## _wp16159 - Section V to explain how the black market rate can rise significantly faster than overall

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### Context and motivation
- Venezuela described as "an oil exporting and import dependent economy with repressed markets for foreign exchange and for intermediate and consumption goods," experiencing inflation and black market premium "bordering on hyper-inflation and hyper-depreciation."
- Plummet in oil receipts "starting in late 2014" led to a massive contraction in the provision of foreign exchange to importers and prompted the analysis.
- Key macro statistics (preserve exact figures):
  - Broad money grew by about 85 percent on average in 2015 and rose to 100 percent at year end.
  - Headline consumer price inflation averaged 88 percent in 2015 and rose to 180 percent by year end.
  - Food inflation ended the year above 300 percent.
  - Tobacco and alcohol increased by nearly as much (relative wording preserved).
  - Black market exchange rate rose 380 percent, ending the year at a rate of 833 bolivars per dollar.
  - Venezuela’s oil basket commanded nearly $100 per barrel in mid-2014.
  - Oil price plunged to $47 per barrel by end-2014 and declined further to $29 per barrel by end-2015.
  - Output contracted 7 percent in the third quarter of 2014; central bank reports output has contracted every quarter since the first quarter of 2014.

### Main critique and alternative explanation
- Cagan model critique:
  - Paper argues the Cagan (1956) model is "not the best explanation for inflation trends in Venezuela."
  - Key objections: unrealistic substitution of bonds for domestic currency under financial repression; "not yet convincing evidence of an increase in velocity or that the elasticity of money demand to inflation has risen" (see Appendix 1).
- Alternative mechanism advanced:
  - Central bank rationing of foreign exchange creates a repressed goods market for imports.
  - Sharp reduction in supply of goods to retail markets propelled inflation "well beyond money growth."
  - Real shock (import supply collapse) generates relative price changes that obscure underlying inflation dynamics.
  - Any Cagan-style de-anchoring of inflation expectations, "if they exist, may comprise only a small part of the rise in inflation so far."

### Stylized general equilibrium model — structure and agents
- Objective: explain dynamics of inflation and the black market rate, showing bt can rise significantly faster than overall inflation without invoking portfolio dollarization or expectation-driven velocity.
- Key agents and institutions:
  - Public enterprise produces oil; export receipts Xt accrue to the state-owned company and are deposited with the central bank at official rate st.
  - Central bank rations dollar allocations each period: fraction (1- φ) to import firms, fraction φ to arbitrage firms.
  - Import firms sell imported consumption good domestically at price Pt; arbitrage firms sell allocated dollars in the black market at rate bt.
  - Holding company consolidates import and arbitrage rents and distributes profits to households each period.
- External and fiscal assumptions:
  - Oil receipts Xt exogenous each period; foreign price P* constant; trade balanced when private sector uses dollar allocations fully for imports: Qt = Xt / P*.
  - Government budget constraint and central bank monetary identity lead to money creation from fiscal deficit:
    - (3) Rt  +  Nt  =  Mt
    - If Rt = 0 and central bank fully distributes dollar receipts:
      - (10) ∆Mt+1  =  ∆Nt+1  =  Tt – st Xt
    - Interpretation: money is created from the fiscal deficit; money creation equals the fiscal deficit because of reserve sales to domestic agents at official rate.

### Pricing, rents, and arbitrage mechanics
- Import firm profits and conditions:
  - (11) ∏^M_t  =  Pt Qt    -   [ (1- φ) st  +  φ bt ]   P* Qt
  - Importer buys from central bank if (12) Pt  ≥  st P*; buys from arbitrage firm if (13) Pt  ≥  bt P*.
  - Rents arise because central bank rationing prevents supply adjustment despite potential prices above marginal cost.
- Arbitrage firm profits:
  - (14) ∏^A_t  =  [ bt  -  st ] * φ Xt
- Competitive implications:
  - When black market dollars used only for imports, black market rate bounded by retail price and official rate:
    - (15) Pt /P*  =  bt  ≥  st
- Holding company profits:
  - (16) ∏t = ∏^M_t + ∏^A_t  =  Pt Qt - st P* Qt  = [Pt – st P*] Qt

### Households, cash-in-advance (CIA) constraint, and demand
- Representative household receives transfers and profits; consumes the import good subject to CIA:
  - Budget constraint: Mt+1 + Pt Ct = Mt + (Tt + ∏t)
  - Cash-in-advance: Mt ≥ Pt Ct
- With goods market clearing Ct = Qt and binding CIA, price level proportional to money supply and inversely proportional to imports:
  - (18) Pt = Mt / Qt
- Equilibrium exchange rate under LOOP:
  - (19) ݏ̃t = Pt / P*
  - Combining (1), (18), (19): (20) ݏ̃t = Pt / P* = Mt / Xt
  - Comparative statics: increase in Mt → proportionate increase in equilibrium nominal exchange rate; increase in Xt → decline in equilibrium nominal exchange rate.

### Mechanisms generating a faster-rising black market rate than aggregate inflation
- Core drivers:
  - Central bank dollar rationing induces excess demand for dollars at st; arbitrage firms capture rents and sell at bt.
  - Retail price Pt linked to effective domestic currency cost of imports; if arbitrage-sourced dollars become more costly (bt rises), Pt is affected through importer cost structure, but pass-through depends on allocations and rents.
  - Arbitrage profits scale with (bt – st) and φ Xt; limited allocations (small φ Xt) can generate large increases in bt even when aggregate Pt evolves more slowly.
  - Monetary expansion via fiscal deficits (∆Mt+1 = Tt – st Xt) raises Pt, but allocation distortions can decouple bt growth from Pt growth: bt reflects prices in the most distorted goods markets and can rise faster when those markets experience higher markups or scarcity.
- Model implication summary:
  - Institutional rationing of foreign exchange plus arbitrage can produce a black market rate that rises significantly faster than overall inflation, even without portfolio dollarization or forward-looking inflation expectations.

