Instrumental Variables

By the end of this lesson, you should be able to: say what an instrument has to satisfy and which of those conditions you can check, compute 2SLS and know what each stage does, read a first-stage F, and recognise that a weak instrument returns a confident number rather than an error.

Where lesson 7 ran out of road

Adjusting Alder Cloud's adoption data on every observable produced near-perfect covariate balance and an estimate 2.6 times the truth. The confounder was team ability, ability was never a column, and no model of the columns you have can remove a confounder that isn't among them.

Regression on this data gives:

7.7 times too large. The problem isn't the estimator. It's that all the variation in adoption is contaminated: teams chose to adopt, and what made them choose is what makes them productive.

Use a different slice of the variation

Alder ran a staggered internal rollout. Some orgs were picked at random for an early enablement push: office hours, a setup guide, a nudge from the platform team.

That push is an instrument. The idea is to stop using all the variation in adoption, and use only the part the coin flip produced.

An instrument $Z$ has to satisfy three things.

Relevance. $Z$ actually moves the treatment. Checkable, and the most important number in any IV analysis.

Independence. $Z$ is unrelated to everything else that affects the outcome. Here it holds by construction because the push was a coin flip, and the covariate table confirms nothing looks unusual:

Exclusion. $Z$ affects the outcome only through the treatment. This one cannot be tested, ever. It's the claim that being in an early wave changes how much a team ships only by changing whether they adopt the assistant. If the push also came with better documentation, or signalled that leadership cared, exclusion fails and the estimate is wrong with no warning.

Monotonicity. The push makes nobody less likely to adopt. Also untestable, and usually reasonable for an encouragement.