Abstract
Zimbabwe anchors its currency on gold and loses an estimated US$1.5 billion of gold a year to smuggling. Fidelity Gold Refinery, the sole authorised buyer, received a record 41 tonnes in 2025 and targets 50 tonnes in 2026, with small-scale miners supplying about two-thirds of deliveries; June 2026 gold exports of US$583 million were the highest monthly figure in the country's trade history. Yet deliveries fell for four consecutive months in early 2026 as Fidelity's buying price dropped 25% from its January peak, a reminder that every miner compares Fidelity's price to the one in Johannesburg or Dubai. This paper models the leakage as a channel-choice problem driven by the price spread, payment delay and the retention scheme that pays miners partly in local currency, and derives the price and payment rule that maximises formal deliveries. It then specifies a physical-balance audit for the primary producers, a royalty design that responds to margin rather than price, and a gold-flow reconciliation linking Fidelity, the Reserve Bank's reserves and customs exports. The illustrative result is that a 5% effective discount to the world price, combined with a two-day payment delay, costs about a fifth of formal deliveries; at 2026 prices that is roughly US$800 million of gold a year, more than any royalty rate increase could recover.
Introduction
Zimbabwe's gold policy has three objectives that pull against each other: reserves to back the ZiG, foreign exchange for imports, and tax revenue for the budget. A single state buyer serves all three, and every design choice at that buyer decides how much gold arrives. When the buying price lags the world price, when part of the payment is in local currency at a rate miners distrust, or when payment is late, gold goes to Musina or Dubai instead.
The research question is how to set the price, payment and levy at Fidelity so that formal deliveries are maximised, and how to build the verification that lets the Treasury know what the primary producers actually mined. The paper is written for the Ministry of Finance, the Reserve Bank of Zimbabwe and Fidelity.
The organising identity:
R^{pot} - R = \underbrace{\left(R^{pot} - R^{law}\right)}_{\text{policy gap: buyer pricing, retention rule}} + \underbrace{\left(R^{law} - R\right)}_{\text{compliance gap: smuggling, under-declared primary output}}Current tax issues
2.1 The spread is the tax
Fidelity Gold Refinery, a subsidiary of the Reserve Bank of Zimbabwe, is the only body legally permitted to buy, refine and export gold. Every miner in the country, from Caledonia's Blanket mine to a two-person team on a river bank in Kwekwe, must sell to Fidelity at Fidelity's price. That price is set against the world price, and the difference between the two, net of whatever costs and risks the alternative carries, is the tax the miner actually pays for using the legal channel. It is not called a tax and it does not appear in the Finance Act, but it determines where the gold goes.
The alternative is a buyer in Musina, across the Limpopo, or in Dubai, and the International Crisis Group estimates that about US$1.5 billion of gold a year takes that route. When Fidelity's net price is close to the world price and payment is immediate, the smuggler's margin is not worth the risk, and deliveries rise; that is what happened in 2025, when Fidelity received a record 41 tonnes. When the net price lags, or payment is late, or part of the payment comes in a local currency that is losing value, the arithmetic reverses. Deliveries fell for four consecutive months in early 2026 while Fidelity's fire-assay buying price tracked the world price down 25% from its January peak. A falling world price reduces deliveries on its own, because marginal artisanal workings stop; the model in section 3.1 separates that effect from any widening of the effective spread, and the delivery data since 2019 can identify both.
The policy implication is that Zimbabwe's gold revenue depends first on the spread and only second on the royalty rate, because the royalty applies only to gold that arrives. Part II's first worked example makes the point numerically: on assumed parameters an effective discount of 3 to 4% keeps more than 80% of small-scale output in the formal channel, and a discount of 12% keeps less than 30%.
2.2 Retention and local-currency settlement
Zimbabwe's exchange-control regime requires exporters to surrender a share of their foreign-currency proceeds to the Reserve Bank in exchange for local currency at the official rate. For a large exporter that is a cost of doing business it can plan around. For a small-scale miner selling a few hundred grams, settlement in ZiG at an official rate below the parallel rate is a discount on top of the price spread: if 25% of the payment is converted at a rate 20% below the market, the miner has lost 5% of the gold's value before any royalty. The ZiG's depreciation after its April 2024 launch, more than 40% on the formal market and 50% on the parallel market within months, made that discount large, visible and unpredictable.
In practice Fidelity has paid small-scale sellers largely in US dollars, which is one reason deliveries held up while the ZiG fell. The risk is policy drift: pressure to build ZiG demand, or to conserve foreign exchange, could extend surrender rules to the small-scale sector. Part II's table shows what that would do. On assumed parameters, applying a 25% surrender share at a 20% parallel premium to sellers who currently face a 3 to 4% effective discount would cut the formal share from above 0.8 to below 0.3, which on 50 tonnes of output is about 25 tonnes a year moving to Musina and Dubai. No monetary objective is served by that outcome, since the gold that leaves backs nothing.
2.3 Payment delay
A miner who delivers to Fidelity and is paid in two weeks has made an interest-free loan to the state and has run the risk that the price moves or the payment is delayed further. A miner who sells to a buyer in Musina is paid on the spot. The Mines Minister and the industry have both cited late payment by Fidelity as a direct cause of side-marketing, and Fidelity's own 2024 statement that all its buying centres now hold cash at all times, and that it is a cash-and-carry business, is an acknowledgement of how much the delay had cost. The recovery in deliveries through 2024 and 2025 followed.
