An RCT Game
The pilot of the household transfer programme falls to you: a cash grant fixed by law at 3 shillings per village — its size is not yours to vary, in the pilot or in the country. What you administer is exactly what cabinet would roll out.
Your laboratory is the Lake Naro district: six market towns, five villages each. My economists have deemed the district representative of the country; on that assumption, what you find here will travel. Note one logistical fact: you and your team can never treat more than four of a town's five villages — in total, across both rounds. Surveying is not so constrained: all five may be surveyed.
Next spring I take one number to cabinet: by how much average village income rises if every village in the country receives the grant. Your final report will state an interval for that effect. Narrow, if you can defend it.
My economists insist the transfers spill through the market towns — helping neighbours, or crowding them out, in proportion to the share of a catchment that is treated. Design your experiment accordingly.
Your budget is 60 shillings, and it pays for everything: 3s to treat a village (a one-off grant, paid once — its effect persists, and it cannot be recalled) and 1s to survey a village's income (paid each round — unsurveyed villages report nothing). You have two survey rounds and my patience for neither more. Nationally, the treasury would pay the same grant once to every village; whether the effect justifies that bill is cabinet's business. Yours is the effect.
First, the timetable:
Then your posting:
Choose the villages to treat and the villages to survey — then run the wave.
One block per market town: its saturation s per wave (the share of its five villages treated), then each surveyed village's income. ● = treated that wave; — = not surveyed. Averages live in the pooled table below.
The same numbers, pooled across market towns that share a saturation s — a caveat: town-level shocks do not cancel in small samples.
| s | treated ȳ (n) | control ȳ (n) |
|---|
Village income: y = base + market shock + τ·treated + spillover. The spillover is proportional to the catchment's saturation s (share of its 5 villages treated): treated villages receive γ_T·s, untreated neighbours γ_C·s. Spillovers run through a village's own market town only — the six catchments do not trade with one another, so an untouched catchment is a clean baseline. Base level and market shocks are unknown; villages are noisy.
Units: incomes are measured in shillings, and the grant itself is worth 3s of village income if simply pocketed. τ is the total direct effect, cash included — τ above 3 means households make the money work; τ below 3 means the cash is leaking out of the village, perhaps towards the market towns.
The minister's number — the effect at national scale, where s = 1 everywhere and every village is treated — is Δ = τ + γ_T.
Treating a village costs 3s, paid once — and its effect lasts: it raises its market's saturation in every later wave, and a market once touched is never again a clean baseline. You can treat at most 4 villages per market town (the fifth must stay untreated), though all 5 may be surveyed. Surveying costs 1s per village per wave; unsurveyed villages report nothing. Market shocks are fixed across waves — a village surveyed twice can be differenced.
The long pilot: a year passes between rounds. One economy-wide shock — unknown in sign and size — shifts every village's round-2 income by the same amount, treated and untreated alike. Any comparison of round 2 against round 1 contains it; only round-2 surveys can reveal it.
You may stop after one wave; unused shillings are returned to the ministry, which does not say thank you.
The final report is an interval for Δ, scored as 100 − 2·(width + 10·miss), where miss is the distance by which the truth escapes your bounds (zero if it doesn't). Under this rule your best strategy is to report the range you believe holds Δ with 80% probability: wider than that wastes points, narrower gambles them.
State an interval for Δ, the income effect of the national rollout — an interval you would defend at 4-to-1 odds: you believe there is an 80% chance the true Δ lies inside it. The ministry works at 80% certainty; it is a busy ministry.
Scoring: 100 − 2 × width if the truth lies inside your interval; every shilling by which it escapes costs 20 more. Narrow and right is a career. Narrow and wrong is also a career, briefer.