### Calibrations and dynamic simulations (one-good and multiple-goods)
- Calibration summary (mid-2015 data and paths preserved exactly):
  - Broad money path: 715 billion bolivars at end 2012 to a projected 2,335 billion bolivars (assuming 65 percent growth in broad money y/y).
  - FX allocations (GlobalSource Partners estimates, daily -> annualized):
    - $170m per day in 2012 → $62 billion in 2012.
    - $130m per day in 2013 → $48 billion in 2013.
    - $90m per day in 2014 → $33 billion in 2014.
    - $30 million per day in May 2015 → $11 billion (annualized) in May 2015.
  - Derived equilibrium exchange rate (M2/FX): rises from 11.5 bolivars per dollar in 2012 to 213 bolivars per dollar in May 2015 (example: May 2015: 2,335 billion bolivars / $11 billion FX sales = 213 bolivars per dollar).
- Dynamic scenarios (one-good model):
  - Scenario: τ = σ = 25%
    - Money growth and inflation reach steady state of 25 percent.
  - Scenario: τ = σ = 95%
    - Inflation converges to steady state of 95 percent.
  - One-off devaluation (holding spending growth at 25 percent; official rate held at 6.3 for four years; in year 5 devalued from 6.3 to 15):
    - Devaluation raises bolivar value of oil revenues → reduces fiscal deficit → reduces money supply → lowers aggregate demand and inflation relative to no-devaluation counterfactual (short-run fall in inflation; long-run converges to 25 percent).
  - Devaluation cycles (every five years, cumulative growth over five years = 205 percent) produce recurrent temporary inflation declines followed by re-accumulation toward long-run inflation (25 percent or 95 percent depending on fiscal spending growth).
  - Oil revenue collapse scenario (assumptions preserved):
    - Fiscal spending growth assumed at 95 percent going forward.
    - Oil prices drop from about $88 per barrel in 2014 to $50 per barrel in 2015 and $30 per barrel in 2016.
    - Simulation result: Inflation would shoot up to over 200 percent in 2015 and 2016 before beginning to converge back to steady-state level of 95 percent.

### Multiple-goods model and black market dynamics
- Rationale: one-good model cannot fully explain much larger rise in bt relative to Pt and widening gap with fitted equilibrium exchange rate.
- Structure and mechanism:
  - Many importing firms compete for black market dollars to import goods i = 1...N; each good has its own markup and marginal willingness to pay for dollars.
  - Break-even black market rate for good i equates retail price to cost (equation (22) in source).
  - Ordering goods by markups: when black market transactions fall, dollars allocated first to goods with highest markups; bt rises because only the most distorted markets can bid up to the higher rates.
- Two-goods simulation highlights:
  - Baseline: fiscal transfers grow by 50 percent driving money growth and spending.
  - 2015–2016: export revenues drop sharply; FX provision assumed to drop more sharply for good 2, driving its price up by more than three times that of good 1.
  - Black market rate reflects large markup in good 2 and rises much above overall inflation.
  - Policy experiment (increasing amount allocated to black market in 2016):
    - Dollars shift into additional imports of scarce good 2 while reducing imports of good 1.
    - Contemporaneous inflation in good 2 falls; inflation of good 1 rises somewhat.
    - Overall inflation lower than baseline and black market rate grows significantly less.
    - Welfare improves because utility gain from the scarce good exceeds utility loss from the less scarce good.

### Capital flight channels and welfare effects (Section VI)
- Two channels simulated:
  A. Overinvoicing and importer dollar savings
  - Importers overinvoice to acquire dollars at official rate for future use; can reallocate imports intertemporally to smooth scarcity.
  - Temporary capital flight used to raise supply in subsequent period can improve welfare (Figure 10 referenced).
  B. Black market dollar savings by arbitrageurs
  - If bt+1 is expected sufficiently higher than bt (accounting for discounting), arbitrageurs save dollars in t to sell in t+1; raises current price of distorted good and lowers it next period, smoothing consumption and improving welfare.
- Aggregate equation for dollar holdings change:
  - (27) Ft+1 - Ft  =  Xt – P1* Q1t - P2*Q2t

### Extensions — price controls, nontraded goods, intermediates, and policy instruments
- Price controls:
  - Binding price control on one good causes shortages and spills demand into other goods, raising their prices; with U(C) = log(C1) + log(C2), households prefer equal money shares across goods.
- Nontraded good:
  - Adding nontraded good with inelastic labor links wage and real exchange rate; export receipts fluctuations affect relative price of nontraded to traded goods.
- Imported intermediate input:
  - Reduced FX allocation for intermediate inputs lowers retail output; import growth rates can be larger in absolute value than output and consumption growth rates.
- Other macro policies:
  - Government dollar purchases reduce FX available for consumption imports (Qt falls).
  - Issuance of external debt increases short-run FX but requires future repayment, reducing future Q and raising future inflation and black market rate.
  - Issuance of domestic debt reduces current monetary financing and money supply relative to no-debt counterfactual but raises future money supplies through debt service.
  - Central bank reserve accumulation raises money supply (relative to selling reserves) and reduces FX for imports, worsening inflation; reserve decumulation (sales) produces more imports and lower inflation.

### Key policy-relevant insights and implications (from conclusions and model experiments)
- Primary insights:
  - FX rationing linked to oil export earnings and multiple exchange rate regimes creates a repressed market for consumer and intermediate goods; consumer prices determined by demand and FX availability; consumer good price determines the black market exchange rate.
  - With multiple goods, the black market rate reflects the subset of goods with the highest markup over international prices; therefore bt can grow faster than aggregate Pt.
  - Capital flight (portfolio choice for dollars) can amplify dynamics but is not necessary to explain rising inflation and steeper black market premium.
  - Two counterintuitive phenomena explained by the model:
    1. A fall in oil revenues can lead to a temporary increase in inflation.
    2. A devaluation can generate a temporary drop in inflation.
- Policy levers and implications:
  - Devaluation can reduce fiscal deficit by raising bolivar value of oil receipts and thus reduce monetary financing and inflation—temporarily—if spending growth is restrained thereafter.
  - Increasing allocation of dollars through black market channels can reallocate imports toward scarce goods, lower their contemporaneous inflation, reduce bt growth, and improve welfare, despite raising imports in some sectors and lowering in others.
  - Accumulation versus sale of FX reserves by the central bank has direct implications for money supply and import availability; selling reserves to domestic agents reduces money supply growth and supports imports, lowering inflation relative to accumulation.

*Content excerpted from _wp16159 - Section V to explain how the black market rate can rise significantly faster than overall*

### References .............................................................................................................

### _wp16159 - References .............................................................................................................

### Appendices, Tables, and Figures (inventory excerpt)
- Appendices listed with page references:
  - Appendix 1. The Cagan Model—Not the Best Explanation for Inflation Surge (page 28)
  - Appendix 2. Numerical example of monetization of deficits, devaluation, and sales of reserves by the central bank. (page 29)
  - Appendix 3. Household optimization with one good and CIA constraint (page 31)
  - Appendix 4. Summary of model equations for dynamic simulations (page 32)
  - Appendix 5. Two imported goods and dollar portfolio holdings (page 33)
  - Appendix 6. Planner’s problem with FX in advance constraint (page 35)
  - Appendix 7. Household portfolio decision with money and black market dollars (page 37)
  - Appendix 8. Traded and nontraded goods (page 39)
- Tables (excerpt):
  - Table 1. Baseline (page 40)
- Figures (excerpt):
  - Figure 1. Typical market for (imported) good (page 41)
  - Figure 2. Money growth raises prices and rents (page 42)
  - Figure 3. A devaluation of the official rate squeezes rent (page 43)
  - Figure 4. Large devaluation to a level above LOOP (pages 44–45)
  - Figure 5. Oil revenue decline (page 46)
  - Figure 6. Two goods economy (page 47)
  - Figure 7. Price controls and scarcity (page 48)
  - Figure 8. Simulation of an increase in allocation to black market (page 49)
  - Figure 9. Simulation of devaluation (page 50)
  - Figure 10. Simulation of overinvoicing good 1 to supply good 2 (page 51)
  - Figure 11. Simulation of capital flight used to supply market in the future (page 52)

### Main substantive findings and analysis (from Introduction)
- Context and motivation:
  - Venezuela is characterized as "an oil exporting and import dependent economy with repressed markets for foreign exchange and for intermediate and consumption goods," and has experienced a surge in inflation and the black market premium—"bordering on hyper-inflation and hyper-depreciation."
  - The plummet in oil receipts, "starting in late 2014," led to a massive contraction in the provision of foreign exchange to importers.
- Critique of the Cagan (1956) explanation:
  - The paper argues that the Cagan model is "not the best explanation for inflation trends in Venezuela."
  - Key objections:
    - The Cagan model assumes individuals can substitute bond holdings for domestic currency; this may be unrealistic for Venezuela due to financial repression.
    - There is "not yet convincing evidence of an increase in velocity or that the elasticity of money demand to inflation has risen" (see Appendix 1).
- Alternative explanation advanced:
  - Venezuela’s system of rationing foreign exchange creates a repressed goods market for imports.
  - The sharp reduction in the supply of goods to retail markets propelled the rise in inflation "well beyond money growth."
  - This real shock generates a relative price change that obscures the underlying inflation dynamics.
  - Any Cagan-style de-anchoring of inflation expectations, "if they exist, may comprise only a small part of the rise in inflation so far."
- Role of devaluation:
  - The model shows how "a devaluation of the official exchange rate could, counterintuitively, lead to a temporary decline in inflation."
  - Mechanism described:
    - A devaluation would reduce the fiscal deficit and, all else equal, would also withdraw domestic money supply "by requiring more bolivars in payment for each dollar of reserves bought from the central bank."
    - A lower fiscal deficit, following the devaluation, would need to be maintained by reducing expenditure growth, even under a crawling peg.
    - The model demonstrates recurrent inflation cycles arising from infrequent devaluations.
- Black market rate interpretation:
  - Over recent years, the black market exchange rate has risen even faster than inflation.
  - The paper argues that "the black market rate reflects prices, not the other way around."
  - When a small share of foreign exchange transactions flows through the black market, its rate reflects prices in the most distorted goods market (i.e., the subset of goods subject to the highest markups over international prices).
  - Depreciation can occur "even without expectations of increasing overall inflation."
- Role of portfolio holdings (capital flight):
  - Portfolio holdings of dollars could further amplify inflation and the black market premium in a given period.
  - The incentive to hold dollars reflects expectations of higher inflation and black market rates in the future, driven by an expectation of a decline (or further decline) in the provision of foreign exchange for imports.
  - Capital flight could nonetheless improve economic welfare if it smooths consumption over time, "by saving dollars in a period of relatively high availability of dollars (due to strong export receipts) to a period of low availiability of dollars (due to weak export receipts)."

### Model and paper structure (overview)
- Sectional structure as described:
  - Section II provides background on the economic developments that motivate this research.
  - Section III presents a one-good general equilibrium model used to derive main results on inflation and the black market rate.
  - Section IV calibrates the one-good model and conducts simulations related to:
    - higher fiscal spending,
    - a devaluation of the official exchange rate,
    - the impact of an oil price collapse.
  - The model is then extended to the case of multiple consumption goods.

*Italic source attribution: Content excerpted from _wp16159 - References .............................................................................................................*

### Section V to explain how the black market rate can rise significantly faster than overall

### _wp16159 - Section V to explain how the black market rate can rise significantly faster than overall

### Background: Venezuela macroeconomic context and recent developments
- Oil exports have constituted about 95 percent of total exports in recent years.
- Oil receipts accrue to the state-owned company, Petróleos de Venezuela (PDVSA), which transfers some of its earnings to the budget and also engages in quasi-fiscal activities focused on social and developmental objectives.
- Venezuela is highly dependent on imports for many food and consumer goods and intermediate inputs.
- Exchange rate regime has frequently included multiple exchange rates. In 2003 the government fixed the exchange rate and introduced foreign exchange controls, including surrender requirements for both current and capital transactions. A government commission administered the controls with broad discretionary powers to allocate foreign exchange to the private sector for current and other transactions.
- Alternative systems for allocating or auctioning foreign exchange were introduced in recent years but usage has been sporadic and transaction volumes low.

Key macroeconomic statistics and episodes (preserve numeric values exactly):
- Broad money grew by about 85 percent on average in 2015 and rose to 100 percent at year end.
- Headline consumer price inflation averaged 88 percent in 2015 and rose to 180 percent by year end.
- Food inflation ended the year above 300 percent.
- Tobacco and alcohol increased by nearly as much (relative wording preserved).
- The black market exchange rate rose 380 percent, ending the year at a rate of 833 bolivars per dollar.
- Venezuela’s oil basket commanded nearly $100 per barrel in mid-2014.
- Oil price plunged to $47 per barrel by end-2014 and declined further to $29 per barrel by end-2015.
- Output contracted 7 percent in the third quarter of 2014; central bank reports output has contracted every quarter since the first quarter of 2014.