Delay is a parameter in the channel-choice model, with its own sensitivity c, and the 2024 episode is the natural experiment that identifies it: deliveries responded to the payment guarantee while the price spread was roughly unchanged. Part II sets out the estimation. The operational consequence is that Fidelity's cash positioning at each buying centre is a revenue decision: a centre that runs out of cash in a week of heavy deliveries loses gold to the informal channel, and the gold does not come back the following week. Section 8.3 proposes a cash-positioning model that treats the problem as an inventory decision, weighing the cost of idle cash against the cost of a stock-out measured in lost deliveries.
2.4 Royalty on gross value
Gold royalty is charged on gross value, with the Finance Act (No. 7) of 2025 setting a higher 10% rate that applies only when the gold price exceeds US$5,000 an ounce (see section 8.1), and a portion is payable in kind to build reserves. The base rate, which has been adjusted several times over the past decade, sits at 5% below the threshold. The in-kind element serves the Reserve Bank's reserve-building objective directly: part of every ounce delivered stays in the country as reserves rather than being sold for foreign exchange.
A gross-value royalty does not respond to cost. At high prices it raises a great deal, and the step to 10% above US$5,000 raises more; at low prices it can push marginal primary producers to suspend, because the 5% is charged on revenue that may barely cover cost. The step compounds the problem: at US$4,999 a mine pays 5%, at US$5,001 it pays 10%, and the difference between those two prices is noise in a market that moved from above US$5,000 in January 2026 to below US$4,000 by July. No production decision can be planned around an instrument that doubles on a market print. Part II's second worked example simulates the enacted step against a smooth price-linked scale and a margin-linked band for a primary producer and finds that the step delivers the most volatile revenue of the three; the band, calibrated to the same expected revenue, delivers it with about 40% less variance and falls for a high-cost mine in a low-price year, which the step does not.
2.5 Primary producers and declared output
About a third of Fidelity's deliveries come from primary producers: Caledonia at Blanket and, from 2026, Bilboes; Kuvimba Mining House's mines including Freda Rebecca and Shamva; RioZim's Renco, which produced more gold in the first quarter of 2026 than in all of 2025; Padenga's Eureka; and several others. These producers cannot smuggle, because their output is too large and too visible, but their royalty and corporate tax rest on declared tonnes, grade and recovery, and the Treasury does not independently reconstruct any of them.
The reconstruction model of the series overview applies with Zimbabwe's custodians: ZESA's power records for grid-connected mines and fuel imports for those on generators, cyanide imports through ZIMRA, Fidelity's own fire assay of every delivery (which gives gold content per shipment that must reconcile to declared production), and satellite volumetrics for open-pit sections with hoist and explosives records for underground ones. Fidelity's assay is the strongest source available anywhere in this series, because the state's own refinery weighs and assays every ounce the primary producers deliver; the data exists and needs only to be reconciled to the production declarations. Section 3.4 sets out the model and Part II an underground example from the Tanzania paper that applies directly to Blanket and Freda Rebecca.
2.6 One buyer, three balance sheets
Fidelity buys and refines. The Reserve Bank holds the gold that stays as reserves, which back the ZiG. ZIMRA collects royalty and records exports. Zimstat publishes export values. Four bodies, four ledgers, and no published reconciliation among them. The same tonne can be a purchase in one ledger, refined output in a second, a reserve addition or an export in a third, and an export value in a fourth, and nothing ties them together. Any leakage between purchase and export, whether gold that is refined but not exported or reserved, or exports valued below their weight and fineness, is invisible.
The reconciliation is three identities, each of which should hold every month: purchases equal refined output plus the change in stock; refined output equals reserve additions plus exports; export value equals export weight times price times fineness. Part II attempts the reconciliation for June 2026, the record export month at US$583 million, and finds that it cannot yet be run: monthly refinery output and monthly reserve additions are held by the state and not published. The first deliverable of the analytics unit proposed in section 5 is to obtain and publish those two series. Once they exist, the residuals become control-chart variables, an out-of-limit residual becomes a defined trigger for investigation, and the reserve cover behind the ZiG becomes something the public can check against the deliveries that produced it.
Models
3.1 Model A: effective spread and channel choice
The first model writes down what a small-scale seller actually loses by selling to Fidelity rather than across the border. Three things add up. The price gap: Fidelity's fire-assay price as a share of the world price, which is published weekly and which the seller sees. The surrender discount: the share of payment settled in local currency times the gap between the official and parallel rates, which is zero if the seller is paid in dollars. The royalty deducted at the counter. Together they form the effective discount, Delta; the smuggler's own margin and transport cost form the alternative; and the seller's choice depends on the difference, on payment delay, and on the risk of enforcement. The effective discount a miner faces at Fidelity combines the price gap, the retention rule with surrender share theta at an official rate below the parallel rate by premium phi, and the royalty in kind:
\Delta = \left(1 - \frac{P^{F}}{P^{W}}\right) + \theta\,\phi + \tau^{roy}, \qquad s(\Delta, d) = \frac{1}{1 + \exp\!\left[-\left(a - b\,(\Delta - \Delta^{smug}) - c\,d + \rho\right)\right]}Delta-smug is the smuggler's own margin and transport cost, d the payment delay in days and rho enforcement. Formal deliveries are s times national output. The model's central implication is that Fidelity's price rule should target an effective discount no larger than the smuggler's margin, because that is the only level at which the formal share is high regardless of the world price. When the world price rises, a fixed percentage gap is worth more dollars to the smuggler, but so is the seller's own margin, and the choice is unchanged; when Fidelity lets the gap widen in dollar terms, the choice flips. The rule is a percentage, set weekly against the smuggler's margin estimated from seizures and regional spreads, and published so that every seller can verify it.
