My paper with Jeff Bloem (IFPRI) and Noah Wexler (UMN, Humphrey School) titled “The Paper of How: Estimating Treatment Effects with the Front-Door Criterion” is now published (and accessible free of charge, thanks to the University of Minnesota libraries covering open access) in the Oxford Bulletin of Economics and Statistics. You can access it here. Here is the abstract, followed by some miscellaneous thoughts about this research project:
We illustrate the use of Pearl’s (1995) front-door criterion with observational data with an application in which the assumptions for point identification hold. For identification, the front-door criterion leverages exogenous mediator variables on the causal path. After a preliminary discussion of the identification assumptions behind and the estimation framework used for the front-door criterion, we present an empirical application. In our application, we look at the effect of deciding to share an Uber or Lyft ride on tipping by exploiting the algorithm-driven exogenous variation in whether one actually shares a ride conditional on authorizing sharing, the full fare paid, and origin–destination fixed effects interacted with two-hour interval fixed effects. We find that most of the observed negative relationship between choosing to share a ride and tipping is driven by customer selection into sharing rather than by sharing itself. In the Appendix, we explore the consequences of violating the identification assumptions for the front-door criterion.
This has been a long project, and publishing this paper has been an uphill battle. It was a long project because Jeff and I started discussing ideas for this paper in the fall of 2019; I know this because I had scribbled a few things on my office whiteboard about it, and those scribblings were still there when I returned to the office after the lockdowns ended. In the meantime, we added Noah as a coauthor since he brought the application to the table.
It was an uphill battle because of the resistance of many to the idea that there are applications for the front-door criterion, which is something we discuss in the conclusion of the paper. While it is difficult to find applications that exactly satisfy the requirements of the front-door criterion, we discuss what happens when those requirements do not hold strictly in the appendix. To me, this is where a lot of the value added of the paper lies, and if you are interested in using the front-door criterion in your own work, I urge you to read the appendix to adapt its use to your specific application.
My view is that the use of instrumental variables is not much easier than the use of the front-door criterion, and that had one never heard of instrumental variables and were told about them today, one’s conclusion would likely be that finding a good instrument would be nearly impossible. And yet, we have learned to live with the difficulty and the (many) imperfections of instrumental variables, so we can almost surely learn to live with the difficulty and the imperfections of the front-door criterion. All along, I’ve suspected that, analogous to how economists prefer probit to logit, economists tend to be skeptical of the front-door criterion because it was derived outside of economics.