Annex F — Formal accounting decomposition and bounded partial attribution framework

Annex 6 of 17 · ≈ 22 min read · 85 paragraphs · section 28 of 40 · search the book

Status and scope. This annex formalises a transparent accounting decomposition and a bounded partial attribution framework for the cross-border spillovers of monetary policy. It produces no new estimate and does not, on its own, permit the identification of a causal policy shock, the establishment of a welfare loss, the determination of legal liability or the justification of a financial consequence. It remains at rungs 1 and 2 of the epistemic ladder used in this document — accounting incidence and plausibly bounded attribution. Rung 3, identified causality, falls under the complementary empirical protocol of Annex G. The purpose here is narrower and more demanding than a calculation for display: every input, allocation, exclusion, counterfactual and stopping rule must be inspectable and refutable line by line.¶ 1

The framework corrects four weaknesses that affect simpler identities. First, a counterfactual is a vector of jointly coherent paths, and not the simple alternative path of a policy rate. Second, an exposure measured after the shock may be endogenous and must be distinguished from an exposure genuinely prior to the shock. Third, overlaps are resolved at the level of primitive economic components, and not by an opaque ex post subtraction. Fourth, costs and offsets are first reported by affected agent; a gain accruing to a central bank, a firm or a household does not automatically offset a loss borne by another agent.¶ 2

Two provisions are added in this revision. A graduated compliance regime (§F.15) defines a minimal configuration under which the framework remains executable by jurisdictions with limited data and limited analytical capacity, so that rigour does not become paralysis. A transitional provision (§F.16) states explicitly the status of the magnitudes reported in Section 9 of the body of the text, computed under the earlier version of this annex and which do not yet satisfy the constitutive rules set out below.¶ 3

F.1 Units of analysis, sets and indices

Let i index a recipient country, j a source monetary jurisdiction, h an affected agent or institutional sector, m a transmission mechanism, k a primitive economic component, and t a period of the cycle, t = 1, …, T. The set of affected agents H must, at a minimum, distinguish the sovereign, the central bank, financial institutions, non-financial corporations, households and, where the data permit, subnational authorities and vulnerable population groups.¶ 4

M = M(A) ∪ M(B) ∪ M(C) ∪ M(O) (F‑1)¶ 5

M is the set of the fifteen mechanisms of Table 24. M(A) = {A1, …, A7} groups the monetary and financial channels; M(B) = {B1, B2} the imported price shocks; M(C) = {C1, C2, C3} the real-economy channels; and M(O) = {O1, O2, O3} the contemporaneous offsets. The memo item for the revaluation of the debt stock, denoted S, lies outside M and enters no cash-flow sum.¶ 6

Each mechanism receives ex ante a sign sₘ ∈ {+1, −1}: +1 for an adverse incidence, −1 for an offset. The sign is fixed by the taxonomy before any measurement and cannot be changed to improve a result. Pre-commitment on signs nevertheless presupposes that the sign is theoretically unambiguous. Where theory admits both directions, the mechanism must be split into primitive components of opposite signs rather than endowed with a net sign by decree. The tourism channel C3 is the case in point: the income effect of tightening at the centre (fewer departures) is adverse, while the relative-price effect of depreciation (a cheaper destination) is favourable. C3 is therefore carried as two primitive components, C3-income (sign +1) and C3-price (sign −1), each measured under §F.3 and allocated under §F.6; the net direction is an empirical result, not a taxonomic assumption.¶ 7

F.2 The counterfactual as a coherent vector of paths

Every magnitude is defined relative to an admissible counterfactual c ∈ Γ. The counterfactual cannot be reduced to a policy-rate path, since each mechanism depends on a jointly determined set of prices, quantities and expectations. Let zₜ(c) be the counterfactual state vector:¶ 8

zₜ(c) = { iⱼ,ₜ(c), yʳᶠⱼ,ₜ(c), eᵢ,ₜ(c), riskₜ(c), yⱼ,ₜ(c), p(com)ₜ(c), qₜ(c), … } (F‑2)¶ 9

The vector may include the source policy rate, the risk-free yield curve, the exchange rate of the recipient country, global risk appetite, the output of the source jurisdiction, commodity prices and other variables specific to each mechanism. The paths must be generated by an explicit model, a reaction function, a market expectations path, a narrative scenario or an identified empirical design; a counterfactual price is a model output, never an observation. Membership of Γ is itself constrained: an admissible counterfactual must describe a policy path that the source jurisdiction could lawfully and plausibly have followed given its mandate and the information available at the time. Holding policy rates at their end-2021 level, denoted c₀ in the body of the text, is admissible as a polar benchmark; it is not an upper bound by definition, and its position within the range is an empirical question. Where the body of the document characterises c₀ as an upper-bound choice, the present annex supersedes that characterisation.¶ 10

At least three counterfactuals must normally be reported: (i) c₀, a constant-rate benchmark; (ii) cᴺ, a neutral-rate or gradual-normalisation path; and (iii) cᴿ, a rule-based or market-expectations path. No scenario may be reported alone, save under a pre-registered and justified exclusion. Under the minimal configuration of §F.15, two counterfactuals — one polar, the other a plausible policy path — constitute the floor.¶ 11

F.3 Mechanism-specific incidence and exposure timing

A single “base × price gap” formula is too restrictive for the fifteen mechanisms; in particular, it cannot represent quantity rationing, where lenders restrict volumes rather than reprice. The generic gross incidence is therefore mechanism-specific:¶ 12

ΔX̃(fix)ᵢⱼₕₘₜ(c) = gₘ( E⁰ᵢⱼₕₘ , zₜ(obs), zₜ(c), θₘ ) (F‑3)¶ 13

ΔX̃(dyn)ᵢⱼₕₘₜ(c) = gₘ( E(obs)ᵢⱼₕₘ,ₜ₋₁ , zₜ(obs), zₜ(c), θₘ ) (F‑4)¶ 14

gₘ is the mechanism-specific measurement function. E⁰ is the exposure fixed before the identified shock or before its credible anticipation; E(obs)ₜ₋₁ is the exposure actually observed before period t. Fixed-exposure measurement is the preferred basis for attribution, because it avoids treating a post-shock adjustment as though it were predetermined. Dynamic measurement is also informative, but it describes an incidence realised after adaptation and must be reported separately.¶ 15

For t > 1, E(obs)ₜ₋₁ may already reflect refinancings, reserve depletion, fiscal adjustment, capital controls or other responses caused in part by the shock. The time lag does not, on its own, make the exposure exogenous. Where the shock alters the exposure base, the analyst must either model the feedback, or instrument the exposure, or freeze the base at E⁰, or report both calculations with an explicit decomposition of adaptation effects.¶ 16

The familiar multiplicative form remains valid as a special case. The floating-rate surcharge A2 may be measured as verified floating-rate principal, multiplied by the contractual reference-rate gap and the accrued fraction. The exchange-rate surcharge A1 may be measured on the foreign-currency debt service actually paid during the period, and not on the total stock outstanding. The real-economy channels C1–C3 generally require elasticities, local projections or structural functions rather than a simple price gap; where credit rationing is material, gₘ operates jointly on quantities and spreads.¶ 17

F.4 Attribution coefficients and structural restrictions

Let αᵢⱼₘ(c) be the fraction of allocated accounting incidence that may plausibly be associated with the monetary policy shock of the source jurisdiction under counterfactual c. Attribution is bounded and joint:¶ 18

αᵢⱼ(c) = ( αᵢⱼₘ(c) : m ∈ M ) ∈ Φᵢⱼ(c) ⊆ [0,1] × … × [0,1] (F‑5)¶ 19

Φᵢⱼ(c) is the set of jointly feasible attribution vectors. It contains the mechanism-specific bounds, the cross-mechanism restrictions, common-shock coherence, the sign restrictions and any constraint induced by the empirical design. The bounds are bounds of documented judgement or of partial identification (Manski, 1990) so long as they are not estimated; they are not confidence intervals.¶ 20

The risk-free refinancing channel A3 must be decomposed before any coefficient is set at unity:¶ 21

Δyʳᶠ = Δy(policy) + Δy(term) + Δy(expectations) + Δy(liquidity) + Δy(residual) (F‑6)¶ 22

α(A3, policy) = 1; 0 ≤ α(A3, other) < 1 unless separately identified (F‑7)¶ 23

Unity applies only to the component identified as a policy shock or surprise, not to the total observed change in the yield curve. The floating-rate channel A2 is the mechanism that can approach full attribution through contractual indexation, subject to verification of reset dates, reference-rate clauses, caps, floors, hedges and arrears. An a priori defensible range is 0.90–1.00 for the mechanically reset component; it is the data, not the label, that determine whether the upper bound is reached.¶ 24

One channel requires a restriction that earlier versions left implicit. The domestic crowding-out channel A7 records the cost of the recipient central bank raising its own policy rate. This response mixes an element of external constraint — the imported tightening the bank cannot escape — and an element of domestic discretion — the stance it chooses within that constraint. The identity cannot separate the two; the separation is an attribution judgement and must reside, visibly, in α(A7). The baseline restriction is therefore an interior interval whose upper bound is strictly below one, with the reasoning for the decision — including the counterfactual domestic reaction function retained — documented in the attribution register (§F.14). Treating the entirety of the domestic rate response as externally caused is not admissible.¶ 25

F.5 Symmetry of proof, joint feasibility and pre-registration of Φ

Costs and offsets must be constructed from the same family of counterfactuals, the same shock definition, the same exposure-timing rule and the same quality threshold. Symmetry means equality of protocol, not equality of numerical coefficients. An income gain on reserves and a debt-service cost may have different attribution bounds, because their contractual and behavioural mechanisms differ.¶ 26

For a central estimate or a named scenario, all coefficients must belong to one and the same jointly coherent vector of Φᵢⱼ(c). For sensitivity extremes, adverse channels may be low when offsets are high, or the reverse, only if that combination is feasible under the common shock and the cross-mechanism restrictions. Selecting every adverse coefficient at its maximum and every offset at its minimum is not admissible where the same shock, the same exchange-rate path or the same global risk factor links them.¶ 27

The joint set Φ disciplines cherry-picking, but it also displaces judgement: the cross-mechanism restrictions that define Φ carry as many researcher degrees of freedom as the coefficients themselves. The restrictions constitutive of Φᵢⱼ(c) — bounds, equalities, monotonicities and common-factor constraints — must therefore be deposited in the attribution register and time-stamped before any aggregate is computed. A restriction added, relaxed or reweighted after a first computation must be recorded as a revision, the pre-revision result being preserved. An unregistered Φ is deemed absent, and §F.13 then blocks the envelope of extremes.¶ 28

F.6 Primitive components and elimination of double counting

Transmission mechanisms are useful reporting channels, but they are not necessarily independent. A single exchange-rate movement may affect debt service, migrants' remittances and the memo item; a single reference-rate shock may affect floating-rate debt and refinancing. Pairwise overlap deductions become unstable as soon as three or more channels share the same determinant. The preferred method therefore allocates primitive economic components once only, before aggregation.¶ 29

Let Dᵢⱼₕₖₜ(c) be the monetary value of primitive component k for agent h in period t, and ωₘₖ the published allocation share of component k to reporting mechanism m:¶ 30

0 ≤ ωₘₖ ≤ 1, and Σ(m ∈ M(k)) ωₘₖ = 1 (F‑8)¶ 31

ΔXᵢⱼₕₘₜ(c) = Σ(k ∈ Kₘ) ωₘₖ · Dᵢⱼₕₖₜ(c) (F‑9)¶ 32

ΔX̃ remains the gross per-channel exposure, published for transparency; ΔX is the overlap-net amount used in aggregation. Every primitive component must have a unique identifier, a source, a sign, a unit, an owner, an allocation rule and a version. The allocation weights may place the component entirely within one mechanism or spread it across several, but they must sum to one. The debt-stock memo item may share a primitive exchange-rate determinant with A1 or O2, while remaining outside the cash-flow aggregate.¶ 33

A pairwise “seam” correction, inherited from the earlier version, may be reported as a robustness test, but must not be the principal estimator. If it is used, all pairwise and higher-order overlaps, their signs and their uncertainty must be published. An unpublished overlap adjustment renders the identity unverifiable.¶ 34

F.7 Offsets, beneficiaries and distributive non-equivalence

Offsets enter once only, contemporaneously with the shock and under the same evidentiary protocol as costs. A capital inflow from the earlier easing phase is not set against a later reversal, in particular where it increased leverage or foreign-currency exposure. Full-cycle analysis must report earlier gains and later costs by beneficiary and by date, rather than presume intertemporal offsetting.¶ 35

The primary object is the per-agent vector. An offset accruing to agent ℓ may reduce a loss borne by agent h only to the extent that an actual or legally committed transfer is documented. Let T(ℓ→h, t) ∈ [0,1] be the share of a gain accruing to ℓ transferred to h in period t. In the absence of transfer data, T is set to zero.¶ 36

O*ᵢⱼₕₘₜ(c) = (1 − Σᵣ≠ₕ T(h→r, t)) · Oᵢⱼₕₘₜ(c) + Σℓ≠ₕ T(ℓ→h, t) · Oᵢⱼℓₘₜ(c) (F‑10)¶ 37

The transfer matrix must not create resources: for each originating agent ℓ and each period t, the shares allocated to other agents cannot exceed the documented transferable gain. Without a documented link, an increased return on central bank reserves offsets neither households facing unemployment, nor firms facing credit contraction, nor the sovereign facing a heavier debt service. This rule prevents a national net from concealing uncompensated distributive losses. The transferred share is deducted from the initial beneficiary, so that consolidation conserves resources (ΣₕO* = ΣₕO).¶ 38

One consequence of the T = 0 default must be stated rather than discovered. Because undocumented gains no longer offset the losses of other agents, the accounting consolidation Σₕ Nᵢⱼₕ under this framework is, mechanically, weakly greater than a national net computed under the earlier version of this annex, in which offsets reduced the aggregate regardless of the beneficiary. The difference is not a revision of the facts; it is the price of refusing to offset a loss with a gain that never reached the party bearing it. Both figures may be presented, labelled respectively “distributive consolidation” and “legacy national net (robustness)”.¶ 39

F.8 Common currency, price base and time

All amounts must be expressed in a single reporting currency, a single price base and at a single reference date. Let dᵢₕₜ be the factor converting the period-t nominal amount borne by agent h into the declared unit:¶ 40

dᵢₕₜ = FX(i, t→b) · [ P(b,0) / P(b,t) ] · δₕ(t, t₀) (F‑11)¶ 41

FX converts into reporting currency b; P(b,0)/P(b,t) converts into the chosen real price base; δₕ(t, t₀) is the declared intertemporal factor, equal to 1 for undiscounted real flows and, where discounting is justified, to 1/(1+rₕ) raised to the number of periods separating t₀ from t. Nominal and real amounts, local currency and foreign currency, discounted and undiscounted totals must never be mixed within a single aggregate.¶ 42

Two coherent methods are permitted, one only per result: (a) conversion into the reporting currency at each period's rate, then deflation by the reporting-currency index; (b) deflation in local currency, then conversion at the base-year rate. Mixing the recipient country's price index and that of the reporting currency within a single ratio is prohibited without an explicit parity model. Equation (F‑11) applies method (a).¶ 43

F.9 Adverse incidence, offsets and net balance by agent

For a feasible parameter vector (α, θ) and a counterfactual c, we define attributable adverse incidence C, attributable offsets O and the net balance N for each affected agent:¶ 44

Cᵢⱼₕ(c, α, θ) = Σₜ dᵢₕₜ · Σ(m : sₘ = +1) αᵢⱼₘ(c) · ΔXᵢⱼₕₘₜ(c, θ) (F‑12)¶ 45

Oᵢⱼₕ(c, α, θ) = Σₜ dᵢₕₜ · Σ(m : sₘ = −1) αᵢⱼₘ(c) · O*ᵢⱼₕₘₜ(c, θ) (F‑13)¶ 46

Nᵢⱼₕ(c, α, θ) = Cᵢⱼₕ(c, α, θ) − Oᵢⱼₕ(c, α, θ) (F‑14)¶ 47

The primary result is the distributive vector Nᵢⱼ(c) = ( Nᵢⱼₕ(c) : h ∈ H ). A consolidated total may be reported in the form Σₕ Nᵢⱼₕ, but it must be labelled an accounting consolidation, not a welfare measure. A welfare aggregate requires explicit social weights, marginal utilities, incidence assumptions and a treatment of non-monetary damages; this annex provides none of them.¶ 48

Where several source jurisdictions contribute to the same global cycle, the bilateral results must be reported before consolidation. Interactions between sources — simultaneous tightening by the Federal Reserve, the European Central Bank and other central banks — require a joint shock model; summing separately estimated bilateral effects may double count the common global component.¶ 49

F.10 Bounds by constrained optimisation, not by independent selection of extremes

Uncertainty arises from the attribution coefficients, the measurement parameters, the allocation weights, the exposure timing and the counterfactual. Let Θ(c) be the admissible set of measurement parameters and Φᵢⱼ(c) the joint attribution set. The per-scenario bounds are written:¶ 50

N⁻ᵢⱼₕ(c) = min { Nᵢⱼₕ(c, α, θ) : α ∈ Φᵢⱼ(c), θ ∈ Θ(c) } (F‑15)¶ 51

N⁺ᵢⱼₕ(c) = max { Nᵢⱼₕ(c, α, θ) : α ∈ Φᵢⱼ(c), θ ∈ Θ(c) } (F‑16)¶ 52

These are partial-identification or sensitivity bounds, not confidence intervals. A probabilistic interval may be reported only if sampling uncertainty, model uncertainty and the probability distribution of the relevant parameters are explicitly estimated. The preferred output is a matrix of bounds by counterfactual, by agent and by mechanism. A global envelope over c ∈ Γ may be added, but it must not replace the per-scenario results, since it masks the assumption that produces each extreme:¶ 53

N⁻ᵢⱼₕ = min { N⁻ᵢⱼₕ(c) : c ∈ Γ } , N⁺ᵢⱼₕ = max { N⁺ᵢⱼₕ(c) : c ∈ Γ } (F‑17)¶ 54

F.11 Gross adverse incidence and corrected ratios

A denominator described as “gross damage” must exclude offsets and unresolved overlaps. We define overlap-net gross adverse incidence G, the bounded attributable share κ and the net incidence ratio ι:¶ 55

Gᵢⱼₕ(c, θ) = Σₜ dᵢₕₜ · Σ(m : sₘ = +1) ΔXᵢⱼₕₘₜ(c, θ) (F‑18)¶ 56

κᵢⱼₕ(c) = Cᵢⱼₕ(c) / Gᵢⱼₕ(c) , ιᵢⱼₕ(c) = Nᵢⱼₕ(c) / Gᵢⱼₕ(c) (F‑19)¶ 57

None of these ratios is a causal probability, a percentage of legal liability or a share of welfare loss. ι may be negative if documented offsets exceed attributable adverse incidence. No ratio may be published until the shock, the population, the time window, the price base, the allocation of primitive components and the denominator are all fixed and reproducible.¶ 58

F.12 The debt-stock memo item

The exchange-rate revaluation of the external debt stock S is a balance-sheet exposure, not a cash flow of the period. It is reported separately:¶ 59

Sᵢⱼₕₜ(c) = D(FX)ᵢₕ,ₜ₋₁ · [ eᵢ,ₜ(obs) − eᵢ,ₜ(c) ] (F‑20)¶ 60

S may affect solvency indicators, collateral constraints, ratings and future refinancing, but these later cash-flow effects enter through their own mechanisms and primitive components. S is never added to C, O, N or G. If a fraction of the stock revaluation is realised through amortisation during the period, that realised flow falls under A1 and is deducted from the memo item for the same period.¶ 61

