Capstone — Should Northbridge Expand Pathways?
Capstone — Should Northbridge Expand Pathways?
Decision brief
Northbridge must decide whether to expand scholarship offers in 2027 from score band 68–72 to applicants scoring 65–72, and from 8 to 20 districts. Funding permits at most 1,200 additional offers. Officials care about degree completion, distributional access, public cost and university capacity.
Your task is not to find the largest coefficient. Build one coherent evidence chain and recommend:
- expand now;
- run a targeted expansion with evaluation;
- redesign delivery;
- or do not expand on current evidence.
Synthetic evidence pack
All records below are teaching data. The historical dates are chosen so five-year outcomes are mature.
A. 2019 lottery cohort: score band 68–72
| Assignment | Applicants | Received scholarship | Completed within 5 years |
|---|---|---|---|
| offer | 500 | 350 (70%) | 290 (58%) |
| no offer | 500 | 100 (20%) | 250 (50%) |
Immediate calculations:
- offer ITT: ;
- first stage: ;
- receipt LATE under IV assumptions: ;
- approximate ITT standard error: ;
- approximate 95% interval: .
The ITT and LATE are not competing estimates of the same parameter.
B. 2021–2023 eligibility cutoff
Applicants at score 70 become eligible. A local-linear analysis reports:
| Bandwidth | Offer-probability jump | Completion jump | Fuzzy-RDD ratio |
|---|---|---|---|
| ±2 points | 0.66 | 0.09 | 0.136 |
| ±5 points | 0.64 | 0.07 | 0.109 |
| ±10 points | 0.61 | 0.12 | 0.197 |
Scores are integer-valued, 18% lie exactly at 70, and one district allowed assessor appeals. Covariates are smooth except adviser recommendation, which rises modestly at 70.
C. 2022–2025 district rollout
Eight districts adopt at different dates; twelve have not adopted by 2025. One-year enrolment is observed for all cohorts.
| Event time | Group-time ATT | 95% simultaneous interval | Supporting cohorts |
|---|---|---|---|
| −2 | +0.01 | −0.03, 0.05 | 6 |
| −1 | +0.02 | −0.01, 0.05 | 8 |
| 0 | +0.05 | 0.01, 0.09 | 8 |
| +1 | +0.07 | 0.02, 0.12 | 6 |
| +2 | +0.09 | 0.01, 0.17 | 3 |
Early-adopting districts had more advisers and falling youth unemployment before adoption. No district reverses treatment, but applicants may apply across district borders.
D. Expansion population and delivery
| Feature | 2019 lottery | 2027 target |
|---|---|---|
| scores 65–67 | 0% | 43% |
| limited adviser access | 22% | 61% |
| rural districts | 10% | 38% |
| scholarship value | £4,000 | proposed £3,200 |
| adviser caseload | 45 | projected 90 |
Estimated public cost is £5,000 per offer including administration. Universities report 700 spare places before accommodation constraints become material.
Required analysis
1. Identification memo
Define one primary treatment, outcome, population, horizon and estimand. Draw the assignment process and state interference, non-compliance and missingness risks.
2. Design-specific evidence
For each source, complete:
| Source | Counterfactual | Estimand | Key assumption | Diagnostic | Scope |
|---|---|---|---|---|---|
| lottery | assigned no-offer applicants | ITT/LATE | random assignment; IV assumptions for receipt | balance, attrition, first stage | 2019 band 68–72 |
| cutoff | just-below applicants | local fuzzy-RDD effect | continuity; no other cutoff change | score density, covariates, bandwidth | near score 70 |
| rollout | never/not-yet districts | cohort-time ATT | conditional parallel trends, no anticipation | event support, sensitivity, spillovers | adopting districts/years |
Do not pool the three estimates until you explain why their treatments, outcomes and populations are commensurable.
3. Reproduce one estimate
Provide code or a transparent hand calculation for one primary estimate. Match inference to assignment, show the denominator and include a static result.
4. Stress the weakest assumption
Choose one:
- weak-IV/exclusion sensitivity;
- RDD manipulation or bandwidth audit;
- DID trend sensitivity;
- attrition bounds;
- transportability weighting and overlap;
- capacity/spillover scenario.
Calibrate the violation using institutional or observed evidence.
5. Move from effect to decision
State separately:
- what the historical evidence identifies;
- what must be assumed to transport it to 2027;
- how reduced scholarship value and adviser congestion alter treatment;
- how capacity, cost and distribution enter the recommendation;
- what new evaluation would reduce the most consequential uncertainty.
Recommended submission
This is a teaching template:
- 1,500-word policy memo for a non-technical committee;
- technical appendix of up to 2,500 words;
- reproducible code and data manifest;
- one-page claim–evidence table;
- five-minute oral defence.
| Criterion | Suggested share |
|---|---|
| estimand and identification | 25% |
| calculation, inference and diagnostics | 25% |
| comparison and sensitivity | 20% |
| transport, costs and policy reasoning | 20% |
| reproducibility and communication | 10% |
Checkpoint answer
What a strong recommendation notices
The lottery gives the cleanest causal offer effect for the original band; its IV ratio is a complier effect under exclusion and monotonicity. The RDD is local and complicated by integer scores, mass at the cutoff and adviser discontinuity. The staggered rollout supports a positive enrolment effect but needs conditional-trend and spillover sensitivity, and it does not yet establish five-year completion.
Direct full expansion is therefore not identified by the historical effect alone: the target contains new score and rural groups, the award is smaller, adviser intensity is lower and capacity may bind. A defensible recommendation is a capacity-limited, stratified lottery among the new eligible groups with protected delivery standards, pre-specified outcomes and district-level spillover measurement. This both provides access and learns the effect under the actual 2027 treatment version. Different recommendations can be excellent if they price the constraints and defend the transport assumptions explicitly.