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---

### Figure and dataset summary
- The figure reports the cumulative distribution of the country-specific standard deviation of changes in reserves, distinguishing between countries that reported FXI data for most of the sample period and those that did not.
- Based on countries that report FXI data at least on a quarterly frequency.
- Sources: IMF, International Finance Statistics; IMF, Information Notice Systems; International Reserves and Foreign Currency Liquidity Template; and authors’ calculations.
- Notes: Non-publishing countries display at least as much, if not more, variation in the change in central bank reserves as countries that publish FXI data.

### Definition and scope of FXI
- FXI defined as “any active transaction that changes the central bank’s foreign-currency position regardless of intent.”
- Key elements:
  - Focus on active transactions: excludes changes arising from interest income on reserve assets or from changes in asset prices.
  - Focus on the central bank as the main entity conducting foreign exchange interventions; excludes FX operations by other public sector entities due to data limitations.
- Dataset reports three proxies:
  - “spot” proxy (operations in spot markets),
  - “derivative” proxy (operations with derivatives),
  - “broad” proxy (includes both spot and derivative transactions).

### Estimating spot interventions: four adjustments to changes in reserves
- Valuation changes:
  - Use country-specific reserve composition from the International Reserves and Foreign Currency Liquidity Template when available (now available for close to 50 percent of the countries).
  - Otherwise use IMF Monetary and Financial Statistics (MFS) and COFER country-group aggregates for currency composition.
  - Needed for monthly-frequency proxies; quarterly BOP transaction-based data generally do not require valuation adjustments unless BOP data are unavailable.
- Investment income:
  - Estimated using reserve composition combined with market interest rates and effective interest rates paid by issuers of reserve currencies.
  - At quarterly frequency use reported investment income on reserves in BOP where available.
- Other foreign currency assets and liabilities vis-à-vis nonresidents:
  - Adjust using IMF Standardized Report Forms of Monetary and Financial Statistics (some provided confidentially).
  - Includes holdings of non-reserve foreign assets and liabilities vis-à-vis all foreign creditors, including IMF and other official creditors.
- Other foreign currency assets and liabilities vis-à-vis residents:
  - Adjust using IMF Monetary and Financial Statistics (some confidential).
  - Key improvement relative to previous proxies in the literature.

### Why the adjustments matter (empirical implications)
- Mean absolute value of the monthly change in reserves (in percent of GDP): 0.18.
- Mean absolute value of the monthly FXI estimate (in percent of GDP): 0.11.
- Distribution of differences (country-month, differences as percent of absolute change in reserves):
  - 16 percent of observations: differences smaller than 10 percent of the coarse proxy.
  - 32 percent of observations: differences between 10 and 50 percent.
  - 52 percent of observations: differences greater than 50 percent of the observed value of the coarse proxy.
- Even excluding small FXI estimates (less than 0.25 percent of GDP in absolute terms), large differences between measures remain.

### Country examples illustrating adjustments
- Argentina: requires accounting for large transactions vis-à-vis non-residents (including the IMF).
- Egypt, Korea, Turkey: adjusting for positions vis-à-vis residents and non-residents is key.
- Six-month moving sum used in several decompositions (change in reserves, valuation effects, income effects, adjustments for positions vis-à-vis non-residents and residents).

### FXI through currency derivatives
- Derivative proxy includes forwards, futures, forward leg of currency swaps, instruments denominated in foreign currency but settled by other means.
- Practical distinction:
  - Some central banks use FX swaps without altering net FX position (e.g., Australia, New Zealand).
  - Other central banks use derivatives that affect net FX position (e.g., Brazil, Thailand, Turkey).
- Empirical findings:
  - 17-18 percent of observations exhibit non-zero differences between the broad (spot plus derivatives) and spot-only measures, indicating some use of derivatives.
  - This 17-18 percent figure likely underestimates true derivative use because reporting to IRFCLT is incomplete; in absence of reported data, derivative transactions are treated as zeros.
  - For frequent FX-swap users, the “broad” proxy is advisable.

