# Causality via potential outcomes

Neyman-Rubin, counterfactuals, conditional treatment effects, and related tricks

October 26, 2016 — December 10, 2021

A sister(?) field of the DAG-centric causal inference. I say *sister field* because the patriarch of the DAG school, Judea Pearl, seems to regard potential outcomes as a special case of causal DAG reasoning, claiming a proud lineage going back to Seward Wright. OTOH, proponents of potential outcomes, especially Rubin, seem to regard it as the actually-practical way to do causal reasoning and claim a proud lineage going to Jerzy Neyman. In practice I suspect we as users do not need to worry excessively about the border disputes.

Rubin and Waterman (2006) comes recommended by Shalizi as:

A good description of Rubin et al.’s methods for causal inference, adapted to the meanest understanding. […] Rubin and Waterman do a very good job of explaining, in a clear and concrete problem, just how and why the newer techniques of causal inference are valuable, with just enough technical detail that it doesn’t seem like magic.

## 1 Relationship to Pearl-style do-calculus

Rubin and Pearl are kind of “academic enemies”. Though neither completely dismisses the other, they both make snide remarks about the other’s work. Pearl shows in his book exactly how Neyman-Rubin potential outcomes can be derived from causal graphs. As far as I know Rubin never really makes an attempt to address Pearl’s ideas directly. However, Rubin, being a statistician, made significant contributions to the practice of real-world causal inference, which go beyond Pearl’s interests. Jamie Robins also made seminal contributions to this subject. You can read some of the debate on Andrew Gelman’s blog here. Pearl writes in the comment section and in that blog post there are links to follow up posts.

I am more familiar with the Pearl-style approach. The two connect by, e.g. Single World Intervention Graphs (Richardson and Robins 2013).

## 2 Heterogeneous treatment effects

See interaction effects for now.

## 3 Instrumental variables

## 4 External validity

Dataset shift etc. See external validity.

## 5 Use in ML

See causality in ML.

## 6 Propensity matching

TODO

## 7 Causal forests

To follow up: proximity matrix in causal random forest.

The GRF Algorithm. Haaya Naushan: Causal Machine Learning for Econometrics: Causal Forests.

## 8 Double learning

See causality and ML.

## 9 References

*arXiv:1902.07409 [Stat]*.

*Proceedings of the National Academy of Sciences*.

*arXiv:1507.03652 [Math, Stat]*.

*The Annals of Applied Statistics*.

*Statistical Science*.

*The Econometrics Journal*.

*Annual Review of Economics*.

*Oxford Statistical Science Series*.

*Journal of Causal Inference*.

*Biometrika*.

*American Journal of Sociology*.

*Applied Bayesian Modeling and Causal Inference From Incomplete-Data Perspectives*.

*British Journal of Mathematical and Statistical Psychology*.

*Epidemiologic Perspectives & Innovations : EP+I*.

*Annual Review of Statistics and Its Application*.

*Statistical Science*.

*The Annals of Statistics*.

*Annual Review of Statistics and Its Application*.

*Annual Review of Statistics and Its Application*.

*International Conference on Artificial Intelligence and Statistics*.

*Proceedings of the National Academy of Sciences*.

*arXiv:1903.03662 [Stat]*.

*Annual Review of Economics*.

*2018 IEEE Data Science Workshop (DSW)*.

*arXiv:2109.00173 [Cs, Stat]*.

*Counterfactuals and Causal Inference*.

*Statistics Surveys*.

*Statistical Science*.

*arXiv:1801.06229 [Stat]*.

*Statistical Science*.

*Proceedings of the 31st International Conference on Neural Information Processing Systems*. NIPS’17.

*arXiv:1606.03976 [Cs, Stat]*.

*Proceedings of the Sixteenth ACM Conference on Economics and Computation - EC ’15*.

*arXiv:1411.2127 [Stat]*.

*Proceedings of the 24th International Conference on Artificial Intelligence*. IJCAI’15.

*Statistical Methods in Medical Research*.

*arXiv:1611.04660 [Cs, Stat]*.

*arXiv:2010.07684 [Cs]*.