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The often (unspoken) assumptions behind the difference-in-difference estimator in practice

Jed Friedman's picture
This post is co-written with Ricardo Mora and Iliana Reggio
The difference-in-difference (DID) evaluation method should be very familiar to our readers – a method that infers program impact by comparing the pre- to post-intervention change in the outcome of interest for the treated group relative to a comparison group. The key assumption here is what is known as the “Parallel Paths” assumption, which posits that the average change in the comparison group represents the counterfactual change in the treatment group if there were no treatment. It is a popular method in part because the data requirements are not particularly onerous – it requires data from only two points in time – and the results are robust to any possible confounder as long as it doesn’t violate the Parallel Paths assumption. When data on several pre-treatment periods exist, researchers like to check the Parallel Paths assumption by testing for differences in the pre-treatment trends of the treatment and comparison groups. Equality of pre-treatment trends may lend confidence but this can’t directly test the identifying assumption; by construction that is untestable. Researchers also tend to explicitly model the “natural dynamics” of the outcome variable by including flexible time dummies for the control group and a parametric time trend differential between the control and the treated in the estimating specification.
Typically, the applied researcher’s practice of DID ends at this point. Yet a very recent working paper by Ricardo Mora and Iliana Reggio (two co-authors of this post) points out that DID-as-commonly-practiced implicitly involves other assumptions instead of  Parallel Paths, assumptions perhaps unknown to the researcher, which may influence the estimate of the treatment effect. These assumptions concern the dynamics of the outcome of interest, both before and after the introduction of treatment, and the implications of the particular dynamic specification for the Parallel Paths assumption.

It’s Time Again for Submissions for our Annual Blog Your Job Market Paper Series

David McKenzie's picture
We are pleased to launch for the third year a call for PhD students on the job market to blog their job market paper on the Development Impact blog.  We welcome blog posts on anything related to empirical development work, impact evaluation, or measurement. For examples, you can see last years series. We will follow the same process laid out by Berk last year, which is as follows: