The Anchor and the Perimeter

Chile's 45%-of-GDP debt anchor is measured on the narrowest slice of the State's balance sheet — 41.5% of GDP. Run the government's own sustainability model on the consolidated public sector it leaves out, and the same standard reads 57–61%. And no one can show where the 45% came from: under the transparency law, neither DIPRES nor the Ministry of Finance holds the model that set it. The anchor is not wrong — it is pointed at the wrong number, and derived by one no one can audit.

Author: David Duarte Arancibia, Austral Fiscal & Infrastructure Intelligence Date: July 2026 Audience: Chile's fiscal-policy community (Ministerio de Hacienda, DIPRES, Consejo Fiscal Autónomo, Congreso); IMF and OECD fiscal surveillance; sovereign credit analysts; fiscal-transparency researchers Companion software & data: the reproducible scripts, all input data, and the de-duplicated component table are published in full, in a public deposit, for independent re-running and audit (see Appendix C). Disclosure: the author was, in a prior role, part of Chile's public-finance apparatus (DIPRES) and a co-developer of the IMF/World Bank PFRAM framework. He is also the founder of Austral, which builds public-sector consolidation and contingent-liability/PPP analytics — the very class of capability this paper argues Chile's anchor lacks; readers should weigh that interest. The paper applies the State's own published method to public data, stands or falls on its reproducible code, and no proprietary Austral product generated any figure in it. It is offered as fiscal-transparency analysis, not as a claim of hidden insolvency.

Abstract

Chile anchors its fiscal rule to a prudent debt level of 45% of GDP. Since the Ley de Responsabilidad Fiscal reform of 2024 (Ley 21.683), that anchor is defined in law on the narrowest available perimeter: the gross debt of the total Central Government. At the end of 2025 that measure stood at 41.5% of GDP — under the anchor, and the basis on which the country is told its finances are sustainable (though DIPRES's own latest projection has the narrow measure breaching 45% in 2029).

That 41.5% is the narrowest number the State could have chosen, and this paper shows what happens when the government's own sustainability model is run not on that slice but on the balance sheet the State actually owes. The result is not a claim of hidden insolvency — it is that the reassurance rests entirely on where the line is drawn, and that a corporate-tax cut already dispatched by Congress and awaiting promulgation is, once its growth assumption is stripped, on its own enough to push even the narrow measure across the anchor.

This paper makes two points, using nothing but the government's own method and the public record.

First, the anchor measures the wrong slice. Once the public sector is consolidated — state-owned-enterprise debt, the present value of public-private-partnership (PPP) and concession commitments, and the contingent-liability stock that DIPRES itself publishes, all de-duplicated — the augmented liability is 57–61% of GDP, twelve to sixteen points above the anchor. We then do what no prior analysis has done: we reproduce the very model the Ministry of Finance used to derive the 45% (a fiscal-space model in which the prudent level is the highest debt from which the primary balance required to stabilise it stays within the maximum feasible primary balance of 2% of GDP, at 90% probability) and re-run it across the perimeter. The model reproduces 45% precisely under a defensible forward calibration; re-run on the consolidated stock, the probability that the required primary balance exceeds the 2%-of-GDP ceiling rises from 8.5% at the central-government measure (just under the 10% tolerance that defines the anchor) to 13–16% at every augmented measure. We are explicit that this re-run is a relabeling, not an independent model verdict: the model is monotone in the debt stock, so any stock above the prudent level necessarily reads above the tolerance. The contribution is that it re-states the perimeter gap in the rule's own metric, on the State's own balance sheet — the slice the anchor measures reads prudent; the consolidated sector it omits, by the same 90%/2%-of-GDP standard, does not.

Second, the 45% itself is an unpublished judgment. DIPRES never released the coefficients of its fiscal-reaction function or the variance-covariance of its shock model. Re-deriving the model from the public methodology, a reasonable range of forward growth-and-rate assumptions reproduces a prudent level anywhere between 31% and 60% of GDP. The anchor's apparent precision is illusory.

We are explicit about the honest cases. Under the narrowest consolidation — counting only the sovereign-dependent SOEs (EFE, Metro) and excluding commercially self-supporting ones (CODELCO, ENAP) — the augmented measure is 44.8%, fractionally under the anchor rather than over (a 9.9% breach probability, just inside the 10% tolerance); we disclose this as the binding robustness floor. And because the model coefficients are not public, this paper is a reproduction, not a replication. We therefore requested the model's parameters from DIPRES under the Ley de Transparencia — and the reply is itself the paper's sharpest finding: neither the agency that set the anchor nor the ministry that houses it can produce the model that derived the 45%. DIPRES, the author of the number, states it "no cuenta con la información" and refers the request onward; the Subsecretaría de Hacienda holds only four general or external documents, none of which contains the coefficients, the shock calibration, or the simulation that produced the 45%. A debt anchor written into law to two significant figures rests on a derivation that no part of the State can show; we have taken the response to the Consejo para la Transparencia and will report its ruling.

Keywords: Chile · prudent debt anchor · fiscal rule · gross central-government debt · state-owned enterprises · contingent liabilities · public-private partnerships · non-financial public sector · fiscal transparency · debt sustainability · fiscal-space model.

Feedback & discussion. Published openly for challenge by Hacienda, DIPRES, the CFA, and the academic community. Comment at https://austral-intelligence.com/research; email [email protected].

Contents

1. The anchor, and the perimeter the law draws
2. The model, reproduced from the public record
3. The perimeter it leaves out — the consolidated public sector
4. The re-run — the State's own model on its own balance sheet
5. How firm is 45%? The threshold as an unpublished judgment
6. Prior work, and what is new here
7. A transparency test — requested, and what came back
8. Limitations
9. The policy lead     Appendices A–C (model in full · glossary · reproducible code)

1. The anchor, and the perimeter the law draws

Chile runs a dual fiscal rule: a structural-balance target, in force since 2001, complemented since 2022 by a debt anchor — a prudent level of gross debt toward which the medium-term structural targets are set. The Executive fixes the anchor's value at the start of its term in the Decreto de Política Fiscal (Decreto 755 of 2022 first set it at 45% of GDP; substituted by Decreto 542 of 2025, which retained the 45% anchor), and the 2024 reform of the Ley de Responsabilidad Fiscal (Ley 21.683) made the anchor a legal requirement, "medido a través de la deuda bruta del Gobierno Central total como porcentaje del PIB."⁷

That phrase is the subject of this paper. Of the choices a debt rule can make — gross or net, central government or general government or the whole non-financial public sector — Chile's law selects the narrowest: gross (not net of the Treasury's substantial financial assets), and Central Government (not the broader general government, and certainly not the consolidated public sector that includes the state-owned enterprises). DIPRES's own methodological review notes that most peers anchoring a debt rule — Colombia, Perú, Costa Rica, Ecuador, Poland — define it at the level of the general government or the non-financial public sector; Chile and Australia are the outliers that limit the ceiling to the central administration.¹¹ The Consejo Fiscal Autónomo, for its part, recommended in 2021 that the anchor be defined on net debt, "pues considera que esta métrica refleja de forma más fiel la posición financiera del Estado" — a recommendation not adopted.¹¹

There is a revealing tension inside the government's own framing. The fiscal-policy decree that sets the 45% anchor states, in the same breath, that the policy will "sostener… la situación patrimonial neta del sector público" — the net worth of the public sector. Decreto 755/2022 (Art. 3°) put it more strongly — "sostener, y, a su vez, fortalecer la situación patrimonial neta del sector público" — and that net-worth objective was carried forward into the current Decreto 542/2025 (Art. 4°), which keeps "sostener" but drops "fortalecer."¹² The aspiration is stated at the level of the consolidated public sector; the operational anchor is measured on the narrowest central-government slice. This paper asks what happens when the two are reconciled.

