How to Use the Front-Door Criterion — New Working Paper

If you follow Marc Bellemare’s blog or specifically his ‘Metrics Monday series, you will already be aware of our new working paper. The paper is titled: “The Paper of How: Estimating Treatment Effects Using the Front-Door Criterion.” The number of people who are reading this post and who do not already read Marc’s blog is probably very small. So, with that in mind, I will offer a few additional thoughts based on the preliminary work writing this paper.

First, here is the abstract of the paper:

Empirical social science nowadays consists largely of attempts at answering questions of the form “Does X cause Y?” As a result, social scientists rely on a number of empirical techniques aimed at disentangling causal relationships from mere correlations. One such technique is Judea Pearl’s (1995, 2000) front-door criterion, which relies for identification on the presence of a single, strictly exogenous mechanism on the causal path between the treatment and outcome. Social scientists in general—and economists in particular—have been resistant to the idea of adding the front-door criterion to the standard empirical toolkit, largely due to the difficulty posed by finding the required mechanism. To help overcome that resistance, we first explain how to use the front-door criterion in a regression context. We then present three empirical illustrations of the front-door criterion. Finally, and most importantly, we look at what happens when some of the assumptions underpinning the front-door criterion are violated.

Second, when writing this paper we discussed an interesting thought experiment. Consider the counterfactual world where applied empirical researchers have not yet discovered instrumental variables. In this world, Angrist, Kruger, et al. have not demonstrated the usefulness of using an exogenous instrumental variable to disentangle the causal effect from a statistical correlation. Instead, I told you that I’ve read about a “new” method that can be used to identify causal effects. It only requires that an instrument Z influences some treatment variable X, but is otherwise excludable from the error term in the equation defining the primary outcome Y. Oh, and the correlation between Z and X must be sufficiently strong, there is another (largely untestable) assumption related to monotonicity, and the resulting estimate is this “new” treatment parameter called a “local average treatment effect.”

How would you respond? I suspect most of us would at least respond extremely cautiously and some of us would outright reject this “new” method. Now, keep this thought experiment in mind when reading about the “new” method of the front-door criterion.

Third, as I wrote on Twitter, one of the more interesting parts of this paper is our exploration of what happens when the mechanism is endogenous. This detail about the exogeneity of a mechanism that lies on the causal path between X and Y is often cited as one of the primary reasons why economists and other social scientists are hesitant to adopt the front-door criterion into their toolkit for causal inference.  We find when the endogeneity of the mechanism is strong (e.g., when the direct effect between the unobserved confounder U and the mechanism is quite a bit stronger than the indirect effect of U on M via X), the front-door criterion yields more biased estimates than the naive estimator. When the endogeneity of the mechanism is relatively weak, however, we find that the front-door criterion yields less biased estimates than the naive estimator. Figure VI (shown below) visualizes this finding. This is still a working paper, and so Marc and I would really appreciate any feedback, comments, or questions you have about this paper. Please feel free to email either of us.

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