Triple Differences Models

We all remember the first time we were introduced to differences in differences models. Was it the Card and Krueger minimum wage paper? Was it Card's Mariel boatlift paper?  You surely saw the nice tables with before and after in the treatment and control groups. Pretty intuitive, right? A bit more complicated to link the tables to regression estimates but doable. Since then, you've added to your difs in difs repertoire and maybe you've even done a few triple differences analyses. Everything is OK until...you go to write up your results and realize that the estimate on that triple interaction is not so easy to explain! Don't worry, we've all been there. 

My suggestion: Have another look at my favorite explanation of differences in differences (in differences) models. This video starring my colleague, Nishith Prakash, and his coauthor, Karthik Muralidharan. Then make similar diagrams for your own paper. Tell your story in the same way that they tell their story about bicycles. Maybe make a video? I think this will help you to tell your story in your paper. 

I also recommend reading the section on triple differences in Scott Cunningham's online book, Causal Inference: The Mixtape. I really like the entire chapter on differences in differences (starts on page 263), but I especially like the discussion of differences in differences in differences (starting on page 273). He provides lots of examples of papers that use triple differences techniques. You can refer to them to help you write up your results. He also provides sample Stata code for a DDD model! 

Thank you, Shiyi, for inspiring this post! I hope it's helpful.