变量上因果关系的定义不清可能使无混杂的因果关联转化为有混杂的关联，反之亦然，具体取决于各自的微观实现。我们论证，在实践中，当我们无法避免这种定义不清时，仅使用聚合因果系统是不可行的。相反，我们需要接受宏观因果关系通常仅参照微观状态来定义这一事实。从积极方面看，我们证明当宏观干预使得微观状态的分布与观测分布相同时，因果关系可以聚合，并讨论了这一观察的推广。