Marginal Priority Group Lottery Instrumentation
Evaluating the causal impact of attending a chosen school is confounded by self-selection and parental preferences. While oversubscribed lotteries provide quasi-experimental variation, including non-random priority tiers where all applicants are accepted or rejected invalidates instrumental variable identifying assumptions.
Picture this
To test if attending a specialty program boosts performance, researchers must ignore applicants who automatically get in due to guaranteed status and applicants who are turned away immediately. Causal evaluation is restricted strictly to the middle group where a random tie-breaker coin flip determined final admission.
What the evidence says
Winning the marginal lottery increased first-choice school attendance by 53.0 percentage points (p < 0.001) and increased attended school test scores by 0.129 standard deviations (p = 0.001), isolating exogenous variation in attendance free from selection bias.
- Who
- N = 3,065 human students in marginal lottery priority groups out of 37,115 total applicants in Charlotte-Mecklenburg Schools, North Carolina (2,591 with complete baseline data).
- How
- Two-stage least squares instrumental variables (2SLS/IV) regression using marginal priority group random lottery numbers as instruments for first-choice school attendance, controlling for lottery fixed effects and baseline covariates.
What to do
Isolate lottery instrumental variables strictly to oversubscribed marginal priority groups where admission probabilities are strictly bounded between 0 and 1.
From the source
"We exploit lottery random assignment by analyzing the subset of students choosing non-home-schools that were oversubscribed and limit our sample to students in marginal priority groups within those schools - priority groups for which lottery number alone determined initial admission."
Heterogeneous Preferences and the Efficacy of Public School Choice