The leverage that was already in the rulebook¶

A plain-language companion to the draft working paper "Leverage Without Additionality: What Co-Funding Ratios Identify in Public Technology Programmes" (v0.2, August 2026). The paper carries the four propositions with their proofs, the numeric cross-checks, the Monte-Carlo report, and the full application to the Digital Europe Programme's published tables; this text carries the ideas.

Read the full draft working paper (PDF)

The short version. European technology programmes report a leverage factor: the co-funding beneficiaries declare per euro of public money, presented as evidence that public money mobilises private money. The paper shows what the number actually identifies. Grant programmes publish the share of project cost they pay. A programme paying half of every project collects one euro of declared co-funding per euro granted and reports a leverage of exactly one, however its beneficiaries behave. The statistic is the funding rulebook, read back. Worse, the caveat funders attach to it points the wrong way: the ratio bounds crowding-in from above, so it flatters rather than understates. Applied to the Digital Europe Programme's own published figures, the headline leverage of 0.79 identifies the share of the envelope spent at full funding rates and nothing about anybody's behaviour.

The identity¶

The arithmetic is short enough to do in the margin. A beneficiary complying with a 50% co-funding rate puts in one euro for every euro it receives. The programme adds these up and reports a leverage of one. At a 25% rate, compliance produces a leverage of three. Nothing about the beneficiary's intentions, its capital constraints, or its alternatives enters anywhere.

Two consequences follow immediately. Two programmes with identical real effects report different leverage when they fund different kinds of action. And a programme can raise its reported leverage by shifting its mix toward lower funding rates while changing nobody's investment by a euro.

The caveat points the wrong way¶

Funders usually attach a warning to the figure saying that it excludes investment induced further down the chain, so the true figure must be higher. The construction says the opposite.

The numerator counts all declared co-funding, including whatever the beneficiary would have spent anyway. Crowding in is the amount above that counterfactual. So the reported ratio equals crowding in minus the counterfactual investment per euro of grant, and that quantity is unobserved and never negative. The reported leverage is an upper bound, and it is reached only under the assumption that no beneficiary would have invested anything at all absent the grant, which is a strong claim and not one funders make out loud.

Where the number does carry information¶

Compliance with the schedule cannot produce a ratio above the highest value the schedule admits. That gives a ceiling, computable by any reader who knows the funding rates, and it turns the published table from a scoreboard into a screen: values at or below the ceiling are accounting, and only values above it require somebody to have contributed more than the rules asked.

For the Digital Europe Programme, the schedule combines a 50% grant rate with action types funded at 100%, so the ceiling is 1.00. The reported headline is 0.79, comfortably below it, and consistent with zero crowding in. What it does identify is the mix: under this two-rate schedule, 0.79 implies that about a fifth of the granted envelope went to fully funded actions. That is a genuine fact about programme composition, and it is the only quantity the headline recovers.

Of the thirteen technology areas with published totals, exactly one exceeds the ceiling: robotics, at 1.08. Three further cells clear it in the within-area breakdowns. Those four observations are the ones that carry behavioural content. Every other published cell is consistent with beneficiaries doing no more than the rules require.

Public money counted as private mobilisation¶

The reported ratio pools other public money with private money. Where the stated justification for the programme is a friction in private capital markets, only the private half speaks to it.

The programme publishes a private-only series, so the split can be computed. The private component is a minority of reported leverage in nine of the twelve areas where both are published. In artificial intelligence, 70 of the 77 points of reported leverage are other public money. In advanced connectivity, all 80 are. Public-to-public cost sharing between the Union and its member states is a real fiscal fact worth reporting; it is not evidence about private financing frictions.

It does not even rank¶

A defender might concede that the ratio is not a level estimate and argue that it still orders programmes correctly. It does not. In 20,000 sampled pairs, ordering programmes by reported leverage inverts the ordering by true crowding in on 25.2% of them. The degenerate case is sharper still: two programmes sharing one rate schedule report an identical ratio by construction, while their true crowding-in ratios span the entire admissible range.

The programme the statistic punishes¶

The clearest illustration sits at the corner of the schedule. One class of public spending funds the maintenance of open-source commons, where the licence prevents the maintainer from capturing the value it creates and the funder screens applicants precisely for the absence of alternative financing. Germany's Sovereign Tech Agency is the reference case, funding critical components at full rates and publishing per-component figures.

A full-funding-rate programme reports a leverage of exactly zero, so this statistic ranks it last in any comparison. It does so for the very feature that makes its additionality plausibly the highest in the set, since selection conditions on nobody else being willing to pay. For this class the informative statistic is coverage: what fraction of the critical substrate is under funded maintenance, the bus factor of each funded component, and funding per unit of criticality.

What to publish instead¶

The fix is small and mostly clerical. Publish the rate schedule and how public contribution is distributed across rates, so any reader can compute the mechanical part of the ratio. Publish the private component separately from the public one. Flag the observations above the ceiling, because those are the ones with behavioural content. Keep causal verbs for quantities estimated against a counterfactual.

Recovering additionality itself needs a research design rather than a reporting change: variation in funding rates or award thresholds unrelated to what beneficiaries intended to invest. Programmes that score and rank applications already generate that variation at the funding cutoff, and the application records that produce the co-funding statistic contain the ingredients.

The small print¶

The application is arithmetic on published aggregates and inherits their limits. The two series cover different windows, the totals are provisional while implementation continues, and the schedule is reconstructed from the programme's stated rates because the distribution is not published, which is itself part of the finding. Compliance is treated as exact, so the four cells above the ceiling should be read as candidates for behavioural content pending reconciliation of application figures against final reporting. Nothing here bears on whether the programme is worthwhile: a programme with zero crowding in can be justified on the appropriability grounds its own design invokes. The claim is about what one statistic supports.