Catchment Cohort Size Instrument

In Simple Words

To measure how school grant size truly affects family spending without getting confused by family choices, researchers look at how many children of school age happen to live in the surrounding area. Since the total grant amount is fixed per school, having more nearby children automatically shrinks the per-child funding without relying on family preferences or behavior.

Research question

Estimating the impact of per-student public funding on household expenditure is prone to endogeneity because school enrollment reflects unobserved household educational demand.

Participants

34 remote primary schools (closest neighboring school ≥5km away) matched to 540 households (1,195 children) in rural Zambia.

Study Design

Two-stage least squares (2SLS) instrumental variable estimation using the total number of school-age children in five primary catchment villages as an instrument for per-student rule-based grants.

Results

The first-stage F-statistic was 23.54 without controls and 10.32 with controls, yielding an IV elasticity estimate of household expenditure to rule-based grants of -0.946 to -1.124 (p < 0.01).

Takeaway

Use demographic catchment size boundaries as exogenous instruments when estimating per-capita public transfer impacts in fixed-grant administrative settings.

Related findings

• Exogenous Failure Assignment →Methods & evidence

  Imagine testing how drivers handle an unexpected patch of black ice on a road. If drivers only go onto the icy road voluntarily, only risk-tolerant drivers are tested; but if a road detour forces a random selection of drivers onto the ice patch, researchers can measure true handling ability and recovery without selection bias.

• Intention-to-Treat (ITT) Instrumentation →Methods & evidence

  When some assigned groups fail to receive a promised intervention, using initial random assignment as an indicator to adjust overall outcomes is like measuring a fitness program's impact based on everyone invited, then mathematically adjusting for those who actually attended the gym.

• Instrumental Variable Estimation under One-Sided Non-Compliance →Methods & evidence

  Imagine testing whether wearing a new type of safety goggles reduces eye injuries in a factory. If workers randomly offered goggles choose to wear them only half the time, while unoffered workers can never get them, researchers can use the initial random offer as a lever to isolate the pure effect of actually wearing the goggles.

• Second-Order Peer Instrumentation (G²X Identification) →Methods & evidence

  Imagine trying to prove whether a student's study habits directly improve a classmate's grades. Instead of measuring the classmate directly, researchers look at the background traits of the classmate's friends from another school—people who affect the classmate but have no direct contact with the original student.