At the end of 2025, gross debt of the total Central Government stood at 41.5% of GDP — 3.5 points under the anchor, after a 2024 structural deficit of 3.3% of GDP that badly missed its 1.9% target.⁸ (This is DIPRES's consistency-revised figure, introduced in the Q1-2026 IFP and carried forward in the Q2-2026 report; the fiscal-policy decree and the 2025 methodological review cite 41.7%.¹¹) On the narrow measure, the country has a thin but positive margin — and a shrinking one. In DIPRES's own latest projection (the Q2-2026 Informe de Finanzas Públicas, Cuadro 5, base scenario on committed spending), the same narrow measure breaches the 45% anchor in 2029 and reaches 45.5% of GDP by 2030 (48% in the adverse scenario, crossing already in 2027); only an optimistic investment-expansion scenario keeps it below the line.⁸ The IMF's 2024 Article IV reached the same conclusion independently, warning the ceiling could be breached as early as 2026 under modest slippage.²¹ And DIPRES reached even that 2028 crossing only after a "consistency re-estimation" (Recuadro 6 of the same report): its previously published path had reflected barely CLP 3,900,000 million of a CLP 13,500,000-million cumulative fiscal deterioration over 2026–30, leaving CLP 9,600,000 million "not reflected in debt" until the reconciliation forced the trajectory up through 45% — the State's own evidence that the headline gross-debt path can badly understate the fiscal picture.⁶ So the anchor gives false comfort twice over: the slice it measures is heading through the line within two years, and — as the rest of this paper shows — the slice it omits is already far past it. The question is whether the narrow measure is the right one.

Figure 1 — Source: DIPRES, Informe de Finanzas Públicas 2T-2026, Cuadro 5 (= Cuadro II.10.5.1), transcribed to data/ifp2t2026_cuadro5_deuda.csv. Supersedes the 1T-2026 base/adverse/expansion figure used in earlier drafts: the 2T revision moves the base crossing from 2028 to 2029 and publishes the Reconstruction-bill scenarios the 1T did not contain. The 2025 close (41.5%) is DIPRES's latest re-estimate, used throughout this paper; the fiscal-policy decree and 2025 methodological review cite 41.7%.

2. The model, reproduced from the public record

The 45% is not a round number plucked from the air; it is the output of a model. In Dipres (2022) — the technical evaluation behind the fiscal-policy decree, summarised in the first-quarter 2022 Informe de Finanzas Públicas — the Ministry of Finance estimated the prudent debt level using three complementary methodologies and took the most conservative.¹³ The load-bearing one is a fiscal-space model: building on the fiscal-space and debt-limit literature (Ghosh et al., 2013; Ostry et al., 2010; Fall, Bloch, Fournier & Hoeller, 2015; Eyraud, Debrun et al., 2018), the OECD's 2020 assessment of Chile's framework, and the CFA's 2021 study, it asks at what debt level the primary balance required to stabilise the debt stops being feasible.¹⁹

The mechanics are standard. Debt evolves as \(d_t = \frac{1+r}{1+g}\,d_{t-1} - pb_t\), so the primary balance that holds debt constant is \(pb^{*}(d) = \frac{r-g}{1+g}\,d\) — the debt times the interest-growth "snowball." The model fixes the maximum feasible primary balance (BPMF) at 2% of GDP — the median of the distribution of fiscal-consolidation efforts in the cross-country record (Escolano et al., 2014) — and defines the prudent debt level as the highest \(d\) at which, under the stochastic distribution of growth shocks (holding the forward real rate at its calibrated value), the required \(pb^{*}(d)\) does not exceed the BPMF with 90% probability.

We reproduce this from the public CFA and World Bank series (1990–2025). The one thing that is not public is the calibration: DIPRES never released its fiscal-reaction-function coefficients, the variance-covariance matrix of its shocks, or the exact forward interest and growth assumptions. So we re-derive them transparently. Chile's historical snowball cannot be used directly — a high GDP deflator makes nominal growth average 7.8%, which would imply an absurdly favourable debt path — so we work in real terms with forward trend assumptions: trend real growth 2.0% (Chile's potential), growth volatility 3.7% (the actual historical standard deviation, 2001–2024), and the BPMF and probability pinned at their published values. Under this calibration, the prudent debt level reproduces the published anchor exactly — d* = 45.0% of GDP — at a forward real effective interest rate of 1.58%. We are careful about what this does and does not show. Reproducing 45% is not an independent validation: \(r\) is the single free parameter, solved by bisection, so some rate always returns the anchor. The substantive question is whether that rate is plausible — and 1.58% is a defensible forward real rate (post-2022 monetary normalisation; new issuance prices above the legacy stock) but it sits above Chile's recently realised real effective cost, which on the deflator spike of 2020–2024 was close to zero. The result therefore rests on a forward assumption, not a historical fact; §5 shows exactly how much weight that assumption bears.

A word on what this reproduction claims and what it does not. The model itself is entirely standard — the fiscal-space method is the IMF's and the OECD's, not ours, and re-running it on a different debt stock is, mechanically, trivial. The contribution is neither the model nor the mechanics but the authority move: this is the calibration that returns Chile's own legal anchor, and §4 turns it on Chile's own consolidated balance sheet. The IMF's 2023 technical-assistance report on Chile had already argued, from a model of its own, that debt should be kept "well below" the 45% ceiling — but on the same central-government perimeter.²⁰ We make the complementary and sharper point: the same 45% rule, re-run through the State's own calibration, condemns a wider perimeter. The novelty is the perimeter, not the ceiling.

3. The perimeter it leaves out — the consolidated public sector

The anchor measures the central government. The State is liable for considerably more.

