Meaningful Causal Aggregation and Paradoxical Confounding
This addresses foundational issues in causal inference for aggregated data, which is incremental as it builds on existing causal theory to clarify and extend aggregation methods.
The paper tackles the problem of ill-defined causality in aggregated variables, showing that macro-interventions can lead to paradoxical confounding or unconfounding depending on micro-realizations, and proposes that causal relations are only meaningful when referenced to micro states, with a solution using natural macro interventions where micro state distributions match observational ones.
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; we term this natural macro interventions. We also discuss generalizations of this observation.