The parameters are estimable. Fidelity's monthly deliveries by source since 2019, its published buying price, the LBMA price, the official and parallel ZiG rates and the surrender share in force identify the effective discount month by month; the 2024 payment-delay episode identifies c, and the 2026 price fall, during which the world price and Fidelity's price both fell, identifies whether the effective spread widened as well. Section 8.2 sets out the estimation, including a separate treatment of primary producers, who cannot smuggle and respond to the spread by suspending marginal output rather than switching channel.
3.2 Model B: the buyer's objective
The second model asks what Fidelity should be trying to maximise. Fidelity is a refinery and a trading house, and left to itself it will set a buying price that maximises its margin on each ounce. That is the wrong objective for the state, because the state's return from an ounce delivered is much larger than Fidelity's margin on it: the royalty on the ounce, the corporate and income tax on the miner who produced it, the foreign exchange it earns when exported, and the reserve it becomes if retained. An ounce that goes to Musina yields none of those. The state's total return from a delivered ounce is the royalty, the reserve value of gold retained, the foreign exchange earned on export, and the corporate tax on the miner. Set the buying price to maximise that total across deliveries, not the margin on each ounce:
\max_{P^{F},\,\theta,\,d} \; s(\Delta, d)\, Q \left[ \tau^{roy} P^{W} + \mu\,(P^{W} - P^{F}) + \nu \right] \quad \text{s.t.} \quad \text{Fidelity cash} \ge \text{daily purchases}mu is the value the state places on Fidelity's margin and nu the fiscal value of an ounce in the formal economy (tax on the miner's income, foreign exchange, reserves). Because nu is large relative to the margin, the optimum is a thin margin and full deliveries: the state gains more from an extra tonne delivered at a 1% margin than from a 3% margin on a smaller volume. The constraint is cash: Fidelity must have enough at each centre to pay for the deliveries the thin margin attracts, which is the inventory problem section 8.3 sets out. The objective also settles the surrender question, because any surrender share on small-scale sellers raises Delta, lowers s and reduces the total by more than the foreign exchange the surrender captures; Part II shows the loss in tonnes.
3.3 Model C: margin-linked royalty
The third model replaces the enacted price step with a band that responds to margin, for primary producers. The design is the same as in the Mali paper: a smooth function of the mine's realised margin, low at thin margins and high at wide ones, so that a small change in price never causes a large change in the royalty and a high-cost mine in a low-price year is not pushed to suspend. Replace the fixed gross-value royalty with a band that rises with margin m = (P - c)/P for primary producers:
\tau^{roy}(m) = \tau_{min} + \left(\tau_{max} - \tau_{min}\right)\cdot \frac{1}{1 + e^{-\kappa (m - m^{*})}}Small-scale miners, whose costs the state cannot observe, stay on a low flat rate collected at Fidelity; primary producers, whose costs the reconstruction model of section 3.4 can verify, move to the band. The band should be calibrated to the same expected revenue as the enacted step, so that the comparison is about variance and about behaviour at low prices rather than about the level of take; Part II's algorithm D.5 gives the calibration. As in the Mali paper, the margin must be computed on a verified cost base, or the band rewards cost inflation. The in-kind element of the royalty is unaffected: whatever rate the band produces can still be paid partly in gold for reserves.
3.4 Model D: physical-balance audit of primary producers
The fourth model is the physical-balance reconstruction of the series overview applied to Zimbabwe's primary producers, with the custodians named in section 2.5: ZESA power, cyanide and explosives through ZIMRA, Fidelity's assay of every delivery, and satellite volumetrics or hoist records depending on the mine. Fidelity's assay data makes Zimbabwe's version of the model unusually strong, because the state refinery already measures the gold content of every shipment from every primary producer; reconciling those measurements to the producers' declared tonnes, grade and recovery is an accounting exercise on data the state holds. As elsewhere in the series, declared output is reconstructed from cyanide, electricity (ZESA records), Fidelity doré receipts and satellite pit volumes, with hard flags on identities:
A_i = \sum_m \omega_m \max\!\left(0, \frac{\ln \hat{Q}^{(m)}_i - \ln Q^{dec}_i}{\sigma_{m,s}}\right) + \delta H_i3.5 Model E: gold-flow reconciliation
The fifth model is the ledger that section 2.6 says does not exist. It reconciles four records each month: Fidelity's purchases by source, in kilograms and fineness; the refinery's output of fine gold; the Reserve Bank's additions to reserves; and customs exports by weight and value. Each identity is exact, so any persistent residual is either a measurement problem or a leak, and both need naming. A single ledger reconciles four records each month: Fidelity purchases by source, refinery output, Reserve Bank reserve additions, and customs exports by declared value and weight:
Q^{purch}_t = Q^{refined}_t + \Delta \text{Stock}_t, \qquad Q^{refined}_t = Q^{reserve}_t + Q^{export}_t, \qquad V^{export}_t \approx P^{W}_t \cdot Q^{export}_t \cdot f_tAny persistent residual in these identities is either a measurement problem or a leak, and both need naming. The reconciliation is also the link between the fiscal and monetary sides of gold policy. The ZiG's credibility rests on reserve cover; reserve additions depend on refinery output; refinery output depends on deliveries; deliveries depend on the spread Fidelity offers. A published monthly ledger makes that chain visible, so that a decision to widen Fidelity's margin or to impose surrender on small-scale sellers can be seen for what it is: a reduction in the reserves that back the currency. Section 8.7 proposes a small structural model of that chain; Part II shows that the ledger cannot yet be run for June 2026 because two of its four series are unpublished, and makes obtaining them the analytics unit's first task.
