The Book of Why: The New Science of Cause and Effect

by Judea Pearl

Yet another reason that the do-calculus remains important is transparency. As I wrote this chapter, Bareinboim (now a professor at Purdue) sent me a new puzzle: a diagram with just four observed variables, X, Y, Z, and W, and two unobservable variables, U1, U2 (see Figure 7.5). He challenged me to figure out if the effect of X on Y was estimable. There was no way to block the back-door paths and no front-door condition. I tried all my favorite shortcuts and my otherwise trustworthy intuitive arguments, both pro and con, and I couldn’t see how to do it. I could not find a way out of the maze. But as soon as Bareinboim whispered to me, “Try the do-calculus,” the answer came shining through like a baby’s smile. Every step was clear and meaningful. This is now the simplest model known to us in which the causal effect needs to be estimated by a method that goes beyond the front- and back-door adjustments. FIGURE 7.5. A new napkin problem?