### Limitations of the dataset
- Valuation changes estimation constrained by limited country-specific currency composition information; aggregate currency shares used for most countries.
- Growing foreign-currency portfolios (more equity, less liquid assets) make valuation changes harder to estimate without granular data.
- Focus on central bank transactions; operations by other public entities are not comprehensively covered due to limited balance-sheet data at monthly or quarterly frequency and currency breakdowns.

### Stylized facts from the FXI estimates
- Cross-country patterns:
  - EMDEs relied significantly more on FXI than AEs before the global financial crisis (GFC); this holds even after excluding China.
  - Post-GFC, use of FXI in EMDEs comparable to that in non-reserve-issuer AEs.
  - Within AEs, economies with large financial sectors (Hong Kong SAR, Singapore, Switzerland) deploy significant FXI.
  - Some AEs pursue narrow band regimes (examples: Hong Kong SAR, Macau SAR, Singapore, Denmark, Taiwan POC).
- Frequency and size:
  - Interventions of absolute size of at least 0.25 percent of GDP per quarter occur nearly ¾ of the time.
  - FXI asymmetric: purchases of foreign currency are significantly more frequent than sales.
  - Use of derivatives limited relative to spot interventions but more prevalent in AEs; financial centers display extensive derivative use.
- Notable historical observation:
  - Period 2021-22: reserve changes suggested large FX sales by EMDEs, but after accounting for valuation losses on fixed income reserve assets (due to rise in global interest rates) and other adjustments, conclusion is little to no FXI during this period.
- Interpretation caveats:
  - Apparent symmetry in FXI through derivatives may reflect unwinding of positions as they come due, or swaps used to manage liquidity without altering FX position.

### Degree of exchange rate management (index)
- Index: FXI_i_NER = ρ_i = (σ_FXIP_i + σ_NEER_i) / (σ_FXIP_i + σ_NEER_i) (index varies from 0 (pure floating) to 1 (peg)).
- σ_FXIP_i: standard deviation of the broad FXI proxy (in percent of GDP) for the full sample period.
- σ_NEER_i: standard deviation of the change in the nominal effective exchange rate for the full sample period.
- Index computed over 2000-20.
- Major reserve-issuing countries (Euro area economies, Japan, the U.K. and the U.S.) are excluded.
- Key findings:
  - On average, AEs allow for slightly greater exchange rate flexibility than EMDEs; distributions not very different with considerable within-group variation.
  - Within AEs, large-financial-sector economies (Hong Kong SAR, Iceland, Singapore, Switzerland) display higher degree of exchange rate management.
  - Within EMDEs, some large EMDEs (Mexico, South Africa, Colombia, Brazil, Turkey) display flexible regimes comparable to flexible AEs; others (Bulgaria, Saudi Arabia) display highly managed regimes.

### Publication and transparency of FXI data
- Officially published FXI coverage in dataset:
  - 43 countries at quarterly frequency.
  - 39 countries at monthly frequency.
  - 14 countries also publish weekly data (subset of the 39 monthly).
- Data collection sources: central bank websites, IMF’s AREAER, hand-collection from reports, country-specific metadata, IMF country teams, direct contact with central banks.
- Definition and comparability issues across official series noted; definitional inconsistencies complicate a unique measurable FXI definition.

### Comparing estimates and official FXI data
- Exclusions from comparison:
  - Freely floating for at least 10 years in AREAER: United States, United Kingdom, Canada, Japan, Euro area, Australia, New Zealand, Mexico.
  - Excluded due to large discrepancies: Angola, Bolivia, Nicaragua, Nigeria, Turkey.
- Correlations:
  - Raw correlation between estimated spot FXI and official FXI: 0.61.
  - Raw correlation between changes in reserves and official FXI: 0.54.
- Sign consistency:
  - Estimated and official interventions rarely have different signs: about 0.5 percent of country/month observations have a meaningfully different sign.
- Caveats:
  - Analysis premised on official series encompassing all central bank transactions that alter foreign exchange position; definitional differences cannot be ruled out.
  - Selection bias: countries publishing FXI may be more transparent and provide more granular data.

