Applied Causal Inference for Observational Research

This sequence is an introduction to basic causal inference. It was originally written as auxiliary notes for a course in Epidemiology, but it is relevant to almost any kind of applied statistical research, including econometrics, sociology, psychology, political science etc. I would not be surprised if you guys find a lot of errors, and I would be very grateful if you point them out in the comments. This will help me improve my course notes and potentially help me improve my understanding of the material.

For mathematically inclined readers, I recommend skipping this sequence and instead reading Pearl's book on Causality. There is also a lot of good material on causal graphs on Less Wrong itself. Also, note that my thesis advisor is writing a book that covers the same material in more detail, the first two parts are available for free at his website.

Pearl's book, Miguel's book and Eliezer's writings are all more rigorous and precise than my sequence. This is partly because I have a different goal: Pearl and Eliezer are writing for mathematicians and theorists who may be interested in contributing to the theory. Instead, I am writing for consumers of science who want to understand correlation studies from the perspective of a more rigorous epistemology.

I will use Epidemiological/Counterfactual notation rather than Pearl's notation. I apologize if this is confusing. These two approaches refer to the same mathematical objects, it is just a different notation. Whereas Pearl would use the "Do-Operator" E[Y|do(a)], I use counterfactual variables E[Y^a]. Instead of using Pearl's "Do-Calculus" for identification, I use Robins' G-Formula, which will give the same results.

For all applications, I will use the letter "A" to represent "treatment" or "exposure" (the thing we want to estimate the effect of), Y to represent the outcome, L to represent any measured confounders, and U to represent any unmeasured confounders.

Outline of Sequence:

I hope to publish one post every week. I have rough drafts for the following eight sections, and will keep updating this outline with links as the sequence develops:

Part 0: Sequence Announcement / Introduction (This post)

Part 1: Basic Terminology and the Assum...