The Useful Silence

Why governments choose the liability they cannot see — the political economy of unrecorded PPP commitments, and why recognition and disclosure, not better valuation, are the reforms that bite

Author: David Duarte Arancibia, Austral Fiscal & Infrastructure Intelligence Date: July 2026 Audience: ministries of finance and fiscal councils; IMF Fiscal Affairs and fiscal-transparency practitioners; supreme audit institutions; academics in public economics and political economy; the informed-policy press Cite as: Duarte Arancibia, David, The Useful Silence (15 July 2026). SSRN: ssrn.com/abstract=7389838 · DOI: 10.2139/ssrn.7389838. Open access under CC BY. Series: paper 12 of the Austral series on the fiscal risks of public-private partnerships; the political-economy companion to The Recognition Rule. Disclosure: the author spent a career on both sides of the incentive this paper names — inside Chile's budget office (DIPRES) and later as head of the PPP unit at Chile's Ministry of Finance, where the pressures described in §6 were not a theory but a working environment; then as a co-developer of PFRAM (the IMF/World Bank PPP Fiscal Risk Assessment Model) and as the World Bank's lead on PPP fiscal-risk assessment, building the pricing tools this paper argues are systematically under-used. He is also the founder of Austral, which sells such tools; readers should weigh that interest. The paper's claims rest on public documents quoted verbatim and on a disclosed, reproducible empirical exercise — including a null result reported as such.

Abstract

Every quantitative paper in this series ends at the same puzzle. The liability is real; the valuation is tractable — a minimum-revenue guarantee is priceable, a foreign-exchange (FX) backstop is priceable, a termination clause is priceable, and this series has priced them; and yet almost no government prices them: in half of the IMF's fiscal-transparency evaluations to date, PPP disclosure is rated "Not Met," the lowest rating the Code awards. The standard explanation is capacity. This paper argues the better explanation is incentive: the silence is useful. When a fiscal rule binds on a measured aggregate — debt, the deficit — any contract form whose obligations escape the measure lets a government buy visible infrastructure now and book the cost later, invisibly. The demand for public-private partnerships is therefore, in part, demand for a recognition treatment rather than for a procurement technology, and the incentive not to price the resulting liabilities is structural, not accidental.

None of this is a heterodox accusation. It is the official sector's own stated view, quoted here at length: the IMF warned in 2004 that "the driving force behind PPPs may be… the ability to bypass expenditure controls, and to move public investment off budget and debt off the government balance sheet, by exploiting loopholes in current fiscal accounting and reporting conventions"; its 2021 guidance concedes that "in many cases PPPs are regarded as a way to spend more in infrastructure circumventing budgetary controls and legislative oversight"; and the European Court of Auditors states plainly that off-balance-sheet treatment under ESA 2010 (the European statistical framework) "incentivises" PPP use "for enhanced compliance with the… Maastricht criteria" — and found on audit that the statistical treatment of PPPs is "an important consideration" in the choice of the procurement option. What the official sector states, the record confirms behaviourally: where the recognition boundary moved, behaviour moved with it — the United Kingdom abolished its flagship Private Finance Initiative (PFI, latterly PF2) once accrual accounting and its own watchdogs exposed the incentive; Portugal's off-book concessions were forced onto the balance sheet at the worst possible moment; Italy created an off-budget agency expressly to form PPPs while complying with the Stability and Growth Pact; and the segment of the European PPP market most sensitive to statistical treatment — government-pay contracts — fell from more than 80% of deals to a trough of 30% over the window in which the statistical rules tightened, a fall that survives, at nearly full magnitude, the exclusion of the UK, whose own exit is the first case.

We are equally candid about what the cross-country data cannot show. We ran the obvious panel — PPP investment against fiscal-rule adoption across 72 emerging economies — and report it as what it is: a null, with the reasons (de-jure rule dummies are not bindingness; the one quasi-experiment in the literature, on French municipalities, likewise rejects the simple debt-hiding channel even while confirming that fiscally constrained governments choose PPPs more). A sharper preview on Eurostat's own off-balance-sheet PPP stocks — the dependent variable, it turns out, that the EU already collects — reads in the predicted direction as fiscal space shrinks, but is honestly underpowered, and we report it in full. The evidence for the mechanism is not a regression coefficient; it is the official sector's own words, the documented behavioural responses to boundary moves, and a worked contract (Box 1) showing the boundary is worth half a point of measured debt per hospital.

The conclusion reframes this series. Valuation engines are necessary infrastructure, but they fight a standing political incentive not to be run. The reforms that bite are the ones that remove the usefulness of the silence: recognition parity between procurement forms, disclosure of the full commitment stock, and fiscal anchors written on a perimeter no contract form escapes. A rule that prices only what it can see will keep purchasing what it cannot.

Keywords: public-private partnerships · fiscal rules · fiscal illusion · creative accounting · off-balance-sheet liabilities · recognition · disclosure · Eurostat · PFI · political economy of public finance.

Feedback & discussion. Published openly for challenge. Comment at https://austral-intelligence.com/research; email [email protected].

Contents

1. The puzzle this series keeps meeting
2. The mechanism — a rule, a boundary, a substitution
3. An old idea with new instruments
4. The record — when the boundary moves, behaviour moves
5. What a cross-country panel can and cannot show — including our own null
6. Why the silence persists
7. Ranking the reforms — what actually removes the incentive
8. Limitations
9. The policy lead     Appendix A — the panel exercises, in full · Appendix B — glossary

1. The puzzle this series keeps meeting

This series has spent eleven papers pricing the fiscal risks of public-private partnerships: the guarantee that pays out when traffic collapses, the exchange-rate backstop that pays out when the currency does, the indexation commitment that binds hardest when inflation is highest, the renegotiation that arrives with near-certainty and the termination clause that prices like a written put. Each paper builds the valuation, shows it is tractable on data a ministry already holds, and ships the instrument. And each paper, at some point, collides with the same observation: almost nobody does this. The record is systematic: across the 37 IMF fiscal-transparency evaluations that have rated the PPP-disclosure principle (2013–2024), half rated it "Not Met" — the lowest rating on the Code's scale — and more than four in five found it short of good practice. Even in Chile — one of the most sophisticated fiscal administrations in the developing world, and by regional standards a disclosure leader (§4) — the evaluation found financial liabilities related to PPPs only "partially reported (0.2 percent of GDP)" and rated the principle "Not Met."¹ When the strong performer fails the test, the gap is not an idiosyncrasy; it is the norm.