### Stylized general equilibrium model: purpose and contrast with earlier literature
- Objective: explain dynamics of inflation and the black market rate, showing how the black market rate can rise significantly faster than overall inflation without invoking inflation expectations or portfolio choice between dollars and domestic currency.
- Contrast with earlier dual-rate models:
  - Earlier models assumed full current account convertibility and a legal parallel market for capital transactions; excess demand for reserves led to an outright balance of payments crisis and unification of rates.
  - The model here incorporates central bank rationing of international reserves (dollar allocations), avoiding an outright reserves collapse but inducing excess demand for reserves and import constraints.
  - Foreign exchange serves as an asset in both approaches; this model assumes no other domestic currency asset other than money and imposes a cash-in-advance constraint on purchases of consumer goods. The micro-founded setup yields a relationship similar to the quantity theory of money.

### Basic structure of the economy (model summary)
- Agents and sectors:
  - Public enterprise produces the only export good (oil), not consumed domestically.
  - Private sector firms: import firms (provide imported consumption good, food, not produced domestically) and arbitrage firms (arbitrate foreign exchange between official market and black market).
  - Government receives oil revenue in dollars from the public enterprise and deposits receipts in the central bank in exchange for bolivars at the official exchange rate st.
  - Central bank rations dollar allocations to the private sector at the official rate; fraction (1- φ) of recipients are import firms; fraction φ are arbitrage firms which sell dollars in the black market.
  - A holding company consolidates profits/rents of import and arbitrage firms and distributes them to households each period.

- External sector assumptions:
  - Oil production and the dollar price of oil are exogenous; dollar value of export receipts denoted Xt is exogenous each period.
  - Stocks of foreign assets and external debt initially zero for public and private sectors.
  - Public sector fully distributes export receipts to private sector each period and does not issue external debt.
  - In sections III–V, private sector uses dollar allocations fully for payment of imports; therefore, trade is balanced each period. (Section VI relaxes this to analyze capital flight.)
  - Foreign price in dollars of the import good is constant at P*, imported quantity denoted Qt.
  - Balanced trade (no capital flows) implies:
    - (1) Qt = Xt / P*

- Fiscal sector:
  - Government receives export receipts Xt and deposits them in the central bank at official exchange rate st. Government makes lump-sum transfers Tt to households in bolivars.
  - Government budget constraint:
    - (2) Tt  -  st Xt  =  Nt+1 – Nt

- Central bank balance sheet and monetary dynamics:
  - Asset side: international reserves (measured in domestic currency) Rt and net domestic credit to government Nt. Liability side: money in bolivars Mt.
  - (3) Rt  +  Nt  =  Mt
  - All money consists of cash in circulation; no deposit money banks assumed.
  - At beginning of each period central bank receives dollar receipts from government and credits government deposits in domestic currency:
    - (4)  (Rt  + st Xt)  +  (Nt  -  st Xt)  =  Mt     Reserves    NDC   Money
  - After government transfers and central bank dollar allocations, if central bank fully distributes dollar receipts and does not accumulate reserves (Rt-1 = Rt = 0), then:
    - (7) Rt = 0
    - (8) Mt+1 = Mt + Tt – st Xt
    - (9) Nt+1 = Nt + Tt – st Xt
    - Therefore:
      - (10) ∆Mt+1  =  ∆Nt+1  =  Tt – st Xt
  - Interpretation: money is created from the fiscal deficit; money creation equals the fiscal deficit only because central bank sells all new reserves each period and private sector pays for dollars at same official rate credited to government. Money creation would be higher if central bank accumulated reserves; a higher volume of dollar sales to private sector or a higher average exchange rate required for dollar purchases would reduce money growth.

### Firms: pricing, rents, and arbitrage
- Market structure: large number of small import and arbitrage firms; representative firms normalized to one each.
- Import firm:
  - Representative import firm buys (1- φ) Xt dollars from central bank at official rate st and φ Xt from arbitrage firm at black market rate bt.
  - Dollars Xt can buy maximum quantity Qt = Xt / P* of import goods at international price P*; firm sells import goods domestically at bolivar price Pt.
  - Revenues and costs:
    - (11) ∏^M_t  =  Pt Qt    -   [ (1- φ) st  +  φ bt ]   P* Qt
      - Profits = Revenues - Average exchange rate cost at world price
  - Rents arise because central bank rationing prevents supply adjustment despite potential prices above marginal cost. Transformation assumed costless (ξt = 0 for remainder).
  - Import firm will buy from central bank if:
    - (12) Pt  ≥  st P*
  - Import firm will buy from arbitrage firm if:
    - (13) Pt  ≥  bt P*
  - With transformation costs ξt > 0, constraints would be:
    - (12′) Pt  ≥  st P* + ξt
    - (13′) Pt  ≥  bt P* + ξt

- Arbitrage firm:
  - Receives allocation φ Xt from central bank and sells it to importers in black market at exchange rate bt.
  - Profits:
    - (14) ∏^A_t  =  [ bt  -  st ] * φ Xt
      - Profits = (MR - MC per dollar) * Amount transacted
  - Competition pushes the import firm–black market relationship toward equality; when black market dollars can be used only for imports (no portfolio holdings), black market rate bounded by retail price and official rate:
    - (15) Pt /P*  =  bt  ≥  st

- Holding company:
  - Consolidates import firm and arbitrage firm profits and distributes to representative household:
    - (16) ∏t = ∏^M_t + ∏^A_t  =  Pt Qt - st P* Qt  = [Pt – st P*] Qt

### Households: cash-in-advance and behavior
- Representative household receives holding company profits and government transfer payments; consumes the import good.
- Government requires retail sales be purchased using domestic currency; household faces a cash-in-advance constraint.
- Household problem (utility maximization, subject to budget and cash-in-advance):
  - (17) max ∑ β^i U(c_{t+i})  s.t.  Mt+1 + Pt Ct = Mt + (Tt + ∏t)   (budget constraint)
  - Cash-in-advance constraint:
    - Mt ≥ Pt Ct

### Mechanisms explaining faster black market rate increases relative to overall inflation (model implications summarized from structure)
- Central bank dollar rationing creates excess demand for dollars that cannot be met at the official rate; arbitrage firms capture rents by selling allocated dollars at black market rate bt.
- Retail price Pt is linked to the effective cost of imports measured in domestic currency; when black market rate bt rises relative to st, import firms face higher costs via purchases from arbitrage firms, transmitting to Pt.
- Because arbitrage profits depend directly on the gap (bt – st) and allocations φ Xt, the black market premium can amplify rapidly when allocations are limited, causing bt to rise more quickly than aggregate money-driven inflation measured by Pt evolution.
- Monetary expansion occurs via fiscal deficits financed by net domestic credit (Tt – st Xt), which increases money (∆Mt+1 = Tt – st Xt). However, allocation rationing and arbitrage-induced transfer of scarce dollars to the black market can generate a faster escalation in bt than in Pt when import availability and effective pass-through differ across goods and markets.
- The model shows how, even absent portfolio dollarization or explicit expectations dynamics, institutional rationing of foreign exchange plus arbitrage can produce a black market rate that rises significantly faster than overall inflation.

