Causal Inference: Selection on Observables (Part 5)

I finish the proofs of the average treatment effect, propensity score and IPW in this video. In addition, I shortly discuss the "Doubly Robust Estimator". At last I make a summary of this topic. My suggestion is that you can focus on the methods of the proofs and pick the one section you want to watch. 00:00 Intro 01:21 Proof of the ATE/ATET 11:24 Theorem: Propensity Score and Balancing Property 21:10 Theorem: Inverse Propensity Score 26:54 Short Preview of Doubly Robust 28:00 Key Takeaways Here I list the references you will probably need, these are bibtex and you can direct search them: @article{abadie_imbens_2016, author = {Abadie, Alberto and Imbens, Guido W.}, title = {Matching on the Estimated Propensity Score}, journal = {Econometrica}, year = {2016}, volume = {84}, number = {2}, pages = {781--807}, doi = {10.3982/ECTA11293}, } @book{frolich_sperlich_2019, author = {Fr{\"o}lich, Markus and Sperlich, Stefan}, title = {Impact Evaluation: Treatment Effects and Causal Analysis}, publisher = {Cambridge University Press}, address = {Cambridge}, year = {2019}, doi = {10.1017/9781107337008}, } @article{hahn_1998, author = {Hahn, Jinyong}, title = {On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects}, journal = {Econometrica}, year = {1998}, volume = {66}, number = {2}, pages = {315--331}, doi = {10.2307/2998560}, } @article{hirano_imbens_ridder_2003, author = {Hirano, Keisuke and Imbens, Guido W. and Ridder, Geert}, title = {Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score}, journal = {Econometrica}, year = {2003}, volume = {71}, number = {4}, pages = {1161--1189}, doi = {10.1111/1468-0262.00442}, } @book{imbens_rubin_2015, author = {Imbens, Guido W. and Rubin, Donald B.}, title = {Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction}, publisher = {Cambridge University Press}, address = {New York}, year = {2015}, isbn = {9780521885881}, doi = {10.1017/CBO9781139025751}, } @article{lalonde_1986, author = {LaLonde, Robert J.}, title = {Evaluating the Econometric Evaluations of Training Programs with Experimental Data}, journal = {The American Economic Review}, year = {1986}, volume = {76}, number = {4}, pages = {604--620}, } @article{manski_1990, author = {Manski, Charles F.}, title = {Nonparametric Bounds on Treatment Effects}, journal = {The American Economic Review}, year = {1990}, volume = {80}, number = {2}, pages = {319--323}, note = {Papers and Proceedings}, } @article{rosenbaum_rubin_1983, author = {Rosenbaum, Paul R. and Rubin, Donald B.}, title = {The Central Role of the Propensity Score in Observational Studies for Causal Effects}, journal = {Biometrika}, year = {1983}, volume = {70}, number = {1}, pages = {41--55}, doi = {10.1093/biomet/70.1.41}, } @article{rothe_2017, author = {Rothe, Christoph}, title = {Robust Confidence Intervals for Average Treatment Effects Under Limited Overlap}, journal = {Econometrica}, year = {2017}, volume = {85}, number = {2}, pages = {645--660}, doi = {10.3982/ECTA13141}, } @unpublished{wager_2024, author = {Wager, Stefan}, title = {Causal Inference: A Statistical Learning Approach}, year = {2024}, note = {Unpublished book draft, Stanford University}, url = {https://web.stanford.edu/~swager/caus...}, urldate = {2026-10-06}, }