### Methodology and validation of FXI proxies — regression evidence
- Regression specification: x*_{i,t} = α_i + β x_{i,t} + ε_{i,t} where x*_{i,t} is official FXI, x_{i,t} is FXI proxy (percent of GDP), ε_{i,t} ~ N(0, σ_ε).
- Full Sample 2000-19 (Table 1) monthly regressions:
  - Change in Reserves coefficient: 0.927*** (0.054).
  - Spot Estimate coefficient: 0.940*** (0.031).
  - BOP Flow coefficient: 0.865*** (0.048).
  - Constants (weighted average country constant): 0.001***, 0.000***, 0.002*** (standard errors (0.000)).
  - Observations: 4177 (monthly columns).
  - # Countries: 23 (monthly change in reserves and spot), 26 for some specifications.
  - R-squared: 0.294 (monthly Change in Reserves), 0.391 (monthly Spot Estimate), 0.500 (monthly BOP Flow).
  - P-value (β = 1): 0.193, 0.067, 0.009 (columns as above).
- Quarterly regressions:
  - Change in Reserves: 0.892*** (0.052).
  - Spot Estimate: 0.918*** (0.048).
  - Observations: 1503.
  - R-squared: 0.462 (quarterly Change in Reserves), 0.626 (quarterly Spot Estimate).
  - P-value (β = 1): 0.048, 0.101 (columns as above).
- Country-by-country median β (equation (2)): median β goes from 0.77 (changes in reserves) to 0.83 (spot) and 0.83 (broad proxy).
- Recent-sample (2010-19) increases the advantage of the spot estimate.

### Horse-race regressions and decomposition of spot estimate
- Horse-race: x*_{i,t} = γ_1 x_{1,i,t} + γ_2 x_{2,i,t} + ξ_{i,t}; spot estimate adds significant information beyond changes in reserves.
- Monthly horse-race (Full Sample 2000-19):
  - Change in reserves alone: 0.317*** (0.080).
  - When spot added: Change in reserves 0.132** (0.056), Spot Estimate 0.316*** (0.059). R-squared rises from 0.294 to 0.420. Observations 4177; # Countries 23.
- Quarterly horse-race:
  - Change in reserves alone: 0.518*** (0.095).
  - With BOP flow and spot: Spot Estimate 0.541*** (0.089) and Change in reserves 0.161** (0.077). R-squared rises to 0.649. Observations 1503; # Countries 26.
- Decomposition (monthly full sample) — incremental adjustments:
  - Valuation and income effects: modest R-squared increase; coefficients sometimes insignificant at 10%.
  - CB position relative to IMF: large positive and highly significant (example coefficient 0.447*** (0.074)).
  - Position relative to residents: largest impact when included; coefficient 0.425*** (0.047); major rise in Within R-squared to 0.464.
  - Across specifications the coefficient on Change in Reserves becomes insignificant when intermediate or final estimates included.

### Sterilization: classification approaches and empirical findings
- Objective: binary classification into ‘fully sterilized’ and ‘not fully sterilized’.
- First step: de jure exchange rate regime — interventions under a fixed exchange rate regime classified as ‘not fully sterilized’.
- For non-pegged regimes two approaches:
  - Interest rate approach rule: FX purchase (sale) is ‘fully sterilized’ when monetary policy rate remains unchanged or increases (decreases) during same period. Only changes ≥ 25 basis points in absolute value considered.
  - Monetary base approach rule: FX purchase (sale) is ‘fully sterilized’ when monetary base remains unchanged or decreases (increases) during same period.
- Empirical cross-tabulation (FXI observations > 0.25 percent of GDP, non-peg regimes):
  - Fully Sterilized under Monetary Base & Interest Rate: 36%.
  - Fully Sterilized under Monetary Base & Not Fully Sterilized under Interest Rate: 6%.
  - Not Fully Sterilized under Monetary Base & Fully Sterilized under Interest Rate: 49%.
  - Not Fully Sterilized under both: 9%.
  - Interest Rate Approach totals: 84% Fully Sterilized; 16% Not Fully Sterilized.
  - Monetary Base Approach totals: 42% Fully Sterilized; 58% Not Fully Sterilized.
- Dataset choice: follows the interest rate approach (classifies 84 percent of FXI operations under non-pegged regimes as fully sterilized); monetary base approach yields lower full-sterilization share.
- Distributional finding: large interventions commonly not fully sterilized; for floating-regime countries not-fully sterilized FXI distribution tilted right — central banks less likely to sterilize when leaning against appreciation than when leaning against depreciation; difference statistically significant.