F.13 Decision, publication and stopping rules

The identity is designed to stop as much as to compute. The following rules are constitutive, not optional caveats:¶ 62

No counterfactual, no figure: every line must identify c and the model generating zₜ(c).¶ 63

No pre-shock or explicitly modelled exposure, no causal interpretation: dynamic realised incidence may nevertheless be reported descriptively.¶ 64

No allocation into primitive components, no aggregate: an unresolved overlap does not disappear through residual deduction.¶ 65

No identified beneficiary or transfer, no distributive offset: gains and losses remain separated by agent.¶ 66

No pre-registered joint attribution set, no envelope of extremes: independent cherry-picking of bounds is prohibited, and an unregistered Φ is deemed absent.¶ 67

No common unit and date, no intertemporal sum.¶ 68

No identified shock and robustness tests, no rung 3 causal claim.¶ 69

No bridge to welfare, no statement of welfare loss; no applicable legal obligation and standard of causation, no statement of legal liability.¶ 70

No pricing at rungs 1 or 2: an accounting incidence, even plausibly attributed, does not by itself justify either compensation or a levy.¶ 71

F.14 Minimum reproducibility package

A result derived from this framework becomes independently inspectable only when the following items are deposited with persistent identifiers and version control. The publication package is part of the method, because each institutional link depends on the provenance of the preceding one.¶ 72

F.15 Graduated compliance: the minimal configuration

Full compliance with §F.1–§F.14 is a research programme, not an afternoon's calculation. If the framework can be satisfied only by jurisdictions endowed with deep data and strong modelling capacity, it betrays the architecture it serves: the measurement layer is meant to be usable, at entry level, by the administrations most exposed to the spillovers it measures. Two configurations are therefore defined. Neither relaxes the stopping rules of §F.13; the minimal configuration restricts the scope, it does not lower the standard of proof.¶ 73

Configuration M (minimal, pilot level). Two counterfactuals — a polar benchmark and a plausible policy path, at least one of which may be narrative provided that its assumptions are written down. Multiplicative gₘ forms permitted for the financial channels where the mechanism is contractually mechanical, with written justification; real-economy channels reported descriptively (dynamic incidence), without attribution, if no elasticity of sufficient quality is available. Allocation into primitive components required only for material overlaps beyond a declared threshold (for example, 5% of gross adverse incidence), the others being published as unresolved. Agent breakdown limited to the sovereign, the central bank and a consolidated private sector. The outputs are labelled “Configuration M” and may serve for measurement, publication and scenario design; they cannot ground any financial consequence.¶ 74

Configuration F (full, regime level). The framework in full: three counterfactuals with modelled zₜ(c), mechanism-specific gₘ functions, a complete register of primitive components, the complete set of agents H, a documented transfer matrix, a pre-registered Φ and the full publication package of Table F3. Only Configuration F outputs may be transmitted to the qualification and pricing layers of the chain, and only after execution of the rung 3 programme of Annex G.¶ 75

The configuration used must be declared on the first page of any result. The move from M to F is a planned trajectory, not a concession: the pilot pathway of Section 12 assumes that the first participants operate under Configuration M and that the support arrangements of the architecture finance the transition.¶ 76

F.16 Transitional provision: status of the Section 9 magnitudes

The magnitudes reported in the body of this document — in particular the Tunisian monetary core of €0.76–1 billion net and the ≈€4.5 billion gross, all causes — were computed under the earlier version of this annex: a national aggregate, a single dominant counterfactual described as an upper bound, a pairwise seam correction, and the absence of a register of primitive components, of an agent breakdown and of a pre-registered Φ. Measured against the constitutive rules of §F.13 as they are now stated, these figures do not constitute verifiable aggregates. They are consequently requalified as follows: they are disciplined illustrations under the legacy framework, retained in the body of the text to make the anatomy of Section 9 legible, and flagged wherever they appear by a cross-reference to the present provision. They ground no claim beyond illustration. Their recomputation under Configuration M is the first deliverable of the empirical programme of this report (Annex I; international extension, Annex J); the convergence or divergence between the legacy figures and the Configuration M results will itself be reported. This provision explicitly resolves the inconsistency that would otherwise exist between the body of the text and its own annex; the silent coexistence of the two standards would offer the critics of the architecture precisely the weapon this annex is intended to take from them.¶ 77

