Random allocation
Every student has the same probability of receiving an offer.
← One-minute overview
Research design / from data to decisions
How to produce a verifiable economic result.
Fix the budget and the objective, compare transparent rules, account for uncertainty, and calculate the maximum justified price of additional information.
01
Need
Mathematics proficiency in PISA
02
Allocation
Equal capacity, different rules
03
Budget
Information costs reduce the number of places
04
Decision
Compare coverage and justified spending
01Question and population
One clear objective:
reach students in need.
The primary criterion is the share of students below basic mathematics proficiency who are offered a place. Additional criteria describe the composition of recipients and their share of the initial skill deficit.
The target population is limited to students of PISA age represented by the survey in 17 covered Ukrainian regions. Weights do not recover unknown outcomes for excluded territories or children outside the survey’s coverage.
War provides the context and the resource-allocation problem. This design does not separate its causal contribution from pre-war differences, the pandemic or selection into the survey.
02Comparing allocation rules
Change the rule.
Keep the number of offers fixed.
The main scenario offers places to 20% of the represented population. Capacities of 10% and 30% are checked separately. These are research scenarios, not existing quotas.
Rural priority
Priority for students in a rural school stratum, identified by STRATUM. This is not a verified residential address.
Family resources
Priority for the bottom weighted quartile of ESCS among nonmissing values. All ties at the threshold are included.
Parental education
Priority for HISCED codes 1–5: highest parental education below short-cycle tertiary education.
How equal capacity is maintained
If the priority group is larger than capacity, each member has the same selection probability. If it is smaller, all members are offered a place and the remainder is allocated randomly among everyone else. We calculate expected coverage rather than draw a lottery of named students.
Students with missing ESCS or HISCED remain in the sample. Missing values do not confer priority under the baseline rule; a separate scenario checks a different treatment.
03Estimation and uncertainty
Skills: 10 plausible values
The basic mathematics proficiency threshold is 420.07. For each of ten plausible values, we separately calculate below-threshold status and the depth of the deficit, max(420.07 − Y, 0).
These values represent uncertainty about the distribution of skills. Averaging them for each child does not produce an exact individual diagnosis.
Sampling: 81 sets of weights
The final weight and 80 replicate weights account for the survey design. The ESCS quartile, priority-group size and selection probabilities are recalculated in every replicate.
We use BRR-Fay with a parameter of 0.5, then add between-imputation variance. Differences between rules are calculated as paired contrasts before pooling.
Uncertainty in the estimateSampling variance + uncertainty about skills
Preliminary intervals: estimate ± 1.96 SE. These do not include future lottery randomness, tutoring effects or unknown properties of a diagnostic test.
Technical specification for the professor
For each plausible value m: Uₘ = 0.05 Σᵣ(θₘᵣ − θₘ)² over 80 replicates. The total is T = mean(Uₘ) + 1.1 × Var(θₘ), where between-imputation variance uses the divisor M − 1; SE = √T.
The original four rules were defined before their pilot results were examined. Missing-data checks, the hybrid rule and capacities of 10%/30% were added after the first calculation and are exploratory. There was no preregistration; the next specification should be fixed before expanding the analysis.
04The economics of additional information
Every screening expense
has an alternative use.
The same money could fund more tutoring places. The model determines how much additional spending is offset by a better composition of recipients.
After paying for screeningq(s) = q₀ − s / c
N is population size; c is the cost of a place; B is the budget after common baseline administrative expenses; q₀ = B / (N × c); and s is the additional information cost per person screened.
Everyone is screened, not just recipients
The screening bill is N × s: recipients have not yet been identified when screening is paid for. The baseline model assumes the same cost of reserving a place for every student.
The objective is to preserve at least the baseline number of offers to students below basic proficiency despite the reduction in capacity.
| Information | Price limit relative to the cost of a place | Conditions |
|---|---|---|
| Perfect knowledge of status | s_max / c = q₀ × (1 − p₀) | The below-threshold share exceeds initial capacity. This is only an upper bound. |
| A test with assumed accuracy | s_max / c = q₀ × (1 − p₀ / pD) | pD > p₀ and there are enough positive results. Otherwise, a separate rule for filling the remaining places is needed. |
Here p₀ is the share below the threshold among recipients under the baseline rule. For a test, pD = aL / [aL + (1 − b)(1 − L)], where L is the below-threshold share, a is sensitivity and b is specificity.
Targeting and learning gains are different objectives
If tutoring has the same effect on every student, more costly screening reduces total learning gains by reducing the number of places. Prioritizing students with insufficient skills has an independent rationale as an access objective. Maximizing returns requires data or explicit assumptions about treatment effects.
05From pilot to paper
Data and reproducibility
The original file has been obtained. Fields, missing values, weights and strata have been checked. Main estimates and standard errors were independently reproduced with separate code.
Pilot and scenario model
Four rules; checks of capacity, missing information and a hybrid. Spending limits calculated for perfect information and a grid of assumed test accuracy.
Robustness of conclusions
Alternative thresholds, leaving out regions one at a time, unequal costs per place and participation scenarios. Fix the primary specification.
The main paper
Update the literature review, identify where policy choices are robust and define limits on applying them to real programs. Interviews are not required for the core paper.