• State-owned enterprises. Hacienda's own Estadísticas de la Deuda Pública reports gross debt of the empresas públicas at 10.5% of GDP (September 2025) — of which only 0.68% carries an explicit State guarantee (DIPRES reports that guaranteed slice as 6.5% of the SOE total, which independently corroborates the ~10% figure). The largest is CODELCO (~7.2% of GDP); ENAP (~0.9%), EFE (~1.1%), and Metro de Santiago, the ports and others make up the rest. The principled split is who services the debt, read from the enterprise's own financial statements — not from whether a guarantee exists. This is not an Austral invention. For EFE and Metro it produces the same answer as the GFSM 2014 market/non-market sectoring test — units that cannot cover even half their costs from sales and rely on sustained government support are reclassified into general government, their debt becoming general-government debt — while CODELCO and ENAP pass that market-producer test and remain public corporations, so the floor excludes them on sectoring and the headline retains them only under the broader gross-public-sector (PSDS public sector debt, D4) concept. It is also the standing IMF and World Bank position that government assumes SOE liabilities "even where those liabilities are not explicitly guaranteed," with railways and metros the textbook government-dependent case.²³ EFE and Metro are served by the Treasury: their audited accounts rest the going concern explicitly on annual Budget-Law transfers (EFE CLP 166,000 million and Metro CLP 419,000 million in 2022 alone; together 89% of cumulative SOE losses 2017–2024), so the full Metro-and-EFE debt — not merely the 0.68% of GDP the State explicitly guarantees — is a sovereign liability. The guarantee is irrelevant to that economic reality. CODELCO and ENAP self-service their debt and remit profits to the Treasury, so they are the defensible exclusion from the conservative floor — with the caveat that CODELCO's investment-grade market access rests on an implicit sovereign uplift: its 2025 ratings are Moody's Baa2 and Fitch BBB+, but its standalone profiles — Moody's ba3 baseline credit assessment and Fitch's "bb" standalone credit profile — are below investment grade, so its market access depends on assumed government support even though its debt is excluded from the floor.²
• PPP and concession commitments. The Informe de Pasivos Contingentes values the minimum-income guarantees (IMG) on the MOP concession programme at 0.87% of GDP in present value — but that is the contingent layer. The firm State-paid subsidies (the SFC/SFO availability-type payments), which sit outside both gross debt and the IMG, are a separate, additive commitment: on the Dirección General de Concesiones' 2022 Compromisos Futuros projection their present value is ~0.4% of GDP — a floor, since concessions awarded since 2022 (e.g. the Talca and Copiapó prisons, the Red O'Higgins hospitals) add further firm subsidies. Crucially, this firm stream is a financial liability under Chile's own accrual standard (§3.1), not a contingency; we keep it out of the headline total here, pending the updated official figure.
• The contingent-liability stock. DIPRES publishes a contingent-liability stock of 8.92% of GDP (2025), spanning the deposit guarantee, student loans (CAE/FES), multilateral commitments, and SOE-guaranteed debt.

These cannot simply be added — that would double-count. We build a de-duplicated perimeter: the SOE-guaranteed debt inside the contingent stock (−0.68% of GDP) is already in the 10.5% SOE figure, and the probabilistic IMG (−0.06%) is already in the 0.87% concession PV; both are netted out. (One line — the 1.86% multilateral commitments — we checked against the primary source for a possible overlap with central-government debt: it is callable shareholder capital Chile holds as a member of the IDB, IBRD and MIGA — Chile as guarantor — categorically distinct from the multilateral loans drawn that already sit inside gross debt; it is a genuine separate contingent, not a double-count.³) The consolidation yields the variants below; the full component build, netting map, and sources are in the note.¹

The thesis survives every consolidation choice but the last. Even counting only hard debt and stripping every contingent liability, the augmented measure is 52.9% — nearly eight points above the anchor. The single framing under which the perimeter is not clearly over the anchor is the narrowest: counting only the SOEs that depend on the Treasury and excluding the commercially self-supporting ones, the perimeter lands at 44.8% — fractionally under the line (a 9.9% breach probability, just inside the 10% tolerance, essentially a tie). We disclose that as the binding robustness floor.

One honesty note on what the total sums. Central-government and SOE debt are face-value gross debt; the IMG (0.87%) and the deposit-guarantee line (3.76%) are DIPRES maximum-exposure figures, not expected cost (the probabilistic IMG is only 0.06%). So part of the headline gap aggregates objects of different valuation basis, PSBS-style. The strict like-for-like against a gross-debt anchor is the hard-debt floor (52.9%) — face-value debt only, no contingents — and it still clears the anchor by nearly eight points and breaches at 13.3%. The broader 57–61% readings are deliberately wide stress aggregates, labelled as such.

Figure 2 — Components and intra-public netting: the note to the table above (de-duplicated per GFSM/PSDS). Built by augmented_components.py.

The table is deliberately a bracket between two rules, and we state which is which rather than mix them. The headline (61.0%) applies the gross-public-sector concept — all public-corporation debt regardless of self-support — which is the perimeter the IMF uses for its own public-sector debt analysis and the broadest defensible measure. The floor (44.8%) applies the stricter debt-service-capacity rule, counting only the Treasury-served SOEs (EFE, Metro) that the §3 split identifies as genuine sovereign liabilities. The two are not in tension once labelled: the first answers "how large is the public sector's gross debt?", the second "how much of it is unambiguously a sovereign liability?" The central case sits between them — under the capacity rule with the contingent stock retained, the perimeter is 53.0% (41.5 central + 2.43 sovereign-dependent SOE + 0.87 IMG + 8.18 contingent-net), numerically all but identical to the 52.9% hard-debt floor in the table but distinct in construction, by coincidence rather than design. Every reading from that capacity-rule central case (53.0%) upward sits well above the anchor; only the narrowest floor — which strips the contingent stock and the self-supporting SOEs — lands fractionally under, at 44.8%. (A reader who prefers the capacity rule as primary should read 53.0% as the central estimate and 61.0% as the upper bracket; the conclusion of §4 is unchanged either way, the breach probability being identical to one decimal at 52.9 and 53.0.)

A word on gross versus net, since §1 flagged the tension. We measure gross throughout, deliberately and consistently: the legal anchor is a gross measure, so a gross consolidation is the apples-to-apples test of that rule, and it matches the IMF's own gross augmented-debt practice. We do not net the sovereign-wealth funds or SOE assets — that would test a different, net rule, and is the natural next study, not this one. We therefore make no claim about a weakening net worth; on the contrary, Chile's net financial position is materially stronger than its gross debt (DIPRES projects it at −43.5% of GDP by 2030). The point is narrower and entirely within the rule's own terms: a gross anchor measured on the narrow perimeter reads comfortable where the gross consolidated perimeter does not. And the assets a net measure would set against the gap are far too small to close it: the sovereign wealth funds (FEES + FRP) totalled about US$14bn — 3.8% of GDP — at end-2025, against a gross consolidated gap of sixteen to twenty points. A full net-augmented perimeter is the natural next study; what is already clear is that netting the State's liquid assets does not rescue the anchor.⁵

3.1 Why the firm concession obligation is debt the anchor omits

The concession commitment is not a footnote to the perimeter; it exposes the perimeter's defining flaw, in three steps, each from a primary standard. That a State-paid concession is economically equivalent to public debt is not itself a new claim — Engel, Fischer and Galetovic established it from Chile's own concession system (a PPP's fiscal impact "resembles public provision, not privatization"), and a long fiscal-transparency literature treats off-balance-sheet PPP commitments as debt the headline statistic hides, "revealed" precisely by moving from a cash to an accrual basis (Irwin, 2012).²² What we add is narrower and Chile-specific: that the State's own recognition standards already book this stream as a financial liability at present value, while the legal anchor is pegged to a statistic that cannot see it.

Chile's own accrual standard already calls it a financial liability. The Contraloría General de la República transposed IPSAS 32 into Chilean public accounting via Resolución CGR N° 16 (2015). Its concessions chapter requires that a State-paid concession give rise to "un pasivo financiero… valorizado inicialmente por el valor actual de dichos pagos" wherever the State holds an "obligación incondicional de pagar efectivo."¹⁶ So the firm subsidy stream is, by Chile's own rules, a financial liability measured at present value — not a contingency.

