Was It Meant to Be? OR Sometimes Playing Match Maker Can Be a Bad Idea: Matching with Difference-in-Differences

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

Do you use diff-in-diff? Then this thread is for you.

You’re no dummy. You already know diverging trends in the pre-period can bias your results.

But I’m here to tell you about a TOTALLY DIFFERENT, SUPER SNEAKY kind of bias.

Friends, let’s talk regression to the mean. (1/N) pic.twitter.com/M2tEEsBiyH

— Laura Hatfield (@laura_tastic) July 27, 2018

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