Economics and social science: the denominator is part of the claim

Research question. Can a portable reliance record preserve the distinction between a registered analysis, an identified sample effect, a transported policy claim, and the population of reviews that actually finishes?

Bounded answer. A declared record can keep these objects separate. Two elementary models show why the separation matters; they do not show that a real institution will honor it. The study, people, outcomes, and effort prices here are synthetic.

The situation

The invented Harbor team evaluates an informational intervention in two types of site. Its versioned plan specifies an average effect for the trial sample. The team obtains a positive estimate and shares code that reproduces its table. A municipal analyst wants to use that estimate for a different mix of sites. A funder also wants an apparently neutral review queue to prioritize its own studies.

These are distinct questions. Registration can document what was planned; reproduction can document what code calculates; identification concerns how the design supports the estimand; transport concerns a new setting. The review queue itself has a selection problem if some reviewers disproportionately decline or finish particular work.

The AEA RCT Registry’s official guidelines distinguish registration review from research-quality or ethics review and support versioned study entries. Its stated eligibility is social-science RCTs, not clinical trials. Use the registry as a source identifier and chronology, not as a quality badge. Guidelines, checked 2026-09-25.

Deaton and Cartwright’s primary paper emphasizes that moving trial findings to other groups requires justification. That motivates our explicit transport assumptions; our numerical example is independently constructed. Primary paper record, search-retrieved abstract checked 2026-09-25.

Model 1: a sample effect is not automatically a target effect

Let $S\in\{A,B\}$ label site type and let $\tau_s$ be its average treatment effect. Under random assignment within the toy trial, an appropriate estimator can estimate the sample mixture

$$\tau_{\mathrm{trial}}=w_A\tau_A+w_B\tau_B.$$

Suppose $\tau_A=2$, $\tau_B=0$, and trial weights are $(0.8,0.2)$. The trial effect is $1.6$. A target population with weights $(0.2,0.8)$ has effect $0.4$ if the within-type effects transfer unchanged and both target types have trial support. The fourfold difference comes entirely from composition. It is not a bias correction that MCRP can infer from a citation.

The elementary transport formula

$$\tau_{\mathrm{target}}=\sum_s v_s\tau_s$$

requires target weights, adequate support, stable definitions of treatment and outcome, and justified within-type transport. Interference, unmeasured effect modifiers, endogenous participation, implementation changes and general-equilibrium effects can break that model. A missing type C cannot be repaired by renormalizing only A and B without changing the target estimand. Report unsupported transport as unknown or partial, not as zero effect for C.

The fixture uses stipulated exact effects, so no confidence interval is claimed. A real analysis would propagate sampling uncertainty and weight uncertainty, and separate confirmatory and exploratory analyses.

Model 2: completed reviews are a selected population

Let an invitation target an adversarial control group with probability $q$, with completion probabilities $c_a$ for adversarial and $c_h$ for other invitees. Then

$$P(a\mid\mathrm{complete})= \frac{q c_a}{q c_a+(1-q)c_h}.$$

At $q=0.1$, $c_a=1$, $c_h=0.01$, the completed share is $100/109\approx0.91743$. An invitation-level “10% maximum” would badly misdescribe completed reviews. This is a conditional-probability identity, not an estimated attack rate.

The repair is not simply to reroll until someone completes. Rerolls spend time, can amplify selection, and may exhaust the only independent experts. Record offered, eligible, invited, accepted, completed and relied-upon denominators, plus refusals and retries. A fair invitation distribution and a fair completion distribution are different design objectives. Neither establishes correct reviews.

Reliance can select once more, independently of allocation. Suppose 10 adverse and 90 other reviews have completed: the adverse completion share is 0.1. If an editor relies only on the adverse 10, the adverse share among relied-upon reviews is 1. That is a separate finite-count fixture, not a continuation of the earlier 100/109 example. Recording every stage exposes the selection; it does not constrain the editor’s legitimate discretion or prove decision quality. Any promised influence bound must specify whether it concerns invitations, completions, or actual reliance. Representation, expertise and decision quality are different objectives.

Four receipts, without upgrading the estimand

In a real application, a substantive identification check would need more than matching a plan and script. Timestamped plans can still be underspecified or amended; protocol records should show both chronology and deviations. An exploratory analysis may be valuable if labeled as such. The framework should not incentivize retroactive relabeling as preregistered.

Scarcity, sponsorship and individual versus team participation

Suppose 20 studies compete for 40 effort tokens. A sponsor submits 15 studies, each requesting 2 tokens; unsponsored authors submit 5. Uniform allocation per study gives 75% of attention to the sponsor even if the verdict function never reads a payment field. This does not prove wrongdoing, but it shows why “no paid verdict” is incomplete as an attention-fairness claim.

Track sponsor/control-group shares separately from judgments. Compare uniform qualified assignment, disclosed principal-level caps, and a newcomer opportunity reserve under matched expertise and total capacity. Caps can themselves deny useful work; publish exclusions and delays. An allegedly additive sponsored pool is not additive if it draws the same scarce reviewers away from the common pool.

A solo researcher can contribute a 1-token estimand check. A large team can prepare a replication bundle and conduct internal checks, but its agents do not become many independent outside reviewers. An economist may model different within-team production functions while retaining one external accountable principal. The protocol needs the boundary, not a theory of every team’s internals.

Failure and repaired workflow

The failure path labels a registered, reproducible estimate “policy-ready,” reports only completed favorable reviews, and cites an invitation cap as protection from capture. The repaired path retains the original estimand, offers transport as a new scoped claim, records unsupported population cells, and reports completion selection separately from allocation. A declined or incomplete check is visible work, not erased from the denominator.

An amendment can change an analysis plan, an estimate, or an intended use. These are different events. A changed city population does not necessarily invalidate the old trial calculation; it can invalidate its relevance to the city. Exact receipt identity permits both statements to coexist without a global trust score.

Human exercise and answer key

Ten-minute entry: Ask participants to compute the two weighted averages and write the population attached to each. Then give them the completion probabilities and ask whether a 10% invitation share ensures a 10% completed-review share.

Answer key: Trial mixture 1.6; target mixture 0.4 conditional on transport; completed adverse share about 91.74%. In the separate final-selection example, a 10% completed share becomes a 100% relied-upon share. An unrepresented target type remains unknown. A perfectly performed arithmetic check does not establish causal identification.

Forty-five-minute clinic: Participants play author, checker, municipal analyst, and resource steward. The author presents a plan deviation; the analyst changes the target population; the steward introduces asymmetric refusal. Each role must preserve the useful narrow result and state which new work is needed. Count the steward’s administrative labor, not just the reviewing economists’ labor.

Agent task and falsifiable evaluation

The domain oracle computes the two mixture effects and conditional completion share with exact rational arithmetic. The implementer should maintain distinct targets for the trial calculation and transport calculation, with transport assumptions as explicit dependencies. A new target mix must not silently mutate the old result. The toy receipt engine checks scopes and declared dependencies; it does not estimate treatment effects or validate randomization.

Proposed evaluation crosses three interfaces (letter, structured template, receipts) with hidden versus explicit population changes. A separate routing experiment varies completion probabilities, sponsor submission share, and principal labeling. Outcomes include estimand errors, unsupported transport, completion concentration, denied work, and total labor. Arithmetic accuracy alone is an inadequate endpoint. No study has been preregistered or run by this packet.

Claim ledger and closest-work boundary

The addition to existing registry, replication and evidence-synthesis practice is a proposed portable boundary around a particular use. It is not a new causal identification theorem, public procurement rule, or mechanism-design equilibrium.