IPSAS 32 and GFSM 2014 agree — and the statistical standard makes it debt. IPSAS 32 places unconditional (or shortfall-guaranteed) grantor payments in the financial-liability model.¹⁷ GFSM 2014 records an on-balance-sheet PPP as an imputed finance lease — an imputed loan — and loans are a debt instrument in every gross-debt measure, so once the concession is judged on-balance-sheet, inclusion in gross debt is automatic, not discretionary (the UK Office for National Statistics books on-balance-sheet PFI exactly this way).¹⁸

Yet the anchor cannot see it. Chile's 45% rule is pegged to the deuda bruta del Gobierno Central — a debt-instrument statistic that, by Hacienda's own definition, contains only bonds, multilateral credits, and instruments recognised by specific law. The firm concession obligation is none of those instruments, so it is invisible to the anchor — even though Chile's own Contraloría rule recognises it as a financial liability and GFSM 2014 would classify the on-balance-sheet portion as a loan. It falls between Chile's two measurement systems: recognised on the patrimonial balance sheet the Contraloría maintains, absent from the debt statistic the anchor uses. (Two honest caveats: GFSM inclusion is conditional on the on/off-balance-sheet risk-and-reward test, and mixed toll-plus-subsidy contracts are split per IPSAS 32; and this is not an accounting error — the gap is that the legal anchor points at the narrow statistic rather than at the balance sheet.)

And the firm payment is not a soft commitment that can be quietly deferred. The Concessions Law obliges the State to pay the contracted subsidies and to settle accrued amounts owed to the concessionaire (valores devengados) in essentially all circumstances; and a material share of these flows is securitised in the capital market as infrastructure bonds (bonos de infraestructura) held by pension funds and insurers. Non-payment of a securitised concession flow is therefore not a budget deferral but a default on a market instrument — the strongest sense in which an obligation can be debt. By that test, too, the firm concession commitment belongs inside the perimeter the anchor draws. We advance this as an argument, not a settled equivalence, and note the honest counterweight: future-flow securitisations are deliberately ring-fenced in special-purpose vehicles structured to rate above the sovereign, and a sponsor can default while the vehicle keeps paying — so non-payment is most precisely a default on the securitised flow that the State backstops, rather than an automatic sovereign credit event.²⁶ The point survives in its weaker, sufficient form: the flow is firm, recognised, and market-held, none of which the anchor's perimeter reflects.

3.2 Which SOEs are sovereign liabilities? The market-producer test, entity by entity

The split between the headline (all SOE debt) and the floor (Treasury-dependent SOEs only) should not rest on the author's judgment. So we apply the GFSM-2014 market-producer test — does the enterprise cover its costs from sales over a sustained window? — to all 28 state firms, on a uniform evidence base: OCEC-UDP's accumulated 2017–2024 results and EBITDA, cross-checked against 2024 filings (CMF/SEP). A firm is non-market (its debt economically sovereign) if its accumulated EBITDA is negative, or it runs persistent losses and depends on recurrent Treasury injections; market otherwise.

The classification is not close: of the 28 firms, the ten carrying accumulated 2017–24 losses (Metro 63% and EFE 26% of the total) are exactly the non-market set, while CODELCO and BancoEstado alone paid 94% of all Treasury inflows. Crucially, the test reproduces the floor as an output, not an assumption: non-market SOE debt sums to ~2.4% of GDP — within a rounding point of the sovereign-dependent figure the floor already used (2.43%). The profitable ports drop out and the small non-market firms enter, roughly offsetting, so the 44.8% floor is robust to the test. The distance between 44.8% and 61.0% is now a question of which statistical perimeter, not whose judgment. (Full 28-firm table and the test: soe_classification.py.)

3.3 The gap is not new — and it is widening

A skeptic might read the consolidated perimeter as a 2025 artefact. It is not. Re-tracing the same construction back through time (Figure 3), the consolidated public-sector perimeter crossed 45% around 2019, and central-government-plus-SOE debt around 2021 — years before the anchor's own measure, which reaches 45% only in DIPRES's 2029 projection. The omitted slice has been over the line for half a decade, and the gap between what the anchor measures and what the State is liable for has widened: the contingent stock roughly doubled (≈4% of GDP in 2015 → ≈9% in 2025) and SOE debt rose from ≈6% to ≈10.5%. The anchor registered none of it — because none of it is in the perimeter it measures.

Figure 3 — Central + SOE gross debt: Hacienda/DIPRES debt statistics; contingent stock: DIPRES Pasivos Contingentes archive (gross, as-reported; SOE intermediate years and contingent 2016/2021/22 interpolated between published anchors — the ~2019 and ~2021 crossings survive even at the conservative published anchors). Built by make_extra_figures.py.

3.4 In international context: Chile anchors on the narrowest perimeter

The perimeter choice is itself an outlier. DIPRES's own review notes that most debt-rule peers anchor on the general government or the non-financial public sector; Chile and Australia are the only ones in its comparison that limit the ceiling to the central administration.⁴

This comparison is about perimeter, not level: on the general-government measure Chile (41.8%) sits mid-panel, unremarkable. The point is that Chile alone tests its rule against a perimeter that omits the SOE, concession and contingent layers — and that, re-measured on a fuller perimeter, Chile's own debt is 52.4% on the central-government-plus-central-bank consolidation DIPRES itself publishes (September 2025), and 53–61% on the consolidation built here. The anchor is not incomplete because Chile's debt is high; it is incomplete because the perimeter is narrow.

4. The re-run — the State's own model on its own balance sheet

The step that puts the perimeter into the rule's own terms is to feed the augmented stock back into the model that produced the 45%. The prudent-debt model does not care, in principle, which liabilities sit inside the perimeter — it asks whether the primary balance needed to stabilise that stock stays feasible. So we re-run it across the debt axis, holding the calibration that reproduces the 45%. We say plainly up front what this is: with the rate held at its calibrated value, the curve is monotone in the stock (Appendix A), pinned to the 10% tolerance at 45% by construction — so it cannot do anything but rise as the perimeter widens. That is not the weakness of the exercise but its discipline: it places the consolidated perimeter on the same axis, in the same units, as the number the rule already blesses.

Figure 4 — Reproduced from prudent_debt_model.py on public CFA/World-Bank series.

The numbers land precisely because they are in the government's own metric. At the central-government measure of 41.5%, the probability that the stabilising primary balance breaches the 2%-of-GDP ceiling is 8.5% — just under the 10% tolerance, which is exactly why the anchor reads as "met." Re-run on the consolidated perimeter, that probability rises to 13.3% at the hard-debt floor (52.9%), 14.9% at the conservative measure (57.3%), and 16.2% at the headline (61.0%). What this contributes is not an independent discovery of risk — the curve is monotone, so larger stock necessarily reads as larger probability — but the fact that it is the rule's own standard on the State's own balance sheet: at the 90%-probability, 2%-of-GDP line the rule itself draws, the slice the anchor measures reads prudent and every consolidated perimeter but the disclosed narrowest floor does not. The anchor reads as satisfied only because it is measured on the slice of the balance sheet that happens to fall below the line.

One mechanical caveat, conservative for the thesis: the single snowball \(s=(r-g)/(1+g)\) applied to the whole stock is exact for central-government debt but an upper bound for the self-supporting SOEs and the deposit-guarantee contingency, which the Treasury does not stabilise in the same way — so the broadest breach probabilities (57–61%) are upper bounds in that respect. The conclusion does not lean on them: it holds at the capacity-rule central case (53.0%, excluding the self-supporting SOEs — 13.3%) and the conservative variant (57.3%, stripping the deposit guarantee — 14.9%), both comfortably above the 10% line.