### Key empirical magnitudes and robustness notes
- R-squared examples:
  - Monthly Spot Estimate R-squared 0.391 (full sample).
  - Quarterly Spot Estimate R-squared 0.626 (full sample).
  - Monthly observations: 4177 (full sample).
  - Quarterly observations: 1503 (varies by specification).
  - # Countries vary by specification (23, 26).
- Diagnostic notes:
  - Adjustments for valuation and investment income matter more as stocks of reserves grow and valuation effects increase.
  - Availability of central bank FX position adjustments typically only after 2002 improves spot estimate accuracy in recent years.
- Robustness: alternative regression ordering does not overturn conclusions; spot estimate consistently shows coefficients closer to 1 and higher R-squared relative to change-in-reserves and BOP flows.

### Data coverage and metadata examples
- Online Appendix metadata preserves frequency notation exactly (examples):
  - Angola: Coverage 2000M1 – 2020M9; Agency Central Bank; Types Spot; Frequency Monthly; Reported format Millions of U.S. Dollars and Euros.
  - Argentina: Coverage 2003M1 – 2020M9; Agency Central Bank; Types Spot; Frequency Daily, Monthly; Reported format Millions of U.S. Dollars.
  - Australia: Coverage 1989M1 – 2020M6; Agency Central Bank; Types Spot; Frequency Daily; Reported format Millions of Local Currency.
  - Brazil: Coverage 2000M1 – 2020M9; Agency Central Bank; Types Spot, forward and forward like (Swap), and other derivatives (Options); Frequency Monthly, daily (from 2009); Reported format Millions of U.S. Dollars.
  - United States: Coverage 1973M3 - 2020M6; Agency Central Bank; Types Spot; Frequency Daily from 1973M3 - 2011Q1, Quarterly from 2011Q2-2020Q2; Reported format Millions of U.S. Dollars.
- Country coverage tables and categorical adjustment codes (Online Appendix 1 Tables 4 and 5) document per-country, per-period basis for valuation and income adjustments.

*Italic source: wpiea2021047-print-pdf*

### Appendix 1 Figure A1.1 f or these f acts).

### Appendix 1 Figure A1.1 (for these facts)

### Figure and dataset summary
- The figure reports the cumulative distribution of the country-specific standard deviation of changes in reserves, distinguishing between countries that reported FXI data for most of the sample period and those that did not.
- Based on countries that report FXI data at least on a quarterly frequency.
- Sources: IMF, International Finance Statistics; IMF, Information Notice Systems; International Reserves and Foreign Currency Liquidity Template; and authors’ calculations.
- Notes: The figure indicates that non-publishing countries display at least as much, if not more, variation in the change in central bank reserves as countries that publish FXI data.

### Key stylized facts (from the new FXI estimates)
- The new FXI estimates confirm some previously discussed stylized facts and reveal new stylized facts missed due to data limitations.
- Consistent with Dominguez et al (2012), EMDEs do not necessarily intervene more heavily in FX markets than AEs beyond non-reserve issuing AEs. While as a group EMDEs relied significantly more on FXI before the global financial crisis, in the post-GFC period the use of FXI in EMDEs has been comparable to that observed in non-reserve issuer AEs.
- The degree of exchange rate management (i.e., the observed use of FXI relative to the observed volatility of the exchange rate) is similar across EMDEs and AEs, contrasting with Hausmann et al (2001).
- Interventions are typically conducted in spot markets; the use of derivatives remains limited in the aggregate, but the use of FX derivatives by central banks has become increasingly important in some countries.
- Some central banks simultaneously deploy spot and forward transactions that offset each other to manage FX market liquidity, without altering their foreign currency position.
- Interventions are mostly asymmetric, with a bias towards FX purchases, in line with Adler et al (2021) but across a wider sample of countries.
- Countries that publish FXI data tend to intervene less in foreign exchange markets, indicating that lack of publication does not reflect a lesser use of FXI as a policy instrument.
- The novel classification of sterilized and unsterilized interventions shows that central banks with (de jure) flexible exchange rates sterilize their FXI operations most of the time but not always: 85 percent of FXI operations are sterilized.
- Central banks are more likely to not fully sterilize FXI when they are leaning against appreciation than when leaning against depreciation of the local currency.

