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---

### Overview and motivation
- Over the past decade, cryptocurrencies have rapidly gained adoption globally, especially in emerging and frontier markets.
- The decentralized, borderless, and pseudonymous nature of cryptocurrencies has propelled their use to transfer funds across borders, especially amid capital controls, as documented by Graf von Luckner, Reinhart and Rogoff (2023).
- For ease of reference, the paper uses the term "capital flight" to refer to capital outflows that circumvent restrictions.
- The paper investigates mechanisms through which crypto markets can undermine capital flow management and exchange rate policies.

### Conceptual mechanism: crypto exchanges as marketplaces for capital flight
- Crypto exchanges match counterparts who want to buy and sell access to foreign exchange (FX) amid restrictions on external transactions.
- In restricted-FX countries:
  - Macroeconomic imbalances and financial stability concerns can lead to excess demand for FX.
  - Residents cannot convert local currency using the official exchange rate and are willing to pay a premium to obtain FX.
- Typical route:
  - Residents convert local currency into crypto on domestic exchanges.
  - They then sell crypto for hard currency on foreign crypto exchanges.
  - Domestic crypto exchanges match counterparties and effectively serve as a marketplace for capital flight.
- Key feature: crypto FX premium — the price of crypto observed in local currency relative to the price of crypto on the global market (expressed in local currency using the official exchange rate).
  - The greater the excess demand for FX, the higher the premium.
  - The more restricted international transactions are, the higher the premium.
  - The premium drives supply of FX to the local crypto market and can be monetized by agents providing FX (including via evasion of controls).

### Stylized illustrative model (portfolio choice setup)
- Purpose: examine interplay of buyers and sellers of crypto under different settings and show why relative prices are more informative regarding capital flight than crypto trading volumes.
- Agents and assets:
  - Economy features N agents allocating savings S across three assets j: local/domestic currency (L), an international crypto currency (B), and a foreign currency (F).
  - Portfolio weights: w_L, w_B, w_F with ∑ w_j = 1.
  - No shorting or leverage: 0 ≤ w_j ≤ 1 ∀ j.
- Exchange rates and asset assumptions:
  - Exchange rate e_F and e_B are the price of the respective currency expressed in terms of the local currency (e^ indicates an anticipated/expected exchange rate).
  - At the onset L and F trade at unitary value; the crypto currency is a stablecoin, so it trades at unitary value with the foreign currency in international markets. Domestic market need not reflect that parity due to FX controls.
- Capital controls:
  - Exchange between domestic and foreign currency is subject to capital controls (a quota Q), restricting how much agents can adjust their foreign currency position.
  - Constraint in the model: S_t Δw_F ≤ Q.
- Portfolio objective (as specified in the source):
  - max(V_{t+1}) = S_t × (w_D + w_F (1 + Δe_{F,t+1}) + w_B (1 + Δe_{B,t+1}))
  - subject to S_t Δw_F ≤ Q
- Interpretation:
  - Crypto can be used for crypto vehicle trades (exchanged for foreign currency abroad) or simply held as an asset.
  - Crypto vehicle trades enable residents to obtain access to FX when formal channels are restricted, effectively converting domestic savings into offshore foreign deposits by selling crypto abroad.
  - Purchasing crypto from another resident may leave the national stock of foreign assets unaffected even as individual agents move savings offshore; the crypto trade operates akin to buying access to FX on a marketplace.

### The modeled confidence shock (section 3.3) and market clearing
- Confidence shock:
  - A confidence shock affects a subset of the population, αN, who now expect a devaluation of the local currency in the near future.
  - αN seek to move their savings into crypto or foreign currencies.
  - They use up their assigned quota, increasing wF up to the constraint and move a stock abroad.
  - The only remaining legal way for residents to move money abroad is to buy the cryptocurrency, B, which is not subject to the quota or any other capital controls or restrictions.
- Demand properties:
  - Residents who expect a devaluation, so that ee > 1, will seek to exchange remaining assets for B, as long as eB = 1.
  - Marginal demand depends on whether the devaluation expected by the agent exceeds the premium of cryptocurrency on the market (unregulated). Total demand for crypto currency, DB, becomes a function of eB.
  - Expected future exchange rate, ee, and hence the degree of expected devaluation, is not uniform over αN, producing a downward sloping marginal demand curve.
  - Note: DB(eB) = ∑i∈/αN wD,i,t−1Si − Qi for eB = 1.
- Market-clearing objective: derive an inverse supply schedule showing who supplies crypto under what conditions and at what prices.
  - Two illustrative points:
    - (1) Whether capital movements are net foreign asset neutral for the country depends on the supplier.
    - (2) What type of supply occurs at higher relative prices.
  - Supply schedule built through three scenarios.

### Scenario one — large domestic stock of crypto (3.3.1)
- Sufficient domestic supply condition:
  - ∑i∈/αN S­i wB,i,t−1 ≥ ∑i ε αN wD,i,t−1 Si − Qi
- If the inequality holds:
  - Sufficient domestic crypto supply satisfies shock-induced demand.
  - Agents exchanging local currency for crypto do not change the country’s net foreign asset (NFA) position.
  - The three currencies continue to trade at unitary value at time t; anticipated devaluation at t+1 does not translate into a devaluation at time t.
  - When eB < 1, demand is infinite (due to unrestricted and technically unlimited arbitrage profits).

### Scenario two — insufficient domestic stock but quotas available (3.3.2)
- Condition:
  - ∑i∈/αN S­i wB,i,t−1 < ∑i ε αN wD,i,t−1 Si − Qi
- Effects:
  - After quotas are used up, demand exceeds domestic supply and crypto prices increase.
  - Relative price must rise to incentivize residents who have unused quotas to use them, exchanging foreign currency for crypto abroad and selling domestically.
  - Assuming a reservation compensation μ above which they do so, a new source of supply arises (residents using their foreign exchange quotas), leading to a new market equilibrium.
  - Key implication: some supply stems from residents using their foreign exchange quotas they otherwise would not have used — crypto market spurs additional capital flight that otherwise would not have occurred and relative prices trade at a premium.

### Scenario three — insufficient stock and additional capital flight channels (3.3.3)
- Condition:
  - ∑i∈/αN S­i wB,i,t−1 + Qi < ∑i ε αN wD,i,t−1 Si − Qi
- Effects:
  - Demand for capital flight via crypto exceeds the sum of domestic holdings and quotas; some agents circumvent capital controls.
  - A small subset ΘN of N can mis-invoice exports/imports and obtain foreign currency beyond their quota.
  - Cost of capital control evasion is θ (including arbitrage reward and risk of detection).
  - A third source of supply arises (illicit channels), further affecting equilibrium.
  - Crypto markets facilitate matching, price discovery and execution; residents can contract to access others’ unused quotas/channels.

### Additional modeled insights (section 3.4)
- Two critical insights:
  - (A) Cryptocurrencies primarily function as tokens for trading access to capital flight.
  - (B) Cryptocurrencies provide valuable information on capital flow pressures by comparing their price in local currency to that in the global market.
- External sector accounting implications:
  - When ∑i∈/αN wB,i,t−1 Si = 0, any crypto transaction facilitating α’s capital flight affects the country’s NFA position.
  - When ∑i∈/αN wB,i,t−1 Si > 0, sales of crypto assets can occur without impacting the country’s NFA; relationship between associated flow and net capital flows is ambiguous.
- Two channels through which tighter capital controls affect crypto relative price:
  - Tighter controls increase the cost to evade restrictions (increase θ), raising the cost of supply at market equilibrium.
  - Holding S and αN constant, a smaller Q increases demand for crypto vehicle transactions.

### Mining (3.4.1)
- When B can be mined (e.g., bitcoin), stock of B inside the country can increase without purchases from abroad by converting electricity into computing power (mining rewards).
- Balance-of-payments effects via energy:
  - Net energy importing country: increased mining raises energy imports.
  - Net energy exporting country: increased mining decreases energy exports.
- Mining implications:
  - Mining may be used to circumvent capital controls or be a source of external revenue if proceeds are repatriated.
  - Energy subsidies can create subsidized exchange-rate advantages; agents could buy energy at the official exchange rate, mine, and sell crypto abroad or domestically at the higher crypto shadow exchange rate.
  - Anecdotal evidence from Argentina and Lebanon: mining activity increased as capital controls and exchange restrictions became binding and subsidized energy prices made mining attractive.

### Empirical approach, hypotheses, and data (section 4)
- Model-generated hypotheses:
  - Hypothesis 1: In the absence of binding capital controls, the law of one price should hold, and there should be no persistent crypto shadow premia.
  - Hypothesis 2: When capital controls are binding in the context of a non-freely floating exchange rate, relative prices of crypto currencies should increase in the domestic market.
  - Hypothesis 3: If regulators are aware of crypto markets rendering capital flow measures less effective, the prevalence of crypto bans should be highest in countries with closed financial accounts.
- Crypto-based shadow exchange rate definition:
  - CryptoShadowRate_LCU_USD = BTC_LCU / BTC_USD
  - Where BTCUSD and BTCLCU are prices of Bitcoin in international markets (quoted in USD) and in the local market (quoted in local currency units), respectively.
- Data:
  - Daily closing price and volume data sourced from centralized exchanges listed with the data provider CC Data (formerly Crypto Compare) for the period between January 1, 2019 and July 13, 2023.
  - For Egypt (no centralized exchanges), P2P buy and sell offers data from Binance are used.
  - Trade-volume weighted average across exchange prices is calculated to reduce exchange-specific noise.

### Case studies and empirical findings (section 4.1)
- Case One — open financial accounts:
  - With open financial accounts and limited external restrictions, arbitrage enforces near price parity ("law of one price").
  - Examples: euro area, Türkiye, Brazil and Mexico show very small price differentials; arbitrage transactions are typically recorded in official financial account data.
- Case Two — binding capital controls and macro imbalances:
  - Argentina (2019): reintroduced restrictions → liquid domestic crypto market and rising parallel exchange rate beginning late 2019.
  - Ukraine (2022): sharp increase in crypto shadow premia after the Russian invasion; post-devaluation official exchange rate coincided with crypto shadow rate levels.
  - Egypt and Nigeria: rises in crypto shadow rates amid excess FX demand; premia can persist after devaluations as long as imbalances and controls coexist.
  - P2P data (Egypt) can be noisier; post Q2 2023 Egypt P2P data became uninsightful due to sudden drop in liquidity.
- Case Three — crypto bans:
  - Strong overlap between countries with capital controls and those that have imposed a ban on crypto assets.
  - Countries classified as closed when their openness index (Baba et al. 2023) is below 0.5.
  - Not all bans are equivalent; enforcement intensity and penalties vary.
- Key empirical pattern:
  - Near price parity under open accounts.
  - Sizable and persistent crypto premia when capital controls are binding, with divergence coinciding with policy changes.
  - Crypto shadow premia serve as a daily-frequency, real-time indicator of FX pressures and tightness of controls in countries with acute FX pressures.

### Limitations and data caveats
- Not every crypto price premia indicates capital controls: illiquid/shallow markets and idiosyncratic exchange events can drive price differences.
- Crypto premia should be interpreted as evidence of capital controls only when observed in liquid markets featuring multiple exchanges.
- P2P markets can be informative but are often noisy and less consistently available.
- Crypto volumes alone reveal little about magnitude of capital flight in tightly restricted countries; relative crypto prices convey more information.

### Policy implications (section 5) and conclusions (section 6)
- Core takeaway: crypto exchanges act as marketplaces for capital flight and can amplify leakages through targeted exceptions to capital controls (e.g., exclusions for certain sectors or agents).
- First-best policy: address underlying macroeconomic imbalances to reduce need for external restrictions, following the IMF’s Institutional View on the Liberalization and Management of Capital Flows.
- Second-best policy: if macro adjustments are not feasible, consider tighter regulation of crypto markets, at least for agents with access to targeted exemptions to controls.
- Regulatory trade-offs:
  - Banning crypto exchanges reduces efficiency of the marketplace for capital flight but forfeits regulatory oversight and potential innovation benefits.
  - Regulating centralized exchanges with AML and KYC provides regulatory control, access to data to identify liquidity providers, and can reveal leaks and loopholes in existing capital flow measures.
- Crypto mining-specific recommendations:
  - Phase out energy subsidies (first-best) or consider limiting mining operations to avoid subsidized exchange-rate advantages and fiscal costs.
  - Account for environmental externalities as social costs of subsidized mining.
- Data policy:
  - Relative crypto prices (crypto-based FX premia) convey information on (a) demand for foreign exchange (proxy for macro imbalances) and (b) the marginal cost of capital flight (indicator of tightness of controls).
  - Crypto-based FX premia complement existing databases on capital controls by providing real-time, hard-to-manipulate signals.
- Conclusions:
  - Crypto markets match counterparts to buy and sell FX but do not create a novel channel for capital flight; they amplify incentives to use traditional channels by monetizing access to FX.
  - Stylized model and empirical analysis (2019–2023 data) support: near parity under open accounts versus sizable premia under binding controls.
  - Recommendation: use crypto-based parallel exchange rate data as a real-time indicator for monitoring currency devaluation pressures and to complement de jure and de facto financial openness measures.

*Source: Introduction, sections 3.3–3.4, 4, 4.1, 5 and 6 from wpiea2024133-print-pdf*

### Introduction ...........................................................................................................

### Introduction

### Overview and motivation
- Over the past decade, cryptocurrencies have rapidly gained adoption globally, especially in emerging and frontier markets.
- The decentralized, borderless, and pseudonymous nature of cryptocurrencies has propelled their use to transfer funds across borders, especially amid capital controls, as documented by Graf von Luckner, Reinhart and Rogoff (2023).
- Policymakers are concerned about implications for macroeconomic and financial stability (Auer and Claessens, 2018; He et al., 2022; IMF, 2022a, 2021; Copestake et al., 2023b).
- For ease of reference, the paper uses the term "capital flight" to refer to capital outflows that circumvent restrictions.
- The paper investigates mechanisms through which crypto markets can undermine capital flow management and exchange rate policies.

### Conceptual mechanism: crypto exchanges as marketplaces for capital flight
- Crypto exchanges provide a platform to match counterparts who want to buy and sell access to foreign exchange (FX) amid restrictions on external transactions.
- In countries that restrict access to foreign exchange:
  - Macroeconomic imbalances and financial stability concerns can lead to excess demand for FX.
  - Residents cannot convert local currency using the official exchange rate and are willing to pay a premium to obtain FX.
- Typical route described:
  - Residents convert local currency into crypto on domestic exchanges.
  - They then sell crypto for hard currency on foreign crypto exchanges.
  - The counterparty is an agent seeking the reverse transaction (e.g., remittances) or someone with access to FX (often illicit).
- The domestic crypto exchange thus matches the two counterparties, effectively serving as a marketplace for capital flight.
- Key feature: a crypto FX premium, defined as the price of crypto observed in local currency relative to the price of crypto on the global market (expressed in local currency using the official exchange rate).
  - The greater the excess demand for FX, the higher the premium.
  - The more restricted international transactions are, the higher the premium.
  - The premium drives supply of FX to the local crypto market and can be monetized by agents providing FX (including via evasion of controls).

### Stylized illustrative model (portfolio choice setup)
- Purpose: examine interplay of buyers and sellers of crypto under different settings and show why relative prices are more informative regarding capital flight than crypto trading volumes.
- Agents and assets:
  - Economy features N agents allocating savings S across three assets j: local/domestic currency (L), an international crypto currency (B), and a foreign currency (F).
  - Portfolio weights: w_L, w_B, w_F with ∑ w_j = 1.
  - No shorting or leverage: 0 ≤ w_j ≤ 1 ∀ j.
- Exchange rates and asset assumptions:
  - Exchange rate e_F and e_B are the price of the respective currency expressed in terms of the local currency (e^ indicates an anticipated/expected exchange rate).
  - At the onset L and F trade at unitary value; the crypto currency is a stablecoin, so it trades at unitary value with the foreign currency in international markets. Domestic market need not reflect that parity due to FX controls.
- Capital controls:
  - Exchange between domestic and foreign currency is subject to capital controls (a quota Q), restricting how much agents can adjust their foreign currency position.
  - Constraint in the model: S_t Δw_F ≤ Q.
- Portfolio objective (as specified in the source):
  - max(V_{t+1}) = S_t × (w_D + w_F (1 + Δe_{F,t+1}) + w_B (1 + Δe_{B,t+1}))
  - subject to S_t Δw_F ≤ Q
- Interpretation:
  - Crypto can be used for crypto vehicle trades (exchanged for foreign currency abroad) or simply held as an asset.
  - Crypto vehicle trades enable residents to obtain access to FX when formal channels are restricted, effectively converting domestic savings into offshore foreign deposits by selling crypto abroad.
  - From a national accounting perspective, purchasing crypto from another resident may leave the national stock of foreign assets unaffected even as individual agents move savings offshore; the crypto trade operates akin to buying access to FX on a marketplace.

### Empirical approach and data highlighted in introduction
- The paper examines crypto price data from centralized exchanges over the 2019-2024 period to provide country case study evidence corroborating model predictions.
- Empirical findings summarized:
  - Near price parity across crypto exchanges under open financial accounts.
  - Substantial deviations in relative prices arise when external transactions are severely restricted.
  - Time series of crypto FX premia show spikes when external restrictions are introduced or tightened.
  - Crypto premia can be interpreted as "shadow exchange rates" reflecting imbalances in supply and demand for FX.
- The authors propose using real-time data on crypto shadow exchange rates as a novel empirical indicator for monitoring buildup of currency devaluation pressures.
- The paper makes a new dataset on crypto shadow exchange rates available online and will update it periodically.

### Key interpretive conclusions from the Introduction
- Crypto assets generally do not create a fundamentally new channel for capital flight; rather, traditional channels (such as trade misinvoicing) persist and can be amplified by crypto exchanges by monetizing access to FX.
- Crypto exchanges reinforce traditional capital flight channels by providing an easy and lucrative marketplace to match counterparties.
- Most countries actively managing capital flows have adjusted crypto regulations in concordance with these dynamics, evidenced by a stark correlation between financial account restrictions and bans on crypto trading.

### Scope and organization (as presented)
- Section 2: brief overview of previous studies on crypto use for cross-border transactions and CFMs.
- Section 3: introduces the illustrative model and explains why relative prices are informative about capital flight.
- Section 4: presents four country case studies and examines crypto regulatory responses.
- Section 5 and the conclusion: discuss policy implications and outline questions for future research.

*Source: Introduction, wpiea2024133-print-pdf*

### 3.3 The Modeled Shock

### 3.3 The Modeled Shock

### Modeled confidence shock and immediate behavior
- A confidence shock affects a subset of the population, αN, who now expect a devaluation of the local currency in the near future.
- αN seek to move their savings into crypto or foreign currencies.
- Using up their assigned quota, they increase wF up to the constraint and move a stock of abroad.
- The only remaining legal way for residents to move money abroad is to buy the cryptocurrency, B, which is not subject to the quota or any other capital controls or restrictions.
- Residents who expect a devaluation, so that ee > 1, will seek to exchange their remaining assets for B, as long as eB = 1, so that the αN’s maximum demand for crypto is ∆wB,iSi = 
- Marginal demand depends on whether the devaluation expected by the agent exceeds the premium of cryptocurrency on the market (unregulated). Total demand for crypto currency, DB, becomes a function of eB.
- Expected future exchange rate, ee, and hence the degree of the expected devaluation, is not uniform over αN, producing a downward sloping marginal demand curve for additional capital flight.
- Note: DB(eB) = ∑i∈/αN wD,i,t−1Si − Qi for eB = 1.