4.1 The forward question — a stochastic projection

The static cross-section answers "where does each perimeter sit relative to the prudent level today?", and — as we have stressed — it answers it monotonically. The harder and more useful question is forward: given the historical distribution of shocks, what is the probability that debt breaches 45% over the coming decade, and on which perimeter? This one is not a relabeling — the answer turns on the joint volatility of growth, the effective real rate and the primary balance, not on the calibration that pins \(d^{*}=45\).

We run an IMF-SRDSF-style stochastic projection to 2035 (Figure 5; method in Appendix A). The central-government baseline is anchored to DIPRES's own published trajectory (41.5% in 2025 rising to 46.5% by 2030); around it we draw correlated annual shocks \((\Delta r,\Delta g,\Delta pb)\) block-bootstrapped from the public CFA/World-Bank panel (2010–24, the COVID years held out of the pool), and propagate them through the debt-dynamics recursion. The augmented perimeter is run through the same dynamics from its 2025 level — again an upper bound, since self-supporting SOE debt is not Treasury-stabilised in the same way.

Figure 5 — Reproduced by dsa_projection.py. SRDSF-style, on an own-estimated shock structure — not DIPRES's unpublished variance-covariance (sought in §7).

Two results follow, and DIPRES publishes neither — its IFP shows only a single deterministic line. First, the probability that the central-government measure breaches 45% rises from 8% in 2026 to 46% by 2028 and about 55% by 2029 — the year DIPRES's own path crosses — settling near 60% through the early 2030s. On the State's own baseline the anchor is not "safely under 45%"; it is a coin-toss-or-worse to be over the line within four years. Second, the consolidated perimeter is above 45% with near-certainty throughout, and its fan carries it to a median near 65% of GDP by 2035, with a 90th-percentile path around 75%. The slice the anchor measures is heading through the line probabilistically; the slice it omits is already past it and pulling away. This forward exercise has independent content — it is, in effect, the fan chart the State has the model for but does not show, on both perimeters. (Honest scope: the shock structure is our own estimate from public data, not DIPRES's variance-covariance; the augmented path is an upper bound; and excluding vs including the COVID years moves the 2030 central breach probability only within a ~60–65% range.)

4.2 The Reconstruction Law — a second bet stacked under the anchor

The Q2-2026 IFP publishes four debt paths, not one, and it is worth setting them out because the disagreement between this paper and the government lives entirely inside them (Cuadro 5, reproduced in Figure 1). On committed spending, gross central-government debt reaches 45.3% in 2029 and 45.5% by 2030 — over the anchor. On spending compatible with the structural target, it holds at 44.1%. And in the two alternative scenarios, which incorporate the Reconstruction bill, debt is lower: 43.6% by 2030 on committed spending, and 40.7% with the target-compatible adjustment.

Read at face value, that is a government publishing the claim that a large permanent tax cut reduces the debt ratio. We take the disciplined pre-law path (44.1% by 2030) as this section's benchmark, precisely because it is the government's own most favourable case — and we take the alternative scenarios seriously enough to say exactly why we do not adopt them.

DIPRES's own decomposition is the reason. The same table splits the improvement into its sources, and the split is decisive: of the 1.9-point gap between the base and alternative paths in 2030, −1.4 points are the nominal-GDP effect — a larger denominator from assumed faster growth — and only −0.5 points the balance effect. The alternative scenario does not show the reform paying for itself out of revenue. It shows the debt ratio falling because the projection assumes a bigger economy, with the numerator barely moving. That is a legitimate way to project, and it is also a bet: strip the growth assumption and four-fifths of the improvement disappears with it.

This paper therefore runs the exercise DIPRES does not publish — the law's mechanical effect, with the growth channel switched off — and reports what happens to the narrow measure under the government's own disciplined baseline.

Between this paper's drafting and September 2026 Chile dispatched the Ley para la Reconstrucción Nacional y el Desarrollo Económico y Social — approved by both chambers and, following a Constitutional Tribunal ruling on unrelated provisions, awaiting promulgation at the time of writing — whose fiscal centrepiece is a cut in the corporate income tax — the Impuesto de Primera Categoría. The bill entered proposing 27% to 23%; an amendment in the Senate's second reading lowered it further, to 22%, and the operative costing is now DIPRES's Informe Financiero N°162 of 9 July 2026 — the tenth in a chain that began with N°84 in April and which also removed the bill's employment tax credit and added a hiring credit for knowledge-services exporters.⁹ That report quantifies the effect on the central-government balance twice, and the two numbers are the point.

Without the dynamic growth effect — the mechanical revenue change — the law is a permanent net loss reaching 0.65–0.70% of GDP a year (−0.02% in 2026, deepening to −0.49% by 2028, −0.65% in 2030 and −0.70% at its trough in 2035; about −CLP 3,300,000 million (2026 pesos) a year by then), with the corporate-rate cut alone accounting for −0.56% of GDP at steady state. With the growth effect the net position stays negative through 2031 (−0.15%) and turns positive only in 2035 (+0.20%). The entire case that the reform pays for itself rests on the growth bet; strip it and the certain residual is a standing two-thirds-of-a-point-of-GDP revenue drain, indefinitely.

Feeding the law's own mechanical (no-growth) balance path (IF N°162, Table 5) into the same stochastic projection, re-anchored to the Q2-2026 disciplined baseline, gives the result in Figure 6. The committed spending adjustment is calibrated exactly to hold the line and has no room for the tax cut on top of it: the median central-government path — which stays below 45% under the disciplined baseline alone — crosses 45% in 2029 and reaches 50.0% of GDP by 2035, and the probability that the narrow measure exceeds 45% rises from 48% to 80%. Even credited with the reform's projected-growth revenue, the path only hovers at the anchor rather than below it. The certain, booked half of the reform — the rate cut — is on its own enough to push the median across the line.

The reassuring "below 45%" reading now rests on two stacked bets: that the anchor's narrow perimeter is the right one (§3–§4), and that the reform's growth materialises. And there is a final, telling asymmetry of disclosure. For the Reconstruction Law, DIPRES publishes the mechanical-versus-dynamic split in full, year by year, across ten successive signed financial reports as the bill changed; for the 45% anchor itself, as §7 records, neither DIPRES nor the Subsecretaría de Hacienda holds the model that produced it. The State shows its work when it cuts revenue; it cannot show it for the line that governs the debt.

Figure 6 — Reproduced by reconstruction_scenario.py, on DIPRES IF N°162 (Tabla 5, transcribed to data/if162_tabla5_efecto_pib.csv) and IFP 2T-2026 (deuda bruta, esc. base con meta). SRDSF-style, on the same own-estimated shock structure as Figure 5.

5. How firm is 45%? The threshold as an unpublished judgment

A second finding falls out of the reproduction. Because DIPRES never published the model's calibration, the 45% is sensitive to assumptions the public cannot see. Holding the pinned inputs (BPMF 2%, probability 90%) and varying the forward real rate and trend growth across reasonable ranges:

The prudent level ranges from 31% to 60% of GDP across this entirely defensible grid. The published 45% sits near the centre — it is not unreasonable — but its precision is an artefact of a particular, unpublished, forward calibration. A rule written into law to two significant figures rests on a model whose parameters are not in the public domain. This is not a criticism of the model; it is an argument for publishing it.