*IMF working paper section V (content unit: _wp16159 - Section V to explain how the black market rate can rise significantly faster than overall).*

### Appendix 3 sets out the optimizing conditions. The discount rate, β, is slightly below unity

### _wp16159 - Appendix 3 sets out the optimizing conditions. The discount rate, β, is slightly below unity

### Optimizing conditions and aggregate demand
- The discount rate, β, is slightly below unity (generally around 0.97-0.99) depending on the rate of time preference.
- Goods market clearing requires that Ct = Qt.
- If import volume is constant over time, the cash-in-advance constraint will be binding with any positive inflation rate.
- Under a binding cash-in-advance constraint with fixed import quantity:
  - The price level is proportional to the money supply and inversely proportional to the quantity of imports.
- Aggregate demand curve (sum of household demand functions):
  - (18) Pt = Mt / Qt

### Equilibrium exchange rate (LOOP framework)
- With only an imported consumption good, the equilibrium nominal exchange rate satisfies the Law of One Price (LOOP) by setting equation (12) to equality.
  - (19) Equilibrium exchange rate: ݏ̃t = Pt / P*
- The equilibrium real exchange rate (= st P* / Pt) equals unity.
- Any official st set lower than Pt/P* implies an overvalued real exchange rate (by LOOP).
- When the official exchange rate equals the LOOP equilibrium, the black market rate equals the official rate.
- Combining equations (1), (18), and (19), assuming no capital flows, yields:
  - (20) ݏ̃t = Pt / P* = [ Mt/ (Xt/P*) ] / P* = Mt / Xt
- Comparative statics from (20):
  - An increase in the money supply leads to a proportionate increase (depreciation) in the equilibrium nominal exchange rate.
  - An increase in export receipts (greater supply of import goods) leads to a decline (appreciation) in the equilibrium nominal exchange rate.
- If the official exchange rate is overvalued (LOOP not binding as equality), import firms earn rents; devaluation toward LOOP reduces those rents and, under many circumstances, will not raise retail prices because retail prices are set above import cost given fixed supply and demand conditions.
- A very large devaluation can raise the price level if it significantly increases import cost such that retail prices must rise to restore LOOP; alternatively, importer losses could reduce supply and increase prices.

### Summary of demand and supply drivers
- Demand side is driven by money growth, which depends mainly on:
  - Fiscal deficits, and
  - Central bank policies for reserve accumulation and allocation of foreign exchange to the private sector.
- Supply side is driven by the receipt of dollars from export earnings, distributed to importers and arbitrageurs through the central bank.

### Calibrations to Venezuelan data (mid-2015)
- Broad money path used:
  - 715 billion bolivars at end 2012 to a projected 2,335 billion bolivars (assuming 65 percent growth in broad money y/y).
- FX allocations (GlobalSource Partners estimates, daily -> annualized):
  - $170m per day in 2012 → annual FX allocations of $62 billion in 2012.
  - $130m per day in 2013 → $48 billion in 2013.
  - $90m per day in 2014 → $33 billion in 2014.
  - $30 million per day in May 2015 → $11 billion (annualized) in May 2015.
- Derived equilibrium exchange rate (M2/FX):
  - Rises from 11.5 bolivars per dollar in 2012 to 213 bolivars per dollar in May 2015.
  - Example: May 2015: 2,335 billion bolivars / $11 billion FX sales = 213 bolivars per dollar.
- Comparison to other models:
  - Monetary model and PPP model are shown for comparison but require normalization (2005Q1=2.1); the M2/FX model uses raw units and fits extraordinarily well without normalization.

### Dynamic simulations of inflation (one-good model)
- Model policy instruments:
  - Fiscal policy: growth rate of transfer payments (t or τ).
  - Exchange rate policy: devaluation rate (s or σ).
- Appendix 4 contains summary of model equations and initial values.
- Scenario: τ = σ = 25%
  - Money growth and inflation reach a steady state of 25 percent.
  - If the initial deficit-to-money ratio is higher than the steady-state ratio, inflation starts above steady state and falls to 25 percent.
- Scenario: τ = σ = 95%
  - Inflation converges to steady state of 95 percent; if initial deficit-to-money ratio is below steady state, inflation rises to 95 percent.
- Impact of one-off devaluation of official exchange rate:
  - Policy: growth rate of spending Tt = 25 percent; official rate held at 6.3 bolivars per dollar for four years; in year 5 official rate devalued from 6.3 to 15 without changing nominal spending growth.
  - Devaluation raises bolivar value of oil revenues → reduces fiscal deficit → reduces monetary financing need → lowers money supply → aggregate demand and inflation fall relative to no-devaluation counterfactual.
  - Short-run effect: lower inflation; long-run: because spending growth remains at 25 percent, inflation still converges to steady state of 25 percent.
  - Temporary rebound in inflation during transition arises because the real value of government spending increases when inflation falls relative to the no-devaluation scenario.
  - Mechanism for limited pass-through: repressed goods market with foreign exchange allocated by official discretion; importers receiving FX at official rate extract rents and keep retail prices above import cost; devaluation reduces rents and purchasing power of rent-recipients, lowering aggregate demand and thus not necessarily increasing retail prices.
- Impact of devaluation cycles (devaluation every five years):
  - Case with fiscal spending growth = 25 percent annually:
    - Every five years official rate devalued by cumulative growth over five years (205 percent).
    - Each devaluation temporarily reduces deficit and inflation; deficit and inflation then rise again as spending continues to grow at 25 percent.
    - Inflation cycles around long-run average of 25 percent.
  - If fiscal spending growth = 95 percent, inflation cycles around 95 percent with similar temporary declines at devaluation years.
- Impact of real shock: oil revenue decline
  - Shock effects:
    - Lower oil revenue → higher fiscal deficit → more monetary financing → higher money growth.
    - Lower oil revenue → fewer resources for imports → lower supply of goods.
    - Combined effect raises inflation.
  - Calibration assumptions for shock scenario:
    - Going forward, fiscal spending growth assumed at 95 percent (roughly observed money growth in 2015).
    - Oil prices assumed to drop from an average of about $88 per barrel in 2014 to $50 per barrel in 2015 and $30 per barrel in 2016.
  - Simulation result:
    - Inflation would shoot up to over 200 percent in 2015 and 2016 before beginning to converge back to the steady-state level of 95 percent (driven by fiscal spending growth).