F.17 Worked example: mechanism A2, sovereign agent

A single worked line shows the framework at human scale. Consider the floating-rate surcharge A2 for the sovereign (h = sov) of recipient country i, vis-à-vis source jurisdiction j, in year t.¶ 78

Exposure. According to the debt register, verified external floating-rate principal before the shock is E⁰ = 2.0 billion (reporting currency), entirely indexed to a single reference rate, with reset dates and the absence of caps and hedges verified in the exposure file. The pre-shock timing satisfies §F.3; no dynamic adjustment is necessary for t = 1.¶ 79

Counterfactuals. Under c₀ (constant-rate benchmark), the reference rate is 0.5%; under cᴺ (gradual normalisation), 2.0%; the observed rate is 5.5%. The gaps are therefore 5.0 and 3.5 points. Both paths, and the model that generates them, are deposited in the shock file.¶ 80

Incidence. With a full-year accrual, gross incidence is ΔX̃ = 2.0 × 5.0% = 100 million under c₀, and 70 million under cᴺ. There is no overlap with A3 for this component — the primitive component “reference-rate gap on verified floating-rate principal” is allocated ω(A2,k) = 1 — so ΔX = ΔX̃.¶ 81

Attribution. Table F2 gives the verified reset range α ∈ [0.90, 1.00]. The attribution register records why the lower bound is not 1: a minor tranche whose reset clause is disputed.¶ 82

Result. The A2 line for the sovereign is 90–100 million under c₀ and 63–70 million under cᴺ, in the declared unit of §F.8, reported by counterfactual and never merged into a single figure. No offset is deducted at this stage (§F.7), no causal claim attaches to it (§F.13), and it prices nothing. The full calculation repeats this discipline for every mechanism, every agent and every counterfactual, under the joint restrictions of Φ.¶ 83

F.18 Epistemic status and bridge to Annex G

Equations (F‑1)–(F‑20) discipline the accounting and the bounds; they do not validate the inputs. Three objects remain beyond the reach of this annex. First, the values and joint restrictions of α require independent estimation or a defensible partial-identification design. Second, the functions gₘ, the primitive components Dₖ, the allocation weights ωₘₖ and the transfer shares T require published data and an audit. Third, causal identification requires an identified monetary policy shock, exposures fixed before the shock or instrumented, multiple counterfactuals, interactions between channels, placebo tests and heterogeneity by exchange-rate regime, capital controls, debt structure and policy credibility.¶ 84

Annex G provides the empirical bridge: high-frequency, narrative or external-instrument monetary shocks; local projections or panel designs interacted with predetermined exposures; explicit cross terms exchange rate × rates × refinancing; placebo and pre-trend tests; state dependence; and a bridge from accounting incidence to output, distribution and welfare. Until that work is completed and replicated, the magnitudes produced here remain an accounting incidence with bounded partial attribution. They may inform measurement and scenario design; they cannot, on their own, establish fault, legal liability, compensation or price.¶ 85

@incollection{yaiche_hc_annexe_f,
  author    = {Yaïche, Nizar},
  title     = {Annex F — Formal accounting decomposition and bounded partial attribution framework},
  booktitle = {The Humanity Compact},
  year      = {2026},
  version   = {2.3},
  doi       = {10.5281/zenodo.22746533},
  publisher = {Zenodo},
  url       = {https://humanitycompact.org/ouvrage/annexe-f/}
}

A book by Nizar Yaïche, former Minister of Finance of the Republic of Tunisia. Who is the author?