3 Selection on Observables (I)

Randomisation is a powerful tool because it means that confounders can be safely ignored by researchers as, in expectation, they will be balanced across treatment and control groups. Sadly, some of the most interesting social science questions cannot be addressed using randomised experiments (Why? First, because experiments are costly, and second, because it would be bad form to randomly assign, for instance, the institutions that govern a country’s electoral system, or whether you get a distinction in your degree). When it is not possible to randomise, how can we make valid causal inferences? In the next two lectures, we discuss methods for non-experimental data which assume that selection into treatment groups is based on observable factors. This week we focus on subclassification and matching.

For a theoretical discussion of the selection on observables identification strategy, the MHE chapter on regression is very good (especially page 51 onwards). There is also a very nice exposition of the conditional independence assumption as it specifically relates to matching in this paper by Jasjeet S Sekhon (that paper also has a fantastic title). For practical advice on matching, the best resource is probably the Elizabeth Stuart paper. This paper gives lots of straightforward recommendations about the different decisions one has to make when implementing different matching estimators. Applied examples are found in Eggers and Hainmueller (2009) and Dehejia and Wahba (1999). There is also a famous example of subclassification in this 1968 paper by Cochran.

Finally, in the lecture we discuss the problem of conditioning on post-treatment variables when estimating causal effects. There are many papers on this subject, but two of the more accessible ones are this one by Montgomery et al, which focuses on post-treatment bias in experimental settings; and this one by Acharya et al, which focuses on post-treatment bias in observational settings. Both are worth reading.

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