The comfortable explanation is capacity: ministries lack the models, the data, the actuaries. This series is itself a refutation of that explanation — every instrument in it runs on public data with published code. A better explanation must account not just for the absence of pricing but for its pattern: where a government is bound, the silence is selective — the liabilities that go unpriced are precisely the ones its rule would have to count if its perimeter were honest (§4 closes on a live example); where the boundary is weakly enforced, there is often not even a test to engineer to, and the commitments simply accumulate unmeasured (§4's emerging-market mirror). That pattern is not what incapacity looks like. It is what an incentive looks like.

So this paper — the political-economy chapter of the series — makes the argument the technical papers only imply. The silence around PPP liabilities is not a bug awaiting a technical fix. It is a feature: for a government operating near a fiscal constraint written on a measured aggregate, the unrecorded liability is the point of the contract form, or at least a substantial part of its attraction. Naming that incentive changes what counts as reform. If the problem were capacity, the answer would be better calculators — and this series' engines would be sufficient. Because the problem is incentive, the answer is to make the silence worthless: recognition rules that treat a debt-financed hospital and a PPP-financed hospital identically, disclosure that publishes the commitment stock whether or not the rule counts it, and anchors written on a perimeter no contract form escapes. The calculators matter — but as the infrastructure those reforms need, not as a substitute for them.

One clarification of scope, before the argument. Nothing here claims that PPPs are only accounting devices, or that every PPP programme is circumvention. PPPs have genuine efficiency rationales — the bundling of construction and operation, whole-of-life maintenance incentives, real risk transfer — established by the same authors this paper leans on.² The claim is about a margin: when a fiscal rule binds, the recognition boundary adds a fiscal-illusion motive on top of whatever efficiency motive exists, and that added motive distorts the choice of contract form, the volume of commitments, and — most relevantly for this series — the willingness to measure what has been committed. The evidence that follows is evidence about that margin.

2. The mechanism — a rule, a boundary, a substitution

The mechanism has three moving parts, none exotic.

The constraint. A government maximises deliverable, visible investment — and the electoral payoff that attends it — subject to a fiscal rule written on a measured aggregate: a debt anchor, a deficit ceiling, an expenditure cap. The rule binds; the shadow price of measured fiscal space is positive. This is not a hypothetical: the companion Chile paper documents a live case, where the government's own projections cross the country's legal debt anchor by 2028 and the fiscal stance has turned contractionary in response.³

The boundary. The recognition rule — the subject of this series' tenth paper — makes the measured aggregate manipulable through contract design. The same hospital can be procured as public works, in which case its financing is debt and scores against the anchor, or as an availability-payment PPP structured to pass the statistical off-balance-sheet tests, in which case a materially identical stream of state obligations scores as nothing at all.⁴ The boundary is not fraud; it is written into the statistical frameworks themselves — for Europe, ESA 2010 (the European System of Accounts, on which the EU's fiscal aggregates are compiled) and its application manual, the MGDD — complete with published criteria a transaction adviser can engineer to. The European Court of Auditors — not a critic of PPPs, an auditor of them — states the consequence plainly: under ESA 2010, "public involvement in PPPs, under certain conditions, [can] be registered as off-balance sheet items," and "this incentivises their use for enhanced compliance with the Euro Convergence Criteria, also known as the Maastricht criteria."⁵

How much the boundary is worth is not rhetoric; it is computable, and Box 1 computes it.

Box 1 — The same hospital, two procurements. One hospital: capex US$300m, 0.5% of a US$60bn GDP, delivered under a 25-year contract. Procured as public works, the state borrows and builds: measured gross debt rises 0.5% of GDP, and the capex hits net lending up front. Procured as an availability-payment PPP engineered to the ESA 2010 boundary, the identical hospital adds 0.0% to measured debt and nothing to the deficit at close. Yet the state's unconditional obligations are the same by construction: the availability fee is set equal to the level debt service on the borrowing alternative — US$21.3m a year for 25 years, a present value of US$300m either way at the 5% government borrowing rate. (A real PPP fee, carrying the private cost of capital, would be larger.)

Run through the recognition engine of the companion paper, the PPP scores off the government balance sheet under both statistical lenses (ESA 2010/MGDD and GFSM 2014) — and on under IPSAS 32, the lens that reads control (the state controls the services, the users, the price, and the residual). The economic-tail test also reads ON here, but for a modelled reason worth stating: unlike the companion paper's stylised availability contract, which abstracts from termination exposure (and whose tail therefore reads off), this contract prices its fair-value termination compensation explicitly — roughly 0.9 × capex, ~0.45% of GDP of contingent exposure — which clears the tail lens's materiality line. The engineering is visible in the parameters, each set one notch inside the line: partner construction and availability risk with automatic deductions; a 49% debt guarantee against a 50% reconsolidation threshold; no government capital contribution against a 50% majority-financing line; termination compensation at fair value rather than debt-based; handback at market conditions; no revenue guarantee. Flip any single one and the contract reconsolidates.

Same asset, same service, same present value of unconditional payments — and a 0.5-percentage-point difference in measured debt. For a government whose rule binds on the measured aggregate, the recognition boundary is worth half a point of debt per hospital, purchased entirely through contract form. Reproducible: worked_example.py alongside this paper, scored through recognition_core.py of The Recognition Rule.

The substitution. With a binding rule and an available boundary, the government substitutes toward the unrecorded form — and here the incentive does its quiet damage, because the substitution operates even where the PPP is the inferior procurement choice, and because it extends beyond the procurement decision to the measurement decision: a ministry that has used the boundary has no appetite for instruments that publicise what crossed it. The theoretical treatment closest to this mechanism is Maskin and Tirole's model of public-private partnerships under government spending limits, and it is worth being precise about what it does and does not show. In their model, a spending-biased official games imperfect public accounting to understate the cost of favoured projects; PPP contracts offer a specific channel — contractor rents backloaded into the unobserved out-years of a strategically incomplete contract — through which a spending cap can be circumvented, even as the bundled PPP form improves cost transparency on another margin. The circumvention motive itself — "the marked increase in PPP contracts worldwide is often attributed less to the intrinsic qualities of such contracts than to governments' attempts to evade budget constraints by taking liabilities off the balance sheet" — appears in their paper as the motivating stylized fact, drawn from the policy record rather than derived in the model.⁶ The formal literature, in other words, supplies the channel and takes the motive from observation. This paper's business is the observation.