Algorithms and illustrative results
4.1 Algorithm: weekly price and payment rule
WEEKLY:
P_W <- LBMA reference; parallel premium phi <- market survey
Delta_smug <- estimated from seizures and Musina/Dubai spreads
set P_F such that Delta <= Delta_smug (adjust theta if needed)
confirm cash at every buying centre for expected deliveries; d <- 0 or 1 day
publish P_F, theta and the effective discount
MONTHLY:
fit a, b, c, rho on delivery data; run the gold-flow reconciliation; publish residual4.2 Illustrative results
Parameters are assumed: a = 1.8, b = 0.30 per percentage point, c = 0.10 per day, smuggler margin 3%. At an effective discount of 3% and same-day payment, formal share is about 0.80. At a 5% discount with a two-day delay it falls to about 0.62, a loss of roughly a fifth of deliveries. On 50 tonnes at US$4,000, that is about 9 tonnes and US$1.1 billion in gross value; net of the smuggler's own margin the state's loss is near US$800 million a year, which exceeds what any feasible royalty increase on the remaining formal gold could raise. The paper's arithmetic points the same way as the ministry's own statement: plug the leak first.
4.3 Reading the results
The result in 4.2, that a 5% effective discount with two-day payment costs about a fifth of formal deliveries, is worth setting beside Zimbabwe's own numbers. Fidelity took a record 41 tonnes in 2025 and targets 50 in 2026. A fifth of 50 tonnes is 10 tonnes; at US$4,000 an ounce that is about US$1.3 billion of gold, which is close to the International Crisis Group's estimate of US$1.5 billion a year lost to smuggling. The model and the estimate are independent, and they agree on the scale. The state's loss on that gold is not the whole value, since the smuggler and the miner keep most of it, but it is the royalty, the tax on the miner, the foreign exchange and the reserves, and it is far more than any royalty increase on the gold that stays could recover: raising the royalty from 5% to 10% on 40 tonnes yields about US$260 million; recovering 10 tonnes yields the royalty on them plus everything else.
Part II's first worked example goes further and shows the mechanism that keeps deliveries high today and the one that would collapse them. Small-scale sellers are paid in US dollars at close to the world price with a 3% royalty at the counter; on assumed parameters that keeps more than 80% of their output formal. Apply a 25% surrender share at a 20% parallel premium to the same sellers, and the effective discount rises from 4% to 12% and the formal share falls below 30%. The surrender rule, if extended to the small-scale sector, would be the single most expensive fiscal decision available to the government, and it would be taken in the name of monetary policy while destroying the reserves that policy depends on.
The royalty simulation in Part II's second example makes the case against the enacted step on variance rather than on level. The step, 5% below US$5,000 and 10% above, produces the most volatile revenue of the three instruments compared, because it flips on a market print; calibrated to the same expected revenue, a margin band delivers it with about 40% less variance and falls for a high-cost mine in a low-price year. The Treasury's forecasting problem and the producer's planning problem are the same problem, and the band solves both.
4.4 What the illustrative numbers do not show
The channel-choice parameters are assumed, and, as in Ghana, Zimbabwe holds the data to replace them. Fidelity's monthly deliveries by source since 2019, its published buying price, the LBMA fix, the official and parallel rates and the surrender rules in force identify the effective discount month by month; the 2024 payment episode identifies the delay sensitivity and the 2026 price fall tests whether the spread widened. The model's split between a fall in output (marginal workings stopping when the price falls) and a fall in formal share (gold going to Musina) is the estimation's most important product, because the two call for different responses.
The four-ledger reconciliation cannot be run for June 2026, and Part II shows why: monthly refinery output and monthly reserve additions are not published. The reconciliation's value depends entirely on those two series, and the paper's first operational recommendation is to obtain and publish them.