### Black market with multiple consumption goods
- Motivation:
  - One-good model explains many dynamics but cannot fully account for the much larger rise in the black market rate relative to overall inflation and the widening gap with fitted equilibrium exchange rate.
  - A multiple-goods model is required to capture how the composition of goods and allocation of limited black market transactions affect the black market rate.
- Structure and mechanism:
  - A large number of importing firms compete for a portion of dollars available in the black market to import goods i = 1...N and sell domestically.
  - Each firm is small in domestic market but the aggregate affects domestic prices.
  - Profit condition for firm selling good i:
    - (21) ߨ௜ܲ = ܾܲെ௜∗ݍ௜
  - Break-even black market rate for good i sets price equal to cost:
    - (22) ܲ௜ݍ௜ܾܲ = ௜∗ݍ௜ or ܾ = ܲ݅ܲ݅∗
  - Ordering goods by markups shows that importers of goods with highest markups will be willing to buy dollars at higher black market rates until their domestic price is driven down to the point implied by their markup.
  - If transactions in the black market fall, the black market rate rises because only goods/markets with the highest markups receive dollar funding.
  - If a monopolist decides allocations, foreign exchange will be used across goods until marginal revenue to marginal cost ratios are equalized across goods.
- Two-goods model:
  - Central bank allocates foreign exchange at the official exchange rate st to import firms that purchase two import goods at fixed world prices.
  - As long as domestic price Pit (marginal revenue) exceeds st Pit* (marginal cost), the importer supplies the good.
  - Central bank also allocates a share φ of dollar export receipts to arbitrage firms at st; arbitrageurs sell dollars in the black market at the highest possible exchange rate.
  - Households maximize intertemporal utility over two consumption goods subject to budget constraint and cash-in-advance constraint (see equations (24) and budget constraint presented in text).

*Source: _wp16159 - Appendix 3 sets out the optimizing conditions. The discount rate, β, is slightly below unity*

### Appendix 5 elaborates the solution. For example, if the CIA constraint is binding and utility

### _wp16159 - Appendix 5 elaborates the solution. For example, if the CIA constraint is binding and utility

### Appendix 5: characterization and implications
- If the CIA (cash-in-advance) constraint is binding and utility is logarithmic, then the expenditure shares on each good are equal (see equation (25) and related text).
- The black market rate grows proportionately to spending on each good (equation (26) and accompanying discussion).
- When utility is logarithmic, expenditure shares satisfy:
  - Equation (25): ܲ
௧
௜
ܥ
௧
௜
ܲൌ
௧
௝
ܥ
௧
௝
- The black market exchange rate is driven by retail goods prices rather than vice versa: the black market rate is based on retail goods prices, and can grow faster than overall inflation if price increases in the most distorted markets exceed those in less distorted markets.

### C. Simulation of black market rate in two goods model
- Central bank supplies dollars proportionally to export revenues (Xt) deposited by the government from state oil company earnings; fraction 1-φ allocated to importers and fraction φ to arbitrageurs.
- Capital account restricted; only capital transactions occur in black market.
- Goods markets clear: imports Qit equal consumption Cit.
- Key simulation assumptions and outcomes:
  - Baseline calibration: fiscal transfers assumed to grow by 50 percent, driving money growth and spending of roughly the same magnitude.
  - In 2015 and 2016, export revenues drop sharply, causing contraction in foreign exchange allocated for imports.
  - Foreign exchange provision assumed to drop more sharply for good 2, driving its price up by more than three times that of good 1.
  - The black market rate reflects the large markup in good 2 and rises with its higher inflation rate; growth of the black market exchange rate is much above overall inflation.
  - Arbitrage and import firms both earn rents from selling dollars and goods.
- Comparative-static mechanism:
  - If the share of dollars channeled through the black market increases, supply of goods in the distorted market rises, reducing its price and slightly lessening the distortion; this can lead to a decline in the black market rate.
  - Arbitrageurs buying dollars from importers in the less distorted market and selling to importers in the more distorted market changes the composition of goods: supply increases in the more distorted market (price declines), and supply decreases in the other market (price rises).
- Policy experiment (Figure 8 referenced):
  - Increasing the amount allocated to the black market (in 2016) shifts dollars into additional imports of good 2 (scarce) while reducing imports of good 1 (abundant).
  - Contemporaneous inflation in good 2 is reduced; inflation of good 1 rises somewhat.
  - Overall inflation is lower than the baseline and the black market rate grows significantly less.
  - Welfare improves because the rise in utility from consumption of the scarce good exceeds the fall in utility from the less scarce good.

### D. Simulation of a devaluation
- Devaluation example (Figure 9 referenced): official exchange rate devalued from 6.3 to 50 (in 2017).
- Effects:
  - Deficit significantly reduces the fiscal deficit, facilitating a decline in money growth.
  - Arbitrageurs and importers face higher costs of purchasing foreign currency, reducing their profits.
  - Lower profits transferred as income to households lead to reduced subsequent spending on both goods, producing lower inflation and a lower black market exchange rate than in the baseline.
- Counterintuitive comparative-statics highlighted:
  - A fall in oil revenues can lead to a temporary increase in inflation.
  - A devaluation can generate a temporary drop in inflation.