The mechanism also predicts its own concealment, which is what makes it this series' concern. A liability that has been kept off the measured aggregate is worth less to its creator if a public valuation puts a number on it. So the same incentive that produces the contract form produces the un-priced portfolio, the guarantee register that stops at enumeration, the contingent-liability report that discloses the probabilistic sliver and omits the firm stream. The general form of this prediction is older than the PPP literature: Milesi-Ferretti showed formally that rules written on measured aggregates invite creative accounting in proportion as they bind; Koen and van den Noord documented empirically, across Europe, that fiscal gimmickry rises when rules tighten; and Irwin catalogued the device inventory — of which the off-balance-sheet PPP is a distinguished member — and observed that such devices are revealed precisely by moving from cash to accrual measurement.⁷ The PPP recognition boundary is the general law's most consequential current instance.

Finally, note what the mechanism implies for a government whose anchor is about to bind. It faces a fork this series' companion paper states from the other side: it can cut capital expenditure — the visible adjustment, and, as that paper shows, the one that sacrifices the highest-multiplier spending — or it can keep building through the form that does not score. The two papers describe the two horns of the same dilemma. A rule that cannot see either the assets that borrowing creates or the liabilities that contracts create will, under pressure, produce both distortions at once: less recorded building, and more unrecorded obligation.³

3. An old idea with new instruments

The intellectual pedigree of the mechanism deserves a paragraph, because it inoculates against the charge of cynicism. That fiscal institutions can be designed to obscure — that the observed architecture of taxes and budgets is better explained by the minimisation of perceived burden than of actual burden — is the founding claim of the fiscal-illusion literature, stated by Amilcare Puviani in 1903, revived for Anglophone public finance by James Buchanan in 1967, and organised into a testable research programme by Wallace Oates in 1988.⁸ The PPP recognition boundary is that literature's modern instrument: an institution that makes a given quantum of state obligation perceptually smaller — to the legislature, the rating agency, the rule — without making it actually smaller. What is new is not the idea but the scale and the specificity: a written, engineerable test, published by the statistical authority itself, that determines whether a thirty-year payment obligation exists, for the purposes of the number the law watches.

And the official sector has known it, in writing, for two decades — which converts this section from accusation to citation. The IMF's 2004 Board paper on PPPs, the founding document of the Fund's engagement with the subject, states it with a bluntness later documents never improved on: "the driving force behind PPPs may be not only a quest to increase economic and social efficiency, but also the ability to bypass expenditure controls, and to move public investment off budget and debt off the government balance sheet, by exploiting loopholes in current fiscal accounting and reporting conventions" — adding, of the Eurostat decision of that year, that it "could open the door to PPPs that are intended mainly to circumvent the SGP" (the EU's Stability and Growth Pact). Even the pre-history fits: the same paper records that the earliest UK private-finance proposals were driven by "a desire on the part of some public enterprises and local governments to bypass expenditure controls imposed by the central government" — the identical mechanism operating one level down, an entity bound by a spending control reaching for private finance to escape it.⁹ Seventeen years later the Fund's operational guidance had not softened: PPPs generate "an illusion of additional fiscal space"; "by keeping PPPs off-budget, governments can increase long-term commitments in infrastructure without legislative scrutiny or oversight, jeopardizing fiscal sustainability. In many cases PPPs are regarded as a way to spend more in infrastructure circumventing budgetary controls and legislative oversight"; and — the sentence closest to this paper's thesis — the Eurostat framework "generates the incentive to structure PPP contracts to circumvent Eurostat rules."¹⁰

That the diagnosis is official and old, while the rules that reward the behaviour remain in force, is itself a datum. It says the obstacle was never analytical. Institutions do not persist for twenty years against their designers' understanding unless someone finds them useful; §6 returns to who, and why.

4. The record — when the boundary moves, behaviour moves

Cross-sectional evidence on this mechanism is treacherous (§5 shows how treacherous, on our own attempt). The evidence that discriminates is dynamic: episodes where the recognition boundary itself moved — was tightened, was bypassed, was forced — and behaviour visibly moved with it. These reveal-events are the empirical spine of the paper.

The United Kingdom: the form died when the advantage died. The UK ran the world's largest PPP programme — over 700 Private Finance Initiative (PFI) deals, roughly £60 billion in capital value, carrying a committed unitary-charge stream of about £199 billion into the 2040s.¹¹ For its first decade and a half the programme lived on both sides of a measurement wedge: from 2009-10, accrual accounting under IFRS (International Financial Reporting Standards) put nearly all PFI on the Whole of Government Accounts balance sheet, while the ESA-based national accounts — the basis of the fiscal rules — kept the majority off headline public sector net debt (PSND). The size of the wedge was quantified by the government's own institutions: the Office for Budget Responsibility (OBR) put off-balance-sheet PFI at roughly £35 billion — 2.5% of GDP — at March 2010, and as late as 2018 the Office for National Statistics (ONS) counted about £6 billion of PFI inside public sector net debt against about £28 billion outside it.¹² Nor was the motive a matter of inference: the Treasury Select Committee concluded in 2011 that the incentive to use PFI rested on its national-accounts invisibility, and the OBR's 2017 fiscal-risks report classified PFI as a fiscal illusion in nearly so many words.¹³ Then the boundary's usefulness collapsed — accrual numbers in the public domain, watchdogs naming the incentive, and the January 2018 collapse of Carillion, one of the programme's biggest contractors, removing the political cover — and the programme did not survive the loss: "I have never signed off a PFI contract as Chancellor, and I can confirm today that I never will," the Chancellor told Parliament in October 2018. "I can announce that the Government will abolish the use of PFI and PF2 for future projects…"¹⁴ No efficiency property of the contract form changed between 2016 and 2018. What changed is that the silence stopped working. The form died with it — the single cleanest behavioural observation the record offers.