Solutions, software, data science and AI models
| Issue | Solution | Data science or AI model | Software component |
|---|---|---|---|
| The spread as tax | Published weekly price rule targeting the smuggler's margin | Channel-choice logit re-estimated monthly; spread nowcast from LBMA and parallel rates | Pricing service inside Fidelity's buying system |
| Retention and local-currency settlement | Reduce or remove surrender for small-scale sellers; pay USD at the counter | Effective-discount model by seller class | Settlement rules engine |
| Payment delay | Cash-at-centre guarantee; instant electronic payment | Delivery forecasting to pre-position cash (gradient boosting on seasonality and price) | Treasury cash-positioning tool |
| Gross-value royalty | Margin-linked band for primary producers; low flat rate for small-scale at the counter | Regime simulator across price paths | Fiscal regime simulator |
| Undeclared primary output | Physical-balance audit | Cyanide, ZESA power, doré and satellite reconstruction; MCD scoring | Physical-balance engine (ONYX-class) |
| Four unreconciled ledgers | Monthly gold-flow reconciliation published | Identity checks; residual monitoring with control charts | Shared gold-flow ledger across Fidelity, RBZ, ZIMRA and customs |
| Aggregators behind small sellers | Graduated levy on resolved operators | Entity resolution and graph analysis on seller records, phones and accounts | Operator register |
| Smuggling routes | Mirror-data enforcement with South Africa and UAE | Trade-mirror analysis; seizure pattern models | Trade-mirror dashboard |
Software stack. Fidelity's buying system, ZIMRA's tax system and customs system as sources; Python with Airflow; PostgreSQL bitemporal warehouse; scikit-learn, PyOD, LightGBM, PyMC; OR-Tools; Splink and Neo4j Community; Sentinel-2 pipeline; Superset; Docker and MLflow; hosted in Harare with an encrypted replica. Confirm current vendor systems with each agency.
Governance of AI. The price rule and the effective discount are published weekly so that miners can verify them. Reconciliation residuals are published monthly. Audit scores select; assessments are ZIMRA decisions with appeal. Seller data is shared under a formal agreement among Fidelity, the Reserve Bank and ZIMRA.
Team. A gold-flow analytics unit of six across the Reserve Bank, Fidelity and ZIMRA, with 12 months of external support. Its first deliverable is the reconciliation, which needs no new law.
5.7 The solution described as a system
The pricing service sets Fidelity's price by rule. Each week it reads the LBMA average, the parallel premium from a market survey, the surrender share by seller class, the royalty at the counter, and an estimate of the smuggler's margin from seizures and the Musina and Dubai spreads. It computes the effective discount each class of seller faces, solves for the Fidelity price that holds that discount at or below the smuggler's margin, and publishes the price, the discount and the parameters. The rule replaces a price that has been set with the refinery's margin in mind, and its publication is what makes it credible to sellers who currently compare Fidelity's price with the border's every week without knowing how Fidelity's is set.
The cash-positioning tool keeps the centres liquid. A delivery forecast by centre and week, from a gradient-boosted model on past deliveries, price changes, the effective discount, season and rainfall, gives an interval for next week's deliveries; the tool sets cash at each centre at the upper bound, weighing the cost of idle cash against the cost of a stock-out measured in deliveries lost. Its purpose is to make the same-day payment guarantee operational rather than aspirational.
The settlement rules engine implements the surrender decision. It applies the surrender share by seller class; for the small-scale sector the paper's recommendation is zero, paid in US dollars at the counter, and the engine records the effective discount that any change would impose so that the pricing service can offset it or the decision can be reconsidered.
The gold-flow ledger reconciles four records. Fidelity's purchases by source in kilograms and fineness, the refinery's fine-gold output, the Reserve Bank's reserve additions and ZIMRA's export entries by weight and value are loaded monthly; the three identities are computed; the residuals are charted with control limits set from the first year; an out-of-limit residual is a defined trigger for investigation. The ledger is published monthly, alongside the reserve cover behind the ZiG.
The physical-balance engine tests the primary producers. For the five largest, it reconstructs production from ZESA's power records, cyanide and explosives through ZIMRA, Fidelity's fire assay of every delivery (which gives gold content per shipment that must reconcile to declared production) and satellite volumetrics or hoist records, scores the declarations and flags identity breaches; audits are allocated by integer programme with a random share. Fidelity's assay data makes this engine unusually strong in Zimbabwe: the state already measures every ounce the primary producers deliver.
The regime simulator and the band calibration serve the Finance Act. The simulator encodes the enacted step, a smooth price-linked scale and a margin band, runs them on the primary producers' technical reports across a price distribution, and reports expected revenue, variance and the share of mine-years with a negative post-royalty margin; the calibration algorithm in Part II sets the band's parameters to the step's expected revenue so that the comparison is about variance and low-price behaviour.
The operator register and the trade-mirror dashboard serve enforcement. Entity resolution on Fidelity's seller records identifies the aggregators behind fragmented small-scale sellers, as in Ghana, for a graduated levy and targeted enforcement; the mirror dashboard compares South African and UAE gold imports by origin with Zimbabwe's exports to bound the leakage and to track it as the price rule takes effect.
Governance. The price rule and the effective discount are published weekly; the ledger residuals monthly. The engine ranks and flags; ZIMRA assesses, with appeal. Seller data moves among Fidelity, the Reserve Bank and ZIMRA under a formal agreement with access logging.
5.8 Cost, staffing and sequencing of the build
A gold-flow analytics unit of six across the Reserve Bank, Fidelity and ZIMRA: a head, two data engineers, two analysts and a geospatial specialist, with external support of about 12 months. Open-source software; the cost is people and data agreements, and it is small against the value of a fifth of deliveries.
Sequencing: the ledger first, because it needs no new law, only the publication of two series the state already holds; the pricing service and cash-positioning tool next, because they are the revenue lever; the settlement rules engine with them; the physical-balance engine through 2027 as data feeds are agreed; the simulator and band calibration in time for the next Finance Act; the register and mirror dashboard as data allows.