That same sensitivity bears on the §4 finding, and we are explicit about its load. Because the prudent level falls as the assumed forward rate rises, the imprudence of the consolidated perimeter is conditional on that rate. Holding growth and volatility at their central values, the headline perimeter (61.0%) reads as imprudent for any forward real rate at or above ≈0.45%, and the hard-debt floor (52.9%) for any rate at or above ≈0.95%; only below those thresholds — at a forward rate near Chile's recently realised, near-zero real cost — would the prudent level rise far enough (to ~60% at r ≈ 0.5%) to bring the perimeter back under the line. Our 1.58% is a forward, post-normalisation rate that clears both thresholds with room to spare; a reader who expects Chile's effective real cost to stay near zero indefinitely should treat the finding as bracketed accordingly.

Volatility is the one parameter the grid above holds fixed, and it is the most load-bearing, so we stress it the right way — conditional on still reproducing the legal 45% anchor. A lower growth volatility forces a higher calibrated rate to return the same 45% (σ = 3.0% → r ≈ 2.5%; σ = 2.5% → r ≈ 3.2%), and under that re-calibration the augmented breach probabilities rise, not fall: at the headline 61.0%, from 16.2% at the base σ = 3.7% to 18.0% (σ = 3.0%) and 20.1% (σ = 2.5%); at the hard-debt floor, from 13.3% to 14.2% and 15.2%. The volatility assumption moves the standalone prudent level enormously, but conditional on reproducing the State's own anchor it leaves the §4 conclusion intact or strengthens it. (The naive alternative — lowering σ while holding r at 1.58% — would appear to rescue the perimeter, but it abandons the very anchor the exercise is calibrated to reproduce, and we do not rely on it.)

6. Prior work, and what is new here

We should be candid about what here is not new, because most of it is not. The concept of a wider, economically-warranted debt perimeter is mature and institutional: the IMF's Managing Public Wealth (Fiscal Monitor, October 2018) makes the case that headline gross debt is the narrowest and least informative slice, and the IMF has published "augmented debt" for China — adding off-budget and local-government-vehicle liabilities to the headline — in every Article IV since around 2014. Re-measuring a sovereign on a broader perimeter is their move, not ours.²⁴ That Chile's SOEs add materially is likewise no discovery: Hacienda itself publishes the 10.5%-of-GDP figure and one partial consolidation; the think-tank Libertad y Desarrollo published a "government + SOE = 59% of GDP" figure against the 45% threshold in 2024;¹⁴ and the IMF's 2021 Fiscal Transparency Evaluation states that "there is no report consolidating the non-financial public sector… but consolidation of at least the NFPS could be easily performed by DIPRES," and finds that financial liabilities related to PPPs are only "partially reported (0.2 percent of GDP)," rating that disclosure principle "Not met."¹⁵ The economic claim that a firm concession is debt-equivalent is older still, and Chilean (Engel–Fischer–Galetovic; §3.1). The IMF's 2024 Article IV had already warned the 45% ceiling could be breached as early as 2026 under modest slippage, and flagged SOE capitalisations and other "below-the-line" operations as a large, under-recognised driver of debt.²¹ On the bare observation — the perimeter is narrow, the SOEs are large, the breach is near — the official sector got there first, and we claim nothing.

What is new is narrower, and it is three things. The first is a standard-compliant, de-duplicated perimeter — SOE debt net of its intra-public guarantees, the concession stock, and the contingent stock net of overlaps, netted per the GFSM/PSDS consolidation procedure with the double-counting map made explicit (the note to the §3 table) — where Libertad y Desarrollo offered a simple sum of two gross figures. The improvement is in rigour and disclosure, not in the existence of a large number. The second is the Chile-specific recognition chain: not the general economics, which is textbook, but the specific fact that the firm concession-subsidy stream is a financial liability under Chile's own CGR/NICSP-32 rule and a loan-equivalent under GFSM 2014 — debt the State's own standards recognise, pegged to an anchor whose debt-instrument perimeter cannot see it. The third is the model-internal re-run: taking the very fiscal-space model the State used to derive 45% and re-expressing the widened perimeter in its metric. We are careful not to oversell it. Mechanically the re-run is a monotone relabeling (§4, Appendix A) — it carries no information beyond "the consolidated perimeter exceeds the prudent level" — so what is genuinely unmatched in the literatures we searched is the move, not a hidden mechanism: the IMF's 2023 technical-assistance report tightened the ceiling on the same narrow perimeter using its own model,²⁰ and the China augmented-debt practice re-measures the stock but does not turn the country's own derived limit model back on it. So the load-bearing contributions are the first two — the standard-compliant, de-duplicated perimeter and the Chile-specific recognition chain — and the re-run is the device that states their consequence in the rule's own terms. If a reader rejects the re-run as mere relabeling, the paper still stands on the perimeter and the recognition argument; that is by design.

7. A transparency test — requested, and what came back

This paper is a reproduction, not a replication: we recovered the published method and re-derived a calibration that returns the published result, but we did not have DIPRES's own coefficients. That gap is itself part of the argument (§5), and it is testable — so we tested it. On 15 June 2026 we filed a request to DIPRES under the Ley de Transparencia (Ley 20.285, folio AE002T0003904) for the technical antecedents of the Recuadro 3 exercise that fixed the 45% anchor: the fiscal-reaction-function specification and estimated coefficients, the variance-covariance matrix of the shock process, the forward interest-rate and growth assumptions, the simulation parameters, the results distribution from which the 45% is read, and any workbook or code.

The response is itself the finding. DIPRES — the author of the Informe de Finanzas Públicas and of the Recuadro 3 exercise — replied (Oficio Ordinario N° 1610, 14 July 2026) that "esta Dirección de Presupuestos no cuenta con la información requerida," and derived the request to the Subsecretaría de Hacienda. The Subsecretaría answered (ORD N° 1633/2026, 21 July 2026) that the only responsive material in its possession is four documents — a 2021 Consejo Fiscal Autónomo report recommending a debt anchor, an IMF comparative note, an OECD methodology assessment, and an unrelated 2021 legislative box — none of which contains the fiscal-reaction-function coefficients, the shock calibration, the BPMF derivation, or the simulation output that produced the 45%, and three of which predate or are external to the April-2022 exercise; it added that no other records exist. In short, neither the institution that authored the anchor nor the ministry that houses it holds a reproducible technical derivation of it.

This is the outcome the design of the request anticipated on its second branch, and it is a fiscal-transparency finding in its own right: a debt anchor written into law (Ley 21.683; Decreto 755 de 2022 and its successor Decreto 542 de 2025) rests on a model whose parameters the responsible institutions cannot produce. Publishing the full model and code (Appendix C) is the reproducibility standard the discipline now expects — deposited data and code a third party can run end-to-end (Christensen & Miguel, 2018; the AEA's data-and-code policy) — and access-to-information requests are an established research instrument, not a stunt, in the study of government conduct (Walby & Luscombe, 2017).²⁵ Measured against that standard, the anchor as published is not audit-ready.