Europe: the auditor names the motive, and the sensitive segment shrinks. The European record adds two things the UK case cannot: an audit finding and a composition test. The audit finding comes from the European Court of Auditors' 2018 special report — whose framing statement §2 quotes — which concluded, after examining twelve co-financed PPPs, that "the statistical treatment of PPPs is an important consideration for public authorities when deciding whether to use this procurement option" and that off-balance-sheet recording "risks undermining value-for-money and transparency."⁵ The composition test comes from the European Investment Bank's own market data, compiled by its European PPP Expertise Centre (EPEC). European PPP volumes have fallen for many reasons — values were already far below their pre-crisis peak when our window opens, the exit of the UK (the largest market) accelerated the decline, the pandemic deepened it — and we make no causal claim about aggregate volumes, whose break points in any case predate the 2016 statistical tightening.¹⁵ But within the shrinking market, the composition shifted in exactly the direction the mechanism predicts: government-pay PPPs — the availability-payment segment whose fiscal attraction is the statistical treatment, since the state pays either way and only the recognition differs — fell from 89% of European deals in 2014 and more than 80% in 2016 to 51% in 2018, 41% in 2020, and a trough of 30% in 2022, before a partial reversion by 2024, across precisely the period in which the revised Eurostat guidance and its secondary provisions made the off-balance-sheet engineering of such contracts materially harder.¹⁷ Part of that shift is country mix — the UK, an overwhelmingly government-pay market that alone closed 28 of Europe's 69 deals in 2016, left over the same window. But the confound is bounded, not merely conceded. Stripping the UK out entirely, under the assumption most adverse to our claim — that every UK deal was government-pay — the ex-UK government-pay share still falls from 84% of deals in 2014 to 38% in 2018 and 27% in 2022 (at most about 31% under the opposite bound): a decline of nearly sixty points, essentially the headline fall.¹⁶ The composition shift is a European phenomenon, not a UK-exit artifact — and the UK's exit is in any case this section's first case: the market's biggest government-pay buyer left precisely because its recognition advantage had died, so the shift registers the mechanism on both margins, exit and substitution. The segment that existed for the treatment is the segment that shrank when the treatment tightened (Figure 1). Italy supplies the reductio: Ispa, an off-budget agency created expressly "to form PPPs and raise capital by issuing state-guaranteed bonds, so as to finance new infrastructure while complying with the European Stability and Growth Pact" — the mechanism of §2 with a legal personality.¹⁸ And Portugal supplies the reckoning: in the 2010 statistical revision, PPPs re-examined against the ESA tests were reclassified into general government, adding half a percent of GDP to the deficit (a further half-point came from reclassified public transport corporations) — the deferred cost surfacing on the eve of the EU/IMF adjustment programme and documented in its reports, at the exact moment the sovereign could least absorb it; the IMF's own guidance notes that the road agency's "off-budget status exempted it from the gateway process," which is the §2 substitution stated as a case history.¹⁹

Figure 1 — The sensitive segment shrinks. Panels 1–2 (context only — no causal claim: values open the window already far below the 2007 peak, counts break in 2015, and the UK's exit and the pandemic dominate the late years): the European PPP market by financing value and transaction count, 2010–2024. Panel 3 (the evidential series): the government-pay share of deals falls from 89% (2014) through 51% (2018) and 41% (2020) to a 30% trough (2022) across the window in which the EPEC–Eurostat Guide (Sep 2016) and the MGDD revisions tightened the off-balance-sheet tests, before reverting to 61.5% by 2024; the fall survives the exclusion of the UK at nearly full magnitude (§4), and the perimeter adds Israel from the 2023 edition. Source: EPEC Market Update series (EIB); each plotted value is mapped to its source edition (and page where recorded) in the table inside make_figure.py, with the restatement convention and its one disclosed exception in the note to that table.

The emerging-market mirror. Outside Europe the boundary is enforced more weakly still, and the pattern shows in the transparency record rather than in reclassification events — quantified, country by country, in the IMF's own evaluations. Jordan, rated Not Met: identified PPP liabilities of 21 percent of 2020 GDP, with power-purchase commitments of 36 percent of GDP in present value to 2045. Georgia (2017, Not Met): gross PPP and power-purchase exposure of 19.8 percent of GDP, with the rights and obligations of legacy PPPs and of the largest projects — the Nenskra plant alone, 6.2 percent of GDP of termination exposure — unreported. Albania (Not Met): at least 55 signed PPPs, present value near 7 percent of GDP, no register. Kenya: unreported PPPs of 5.7 percent of GDP at its 2016 evaluation — and still Not Met at its 2020 re-evaluation. Peru: a net ~4 percent of GDP published while gross commitments near 20 percent went unpublished. Even Portugal's evaluation, four years after §4's reclassification reckoning, found €21.3 billion of concessions — 13 percent of GDP — outside its monitoring unit's coverage.¹ And Chile — a top-tier administration and a regional disclosure leader — had its PPP stock found only fragmentarily reported and the principle unmet. Where the European story is "engineered to the test," the story in emerging markets and developing economies (EMDEs) is quieter — there is often no binding test to engineer to, and the commitments simply accumulate unseen. The instruments differ; the silence is the same.

