Last week, Jeff Bloem, new coauthor Noah Wexler, and I released a new version of our paper titled “The Paper of How: Estimating Treatment Effects with the Front-Door Criterion.”
Ever since the semester ended about a month ago, all three of us have been hard at work on this new version. The biggest difference between this and the previous version is the addition of an application to observational data where the assumptions for the front-door criterion (FDC) to estimate an average treatment effect (ATE) plausibly hold.
Specifically, using data on Lyft and Uber rides in Chicago during the summer of 2019, we look at the effect of choosing to share a ride (i.e., the treatment variable X) on tipping at the intensive and extensive margins (i.e., the outcome variable Y).
Obviously, because the price of a sharing-authorized ride tends to be significantly lower than the price of a solo ride, the decision to allow a shared ride is endogenous to tipping: in principle, cheapskates frugal consumers are more likely to select into authorizing a shared ride and they are less likely to tip and more likely to tip less when they do tip.
To identify the ATE of X on Y, we exploit as exogenous mediator M on the causal path from X to Y a variable which captures whether a ride is actually shared, since authorizing a shared ride does not guarantee one. To make M (conditionally) exogenous to X and Y, we rely on a battery of fixed effects (i.e., date, hour, day of the week–hour, and origin–destination fixed effects) which serve to account for the supply and demand of shared rides when the decision to authorize a shared ride is made.
What we find is that, compared to the naïvely estimated ATES obtained from simple regressions of Y at the intensive or extensive margins on X, the ATEs obtained by the FDC are more than an order of magnitude lower. In other words, it looks as though a lot of the naïve ATEs are due to the selection of cheapskates frugal consumers into authorizing a shared ride.
We also do a number of other things in the paper. Among other things, we present a “how-to” for applied economists interested in using the FDC in their own work. We identify an additional “double relevance” for the FDC to identify an ATE wherein the two constituent coefficients have to be nonzero (no matter how plausibly the theoretical story behind them). Finally, we explore departures from some of the assumptions necessary for the FDC to estimate an ATE, and what can be done in those cases.
Here is the abstract:
We present the first application of Pearl’s (1995, 2000) front-door criterion to observational data in which the required assumptions plausibly hold. For identification, the front-door criterion relies on the presence of a single, strictly exogenous mediator variable on the causal path between the treatment and outcome variables. After first explaining how to use the front-door criterion in practice, we present empirical illustrations. Our core application uses data on over 890,000 Uber and Lyft rides in Chicago to estimate the average treatment effect of the authorization of ride sharing—that is, the decision to authorize the app to overlap one’s ride with a stranger’s ride—on tipping behavior. We exploit as mediator the (conditionally) exogenous variation in whether one actually gets to share a ride, since authorizing a shared ride does not necessarily result in sharing a ride. Comparing our front-door criterion results to those of naïve regressions of tipping on the decision to authorize ride sharing, we find that almost all of the naïve negative relationship between authorizing a shared ride and tipping is due to selection effects. Finally, we explore the consequences for applied work of violating some of the assumptions underpinning the front-door criterion approach.
We have been fortunate to receive a number of comments from colleagues after discussing the paper in a Twitter thread at the end of last week. We welcome additional comments and suggestions between now and mid-July, when we were thinking of submitting.
(Want more content like this? Although I have slowed down on the ‘Metrics Monday–I only have so many things I can talk about–and on blogging in general, my friend Dan Millimet has a blog that is entirely dedicated to econometrics. You can find Dan’s blog here.)