### Market clearing and inverse supply schedule — overview
- Objective: derive an inverse supply schedule showing who supplies crypto under what conditions and at what prices.
- Two illustrative points of the exercise:
  - (1) Whether capital movements in the portfolio are net foreign asset neutral for the country depends on the supplier.
  - (2) What type of supply occurs at higher relative prices.
- Supply schedule built gradually through three scenarios.

### 3.3.1 Scenario one — large domestic stock of crypto
- Crypto assets can be bought abroad with foreign currency or domestically with domestic currency.
- Domestic demand can be satisfied from domestic crypto holdings (purchased before) and from abroad with foreign currency.
- Sufficient domestic supply condition:
  - ∑i∈/αN S­i wB,i,t−1 ≥ ∑i ε αN wD,i,t−1 Si − Qi
- If the inequality holds, there is sufficient supply of crypto to satisfy shock-induced demand. Agents exchanging local currency for crypto do not change the country’s net foreign asset (NFA) position.
- With sufficient domestic stock, the three currencies continue to trade at unitary value at time t; anticipated devaluation at t+1 does not translate into a devaluation at time t.
- When eB < 1, demand is infinite (due to unrestricted and technically unlimited arbitrage profits).

### 3.3.2 Scenario two — insufficient domestic stock of crypto (but quotas available)
- Condition: ∑i∈/αN S­i wB,i,t−1 < ∑i ε αN wD,i,t−1 Si − Qi
- After quotas are used up, stock of savings held by residents expecting devaluation exceeds available cryptocurrency; demand exceeds supply and crypto prices increase.
- Because residents i ∈/ αN have not used up their quotas, relative price must rise to incentivize them to use their quota, exchange foreign currency for crypto abroad and sell it domestically.
- Assuming a reservation compensation μ above which they do so, a new source of supply arises (residents using their foreign exchange quotas), leading to a new market equilibrium.
- Key implications:
  - Some supply now stems from residents using their foreign exchange quotas they otherwise would not have used—crypto market spurs additional capital flight that otherwise would not have occurred.
  - Relative prices of crypto trade at a premium relative to the domestic market.

### 3.3.3 Scenario three — insufficient domestic stock and additional capital flight channels
- Condition: ∑i∈/αN S­i wB,i,t−1 + Qi < ∑i ε αN wD,i,t−1 Si − Qi
- Demand for capital flight via crypto exceeds the sum of domestic crypto holdings and quotas; some agents circumvent capital controls.
- A small subset ΘN of N can mis-invoice exports/imports and obtain foreign currency beyond their quota.
- Cost of capital control evasion is θ (including arbitrage reward and risk of detection).
- A third source of supply arises (illicit channels), further affecting equilibrium.
- In scenarios two and three, residents can engage in contracts to access others’ unused quotas/channels; crypto markets facilitate matching, price discovery and execution.

### 3.4 Takeaways from the stylized model
- Two critical insights:
  - (A) Cryptocurrencies primarily function as tokens for trading access to capital flight.
  - (B) Cryptocurrencies provide valuable information on capital flow pressures by comparing their price in local currency to that in the global market.
- External sector accounting implications:
  - Methods to determine the size of flows may not equate to net capital flows due to existing crypto stocks.
  - Role of resident crypto stocks:
    - When ∑i∈/αN wB,i,t−1 Si = 0, any crypto transaction facilitating α’s capital flight affects the country’s NFA position.
    - When ∑i∈/αN wB,i,t−1 Si > 0, sales of crypto assets can occur without impacting the country’s NFA. Thus, the relationship between associated flow and net capital flows is ambiguous.
- Relative price of the crypto currency is a clearer macro indicator, containing information on:
  - (1) Macro imbalances that spur outflow pressures (affecting eB via demand shifts).
  - (2) Tightness of capital controls.
- Two channels through which tighter capital controls affect crypto relative price:
  - Tighter controls increase the cost to evade restrictions (increase θ), raising the cost of supply at market equilibrium.
  - Holding S and αN constant, a smaller Q increases demand for crypto vehicle transactions.

