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

by Judea Pearl

In this approach we pretend that the data came from some unknown random source and use standard statistical methods to find the line (or, in this case, plane) that best fits the data. The output of such an approach might be an equation that looks like this: S = $65,000 + 2,500 × EX + 5,000 × ED (8.1) Equation 8.1 tells us that (on average) the base salary of an employee with no experience and only a high school diploma is $65,000. For each year of experience, the salary increases by $2,500, and for each additional educational degree (up to two), the salary increases by $5,000. Accordingly, a regression analyst would claim, our estimate of Alice’s salary, if she had a college degree, is $65,000 + $2,500 × 6 + $5,000 × 1 = $85,000. The ease and familiarity of such imputation techniques explain why Rubin’s conception of causal inference as a missing-data problem has enjoyed broad popularity. Alas, as innocuous as these interpolation methods appear, they are fundamentally flawed. They are data driven, not model driven. All the missing data are filled in by examining other values in the table. As we have learned from the Ladder of Causation, any such method is doomed to start with; no methods based only on data (rung one) can answer counterfactual questions (rung three).