Chile, in real time. The author's home system supplies the live case, and an honest complication. Chile is, by regional standards, the positive template — its budget office has published an annual contingent-liability report since 2007, disclosing and probabilistically valuing the concession minimum-income guarantees.²⁰ Yet exactly as Chile's legal debt anchor begins to bind — the government's own projections cross the 45%-of-GDP prudent level by 2028, and the fiscal stance has tightened in response — the State has announced a US$17.6 billion concession tender pipeline for 2024–28 (transport-dominated, from the Valparaíso–Santiago rail to the Route 5 relicitations), a concession-based prison programme of roughly US$4.2 billion partly overlapping that pipeline's near-term tranche, and an award record (the Talca and Copiapó prisons, the Red O'Higgins hospitals) already carrying firm availability subsidies.²⁴ We are careful about what this coincidence is: an illustration of the mechanism, not evidence for it — §6 concedes that a fiscal-stress/concession-enthusiasm correlation is overdetermined, and this paragraph obeys that concession. What does discriminate is the disclosure pattern. The firm subsidy stream of exactly these contracts is absent from every ledger the rule and the public debate do read: gross debt, the debt anchor's perimeter, and the contingent-liability report, which covers the guarantees but not the unconditional payments. It is partially carried on the one ledger no rule reads — the accrual balance sheet kept by the Contraloría, Chile's comptroller-general — and the qualification matters more than the recognition. That balance sheet does carry explicit concession lines: a Bienes Concesionados asset of CLP 886bn net at end-2023, composed almost entirely of the subsidised social infrastructure (prisons CLP 575bn, hospitals CLP 166bn — reported by a single health service — airports CLP 100bn, and CLP 287bn of "other," four-fifths of it from the concessions directorate), and a Pasivos por Concesiones liability. But that liability is CLP 294bn current against CLP 59bn non-current, and the non-current portion has fallen across the five years reported while the programme grew. A balance sheet carrying the present value of two- and three-decade availability streams does not look like that; one recognising amounts falling due does. The inference is ours and we mark it as such — the statements do not disclose the liability's composition as they do the asset's — but the shape of the number is hard to reconcile with recognition of the contractual stock.²¹ The correction this forces on our own framing is worth stating plainly: it is not that the firm stream sits on an unread ledger. It is that no ledger carries it whole. Disclosure of the contingent layer coexists with silence on the firm layer, because what governs is not transparency culture in general but what the binding rule counts. Chile discloses what its anchor ignores and stays silent on what its anchor would have to count if its perimeter were honest. Even the positive template is silent exactly where silence is useful. And the silence survives being asked. In July 2026 the author requested, under Chile's access-to-information statute, the concessions directorate's own projection of the system's future commitments — the Gasto Sectorial — Compromisos Futuros model — contract by contract, distinguishing the fixed construction and operation subsidies, compensations, minimum-income guarantees and the remaining firm obligations of the Treasury, together with the projection's discount rate, horizon and methodological note. The request was derived to the budget office, which refused it in August, invoking the statute's commercial-interest exception: the current version incorporates estimates of contractual modifications and compensations for concessions "in the process of negotiation with the respective concessionaire," and disclosure would prejudice "the negotiating position of the Treasury." Applying the statute's severability principle, the office directed the requester instead to the tender documents and award decrees published on the works ministry's site — that is, to the contracts, not to the aggregate.²³ The instrument exists; the State maintains and updates it; and the number it produces is withheld on a ground that has nothing to do with analytical capacity. What the same State does publish, in the very same period, sharpens rather than softens the point. Chile's budget-execution data are released monthly and openly to sub-allocation level, and the concession payments are in there — scattered across at least six ministries. In the first half of 2026 the payments to concessionaires that can be identified as such — not a programme total, which these files do not support constructing — came to about CLP 201 billion (roughly US$220 million): the health ministry's hospital programme naming its instruments precisely — Subsidio Fijo a la Construcción CLP 55.8bn, equipment and non-clinical furniture subsidies a further CLP 13.1bn, contract-modification payments CLP 3.3bn — and the civil-aviation directorate reporting CLP 17.4bn under the plain heading "payments to airport concessionaires." Alongside them sits some CLP 540bn of value-added-tax mechanics (the IVA Concesiones line in the Treasury vote and the input-credit reimbursements in public works, health and interior), which is circulation rather than subsidy and which dominates the visible numbers.

Three features of that record matter. First, the largest single line is the least informative: the justice ministry's concession programme — the prisons — executed CLP 111.3bn in six months under an item styled "other goods and services" and an allocation styled "other." The programme is named; the payment is not. Second, no line anywhere in the central-government budget identifies an operation subsidy (the SFO, the recurring availability payment that is the firm stream this paper is about), and no minimum-income guarantee registers execution — consistent with a contingent instrument that has not been called, and with a firm instrument that has no line of its own. Third, and decisively, not one of these allocations is attributable to a contract. One can watch the money leave; one cannot say which concession received it, aggregate what remains owed, or place any of it on a payment schedule.²²

A fourth feature is methodological, and it belongs in the argument rather than in a footnote. Reconstructing even the programme's own annual budget from these releases is not straightforward: the execution files are clean at allocation level and reconcile exactly against the published chapter aggregates, but the companion budget-law files carry subtotal rows at each level of the classification, so a naive sum of the concessions directorate's vote inflates it several-fold. The point is not that the data are bad — they are unusually good by regional standards, open, monthly and granular. It is that granular cash-flow releases and an attributable commitment stock are different objects, and possessing the first at this quality does not deliver the second. That is precisely the gap the reserved projection occupies.

The two halves fit together exactly. What Chile publishes is the disaggregated cash flow, ministry by ministry, in the period it occurs. What it declines to release is the one instrument that turns those flows into an attributable, projected stock. This is not an accusation of concealment: road concessions are overwhelmingly user-paid, so the absence of construction subsidies in the public-works vote is a fact about the contracts, not about the disclosure; and the health ministry's naming practice shows the system is perfectly capable of transparency when nothing in the fiscal aggregates turns on it. The asymmetry of §4 is therefore not only a publication choice observable from outside: it holds when the aggregate is formally requested, and it survives the fact that the pieces are public. The silence is not about the payments. It is about the sum.

5. What a cross-country panel can and cannot show — including our own null

A reader persuaded by §4 will ask for the regression: across countries and years, does PPP investment rise when fiscal rules bind? We asked it, ran it, and report it — in full in Appendix A — as what it turned out to be: a null. Merging the IMF Fiscal Rules Dataset with the World Bank's Private Participation in Infrastructure (PPI) investment series (72 emerging economies covered by both datasets, 1990–2023, N = 2,324 country-years), two-way fixed-effects estimates of PPP investment on rule-in-force indicators are positive but statistically indistinguishable from zero in every specification (t ≤ 1.1), the headline estimate shrinks under outlier treatment, and an event study around 43 national rule adoptions is flat — the median within-country change in PPP investment after rule adoption is exactly zero. This is "no evidence of an effect," not "evidence of no effect": a de-jure rule dummy is a poor proxy for a binding constraint (most rules, most years, do not bind — and the mechanism operates only when they do), and the dependent variable is zero-inflated and noisy. But the honest reading is that the naive cross-country design cannot see the mechanism, and we decline to torture it until it confesses.²⁵