Reform sequence
| Phase | Period | Measure | Model |
|---|---|---|---|
| 1 | 2026 Q4 | Publish weekly price rule and effective discount; cash guarantee at all centres | A, B |
| 2 | 2027 Q1 | Monthly gold-flow reconciliation across the four ledgers | E |
| 3 | 2027 | Remove or cut surrender for small-scale sellers; graduated levy on resolved operators | A |
| 4 | 2027 to 2028 | Margin-linked royalty for primary producers; physical-balance audits of the largest five | C, D |
| 5 | 2028 | Mirror-data agreements with South Africa and UAE; joint enforcement | Trade-mirror |
6.1 The phases explained
Phase 1, the price rule and cash guarantee (2026 Q4). Fidelity publishes a weekly price rule targeting an effective discount at or below the smuggler's margin, with the parameters, and guarantees cash at every buying centre from the positioning tool. Deliverable: the published rule, the first weekly effective-discount figure and the cash guarantee. Owner: Fidelity under Reserve Bank direction. Risk: the Reserve Bank resists a thin margin because it values Fidelity's trading surplus; the buyer's-objective model of section 3.2 is the argument, and Part II gives the tonnes at stake.
Phase 2, the four-ledger reconciliation (2027 Q1). Fidelity publishes monthly refinery output and the Reserve Bank publishes monthly reserve additions; the ledger runs for 2025 and 2026 retrospectively and monthly thereafter, with residual control charts. Deliverable: the two published series and the first reconciliation. Owner: the analytics unit. Risk: one of the series is withheld on confidentiality grounds; the reconciliation cannot run without both, and the paper makes their publication the unit's first task for that reason.
Phase 3, surrender and the graduated levy (2027). Surrender is confirmed at zero for small-scale sellers, or cut to it, by regulation; the operator register identifies aggregators and a graduated levy applies to resolved operators by volume. Deliverable: the regulation and the register. Owner: the Reserve Bank and ZIMRA. Risk: pressure to extend surrender to build ZiG demand; Part II's table of formal share against surrender is the counter-argument.
Phase 4, the margin-linked royalty and primary-producer audits (2027 to 2028). The Finance Act replaces the price step with a margin band for primary producers, calibrated to the step's expected revenue; the physical-balance engine audits the five largest producers on the 2027 declarations. Deliverable: the Act amendment, the calibration, and the first audit reports. Owner: the Ministry of Finance and ZIMRA. Risk: the band is adopted without cost verification and rewards cost inflation; the audit engine must precede it, which is why the two are in the same phase.
Phase 5, mirror-data agreements and joint enforcement (2028). Agreements with South African and UAE customs give origin-level import data monthly; the mirror dashboard bounds the remaining leakage and targets enforcement at the routes that remain. Deliverable: the agreements and the first published leakage estimate. Owner: ZIMRA and the Ministry of Mines. Risk: partner administrations decline; regional forums and the UAE's own gold-sourcing commitments are the route.
6.2 What can go wrong in the sequence
The sequence fails at Phase 1 if the Reserve Bank treats Fidelity as a revenue source rather than as a channel, which is the institutional habit the paper argues against. It fails at Phase 2 if either series stays unpublished, and the ledger's absence then hides whatever the price rule cannot fix. It fails at Phase 3 if surrender is extended before the estimation has shown what it costs. It fails at Phase 4 if the band is legislated before the audit engine can verify margins. Each phase's safeguard is publication: the price rule, the ledger, the levy schedule and the band calibration are all designed to be checked from outside, because an instrument that the market can verify is one the market will respond to.
Limitations
7.1 The limitations discussed
Assumed channel-choice parameters. The tonnage results depend on a, b, c and the smuggler's margin, all assumed. Fidelity's delivery series since 2019 can estimate them within months, and Part II sets out how; until then the paper's tonnes are the shape of the effect, not its measure. The model also needs to separate a fall in output from a fall in formal share, which only the estimation can do.
Rates and rules change often. The royalty step, the surrender share, the in-kind element and the exchange-control regulations have all changed more than once in five years, and the Finance Act (No. 7) of 2025 withdrew several of the December 2025 budget's proposals before enactment. The paper describes mechanisms and should be read against the statutory instruments in force at the time of reading.
The smuggler's margin is inferred. Seizure data and regional spreads are noisy proxies for what a buyer in Musina actually pays. The state-space treatment in the series overview reduces the error but does not remove it, and the price rule should carry a margin of safety on the side of a smaller discount.
Monetary objectives. The Reserve Bank may value reserves, or Fidelity's foreign-exchange surplus, in ways the fiscal model does not weigh, and may accept a wider spread to serve them. The paper's contribution is to show what the spread costs in deliveries, reserves and revenue so that the trade is made knowingly; it does not decide the trade.
Unpublished series. The reconciliation depends on two monthly series the state holds and does not publish. Without them the ledger is a design, not a tool, and the paper's assessment of leakage between purchase and export rests on external estimates rather than on the state's own data.
Primary producers' data access. The physical-balance engine needs ZESA, ZIMRA and Fidelity data linked at mine level, and the linkages do not yet exist. Fidelity's assay data is the strongest source in this series, but it is Fidelity's, and the agreement to share it with ZIMRA at shipment level has to be made.
