Previously I discussed the

unique aspects of modeling claims and addressing those with generalized linear models. I followed that with a discussion of the challenges of using

difference-in-differences in the context of GLM models and some ways to deal with this. In this post I want to dig into into what some folks are debating in terms of issues related to combining matching with DID. Laura Hatfield covers it well on twitter:

Link:

https://twitter.com/laura_tastic/status/1022890688525029376
Also, they picked up on this it at the incidental economist and gave a good summary of the key papers

here.
You can find citations for the relevant papers below. I won't plagerize what both Laura and the folks at the Incidental Economist have already explained very well. But, at a risk of oversimplifying the big picture I'll try to summarize a bit. Matching in a few special cases can improve the precision of the estimate in a DID framework, and occasionally reduces bias. Remember, that matching on pre-period observables is not necessary for the validity of difference in difference models. There are cases when the treatment group is in fact determined by pre-period outcome levels. In these cases matching is necessary. At other times, if not careful, matching in DID introduces risks for regression to the mean…what Laura Hatfield describes as a ‘bounce back’ effect in the post period that can generate or inflate treatment effects when they do not really exist.

Both the previous discussion on DID in a GLM context and combining matching with DID indicate the risks involved in just plug and play causal inference and the challenges of bridging the

gap between theory and application.
**References:**
Daw, J. R. and Hatfield, L. A. (2018), Matching and Regression to the Mean in Difference‐in‐Differences Analysis. Health Serv Res, 53: 4138-4156. doi:10.1111/1475-6773.12993

Daw, J. R. and Hatfield, L. A. (2018), Matching in Difference‐in‐Differences: between a Rock and a Hard Place. Health Serv Res, 53: 4111-4117. doi:10.1111/1475-6773.13017