
"In this second edition of Counterfactuals and Causal Inference, completely revised and expanded, the essential features of the counterfactual approach to observational data analysis are presented with examples from the social, demographic, and health sciences. Alternative estimation techniques are first introduced using both the potential outcome model and causal graphs; after which, conditioning techniques, such as matching and regression, are presented from a potential outcomes perspective. For research scenarios in which important determinants of causal exposure are unobserved, alternative techniques, such as instrumental variable estimators, longitudinal methods, and estimation via causal mechanisms, are then presented. The importance of causal effect heterogeneity is stressed throughout the book, and the need for deep causal explanation via mechanisms is discussed"
The reason I didn't like the book is that I found it insufficiently rigorous to really engage with the "how" of doing causal inference, but excessively mathematical as a theoretical introduction to causality.
"Causality: A Primer" (also written by Pearl) is a very short book that I think does a good job of surfacing some of the same theoretical background while also explaining how to use Pearl's causality. If you exhaust that, I'd recommend moving to the full "Causality" book.
But otherwise I'd recommend actually looking into the counterfactual / potential outcomes view of causality. The set of questions it answers are about 80% overlapping (although both Pearl and POs have their own 20%), but I find the vocabulary a little more intuitive. Canonical books include Morgan and Winship "Counterfactuals and Causal Inference" or Imbens and Rubin "Causal Inference for Social Scientists".
As to the blog post, Pearl is correct that causality requires qualitative assumptions about design to justify assumptions required to do causal inference. In Pearl's work this is often motivated as qualitative knowledge informing the structure of the DAG before any estimation. But recent advances in causal discovery have actually rendered it possible to black box the structure of a DAG from data -- happy to provide citations if this is down the rabbit hole. By contrast, I agree with Gelman that Pearl is an irritating writer and that in "The Book of Why" he gives a sloppy intellectual history of causation.
Morgan and Winship's Counterfactuals and Causal Inference: Methods and Principles for Social Research [1] is also really good. Be sure to get the second edition; it's much better than the first.
[0] http://www.amazon.com/Analysis-Regression-Multilevel-Hierarc...
[1] http://www.amazon.com/Counterfactuals-Causal-Inference-Princ...
Take for instance the running example of catholic schoolings effect on test scores used by the boook Counterfactuals and Causal Inference. Subsequent chapter re-treat this example with increasingly sophisticated techniques and more complex assumptions about causal mechanisms, and each time they uncover a flaw in the analysis using techniques from previous chapters.
My lesson from this: outcomes causal inference is very dependent on assumptions and methodologies, of which the options are many. This is a great setting for publishing new research, but its the opposite of what you want in an industry setting where the bias is/should be towards methods that are relatively quick to test and validate and put in production.
I see researchers in large tech companies pushing for causal methodologies, but I'm not convinced they're doing anything particularly useful since I have yet to see convincing validation on production data of their methods that show they're better than simpler alternatives which will tend to be more robust.