Linear Statistical Models for Causation: A Critical Review

Regression models are often used to infer causation from association. For instance, Yule [79] showed – or tried to show – that welfare was a cause of poverty. Path models and structural equation models are later refinements of the technique. Besides Yule, examples to be discussed here include Blau and Duncan [12] on stratification, as well as Gibson [28] on the causes of McCarthyism. Strong assumptions are required to infer causation from association by modeling. The assumptions are of two kinds: (a) causal, and (b) statistical. These assumptions will be formulated explicitly, with the help of response schedules in hypothetical experiments. In particular, parameters and error distributions must be stable under intervention. That will be hard to demonstrate in observational settings. Statistical conditions (like independence) are also problematic, and latent variables create further complexities. Causal modeling with path diagrams will be the primary topic. The issues are not simple, so examining them from several perspectives may be helpful. The article ends with a review of the literature and a summary.