The published literature, read carefully, lands in the same nuanced place — and we cite its strongest counter-result with the prominence it deserves. Three findings bracket the question. In the European Union — where rules are supranational, monitored, and enforced — Cepparulo, Eusepi and Giuriato find that stringent numerical budget-balance rules do foster "government's opportunism in the choice of PPPs": the rules-to-PPP margin, visible where rules actually bind.²⁶ Across emerging markets, Hammami, Ruhashyankiko and Yehoue find PPPs significantly more common under heavy debt burdens — though their deficit variable is never significant, and their own interpretation is benign leverage rather than circumvention.²⁷ And in the one quasi-experiment that could isolate the channel — France's 2011 decree putting local-government PPP debt on-balance-sheet, which removed the accounting advantage while leaving every other property of the contract intact — Buso, Marty and Tran find that budget-constrained municipalities chose PPPs more both before and after the change, and conclude that "debt hiding is a relevant, but not a sufficient element" in the choice: in their published summary, the constrained-government preference for PPPs "is not explained by the possibility of debt-hiding."²⁸ That result is the strongest published counterweight to this paper's mechanism, and we do not wave it away. Our reply is scope, and it is §4's reply: the French decree changed municipal accounting inside a national fiscal framework whose sovereign-level rules were untouched — French mayors face financing constraints, not Maastricht. The mechanism this paper describes operates at the boundary between contract design and the sovereign fiscal rule; and at that boundary the discriminating evidence is not cross-sectional association but the reveal-events of §4, where the boundary itself moved and the sovereign's behaviour — abolition, reclassification, re-engineering, composition shift — moved with it. The identification that could settle the panel question properly — continuous distance-to-limit within the EU's uniform rule framework, rather than de-jure dummies across heterogeneous ones — turns out to be partially runnable now, and we ran its first pass rather than merely flag it. Eurostat, it emerges, collects exactly the dependent variable this design needs: the adjusted capital value of off-balance-sheet PPPs by member state — the stock of precisely the object this paper is about — reported annually since 2010 in the supplementary table to the EDP notification (dataset gov_cl_ppp), near-complete for all 27 members (a handful of pre-2013 cells are unreported). The preview (Appendix A.2) reads as the mechanism predicts, and no stronger: within countries, off-balance-sheet PPP stocks rise as fiscal space to the 60% debt reference shrinks, with the predicted sign but marginal significance in the levels specification (p ≈ 0.09) and nothing in flows; the binding dummies are dead (p ≈ 0.8) — the de-jure lesson again; the cross-section is right-signed and insignificant at N = 27, with essentially all off-balance stock held by a handful of members (Portugal, Hungary, Slovakia, Spain, Belgium, Ireland — all but Slovakia carrying high debt) and nine members — Germany and France among them — reporting zero in every year they report. Directionally consistent, honestly underpowered: 41% of the panel is zeros and Portugal's post-programme drawdown dominates the within variation. The design that could actually identify is an event study around Eurostat reclassification decisions, and that is future work. One exploratory by-catch, reported with the multiplicity warning it requires (it is one coefficient among the dozen we ran): government guarantee stocks rise significantly as the deficit limit binds (p ≈ 0.02) — if it survives dedicated scrutiny, substitution across silent instruments is §6's common-pool prediction operating one instrument over.

There is also a fitting irony in the null, which we note rather than hide: the reason the panel fails is the gap between rules as written and rules as they bind — the de-jure/de-facto gap. A paper about what measured aggregates fail to capture should not be surprised when a measured rule dummy fails to capture its subject.

6. Why the silence persists

If the incentive has been named in official documents for twenty years, why does it survive? Four reasons, none flattering, all structural.

Time horizons and blame asymmetry. The benefits of the unrecorded form arrive within the electoral cycle — the ribbon, the jobs, the rule formally complied with. The costs arrive on someone else's watch: renegotiations cluster years after award, guarantee calls arrive in downturns, termination and handback liabilities mature in decades. The asymmetry is not incidental to the contract form; long-duration incompleteness is what makes the backloading channel of §2 work. A liability whose recognition can be deferred past the horizon of the officials who created it will find creators.

The sophisticated-ministry problem. It is tempting to model the finance ministry as the dupe of line ministries' enthusiasm. The record — and the author's professional experience inside two of these institutions — supports a less comfortable model: the finance ministry is frequently the user. When the rule binds the government as a whole, it binds the ministry that must deliver the government's programme within it, and the recognition boundary is then the ministry's own margin of adjustment. This is why technical assistance aimed at "building ministry-of-finance (MoF) capacity to assess PPP fiscal risks" so often produces capacity that is not used: the constraint was never analytical. The ministry that declines to run the valuation is not failing to understand the liability; it is declining to create the number that would have to be explained — or, where the number already exists and is maintained, declining to release it, as §4's refusal shows.

The common-pool of the rule itself. A fiscal rule converts fiscal space into a scarce common resource; each claimant — sector ministries, subnationals, state enterprises — has the standard common-pool incentive to appropriate it through whichever channel is not metered. The unrecorded PPP is the unmetered channel. This predicts, correctly, that circumvention pressure rises with the tightness of the rule — the Koen–van den Noord finding — and that it migrates across instruments as each is successively closed: off-budget funds, then public enterprises, then PPPs, then whatever is next. The reform problem is therefore not "fix the PPP loophole" but "meter the perimeter," which is §7's argument.

And the honest counterweights. Three concessions keep the argument calibrated. First, PPPs have real efficiency rationales, and some programmes are dominated by them; observed PPP use is never all circumvention, and the efficiency and circumvention motives coexist within single programmes and single contracts.² Second, constrained governments also have genuinely larger unmet infrastructure needs — the correlation between fiscal stress and PPP enthusiasm would exist in a world of pure efficiency motives too, which is exactly why §5's cross-sections cannot settle the question and this paper leans on reveal-events instead. Third, self-correction happens: the UK closed its programme, Eurostat tightened its tests, Chile built a contingent-liability report that most OECD members still lack, and Georgia moved its PPP-disclosure rating from Not Met to Good between its 2017 and 2024 evaluations — the only country in the FTE record to do so. The mechanism is not destiny. It is a standing pressure that institutions can be designed against — which is the point of designing them.

7. Ranking the reforms — what actually removes the incentive

If the diagnosis is incentive rather than capacity, reforms should be ranked by how much of the incentive they remove — not by how much analytical sophistication they add. Four tiers, in descending order of bite.

1. Recognition parity. The root reform is to make the recognition boundary worthless: a procurement-neutral rule under which a given stream of unconditional state obligations scores identically whether it was created by a bond issue or an availability contract. This is the standard this series' Recognition Rule paper derives and the direction the frameworks have been crawling — the control test of IPSAS 32 (the international public-sector accounting standard for service concessions) already puts most grantor obligations on the accounting balance sheet; the gap that remains, and that the cases of §4 exploited, is between the accounting books and the statistical aggregates — ESA in Europe, elsewhere the IMF's government finance statistics framework codified in the GFSM — that the fiscal rules actually watch.⁴ Parity between those two is the reform that kills the §2 substitution at its source — and the UK case quantifies exactly what it would remove: a 2.5%-of-GDP wedge between what the accounting books recorded and what the rule's measure saw. (The UK, note, closed its programme rather than its wedge — the abolition is tier 2's visibility case, not a parity reform; the wedge on the legacy stock persists.) One honest qualification from §5: the single direct test of parity in the literature — France's 2011 decree, which consolidated municipal PPP debt — did not stop constrained mayors choosing PPPs, because it moved a ledger no sovereign fiscal rule watches. Parity bites where the binding rule reads the number being equalised; that is the sovereign statistical boundary — the number the UK's rules watched, and the one its programme was built against.

