Three facets of causal inference: Identification, explanation, and generalization

I formally characterize three objectives of causally-oriented empirical research: identification, explanation, and generalization. I then analyze some logical relationships between them. Loosely, causal identification is measurability of treatment effects from data; causal explanation occurs when a unique theoretical model is consistent with observed data; and causal generalization is application of a causal model from one setting to another. I show that explanation implies identification but not vice versa; that explanation is possible even if no pairwise causal effects are identified for any variables; and that improvement in identification also improves explanation. Causal generalization requires a known mapping of causal models across cases based on the background or contextual characteristics of each case. Necessary conditions to recover this mapping empirically are stringent and require theoretical commitments. Overall the results show a strong connection between theoretical models and causal inference.