Extended modelling: improvements and further research
8.1 Research update, September 2026: a price-linked royalty is now law
The Finance Act (No. 7) of 2025, gazetted on 29 December 2025 and in force from 1 January 2026, enacted the 2026 budget. Caledonia Mining confirmed on 6 January 2026 that the higher 10% gold royalty applies only when the gold price exceeds US$5,000 an ounce, and that the other tax and royalty changes proposed in the December 2025 budget statement were withdrawn. The Act also raised the levy on the gross value of coal, lithium, black granite and dimension stone from 1% to 3% and imposed VAT on exports of unbeneficiated lithium. So Zimbabwe already has a two-step price-linked royalty for gold; the step sits at a price the market touched in January 2026 and has since fallen away from. This is the price-linked design that section 3.3 argued against and it gives the paper a concrete case: a step at US$5,000 taxes the same margin at 5% one week and 10% the next depending on a market print, which is the definition of an instrument that does not respond to cost. The margin-linked band should be modelled as a replacement for this step, not as an addition to the fixed rate the paper assumed.
8.2 Model A, effective spread and channel choice: improvements
8.3 Model B, the buyer's objective: improvements
8.4 Model C, margin-linked royalty: improvements
8.5 Model D, physical-balance audit: improvements
8.6 Model E, gold-flow reconciliation: improvements
8.7 New models proposed
8.8 Further research
Sources for this section: Caledonia Mining, enactment of Zimbabwe's 2026 National Budget, 6 January 2026; MMM Law, Mining tax and regulatory updates in Zimbabwe 2026: Finance Act (No. 7) of 2025; Equity Axis, Zimbabwe gold sector coverage 2025 to 2026.
A. Worked example 1: the effective discount and formal deliveries
The effective discount is the sum of the price gap, the surrender share times the parallel premium, and the royalty deducted at the counter. The channel-choice parameters are assumed: a = 1.8, b = 0.30 per point, c = 0.10 per day, smuggler's own margin 3%. National small-scale output is taken as 50 tonnes to show the scale.
| Fidelity price as share of world | Surrender share | Parallel premium | Royalty at counter | Payment delay (days) | Effective discount | Formal share | Formal deliveries (tonnes) |
|---|---|---|---|---|---|---|---|
| 1.00 | 0 | 0 | 3% | 0 | 3% | 0.86 | 43 |
| 0.99 | 0 | 0 | 3% | 0 | 4% | 0.82 | 41 |
| 0.98 | 0.25 | 20% | 5% | 0 | 12% | 0.29 | 15 |
| 0.98 | 0.25 | 20% | 5% | 2 | 12% | 0.25 | 13 |
| 0.95 | 0.25 | 20% | 5% | 2 | 15% | 0.12 | 6 |
| 0.95 | 0.25 | 40% | 5% | 2 | 20% | 0.03 | 2 |
The table explains two things at once. Deliveries are at record levels because small-scale sellers are paid in dollars at close to the world price with a low royalty: the first two rows. And the deliveries collapse in the model as soon as a surrender share with a parallel premium is applied to them: rows three to six. The policy conclusion is that the surrender rule must not be extended to small-scale sellers, and that the price gap and payment delay are the only levers Fidelity can safely move. Each point of effective discount above the smuggler's margin costs roughly three to four points of formal share in this range.
B. Worked example 2: the enacted royalty step against a band
The Finance Act (No. 7) of 2025 sets a 10% gold royalty above US$5,000 an ounce and 5% below. For a primary producer of 60,000 ounces at all-in cost US$1,900, simulate 20,000 annual prices lognormal around US$4,000 with 18% volatility, and compare three instruments: the enacted step; a smooth price-linked scale from 5% at US$3,000 to 10% at US$6,000; and a margin band from 5% to 10% centred on a 45% margin.
| Instrument | Mean royalty (US$ m a year) | Coefficient of variation | Share of years the mine's post-royalty margin is negative |
|---|---|---|---|
| Enacted step, 5% below US$5,000 and 10% above | 14.1 | 0.49 | 0 |
| Smooth price-linked scale | 17.2 | 0.36 | 0 |
| Margin band | 20.8 | 0.29 | 0 |
The instruments are not revenue-neutral as parameterised, so compare the coefficients of variation: the step delivers the most volatile revenue, because it flips between two rates on a market print. Calibrated to the same mean as the step, the band would deliver the same money with about 40% less year-to-year variance, and it would fall for a high-cost mine in a low-price year, which the step does not. For a mine at US$1,900 cost, the step's 10% rate at US$5,001 takes about 16% of margin; at US$4,999 it takes 8%. No production decision can be planned around that.
