Instrumental Variables in Education Research

A good instrument must be strongly correlated with the educational treatment (relevance), must not directly affect the outcome (exclusion restriction), and must satisfy monotonicity — meaning the instrument shifts treatment in the same direction for all units. Common credible instruments include lottery randomisation, compulsory schooling law cutoffs, quarter of birth, and geographic proximity to colleges.

Compute the first-stage F-statistic on the excluded instruments. A widely used rule of thumb is F > 10. When F is below this threshold, 2SLS estimates can be severely biased toward OLS. In cases of weak instruments, robust methods such as the Anderson-Rubin test or LIML estimation are preferred.

The Local Average Treatment Effect is the causal effect for compliers — those whose treatment status was changed by the instrument. If your policy targets the full population or a specific subgroup that differs from compliers, the LATE may not directly answer your question. Always characterise the complier population to assess the policy relevance of the estimate.

2SLS can be applied with a binary outcome, but the estimates are interpreted as linear probability model coefficients. Non-linear IV estimators exist (e.g., bivariate probit) but impose stronger assumptions. For many education applications, linear 2SLS with a binary outcome is an acceptable and standard practice.

When a sharp administrative cutoff determines treatment eligibility — such as a test score threshold for a remedial program or a birthday cutoff for school entry age — regression discontinuity is often preferable because the identifying assumption (continuity of potential outcomes at the cutoff) is more transparent and testable than the IV exclusion restriction.