### Definition and scope of FXI used in the estimates
- FXI is defined as “any active transaction that changes the central bank’s foreign-currency position regardless of intent.”
- The definition has four key elements; two highlighted in the text:
  - A focus on active transactions: changes arising from interest income on reserve assets or from changes in asset prices are not considered interventions.
  - A focus on the central bank as the main entity conducting foreign exchange interventions, excluding foreign currency operations by other public sector entities due to data limitations.
- For most countries, omission of FX transactions by other public sector institutions is likely innocuous as typically FXI is undertaken by central banks, although there may be exceptions.

### Paper organization (as stated)
- Section II explains in broad terms how the FXI estimates are constructed.
- Section III presents stylized facts based on these estimates.
- Section IV describes the dataset of publicly available FX interventions.
- Section V assesses the performance of the estimates relative to other proxies.
- Section VI discusses the construction of the classification of FXI into ‘fully sterilized’ and ‘not fully sterilized’.
- Section VII concludes.

*Sources: IMF, International Finance Statistics; IMF, Information Notice Systems; International Reserves and Foreign Currency Liquidity Template; and authors’ calculations.*

### Section II.

### Section II.

### Definition and scope of FXI
- FXI is defined as operations that affect the central bank’s foreign currency position, encompassing any exchange between foreign and domestic currency assets.
- The definition:
  - Is consistent with the portfolio balance channel.
  - Delineates clear boundaries for FXI by excluding foreign currency borrowing/lending operations whose impact on exchange rates is less clear.
  - Encompasses all transactions that meet the above criteria, irrespective of stated intent.
- The dataset reports three proxies:
  - “spot” proxy (operations in spot markets),
  - “derivative” proxy (operations with derivatives),
  - “broad” proxy (includes both spot and derivative transactions).

### Estimating spot interventions: adjustments to changes in reserves
To derive a ‘spot’ FXI estimate from the change in the stock of reserves, four adjustments are applied:
- Valuation changes
  - Use country-specific information on the composition of reserve assets by asset type and currency from the International Reserves and Foreign Currency Liquidity Template when available (now available for close to 50 percent of the countries).
  - For countries without template information, use IMF Monetary and Financial Statistics (MFS) to break down reserve assets into SDR holdings, gold, and all others.
  - For currency composition, use the International Reserves and Foreign Currency Liquidity Template when available, or country-group aggregates from COFER.
  - Valuation changes are necessary for monthly-frequency proxies because the change in the stock of reserves is affected by market valuation; quarterly estimates use transaction-based BOP data and generally do not require valuation adjustments unless BOP data are unavailable.
- Investment income
  - Estimate investment income on reserve assets using composition of assets combined with market interest rates and effective interest rates paid by issuers of reserve currencies.
  - At quarterly frequency, use investment income on reserves reported in BOP statistics where available.
  - Investment income estimates are applied to both monthly and quarterly FXI estimates.
- Other foreign currency assets and liabilities vis-à-vis nonresidents
  - Adjust for changes in other foreign assets and liabilities using IMF Standardized Report Forms of Monetary and Financial Statistics (some provided on a confidential basis).
  - Includes holdings of non-reserve foreign assets and liabilities vis-à-vis all foreign creditors, including IMF and other official creditors.
- Other foreign currency assets and liabilities vis-à-vis residents
  - Adjust for variations in foreign currency assets and liabilities vis-à-vis domestic entities using IMF Monetary and Financial Statistics (some confidential).
  - This adjustment is a key improvement relative to previous proxies in the literature.