We have contested the response before the Consejo para la Transparencia (amparo, folio AE002T0003904, filed 21 July 2026) on two grounds: that derivation to the Subsecretaría was improper for a product DIPRES itself authored, and that a bare declaration of non-possession does not satisfy the Council's established standard for a founded claim of inexistence (which requires the organ to document an exhaustive search). Either resolution sharpens the finding rather than softening it: if the amparo surfaces the parameters, we replace our calibration with the official one and report any difference; if the Council confirms that no reproducible derivation exists, the non-reproducibility of the anchor is established by the transparency authority itself. We will publish the full exchange and the Council's ruling as an addendum. A parallel request to the Dirección General de Concesiones (DGC/MOP) for the current Gasto Sectorial — Compromisos Futuros workbook — which would replace the 2022 firm-commitment floor (§8) with a live figure — remains outstanding.

8. Limitations

(1) Reproduction, not replication (§7): the calibration is ours, bracketed against the published result; the transparency request was the remedy, and it returned no official parameters — DIPRES and the Subsecretaría de Hacienda both disclaim holding a reproducible derivation (§7), a finding now before the Consejo para la Transparencia. (2) The SOE perimeter is a deliberate two-rule bracket (§3): the headline 61.0% applies the gross-public-sector concept (all public-corporation debt, the IMF's own measure), the floor 44.8% the stricter debt-service-capacity rule (Treasury-served SOEs only). Counting CODELCO's debt as a sovereign liability is defensible (100% state-owned, historically backstopped, with an implicit rating uplift) but contestable (asset-backed and profit-generating); a reader who takes the capacity rule as primary should read the central case as 53.0% and 61.0% as the upper bracket. The conclusion of §4 holds across the bracket. (3) Vintages span 2024–2025 across components; the firm MOP concession-subsidy PV is ~0.4% of GDP on the 2022 DGC projection — a floor, additive to (not part of) the 0.87% IMG, which is contingent not firm — and is held out of the headline 61.0% pending the updated official workbook. This ~0.4% is the present value of the State's net firm availability subsidies, a deliberately narrow measure; it is not comparable to, and far below, the gross committed-investment stock that wider studies report (the IDB sizes Chile's committed concession-investment stock at ~6.2% of GDP, 1994–2015), which bundles the full contracted CAPEX rather than the net cash the Treasury pays — a difference of scope, not a contradiction.²⁷ (4) The multilateral-commitments line (1.86%) is confirmed (against the DIPRES contingent-liability report and Hacienda's gross-debt composition) to be callable shareholder capital — Chile as guarantor to the IDB/IBRD/MIGA — not the multilateral loans already inside gross debt, so it is a genuine separate contingent and no double-count; the earlier overlap caveat is resolved. (5) The fiscal-space model is one of several debt-limit methodologies; the Fournier–Bétin default-probability model (which DIPRES also cites, with a 48% median) is a robustness cross-check, not a substitute, and should never be read as a model-solved limit. (6) Model simplifications (Appendix A): the §4 re-run holds the rate deterministic, draws growth i.i.d.-normal with no persistence, and sets the growth–rate correlation to zero — each conservative on tail risk — and applies one snowball to the whole perimeter, which is exact for central debt but an upper bound for the self-supporting SOEs and the deposit guarantee; the §7 transparency request sought DIPRES's actual shock variance-covariance to replace these with the official structure, but DIPRES declared it holds no such parameters (§7). (7) The §4 re-run is a relabeling in the rule's own metric, not an independent model verdict (§4, Appendix A); the paper's weight rests on the de-duplicated perimeter (§3) and the recognition chain (§3.1).

9. The policy lead

The recommendation is not that Chile is insolvent — it is not — nor that 45% is the wrong number. It is that the anchor should be measured on the perimeter the State is actually liable for, or the consolidation and the model should be published so the public can measure it themselves. A prudent-debt rule that anchors on the central-government slice, while the same government states its goal as the net worth of the public sector, gives a reading of comfort that the consolidated balance sheet does not support: 41.5% under a 45% line, when the consolidated perimeter is 57–61% — which, expressed in the rule's own metric, reads as imprudent where the narrow slice reads as prudent. The fix is the one the IMF already named: consolidate the non-financial public sector, which "could be easily performed by DIPRES," and anchor the rule to it. Measuring the right slice is the difference between a rule that disciplines fiscal policy and one that reassures it.

The narrow measure has a second cost, and it points the other way. A gross-debt anchor cannot see assets: it registers the liability side of a debt-financed hospital and nothing else, so it treats borrowing to build and borrowing to consume as the same act. When the anchor binds — and on DIPRES's own projection it binds in 2029 — the rule offers no reason to protect the expenditure that creates assets, and the easiest line to defer is always the project not yet started. That the composition of an adjustment matters is not speculation: the Central Bank's own researchers estimate Chile's cumulative public-investment multiplier at around 2 — roughly double the multiplier of total spending — and the regional evidence puts the public-investment multiplier near 1 two years out, rising toward 2.5 precisely where investment is executed efficiently, while short-run public-consumption multipliers sit at or below zero.²⁸ We do not argue here that Chile's remaining fiscal space should be spent on debt-financed investment. That is a different question — it requires the multiplier evidence, the efficiency conditions, and the monetary-policy response to be brought into one frame, and we take it up in a companion paper, under the same discipline this paper imposes: any case for using fiscal space must be made on the consolidated perimeter, not the narrow slice. The point that belongs to this paper is narrower, and it is symmetric with everything above. An anchor that omits the liabilities of the wider public sector also omits the assets that borrowing can create; it can therefore neither certify prudence nor allocate restraint — and a rule that cannot distinguish borrowing to build from borrowing to consume will always cut the building first.

Appendices

Appendix A — The model, in full

We state the whole model, so it can be audited and reproduced without any private input.

Debt dynamics. With gross debt-to-GDP \(d_t\), real effective interest rate \(r\), real GDP growth \(g\) and primary balance \(pb_t\) (all real): \[d_t = \frac{1+r}{1+g}\,d_{t-1} - pb_t.\] Debt is stabilised (\(d_t=d_{t-1}=d\)) by the primary balance \[pb^{*}(d) = \frac{r-g}{1+g}\,d \equiv s\,d, \qquad s \equiv \frac{r-g}{1+g}\ \text{(the snowball)}.\]

Prudent debt level (BPMF route). The maximum feasible primary balance is \(\mathrm{BPMF}=2\%\) of GDP (Escolano et al. 2014; pinned by DIPRES). The prudent level \(d^{*}\) is the highest debt at which the required stabilising primary balance does not exceed the BPMF with probability \(\ge 90\%\) — equivalently, where the 90th percentile of the snowball satisfies \[q_{90}(s)\cdot d^{*} = \mathrm{BPMF} \;\Longrightarrow\; d^{*} = \frac{\mathrm{BPMF}}{q_{90}(s)}.\]

Shock distribution. Real growth is drawn \(g\sim\mathcal{N}(\bar g,\sigma_g)\) and the snowball \(s=(r-g)/(1+g)\) is evaluated over \(10^{6}\) draws; \(q_{90}(s)\) is its 90th percentile. (Working in real terms is essential: Chile's high GDP deflator inflates nominal growth to ~7.8%, which would make the nominal snowball spuriously favourable.)

