Parameter identification and causal identification

Question

1. When people say identification, do "parametric identification" and "causal identification" mean completely different?

   Ex) When performing ML estimation, the sentence that one parameter is identified seems to mean that there are no observationally equivalent parameters in a given model. (i.e. when the parameter that maximizes the likelihood function given a model is unique (I think, it is a mathematical concept))

   And the sentence that the causal relationship has been identified seems to mean that we can accept the parameter as a causal relationship (I think, it is a conceptual problem) (For example, we only use the adopted child sample (to remove genetic factors) to identify the impact of home education on children's output)

The question here is whether parameter identification and causal relationship identification have completely different meanings?

2. If the meaning of parameter identification and causal relationship identification in question 1 is completely different, when we perform ML estimation. Are the mathematical conditions for parameter identification? and does the identification strategy in imperial papers mean the causal identification?

• In my personal opinion, parameter identification and causality identification are different, and the identification conditions attached to the ML estimation method are mathematical conditions for parameter identification, and the identification strategy in imperial papers is the concept for identifying causal relation. But I am not sure.

Answer 1

I found David Card's Woytinsky lecture and slides very helpful for thinking about this. He distinguishes between two meanings of identification:

1. Econometric identification is about exclusion/functional form assumptions that invert the data to the model parameters. Linear supply and demand are an example, and also partial identification to set or a region.
2. Substantive identification is ruling out alternative explanations for the data.

This mirrors the distinction between model-based and design-based empirical work.

If you want to delve even deeper, I would recommend Lewbel, Arthur. 2019. "The Identification Zoo: Meanings of Identification in Econometrics." Journal of Economic Literature, 57 (4): 835-903. He argues that there are at least two dozen varieties.