2. Disclosure of the full commitment stock. Where parity is not yet won, publication is the fallback that devalues the silence: an annual, audited statement of the state's firm and contingent PPP commitments — present values, payment schedules, guarantee exposures — published whether or not the fiscal rule counts them. Disclosure does not remove the rule-arbitrage, but it removes its invisibility, and the UK case shows how much visibility can do: the accrual numbers and the watchdog reports had stripped the programme of its accounting rationale before Carillion's failure removed its remaining political cover, and the abolition invoked no change in the statistical rules the UK's fiscal targets were written on — visibility was central to the form's death, even if it did not act alone. The design of such a disclosure regime — what must be published for a programme's numbers to be trustable — is the subject of a forthcoming paper in this series; Chile's contingent-liability report is the regional proof of feasibility and, per §4, also the proof that disclosure must cover the firm stream to close the loop.²⁰

3. Anchors on an honest perimeter. Fiscal rules themselves can be written so that no contract form escapes them: anchor debt on the consolidated public sector, count recognised concession liabilities in the anchor's perimeter, and let the rule see what the state owes rather than what one statistical slice records. This is the Chile companion paper's recommendation, generalised: a rule that cannot be arbitraged by reclassification is a rule with nothing to be silent about.³

4. Valuation engines — necessary, and insufficient alone. Last, deliberately, come this series' own instruments. Pricing the guarantee book, stress-testing the portfolio, valuing the FX and indexation tails: all of it is the infrastructure the first three reforms need — a disclosure regime with no valuations discloses nothing, and a consolidated anchor needs the concession stock in present value. But supplied without the first three, the engines are tools awaiting a user with a motive not to use them. Maskin and Tirole's closing policy line points the same way: PPP contracts "need to be carefully reviewed by independent authorities that can expose hidden rent backloading" — the operative word being independent, because §6's user cannot be the auditor of its own silence.⁶

The reframing of the series, then, in one sentence: these papers built the pricing engines; this paper explains why they will sit idle unless the recognition and disclosure reforms give someone standing, and a reason, to run them — and why fiscal councils, supreme audit institutions and statistical offices, not the transacting ministry, are the natural operators.

8. Limitations

(1) The claim is a margin, not a totality. The paper establishes that a recognition-arbitrage motive exists, is officially acknowledged, and has visibly moved behaviour where the boundary moved; it does not — and cannot — decompose any given PPP programme into efficiency and circumvention shares. (2) The econometrics is weak and is reported as such (§5, Appendix A): the cross-country panel is a null, and the EU distance-to-limit preview is directionally consistent but underpowered (p ≈ 0.09 in its best specification, with 41% zeros and Portugal dominating the variation) — the thesis was never staked on either, but a reader who weighs only regression evidence should weigh this paper accordingly. The strongest published quasi-experiment (France, 2011) rejects the simple debt-hiding channel at the municipal level while confirming the constrained-government preference for PPPs; our scope reply (§5) is an argument, not a proof. (3) Reveal-events are selected by visibility. Boundary moves that produced no behavioural response generate no headline; the §4 record cannot exclude survivorship, though the UK, Portugal and composition cases are large enough that their absence would be equally visible. (4) The composition evidence is descriptive, but its principal confound is bounded. The collapse of the government-pay share of European deals coincides with the statistical tightening; rate environments and national programme decisions moved over the same window, and no causal decomposition is attempted. The largest confound — the UK's exit — is however bounded rather than conceded: the ex-UK share falls essentially as far as the headline series under the assumption most adverse to the claim (§4, ¹⁶). Residual caveats: the 2018–2022 UK counts are chart-read (verified by summing to each edition's total, exactly for 2018–2021 and to 43 of 45 for 2022), and the EPEC perimeter adds Israel from the 2023 edition. (5) The author's seat — inside DIPRES, the Chilean MoF, and the PFRAM/World Bank apparatus — is both the paper's authority and its bias; the argument has been kept, deliberately, to quotable documents and reproducible exercises so that it does not rest on testimony. (6) No new engine ships with this paper — the Box 1 vignette runs on the companion paper's recognition classifier, and the appendix scripts are estimation code, not product; it is an argument built on the series' instruments, the official record, one disclosed null, and one disclosed underpowered preview.

9. The policy lead

The recommendation follows from the diagnosis. Stop treating the un-priced PPP portfolio as an analytical failure to be fixed with training and toolkits — the tools exist, and this series is evidence. Treat it as what the official record has called it for twenty years: an incentive problem created by rules that watch one slice of the balance sheet. The reforms that bite are the ones that remove the incentive — recognition parity between procurement forms; an audited, published statement of the full commitment stock, firm and contingent; fiscal anchors written on a perimeter no contract form escapes; and independent institutions, not the transacting ministry, holding the valuation pen.

Two clarifications keep the close honest. The incentives that have actually been removed were removed this way — the UK by abolishing the programme once the accrual numbers spoke, Eurostat by tightening the test, Chile, partially, by publishing the report; none by calculator acquisition alone, though Chile's report, note, embeds valuation (the guarantees are probabilistically priced), which is tier 4's point exactly: the calculator matters once an institution with standing runs it. And the thesis is falsifiable. It would be reversed by sovereign-level boundary tightenings followed by no change in the contract-form mix, or by the §5 distance-to-limit design returning a robust null on the government-pay margin — the observations that would say the silence was incidental after all.

The silence around PPP liabilities is useful to its keepers. The task of reform is not to lament that fact but to repeal it: make the liability visible wherever it is created, count it wherever the rule looks, and the contract form will finally have to compete on the only ground where it was ever legitimately attractive — whether it builds and runs infrastructure better than the state can. Where it does, it will survive honest accounting. Where it survives only by accounting, that is the finding.

Appendices

Appendix A — the panel exercises, in full

Reported per the series' practice of publishing negative results with the same care as positive ones.