### Empirical examples and relevance
- Hu et al. (2021) example: when cryptocurrency transactions were unregulated and China had a USD 50,000 dollar quota on foreign transactions, individuals bought cryptocurrencies more cheaply in neighboring countries to sell them at a risk-free profit in China — behavior captured by scenarios one and two.
- Model applies also when capital controls are not quota-based, as long as certain sectors/agents have privileged access to foreign currency (e.g., foreign financial firms excluded from capital controls).
- Crypto markets allow monetization of privileged channels (e.g., trade misinvoicing) on a widely accessible marketplace.
- Argentina example:
  - Since 2019, Argentina has had tight restrictions on external transactions, strictly limiting movement of capital abroad through official channels.
  - Exporters of commodities/agricultural products often required to repatriate proceeds at a less favorable exchange rate than the market exchange rate, creating incentives to understate exports and repatriate only a portion officially.
  - Commodity exporters can purchase large amounts of crypto assets, move them into local exchanges, and repatriate FX proceeds at a more favorable rate, with crypto markets matching exporters with individuals seeking to move capital abroad.

### 3.4.1 When B can be mined
- Some crypto assets (e.g., bitcoin) can be mined, so the stock of B inside the country can change over time without purchases from abroad.
- In the case of bitcoin, the stock in a country can be increased by converting electricity into computing power, yielding mining rewards.
- Because energy is tradable (oil, gas, electricity), marginal increases in energy consumption for mining can affect the country’s balance of payments:
  - For a net energy importing country: increased energy imports.
  - For a net energy exporting country: decreased energy exports.
- Crypto mining’s role differs by country:
  - In some countries, mining may be used mainly to get around capital controls (mining becomes the channel for capital flight).
  - In others with open financial accounts, mining may be a source of external revenue.
- Mining may provide a channel to transfer money abroad at the more favorable official exchange rate because energy is typically imported at the official exchange rate (a discount/subsidy financed with foreign reserves).
- Agents with mining rigs could purchase energy, mine bitcoin, and sell it abroad or domestically at the higher crypto shadow exchange rate.
- Anecdotal evidence from Argentina and Lebanon in the early 2020s: mining activity increased as capital controls and exchange restrictions became binding and subsidized energy prices made mining especially attractive.

### 4 Empirical analysis — hypotheses and data
- Model-generated hypotheses:
  - Hypothesis 1: In the absence of binding capital controls, the law of one price should hold, and there should be no persistent crypto shadow premia.
  - Hypothesis 2: When capital controls are binding in the context of a non-freely floating exchange rate, relative prices of crypto currencies should increase in the domestic market.
  - Hypothesis 3: If regulators are aware of crypto markets rendering capital flow measures less effective, the prevalence of crypto bans should be highest in countries with closed financial accounts.
- Crypto-based shadow exchange rate definition:
  - CryptoShadowRate_LCU_USD = BTC_LCU / BTC_USD
  - Where BTCUSD and BTCLCU are prices of Bitcoin in international markets (quoted in USD) and in the local market (quoted in local currency units), respectively.
- Data:
  - Daily closing price and volume data sourced from centralized exchanges listed with the data provider CC Data (formerly Crypto Compare) for the period between January 1, 2019 and July 13, 2023.
  - For Egypt (no centralized exchanges), P2P buy and sell offers data from Binance are used.
  - Trade-volume weighted average across exchange prices is calculated to reduce exchange-specific noise (removing P2P counterparty risk and leveraging greater liquidity of centralized exchanges).

*Source: IMF Working Paper chapter 3.3 and related sections in the supplied PDF content.*

### 4.1 Case  Studies

### 4.1 Case Studies

### 4.1.1 Case One: When external restrictions are limited the law of one price holds
- Central insight: with an open financial account and only limited restrictions on external transactions, arbitrageurs can use legal channels to eliminate significant price premia between domestic crypto prices and global market prices ("law of one price").
- Mechanism: when domestic demand for crypto exceeds domestic supply, arbitrageurs move capital abroad, purchase crypto, and supply the local market until the arbitrage spread is minimal.
- Empirical evidence: selected economies with relatively open financial accounts (the euro area, Türkiye, Brazil and Mexico) show very small price differentials between crypto in local currency and the global market; the law of one price is enforceable by arbitrage traders even during periods of financial stress when regulators allow free financial flows (example: Türkiye).
- Accounting implication: arbitrage transactions that facilitate crypto vehicle flows would typically be recorded in official financial account data (or in the current/capital account, depending on accounting conventions). Example: Brazil’s central bank publishes estimates of capital in- and outflows made to purchase/sell crypto in its balance of payments statistics.