### VI. Capital flight (extensions and simulations)
- Model extension: changes in stock of dollars held by domestic households must equal central bank distributions from export revenues minus value of imports:
  - Equation (27): Ft+1 - Ft  =  Xt – P1* Q1t-P2*Q2t
- Two simulated channels of capital flight:
  A. Overinvoicing and dollar savings by importers
  - Importers selling both goods can overinvoice to acquire dollars at the official rate and use them to import in the distorted market now or later.
  - If FX expected to become scarcer in the distorted market next period, importers may reduce current imports of the less distorted good and shift dollars to increase imports of the distorted good in the next period.
  - Figure 10 (referenced) shows temporary capital flight used to raise supply in the subsequent period of increased scarcity improves overall welfare.
  - In general equilibrium, importer revenue after quantity reallocation remains the same because price changes offset quantity changes; cost of acquiring dollars from arbitrageurs falls as black market rate and distorted-market good price decline when its supply increases.
  B. Black market dollar savings (by arbitrageurs)
  - If black market rate expected to increase (enough to offset time discount), arbitrageurs save dollars in period t (losing bt revenue per dollar) and sell in t+1 (gaining bt+1 per dollar), gaining extra profits up to the point where black market rate equalizes across t and t+1.
  - This dollar saving is capital flight: current dollars are withdrawn from imports to be sold later, raising current price of the distorted good and lowering it next period, smoothing imports and consumption over time and improving welfare.

### VII. Extensions of the model
A. Price controls
- Two-good case with a price control on one good and a binding cash-in-advance constraint reduces household allocation to a static problem each period (equations (28)–(31)).
- First-order condition when price control not binding:
  - Equation (29): U1 / U2 = P1 / P2
- With U(C) = log(C1) + log(C2), households prefer equal money shares on each good (equation (30): P1 C1 = P2 C2).
- If price control binds on good 2 (P2 constrained below optimal), excess demand causes shortage; households’ unsatisfied spending spills over into additional demand for good 1, raising P1 beyond the unconstrained level.
- Equilibrium P1 determined by money supply and import supplies:
  - Equation (31): P1 = (P̄ M / P̄) Q2 / Q1  (preserve original notation as presented)

B. Nontraded good
- Add non-traded good produced with inelastic labor; wage tied to price of non-traded good.
- Household optimization includes utility of traded and non-traded consumption (equations (32)–(35)).
- If utility is logarithmic, expenditure shares on each good are equal (equation (36): ܲ
௧
்
ܥ
௧
்
ܲൌ
௧
ே
ܥ
௧
ே).
- With inelastic labor supply = 1, ܥ
ே
ܻൌ
ே
ൌܮൌ1 and equation (37) holds.
- Real exchange rate intuition: when export receipts rise, real exchange rate (relative price of non-traded to traded goods) rises; when export wealth falls, equilibrium real exchange rate falls.

C. Imported intermediate input
- Model variant: import is intermediate input combined with domestic labor to assemble retail good; production function (equation (38)): ܻ
௜
ݍൌ
௜
ఈ
ܮ
௜
ଵିఈ.
- Firm chooses labor and imported intermediate to maximize profits (equation (39)); first-order conditions (equations (40)–(41)).
- Aggregation with inelastic labor L=1 yields equations (42)–(43).
- Zero-profit black market exchange rate depends on domestic/foreign inflation and growth of imports (equation (44)):
  - A fall in Q leads to higher growth in black market rate compared with inflation.
- Aggregate demand in terms of output (equation (45)): ܯ
௧
ܲൌ
௧
ܥ
௧
ܲൌ
௧
ܻ
௧
ܲൌ
௧
ܳ
௧
ఈ.
- If intermediate input is reduced due to limited FX allocation, retail output falls; link between output, consumption, and import good implies import growth rates are larger in absolute value than output and consumption growth rates (empirically evident for Venezuela).

D. Other macro policies and their effects
- Government spending in dollars:
  - Government purchases of foreign goods/services using dollars decrease supply of dollars for consumption imports (Qt falls); effects similar to a reduction in Xt unless government purchases satisfy consumption demand.
- Issuance of external debt:
  - Increases FX for imports in short run (Qt rises), but requires future repayment reducing future Q; external debt service reduces FX for imports, driving up inflation and black market rate.
- Issuance of domestic debt:
  - Financing deficit via domestic debt reduces monetary financing and lowers money supply relative to no-debt counterfactual; future debt service raises future money supplies.
- Accumulation/decumulation of FX reserves:
  - If central bank builds FX reserves instead of selling them, money supply will be higher than if reserves sold to domestic agents, and less FX will be available for imports → higher inflation and lower consumption versus full sale scenario.
  - Decumulation (selling reserves) produces more imports and lower inflation.

### VIII. Conclusions — key insights
- The stylized general equilibrium model captures key features of the Venezuelan economy: FX rationing linked to oil export earnings and multiple exchange rate regime create a repressed market for consumer and intermediate goods.
- Domestic price of consumer goods is determined by demand and FX availability; the consumer good price determines the black market exchange rate.
- With multiple goods, arbitrary allocation to import and arbitrage firms creates varying subsidies; black market rate reflects subset of goods with highest markup over international prices.
- Capital flight (portfolio choice between dollars and domestic currency) can contribute to dynamics, but is not necessary to explain rising inflation and steeper black market premium.
- The model explains two counterintuitive phenomena:
  1. A fall in oil revenues can lead to a temporary increase in inflation.
  2. A devaluation can generate a temporary drop in inflation.

*Source: _wp16159 - Appendix 5 elaborates the solution. For example, if the CIA constraint is binding and utility (PDF chapter/section).*

### Appendix 1. The Cagan Model—Not the Best Explanation for Inflation Surge

### Appendix 1. The Cagan Model—Not the Best Explanation for Inflation Surge

### Cagan model mechanics (as described)
- Hyperinflation driven by severe drops in money demand dominated by rising inflation expectations.
- Mechanisms: a rise in money growth that feeds inflation expectations and/or an increased elasticity of real money demand to expected inflation, which destabilizes inflation expectations and raises velocity.
- Money demand specification referenced in the text: m = f(i) where i is the nominal interest rate and expected inflation enters (symbols appear in source).

### Empirical fit to Venezuela (main findings)
- Through 2014, there is no evidence that velocity was increasing or that the elasticity of money demand rose.
- Velocity has been on a steady decline, irrespective of whether it is measured using GDP, aggregate demand, private consumption, or imports.
- The data for 2015 is incomplete:
  - At end-December, the monetary base grew by 111 percent yoy.
  - Consumer price inflation reached at least 180 percent by the end of the year.
  - On the surface, the increase in inflation above money growth may show first signs that velocity has finally started to rise and that the Cagan model may be relevant, but national accounts data for 2015 (including GDP and its components) were not yet published, so velocity cannot be updated at that time.

