In the main text, I discussed making causal claims from non-experimental data using natural experiments and matching. In this appendix, I will introduce the potential outcomes model, and define more precisely the conditions that are required for causal inference from observational data. This chapter will draw on Morgan and Winship (2014) and Imbens and Rubin (2015).
My preference would be for a discussion that includes Pearl's DAGs as well as Rubin's potential outcomes framework.
Edit: My take is that Rubin's framework is rooted in a 20th century Fisherian orientation (which is why it's especially popular among statisticians), while Pearl's framework in part reflects new insights on probabilistic graphical models (which is why it's popular among computer scientists). The future, I suspect, will entail both approaches.