### 4.1.2 Case Two: Binding capital controls in the presence of macroeconomic imbalances
- Model prediction: when restrictions on external transactions are introduced or suddenly tightened, significant crypto shadow rates should arise (hypothesis 2), reflecting excess demand for foreign currency.
- Argentina (2019):
  - Context: significant imbalances in the 2019 election year; outgoing government reintroduced restrictions and set a narrow band for maintaining the exchange rate.
  - Outcome: residents developed a liquid domestic market for crypto as a marketplace for capital flight; crypto trading increased in lockstep with a rising parallel exchange rate beginning late 2019.
- Ukraine (2022):
  - Context: FX imbalances arose suddenly following the Russian invasion.
  - Outcome: sharp increase in crypto shadow premia; the post-devaluation official exchange rate coincided with the level where the crypto shadow rate was trading, suggesting crypto-based implicit parallel exchange rates can be informative for policy decisions on devaluation levels.
- Egypt and Nigeria:
  - Observation: rises in crypto shadow rates amid signs of excess demand for foreign currency; premia can persist after significant devaluations as long as imbalances and capital controls coexist.
- Data considerations:
  - Crypto-based parallel exchange rates can provide important, real-time signals for policymakers where other parallel exchange rate data are not systematically available.
  - P2P data (example noted for Egypt) can be noisier and less consistently available; post Q2 2023 Egypt data became uninsightful due to a sudden drop in liquidity in these markets.

### 4.1.3 Hypothesis Three: Crypto Bans
- Question: Do governments seeking to restrict capital mobility regulate or ban crypto markets?
- Empirical pattern: strong overlap between countries that have capital controls and those that have imposed a ban on crypto assets.
- Classification detail: countries are classified as closed when their openness index (Baba et al. 2023) (ranging from zero to one) is below 0.5.
- Interpretation: the correlation suggests policymakers view crypto exchanges as contributing to capital outflow pressures by providing a marketplace for capital flight.
- Caveat: not all crypto bans are equivalent; enforcement intensity and penalties vary across jurisdictions.

### Key empirical pattern across case studies
- Near price parity in crypto markets under open financial accounts.
- Sizable and persistent crypto premia when capital controls are binding, with divergence timings coinciding with policy changes to restrict capital flows.
- Crypto shadow premia serve as a daily-frequency, real-time indicator of FX pressures and tightness of controls in countries with acute FX pressures.

### Limitations and data caveats
- Not every crypto price premia indicates unrevealed capital controls: illiquid/shallow crypto markets and idiosyncratic exchange events can also drive price differences.
- Crypto-based premia should be interpreted as evidence of capital controls only when observed in liquid markets featuring multiple exchanges.
- P2P markets can be informative but are often noisy and less consistently available.

### Accounting and measurement implications
- Crypto trades generally do not create a novel channel for capital flight; capital has typically already moved via traditional channels before the crypto vehicle trade occurs.
- Therefore, the underlying crypto transaction per se does not affect the country’s net foreign asset position.
- Conclusion for balance-of-payments statistics: growing crypto use is not necessarily making BoP statistics less accurate; however, if crypto use propels an overall increase in capital flight via traditional channels, inaccuracies may increase net errors and omissions.

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### 5 Policy Implications
- Core takeaway: crypto exchanges can act as marketplaces for capital flight and can amplify leakages through targeted exceptions to capital controls (e.g., exclusions for certain sectors or economic agents).
- First-best policy: address underlying macroeconomic imbalances to reduce the need for external restrictions, following the IMF’s Institutional View on the Liberalization and Management of Capital Flows.
- Second-best policy: if macro adjustments are not feasible, consider tighter regulation of crypto markets, at least for agents with access to targeted exemptions to controls.
- Regulatory options and trade-offs:
  - Banning crypto exchanges reduces efficiency of the marketplace for capital flight but forfeits regulatory oversight and potential innovation benefits.
  - Regulating centralized exchanges with AML and KYC provides regulatory control, access to data to identify liquidity providers, and can reveal leaks and loopholes in existing capital flow measures.
- Crypto mining-specific implications:
  - Mining can create direct channels for capital flight if foreign currency proceeds are not repatriated, or it can be a source of FX revenue if proceeds are repatriated.
  - Energy subsidies used by miners can create fiscal costs and provide subsidized exchange-rate advantages; phasing out subsidies is first-best, or otherwise consider limiting mining operations.
  - Environmental externalities add to the social costs of subsidized mining.
- Data policy implication:
  - Crypto volumes alone reveal little about the magnitude of capital flight in tightly restricted countries.
  - Relative crypto prices (crypto-based FX premia) convey information on (a) demand for foreign exchange (proxy for macroeconomic imbalances) and (b) the marginal cost of capital flight (indicator of tightness of controls).
  - Crypto-based FX premia complement existing databases on capital controls (for example, the IMF’s Taxonomy of Capital Flow Management Measures and the AREAER) by providing real-time, hard-to-manipulate signals.

### 6 Conclusion
- Main findings:
  - Crypto markets match counterparts to buy and sell FX but do not create a novel channel for capital flight.
  - Crypto exchanges amplify incentives to use traditional channels to evade capital controls by serving as marketplaces to efficiently trade access to cross-border capital flight channels.
  - A stylized model shows excess demand for FX amid binding external restrictions leads to persistent crypto shadow premia relative to global market prices; crypto trading volumes need not correlate with cross-border capital flows.
- Empirical support:
  - Analysis of crypto price data from centralized exchanges over 2019-2023 supports model predictions: near parity under open accounts versus sizable premia under binding controls.
- Policy recommendation:
  - Use crypto-based parallel exchange rate data as a real-time indicator for monitoring currency devaluation pressures and to complement de jure and de facto financial openness measures.
- Research directions:
  - Panel data regression approaches to analyze relationships between crypto-based FX premia, capital control measures, and macro fundamentals.
  - In-depth analysis of heterogeneity in regulatory responses and the drivers of policy differences across countries.