### Why the adjustments matter (empirical implications)
- Valuation changes: changes in the stock of reserves can reflect market price or exchange rate valuation changes that affect the central bank’s foreign currency position but are not active transactions.
- Investment income: passive returns on reserves contribute positively to changes in reserves by definition and can bias coarse measures toward indicating reserve accumulation (important for large reserve holders).
- Reallocations vis-à-vis nonresidents: reallocations between reserve and non-reserve assets or foreign borrowing/repayment can change reported reserves without altering the central bank’s net foreign currency position.
- Operations vis-à-vis residents: foreign currency operations on behalf of domestic entities (e.g., general government) can change reserves with offsetting changes in domestic liabilities, leaving the net foreign currency position unchanged.
- Empirical contrasts (country-month and aggregate evidence):
  - Mean absolute value of the monthly change in reserves (in percent of GDP) is 0.18.
  - Mean absolute value of the monthly FXI estimate is 0.11.
  - Distribution of differences between FXI estimate and change in reserves (country-month level, differences expressed as percent of the absolute value of change in reserves):
    - 16 percent of observations entail differences smaller than 10 percent of the coarse proxy.
    - 32 percent of observations entail differences between 10 and 50 percent.
    - 52 percent of observations display differences greater than 50 percent of the observed value of the coarse proxy.
  - Even excluding small FXI estimates (less than 0.25 percent of GDP in absolute terms), large differences between the measures remain.

### Country examples illustrating the importance of adjustments
- Argentina: capturing FXI accurately requires accounting for large transactions vis-à-vis non-residents (including the IMF).
- Egypt, Korea, Turkey: adjusting for positions vis-à-vis residents and non-residents is key to accurate FXI measurement.
- Empirical note: the six-month moving sum is used in several decompositions (change in reserves, valuation effects, income effects, adjustments for positions vis-à-vis NR and residents).

### FXI through currency derivatives
- Derivatives (forwards, futures, forward leg of currency swaps, instruments denominated in foreign currency but settled by other means) are included in the “derivative” proxy and are reported separately.
- Practical distinction:
  - Some central banks use FX swaps without altering net FX position (often to manage FX market liquidity and smooth market functioning), e.g., Australia or New Zealand.
  - Other central banks actively use derivatives as part of FXI (affecting net FX position), e.g., Brazil, Thailand, Turkey.
- Empirical findings on derivatives:
  - Including derivatives changes the picture for some countries; derivatives sometimes offset spot operations and sometimes add to them.
  - 17-18 percent of observations exhibit non-zero differences between the broad (spot plus derivatives) and spot-only measures, indicating some use of derivatives.
  - The 17-18 percent figure likely underestimates true derivative use because reporting to the International Reserves and Foreign Currency Liquidity Template is incomplete; in absence of reported data, derivative transactions are treated as zeros.
  - For countries that frequently use FX swaps, the “broad” proxy is advisable because it combines spot and forward legs and better reflects net foreign currency position.

### Limitations of the dataset
- Valuation changes estimation is constrained by limited country-specific information on currency composition of reserves; for most countries valuation changes are estimated using aggregate currency shares.
- As foreign currency holdings grow and portfolios diversify into higher-return and less liquid assets (including equity), valuation changes may become more volatile and harder to estimate without granular data.
- Focus is on central bank transactions; operations by other public entities (central government, public banks, sovereign wealth funds, state-owned enterprises) can share characteristics with central bank interventions but are not comprehensively covered due to limited balance-sheet data at monthly or quarterly frequency and currency breakdowns.

### Stylized facts from the FXI estimates
- Broad cross-country patterns:
  - EMDEs relied significantly more on FXI than AEs before the global financial crisis (GFC); this holds even after excluding China.
  - In the post-GFC period, the extent of FXI in EMDEs has been comparable to that observed in non-reserve-issuer AEs.
  - Within AEs, patterns are dominated by economies with large financial sectors (examples: Hong Kong SAR, Singapore, Switzerland) that deploy significant FXI to cope with sizable capital flows.
  - Some AEs pursue narrow band regimes (examples include Hong Kong SAR, Macau SAR, Singapore, Denmark, Taiwan POC), which affects comparisons with EMDEs.
- Frequency and size of interventions:
  - Both EMDEs and AEs intervene frequently: interventions of absolute size of at least 0.25 percent of GDP per quarter occur nearly ¾ of the time.
  - FXI exhibits asymmetry: purchases of foreign currency are significantly more frequent than sales (visible for both EMDEs and AEs).
  - Use of derivatives is limited relative to spot interventions but more prevalent in AEs than in EMDEs; within AEs, financial centers display particularly extensive use of FXI through derivatives.
- Notable historical observation:
  - The period 2021-22: reserve changes suggested large FX sales by EMDEs, but after accounting for valuation losses on fixed income reserve assets (due to the rise of global interest rates) and other adjustments, the conclusion is that there was little to no FXI during this period.
- Interpretation caveats:
  - Apparent symmetry in FXI through derivatives may reflect unwinding of positions as they come due, or swaps used to manage liquidity without altering FX position; in such cases the broad FXI measure may better represent true intervention.