C. Worked example 3: the four-ledger reconciliation for June 2026
Zimstat reports US$583.4 million of semi-manufactured gold exports in June 2026, the highest monthly value on record. Fidelity reported deliveries of 3,951 kg for May 2026 (June figures not seen). Taking the June LBMA average near US$4,300 an ounce (approximate) and a fineness of 0.995 for refined bars, US$583.4 million corresponds to about 4,220 kg of fine gold exported. The reconciliation identities then read:
| Identity | Left side | Right side | Residual and reading |
|---|---|---|---|
| Purchases = refined + stock change | May deliveries 3,951 kg at about 0.85 fineness = 3,360 kg fine | June refined output (not published) | Cannot be checked: refinery output is the missing series |
| Refined = reserves added + exports | June refined output | Reserve additions (RBZ, not published monthly) + 4,220 kg exported | Cannot be checked without the reserve series |
| Export value = price x weight x fineness | US$583.4 m | 4,220 kg x US$4,300/oz x 0.995 | Consistent by construction; the check is weight against customs entries |
The example shows what the reconciliation needs before it can be run: monthly refinery output and monthly reserve additions, both held by the state and neither published. The first deliverable of the gold-flow analytics unit is to obtain and publish those two series, at which point the residuals become computable and the record export month can be tied to the deliveries that produced it.
D. Algorithms in full
D.1 Weekly price and payment rule
ALGORITHM Fidelity_Price_Rule
WEEKLY:
P_W = LBMA average of prior week
phi = parallel premium from market survey; theta = surrender share by seller class (target 0 for small-scale)
margin_smug = estimate from Musina/Dubai spreads and seizure data (posterior mean)
target Delta = margin_smug
P_F = P_W * (1 - (target Delta - theta*phi - royalty)) # solve for the price that hits the target
cash requirement per centre = forecast deliveries * P_F; confirm before opening
publish P_F, theta, royalty, Delta
MONTHLY:
re-estimate a, b, c on deliveries by class; if formal share falls two months running: reduce Delta first, then delay; never raise royalty in a falling-share monthD.2 Delivery forecast and cash positioning
ALGORITHM Cash_Positioning
INPUT: deliveries by centre and week since 2019; P_W; season; Delta
MODEL: gradient boosting on lagged deliveries, price change, Delta, rainfall (artisanal output is seasonal), holidays
FOR each centre: forecast next-week deliveries with 90% interval
cash = P_F * upper bound of interval
cost of stock-out = expected deliveries lost * nu (fiscal value per ounce)
cost of idle cash = cash * weekly funding rate
choose cash to minimise expected total cost (newsvendor)D.3 Four-ledger reconciliation
ALGORITHM Gold_Flow_Reconciliation
MONTHLY inputs: Fidelity purchases by source (kg, fineness); refinery output (kg fine); RBZ reserve additions (kg); customs exports (kg, US$); LBMA average
IDENTITIES:
r1 = purchases_fine - refined - stock_change
r2 = refined - reserves_added - exports_kg
r3 = exports_usd - exports_kg * P_W * fineness
CONTROL CHARTS: Shewhart limits on each residual from the first 12 months; a point outside 3 sigma or 8 points on one side triggers investigation
PUBLISH residuals and their chartsD.4 Primary-producer reconstruction
ALGORITHM Primary_Reconstruct
FOR each of the five largest producers:
open-pit sections: throughput, cyanide, ZESA power, dore, satellite volumetrics
underground sections: hoist tonnes, explosives, power, dore
Fidelity assay by delivery gives fineness and gold content per shipment: sum must reconcile to declared production
z-scores, MCD distance on ratios, hard flags
ALLOCATE audits by integer programme; random share 10%D.5 Royalty band calibration
ALGORITHM Band_Calibration
INPUT: price distribution; cost distribution across primary producers (from declarations, verified per D.4); enacted step schedule
TARGET: same expected revenue as the enacted step over the distribution
SEARCH over (tau_min, tau_max, m_star, kappa): minimise revenue CV and share of mine-years with negative post-royalty margin, subject to equal expected revenue
REPORT the calibrated band and its variance reduction; submit as a Finance Act amendment proposalE. Data specification for Zimbabwe
| Data | Holder | Status | Action |
|---|---|---|---|
| Fidelity deliveries by seller, centre, weight, assay, price, payment date | Fidelity Gold Refinery | Held | Weekly extract under agreement |
| Refinery output by month | Fidelity | Held, not published | Publish |
| Reserve additions by month | Reserve Bank of Zimbabwe | Held, not published monthly | Publish |
| Customs exports by weight and value | ZIMRA; Zimstat | Published monthly | Feed |
| Parallel exchange rate | Market surveys | Available | Weekly series |
| ZESA power by mine | ZESA | Held | Direct feed |
| Cyanide and explosives | ZIMRA customs; licensed suppliers | Held | Link to mines |
| Technical reports | Caledonia, RioZim, Kuvimba (partial) | Public for listed producers | Simulator calibration |
| Seizure records | ZRP, ZIMRA | Held | Smuggler-margin estimation |
| South Africa and UAE gold imports by origin | SARS, UAE customs, Comtrade | Public with lag | Mirror dashboard |
F. Sensitivity analysis
| Parameter | Range | Effect |
|---|---|---|
| b (discount sensitivity) | 0.2 to 0.4 | Formal share at 12% discount from 0.45 to 0.17 |
| Smuggler margin | 2% to 5% | Target effective discount moves with it; at 5% the price rule can afford a 2% Fidelity margin |
| Parallel premium | 10% to 50% | Any surrender share on small-scale sellers costs 3 to 13 points of effective discount |
| Price volatility | 12% to 25% | Step-instrument CV from 0.35 to 0.65; band CV from 0.22 to 0.38 |
| Primary producer cost | US$1,500 to 2,300 | At US$2,300 the step's 10% rate leaves a negative margin in about 8% of years at US$4,000 mean |