*Source: 4.1 Case Studies (excerpts) from wpiea2024133-print-pdf*

### References

### References

### Major themes in the cited literature
- International capital flows and cryptocurrencies
  - Works examining cross-border crypto flows, measurement, drivers, and policy implications: Cardozo et al. (2023) and Cerutti, Chen, and Hengge (Forthcoming).
  - Studies on using bitcoin to avoid capital controls and capital flight: Chen and Sarkar (2022); Hu, Lee, and Putniņš (2021); Ju, Lu, and Tu (2016); Cuddington (1986).
  - Research on crypto, corruption, and capital controls: Alnasaa et al. (2022).
  - Graf von Luckner, Reinhart, and Rogoff (2023) on "Decrypting new age international capital flows."

- Market structure, pricing, and returns of cryptocurrencies
  - Cross-section and risk-return analyses: Borri and Shakhnov (2022); Liu and Tsyvinski (2021).
  - Trading, arbitrage, and price inconsistencies across markets: Makarov and Schoar (2020); Pieters and Vivanco (2017); Pieters (2016).
  - Competition in exchange markets: Hu and Zhang (2023).

- Policy, regulation, and macro-financial implications
  - Regulatory responses and market reactions: Auer and Claessens (2018); Copestake, Furceri, and Gonzalez-Dominguez (2023a); Copestake et al. (2023b).
  - IMF analyses and policy notes: IMF (2021); IMF (2022a); IMF (2022b); IMF (2022c); IMF (2023a); IMF (2023b); IMF (2023c); IMF (2023d).
  - Capital Flow Management Measures and digital-age challenges: He et al. (2022).

- Theoretical and empirical links to exchange rate regimes and international finance
  - Foundational and reinterpretative works on exchange arrangements and "fear of floating": Calvo and Reinhart (2002); Reinhart and Rogoff (2004); Ilzetzki, Reinhart, and Rogoff (2019).
  - Currency competition and the impossible trinity in the context of crypto: Benigno, Schilling, and Uhlig (2022).
  - Money-demand and Mundell–Fleming model applications: Enajero (2021).

- Behavioral, informational, and socio-economic signals in crypto markets
  - Studies on bubbles, social feedback, and user intentions: Garcia et al. (2014); Glaser et al. (2014); Tang and You (2021).

### Representative bibliographic details and numeric citations preserved
- Akbalik, M., Apergis, N., Zeren, M., and Sarigül, Ö. (2021). Finansal Ara̧stırmalar ve Çalı̧smalar Dergisi, 13(24):16–35.
- Benigno, P., Schilling, L. M., and Uhlig, H. (2022). Journal of international economics, 136:103601.
- Borri, N. and Shakhnov, K. (2022). The Review of Asset Pricing Studies, 12(3):667–705.
- Calvo, G. A. and Reinhart, C. M. (2002). The Quarterly journal of economics, 117(2):379–408.
- Cuddington, J. T. (1986). Volume 58. International Finance Section, Department of Economics, Princeton University.
- Garcia, D., Tessone, C. J., Mavrodiev, P., and Perony, N. (2014). Journal of the Royal Society Interface, 11(99):20140623.
- Graf von Luckner, C., Reinhart, C. M., and Rogoff, K. (2023). Journal of Monetary Economics, 138:104–122.
- Ilzetzki, E., Reinhart, C. M., and Rogoff, K. S. (2019). The Quarterly Journal of Economics, 134(2):599–646.
- IMF (2021). Global Financial Stability Report. October 2021.
- IMF (2022a). Fintech Note 2022/005.
- IMF (2023a). Elements of Effective Policies for Crypto Assets. Policy Paper.
- Ju, L., Lu, T., and Tu, Z. (2016). International Review of Finance, 16(3):445–455.
- Liu, Y. and Tsyvinski, A. (2021). The Review of Financial Studies, 34(6):2689–2727.
- Makarov, I. and Schoar, A. (2020). Journal of Financial Economics, 135(2):293–319.
- Pieters, G. and Vivanco, S. (2017). Information Economics and Policy, 39:1–14.
- Reinhart, C. M. and Rogoff, K. S. (2004). The Quarterly Journal of economics, 119(1):1–48.
- Tang, B. and You, Y. (2021). Available at SSRN 3981990.

### Appendix reference
- Appendix A.1 titled "Crypto Shadow Rates" notes presentation of crypto shadow rates and official exchange rates for thirty economies with continuous centralized-exchange data since January 2020.

*Source: References section of the PDF "wpiea2024133-print-pdf - References"*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024133-print-pdf.pdf_