Instrumental Variables

The one idea: When you can't fairly compare treated and untreated people, look instead for a nudge that pushed some of them into treatment for reasons unrelated to the outcome, and measure what happened to the people the nudge moved. It only works if that nudge could not have changed the outcome by any other route.

⚠️ The trap: "Any variable that's correlated with the treatment can serve as my instrument." That feels right and it's wrong. A valid instrument must move the treatment AND reach the outcome only through the treatment — a lever with any other path (like rainfall standing in for TV, where geography also drives diagnosis rates) is disqualified no matter how strong the correlation.

Sometimes the treatment you care about is hopelessly confounded and always will be. Who gets health insurance, who finishes more school, who adopts your premium feature — people sort themselves into these, and no amount of controlling-for-covariates fixes sorting you can't see. Instrumental variables (IV) is the escape hatch: instead of comparing treated to untreated people, find a lever that pushes people into treatment for reasons unrelated to the outcome, and study the push.

Call the lever Z, the treatment T (the thing whose effect you want), the outcome Y. A valid instrument moves T, and it touches Y only through T — no side doors. Here is the whole method in words: divide how much the outcome moved by how much the lever moved the treatment.

This is a single division — the AI or a stats package runs it. The plain-English rule above is the part to remember. Effect of T on…