🔎 What this note addresses

The use of draft lottery numbers (U.S. lotteries held 1969–1972) has become a common instrument in studies of political attitudes and behavior because, in principle, they provide true randomization of exposure to military service or its threat. However, the first lottery conducted in 1969 was not drawn randomly: citizens born in the fourth quarter of the year had disproportionately higher draft risks. This note explains that randomization failure and how it could, in theory, undermine the draft lottery’s role as an instrumental variable.

🧾 What the evidence shows from national survey data

• Data source: American National Election Studies (ANES).
• Key empirical result: individuals most affected by the 1969 randomization failure (those born in the fourth quarter) largely do not appear statistically distinct from those born at other times of year.
• Main implication: with some caveats, researchers should be able to treat the 1969 draft numbers as if they were assigned at random.

⚠️ How the 1969 flaw could still matter in theory

• A nonrandom draw could bias estimates if birth-quarter correlates with unobserved confounders.
• Potential problems highlighted include:
• failure of randomization,
• sample attrition that interacts with birth-quarter,
• choices of treatment or dependent variables that pick up birth-quarter differences, and
• possible violation of the exclusion restriction for instrumental-variable use.

🔧 Practical guidance for researchers using this instrument (and others with imperfect randomization)

• Carefully assess sources of randomization failure and whether they correlate with outcomes.
• Check for differential attrition by instrument status.
• Consider how treatment and outcome selection might amplify or mitigate biases tied to the instrument.
• Evaluate the plausibility of the exclusion restriction in the specific substantive application.

✨ Why this matters

This note reconciles the documented procedural flaw in the 1969 draft lottery with empirical evidence from ANES showing little observable difference for the most affected cohort. It concludes that the 1969 numbers can often be treated as effectively random, while underscoring concrete checks and caveats that apply both to the draft-lottery instrument and to other natural experiments with imperfect randomization.