Calibration — every value sourced or pinned; only \(r\) is calibrated:

The sensitivity of \(d^{*}\) to \((\bar g, r)\) is the table in §5 (31–60% across the plausible grid). Note that \(r\) is the single free parameter, solved by bisection, so reproducing 45% is a calibration, not an independent validation — the substantive question (§2, §5) is whether the calibrated rate is plausible.

The augmented re-run. Holding that calibration, for each perimeter \(d_0\) the model reports the imprudence probability \[\Pr\!\left[\, s\,d_0 > \mathrm{BPMF}\,\right], \qquad s=\tfrac{r-g}{1+g},\ g\sim\mathcal{N}(\bar g,\sigma_g),\] imprudent when this exceeds \(1-90\%=10\%\). Results: 41.5% → 8.5%; 45.0% → 10.0%; 52.9% → 13.3%; 57.3% → 14.9%; 61.0% → 16.2% (§4, Figure 4).

Because \(\Pr[s\,d_0 > \mathrm{BPMF}] = \Pr[s > \mathrm{BPMF}/d_0]\) and \(r\) (hence the distribution of \(s\)) is held fixed, the imprudence probability is a strictly increasing function of \(d_0\), equal to exactly \(10\%\) at \(d_0 = d^{*} = 45\%\) by the calibration. The augmented breach probabilities are therefore entailed by the calibration that pins \(d^{*}=45\), not independently discovered: the re-run (§4) is a monotone relabeling of the debt axis into the rule's own probability units, and its value is presentational — same metric, same balance sheet — not a separate test.

Forward stochastic projection (§4.1). The fan chart projects \(d_t = \frac{1+r_t}{1+g_t}\,d_{t-1} - pb_t\) to 2035 over \(10^{5}\) paths. The central baseline median is anchored to DIPRES's published trajectory (the implied per-year baseline primary balance is backed out at the \(r=1.58\%,\ g=2.0\%\) calibration; it runs from a \(-1.8\%\) primary deficit in 2026 to \(-0.4\%\) by 2030). The fan is generated by drawing each year's shock vector \((\Delta r,\Delta g,\Delta pb)\) jointly from the demeaned historical panel (2010–24, COVID 2020–21 held out), which preserves the contemporaneous cross-correlation (estimated \(\mathrm{corr}(r,g)\approx0.6\), \(\mathrm{corr}(g,pb)\approx0.7\); shock s.d. \(\approx 3.0/2.0/1.4\) pp for \(r/g/pb\)). Crucially, this relaxes the three simplifications of the static re-run noted below — the rate is now stochastic and the shocks correlated — so the breach probabilities it reports are discovered, not entailed by the calibration. The augmented perimeter is propagated through the same recursion from its 2025 level (an upper bound).

Honest scope. DIPRES did not publish its fiscal-reaction-function coefficients or shock variance-covariance, so this is a reproduction of the published method, not a replication of the official run; the calibration is ours and bracketed (§5), and the transparency request (§7) sought the official parameters but established that DIPRES holds none. Three simplifications relative to DIPRES's unobserved model are worth naming, and each is conservative on tail risk (i.e. understates breach probabilities): the forward real rate is deterministic (a stochastic rate, positively shocked in bad states, would widen the snowball and raise breach probabilities); growth is drawn i.i.d. normal with no AR(1) persistence; and the growth–rate correlation is set to zero (a negative correlation — high rates in low-growth states — would also raise them). The single snowball applied to the whole perimeter is, conversely, an upper bound for the self-supporting SOEs and the deposit guarantee (§4). The code that implements all of the above is in Appendix C.

Appendix B — Glossary

• Deuda bruta del Gobierno Central total — gross debt of the total central government, the legal anchor perimeter.
• NFPS — non-financial public sector (general government + non-financial SOEs).
• BPMF — balance primario máximo factible, the maximum feasible primary balance (2% of GDP).
• Snowball — \((r-g)/(1+g)\), the automatic debt dynamics.
• Fiscal-space / prudent-debt model — the IMF/OECD method deriving the highest debt from which stabilisation stays feasible at a given probability.
• IMG — ingreso mínimo garantizado, the minimum-income guarantee on MOP concessions.

Appendix C — Reproducible code

A paper that asks the State to publish its model must publish its own. The core — the three functions that are the model (reproduce the prudent level, calibrate the rate, and re-run the breach probability across the perimeter) — is reproduced verbatim below. The complete runnable scripts (prudent_debt_model.py, the perimeter build augmented_components.py, the firm-commitment PV concession_commitments_pv.py, and the forward stochastic projection dsa_projection.py behind §4.1) and all input data — the CFA fiscal series, World Bank growth/inflation, the DIPRES debt and contingent-liability reports, and the MOP/DGC Compromisos Futuros workbook — are published in full in the public reproducibility deposit accompanying this paper (a neutral repository, not a product page), and the entire analysis reproduces end-to-end with python prudent_debt_model.py (seed 42, 10⁶ draws). BPMF = 2.0, SEED = 42.

def prudent_level(r_real, g_bar, g_sigma, n=1_000_000, seed=SEED):
    """Analytical BPMF route, real terms. The stabilising primary balance is
    pb*(d) = ((r-g)/(1+g))*d; the prudent level d* is the debt at which its
    90th-percentile (over the growth draw) equals the BPMF (2% of GDP)."""
    rng = np.random.default_rng(seed)
    g = rng.normal(g_bar, g_sigma, n) / 100.0     # real growth, decimal
    snow = (r_real / 100.0 - g) / (1.0 + g)        # snowball (r-g)/(1+g)
    q90 = np.percentile(snow, 90)
    d_star = (BPMF / 100.0) / q90 * 100.0 if q90 > 0 else np.inf
    return dict(d_star=float(d_star), q90=float(q90 * 100),
                mean_snow=float(snow.mean() * 100))   # d* in % of GDP

def calibrate_rate(g_bar, g_sigma, target=45.0):
    """Forward real effective rate that reproduces d* = target (bisection)."""
    lo, hi = -2.0, 8.0
    for _ in range(60):
        mid = (lo + hi) / 2
        d = prudent_level(mid, g_bar, g_sigma)["d_star"]
        if d > target:          # rate too low -> d* too high
            lo = mid
        else:
            hi = mid
    return mid

def breach_prob(d0, r_real, g_bar, g_sigma, n=1_000_000, seed=SEED):
    """P(stabilising primary balance at debt d0 > BPMF) — imprudent if > 10%."""
    rng = np.random.default_rng(seed)
    g = rng.normal(g_bar, g_sigma, n) / 100.0
    snow = (r_real / 100.0 - g) / (1.0 + g)
    req_pb = snow * d0          # required stabilising primary balance, % of GDP
    return float((req_pb > BPMF).mean())

# Reproduce the 45% anchor, then re-run on the augmented perimeter:
#   g_bar, g_sigma = 2.0, 3.7        # trend real growth; historical volatility
#   r = calibrate_rate(g_bar, g_sigma)           # -> 1.58%
#   prudent_level(r, g_bar, g_sigma)["d_star"]   # -> 45.0  (the legal anchor)
#   breach_prob(41.5, r, g_bar, g_sigma)         # -> 0.085 (central: prudent)
#   breach_prob(61.0, r, g_bar, g_sigma)         # -> 0.162 (public: imprudent)