### Reasons the Cagan model may not fit Venezuela in 2015 (arguments)
- Real GDP is not constant in Venezuela in 2015: real GDP is estimated to have fallen sharply (based on indicators of activity). The Cagan model assumes real GDP constant and simplifies to a relationship between money and expected inflation—an assumption judged unrealistic for Venezuela in 2015.
- Real private consumption and imports may have fallen even more than output, a development the Cagan model does not account for; therefore, model estimates are not reliable under these conditions.
- Financial repression: the Cagan model is based on a money demand equation involving the choice between money and bonds. It is likely that households do not have the option of buying bonds as an alternative asset to holding money in Venezuela’s economic structure, undermining the model’s applicability.

### Illustrative data/figure notes (as presented)
- A figure/table in the source displays Velocity = X / Money with series for GDP, Domestic demand, Private consumption, Imports over the period 2000–2014 and indicates steady decline in velocity measures (figure axis labels and years preserved in source).

### Implications (for interpretation and modeling)
- The Cagan explanation (expectations-driven velocity rise) is not validated by pre-2015 Venezuelan data; analysts should not rely on the standard Cagan framework without accounting for:
  - Large declines in real GDP, consumption, and imports.
  - Binding financial repression that limits households’ portfolio choices (money vs. bonds).
  - Missing or lagged national accounts data (2015) that prevent timely velocity updates.
- Caution in attributing inflation surge solely to expectation-driven money demand collapses when real activity and portfolio constraints are changing.

### Key numeric facts extracted from the text
- Monetary base growth at end-December 2015: 111 percent yoy
- Consumer price inflation by end-2015: at least 180 percent
- Time span referenced for velocity series: 2000 through 2014

*Source: Appendix 1. The Cagan Model—Not the Best Explanation for Inflation Surge (from the supplied IMF Appendix content).*

### Appendix 7. Household portfolio decision with money and black market dollars

### Appendix 7. Household portfolio decision with money and black market dollars

### Model setup
- Households maximize discounted utility over consumption and choose a portfolio between holding dollars (F) and domestic money (M).
- Purchases of domestic goods are subject to a cash-in-advance (CIA) constraint: only domestic currency is acceptable for spending.
- Dollars cannot be used for consumption immediately; dollars must first be converted into bolivars with a one period lag in order to be used for consumption purchases.
- The CIA constraint implies Pt Ct predetermined by Mt / Ct (i.e., Pt = Mt / Ct when binding).

### First-order conditions and Kuhn–Tucker conditions
- Let λt be the Lagrange multiplier on the CIA constraint. The Kuhn–Tucker conditions imply:
  - λt ≥ 0 and the rate of inflation must be at least as high as the discounted marginal rate of substitution in consumption.
  - The rearranged FOC yields an inequality: inflation ≥ discounted marginal rate of substitution (preserved in symbolic form in the source).
- The second FOC relates returns on holding domestic money versus black market dollars. Key qualitative relation:
  - The right-hand side of the expression is > 1 if the CIA constraint is binding.
  - In particular, the black market rate must be increasing slightly faster than inflation to be consistent with constant consumption.

### Intuition and required premium on black market dollars
- Because dollars require a one period wait before being usable for consumption, the return on black market dollar holdings must compensate households for the intertemporal waiting (the rate of time preference).
- If there is a security/evasion cost to purchasing dollars in the black market, the required black market return would need to be even higher to induce dollar holdings.
- Summary statement from the model: the return on the black market rate must be slightly higher than inflation by the rate of time preference.

### Portfolio dominance scenarios and aggregate implications
- If the black market return on dollar holdings is higher than implied by the FOC:
  - Dollar holdings dominate bolivar holdings.
  - Households hold only as much bolivars as needed for next period consumption; the rest is saved in dollars.
  - Aggregate consequence: savings in dollars reduce imports; aggregate imports must be consistent with aggregate consumption.
- If the black market return on dollars is lower than the FOC (e.g., equal to price inflation rather than higher than inflation):
  - Bolivars dominate dollars and only domestic money is used as an asset.
  - Dollars are not used as assets, but merely to purchase import goods.

### Special cases: always-binding CIA constraint and absence of dollar saving
- When the CIA constraint is always binding (Mt+1 determines next period consumption):
  - Pt Ct = Mt / Ct and Mt+1 will determine next period’s consumption since CIA binds for all t.
  - The only portfolio choice reduces to Ft+1 versus Mt+1.
  - Money holdings must be at least as great as the optimal path of consumption spending.
  - If the return on dollars is not high enough (if the black market rate only increases with inflation), households will choose F = 0.
- If there is no ability to save in dollars (only in money):
  - The budget and CIA constraints imply the household’s only decision is whether to consume up to money holdings or to save.
  - If households spend all their money holdings, next period money stock equals their current income.

### Appendix 8 connection: traded and nontraded goods (brief)
- Non-traded good produced with inelastic labor; wage tied to the price of the non-traded good.
- Household utility extended to include both traded and nontraded consumption goods; CIA constraint applies to traded goods expenditures as specified.
- First-order conditions imply again that inflation must be at least as high as the discounted marginal rate of substitution and include conditions equating marginal utilities across consumption goods.

### Key model implications for policy and market behavior
- A necessary premium on black market returns: Black market dollar returns must exceed inflation by the household time preference to induce dollar saving.
- Exchange rate and price policy interactions:
  - Official devaluation increases unit costs of imports (st P*), squeezing importer rents and, if large enough (above LOOP), can lead to pass-through to domestic prices and import compression.
  - Money growth raises prices and rents when CIA is binding because Pt = Mt / Ct and Ct = Qt.
  - Declines in export receipts (e.g., oil revenue decline) reduce FX supply, widen fiscal deficits, increase money creation, and raise inflation (aggregate demand increases while aggregate supply contracts).
- Allocation distortions across goods:
  - In a multi-good economy, the black market rate tends to reflect prices in the most distorted goods markets (those with highest rents or highest relative prices P_i/P*_i).
  - Price controls reduce importer rents but create excess demand (shortages/scarcity).

*Source: Appendix 7. Household portfolio decision with money and black market dollars (from the provided content unit).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16159.pdf_