A.1 The cross-country panel (EMDEs, fiscal-rule dummies)

Data. (i) IMF Fiscal Rules Dataset (1985–2024 vintage): country-year indicators for national and supranational expenditure, revenue, budget-balance and debt rules, 123 economies. (ii) World Bank Private Participation in Infrastructure (PPI): total PPI investment by country-year, 1990–2023, retrieved via the World Bank Data360 API; no-deal years coded as zero investment throughout. (iii) GDP (current US$), World Bank World Development Indicators (WDI), for scaling. Merged panel: 72 PPI-covered emerging and developing economies also covered by the rules dataset, 1990–2023, N = 2,324 country-years — below 72 × 34 because (i) the rules dataset covers four economies (Kiribati, Tonga, Vietnam, Vanuatu) for only part of the window and (ii) some country-years lack WDI GDP; N = 4,366 when the 58 PPI economies not covered by the rules dataset, and the uncovered country-years of the four above, are additionally retained with their rule indicators coded as no-rule-in-force. Dependent variable: PPI investment in % of GDP (analysis-sample mean 0.38, s.d. 1.34 — heavily zero-inflated and right-skewed).

Specifications and results. Two-way fixed effects — TWFE: country + year fixed effects — with standard errors clustered by country; the full grid, as produced by estimate_panel.py:

Event study around the 43 national-rule adoptions inside the panel with an observed pre-period (±5-year window): mean PPI/GDP 0.49 pre vs 0.50 post; within-country post-minus-pre mean −0.02, median exactly 0.00.

Reading. The sign is positive in every fixed-effects specification and the magnitude is not economically trivial at face value (≈0.1% of GDP), but nothing approaches significance anywhere on the grid (max t = 1.09, spec 6); the headline any-rule estimate shrinks under winsorising and the asinh transform — what little there is rides on outlier deal-years — while the debt-rule estimate moves slightly up ex-big-four; and the event study is flat, with a within-country median change of exactly zero. Two structural reasons to expect exactly this even if the mechanism is real: a de-jure rule indicator does not measure bindingness (most rules, most years, are slack — and §2's mechanism operates only at a binding constraint); and the dependent variable mixes the mechanism's margin (government-pay PPPs substituting for public works) with demand-risk concessions that carry no recognition advantage. The design that could identify — continuous distance-to-limit within a uniform rule framework (the EU), with government-pay PPPs separated from demand-risk concessions — is future work. On the gate: the pre-committed rule was a confirmatory table if the design identified, an honest-null paragraph if not; it did not identify, §5 carries the null paragraph, and this appendix reports the full grid — beyond the committed minimum — for reproducibility. Replication artifacts ship in the panel/ directory alongside the paper's source: merged_panel.csv, the estimation script estimate_panel.py (which reproduces every number above end-to-end), regression_results.csv, the original preview verdict, and the gate text.

A.2 The EU distance-to-limit preview (Eurostat off-balance-sheet PPP stocks)

Data. Dependent variable: Eurostat dataset gov_cl_ppp, national-accounts item OFF_PPP — the "adjusted capital value of off-balance-sheet PPPs," general government, % of GDP — reported by every member state in the supplementary table accompanying the EDP notification, annual 2010–2024, EU-27: N = 391 of a possible 405 country-years — 14 early cells (Germany 2010–11; Denmark, Estonia, Spain, Ireland 2010–12) are not reported; the DV is zero in 41% of the observed cells, and nine members — Bulgaria, Germany, France, Luxembourg, the Netherlands, Poland, Romania, Sweden, Slovenia — report zero in every year they report. This series is government-pay by construction: ESA records demand-risk concessions separately. Regressors from gov_10dd_edpt1: continuous distance of gross debt to the 60% reference value and of the deficit to 3%, plus binding indicators; gov_cl_guar (guarantee stocks) for the context regression.

Results (country + year fixed effects, standard errors clustered by country, 27 clusters):

Negative distance coefficients are the mechanism's predicted sign: less fiscal space, more off-balance-sheet PPP. At the point estimate of spec (2), ten points less debt-distance associates with ≈0.05 pp of GDP more off-balance PPP stock. Cross-section: mean off-balance stock is concentrated in Portugal (2.7% of GDP on average), Hungary (1.5), Slovakia (1.4), then Ireland, Spain and Belgium — all but Slovakia high-debt members (Slovakia's mean debt over the window is ~52% of GDP) — right-signed and insignificant at N = 27.

Reading. Directionally consistent with the mechanism in levels, marginal at conventional thresholds, null in flows — and the binding dummies are dead while the continuous measure carries what signal there is, which is §5's de-jure/de-facto argument re-materialising inside the EU. Structural limits: a stock DV conflates classification choices with mechanical amortisation of legacy contracts; Portugal's post-programme drawdown dominates the within variation; 27 clusters. The guarantee-substitution coefficient (spec 9) is exploratory — one significant coefficient among the dozen run, reported under a multiplicity warning, not a finding. The identifying design this preview motivates — an event study around individual Eurostat reclassification decisions — is left for dedicated work. Artifacts in panel/eu/: the raw Eurostat API extracts (gov_cl_ppp_raw.json, debt_gd.json, deficit_b9.json, gov_cl_guar.json), eu_panel.csv, build_and_estimate.py (runs from the directory and reproduces every number above from the extracts), and the full estimation output.

Appendix B — glossary

• Recognition boundary — the set of statistical/accounting tests determining whether a PPP's asset and liability score on the government balance sheet: ESA 2010 (the European System of Accounts) as applied by the MGDD (Eurostat's Manual on Government Deficit and Debt), IPSAS 32 (the International Public Sector Accounting Standard on service concession arrangements), and GFSM 2014 (the IMF's Government Finance Statistics Manual).
• PFI / PF2 — the UK's Private Finance Initiative (from 1992) and its successor Private Finance 2 (from 2012); the world's largest PPP programme until its abolition in October 2018.
• Government-pay PPP — availability-payment contract in which the state is the payer; the segment whose fiscal attraction depends on statistical treatment.
• Fiscal illusion — systematic misperception of the fiscal burden induced by the design of fiscal institutions (Puviani 1903).
• Reveal-event — an episode in which the recognition boundary moves (tightening, reclassification, accounting reform) and behaviour responds, exposing the incentive.
• De-jure vs de-facto rule — a fiscal rule as legislated vs a rule as it actually binds in a given year; the gap that defeats naive panels (§5, Appendix A).