A variable that changes the treatment but affects the outcome only through the treatment, used to estimate a causal effect when unmeasured confounders make a direct comparison biased. The effect is the instrument's effect on the outcome divided by its effect on the treatment.
Card 1 of 276. Answer: A variable that changes the treatment but affects the outcome only through the treatment, used to estimate a causal effect when unmeasured confounders make a direct comparison biased. The effect is the instrument's effect on the outcome divided by its effect on the treatment.
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An instrument needs two properties. Relevance: it must move the treatment, which you can check from the data; a first-stage F statistic below about 10 signals a weak instrument. Exclusion: it must have no other path to the outcome, which can't be tested and has to be argued. Estimation usually uses two-stage least squares: predict the treatment from the instrument, then regress the outcome on that prediction.
Example: you can't force users to adopt a feature, but you can randomly show half of them a prompt to try it. Adoption is 60% with the prompt and 20% without, and revenue per user is 10.80 against 10.00. The random prompt is the instrument: (10.80 − 10.00) / (0.60 − 0.20) = 2.00 per user, the effect on users who adopt because of the prompt, called the local average treatment effect.
Philip Wright used the idea in 1928 to estimate supply and demand for animal and vegetable oils. Angrist and Krueger's 1991 study used quarter of birth, which shifts years of schooling through school-entry and compulsory attendance rules, to estimate the return to education. Angrist and Imbens shared the 2021 economics Nobel for this line of work, with David Card.