*Source: wpiea2021047-print-pdf - Section II.*

### Appendix 1.

### Appendix 1.

### Degree of exchange rate management
- Index definition: FXI_i_NER = ρ_i = (σ_FXIP_i + σ_NEER_i) / (σ_FXIP_i + σ_NEER_i) as presented in equation (1) (index varies from 0 (pure floating) to 1 (peg)). The index uses:
  - σ_FXIP_i: standard deviation of the broad FXI proxy (in percent of GDP) for the full sample period.
  - σ_NEER_i: standard deviation of the change in the nominal effective exchange rate for the full sample period.
- Sample and scope:
  - Index computed over 2000-20 (full sample period).
  - Major reserve-issuing countries (Euro area economies, Japan, the U.K. and the U.S.) are excluded.
- Key findings:
  - On average, AEs allow for slightly greater exchange rate flexibility than EMDEs, but the distributions are not very different and there is considerable variation within both groups.
  - Among AEs, economies with large financial sectors (examples in text: Hong Kong SAR, Iceland, Singapore, Switzerland) tend to display a higher degree of exchange rate management.
  - Within EMDEs, some large EMDEs display flexible regimes comparable to flexible AEs (examples in text: Mexico, South Africa, Colombia, Brazil, Turkey), while others display highly managed regimes (examples in text: Bulgaria, Saudi Arabia).

### Spot interventions versus derivatives
- Dominance and use:
  - Interventions remain dominated by transactions in spot markets.
  - Interventions in foreign currency derivatives have become more frequent, but their size remains smaller than interventions in spot markets.
- Use during stress:
  - Derivatives are used significantly during periods of stress, as shown by spikes during the Global Financial and European crises.
  - Derivatives allow central banks to preserve liquidity buffers while providing foreign currency hedging during episodes of heightened exchange rate market pressures.
- Figure guidance:
  - Figure 10 presents spot and derivatives absolute FX interventions at quarterly level aggregated across countries weighting by 3-year moving average GDP.

### Publication and transparency of FXI data
- Dataset of officially published FXI:
  - The dataset includes officially published FXI for 43 countries at quarterly frequency and for 39 countries at monthly frequency.
  - Fourteen of these countries also publish weekly data; annual-only reported FXI series are not included in the dataset.
- Data collection process:
  - Sources included central bank websites, IMF’s AREAER, hand-collection from reports (monthly/quarterly monetary and exchange rate policy reports), country-specific metadata in Appendix Table A1.2, discussions with IMF country teams, and, in some cases, direct contact with central banks.
- Definition and comparability issues:
  - Definitions of officially published FXI may not be uniform across countries and may not correspond to the paper’s transaction-based definition of FXI.
  - Treatment differences include operations done with or on behalf of the government or state-owned enterprises, treatment of export surrender requirements, and whether series encompass only FX market operations or any exchange of foreign and domestic currency assets.
  - These definitional inconsistencies complicate establishing a unique and measurable definition of FXI.

### Comparing estimates and official FXI data
- Sample selection for comparison:
  - Excluded from the comparison: countries classified as freely floating for at least 10 years in AREAER (United States, United Kingdom, Canada, Japan, Euro area, Australia, New Zealand, and Mexico).
  - Also excluded due to large discrepancies between official FXI and change in reserves: Angola, Bolivia, Nicaragua, Nigeria, and Turkey.
  - The comparison focuses on countries that are non-pure floaters and publish intervention data.
- Correlation and sign consistency:
  - Raw correlation between the estimated spot FXI and official FXI: 0.61.
  - Raw correlation between changes in reserves and official FXI: 0.54.
  - Estimated and official interventions rarely have different signs: only about 0.5 percent of country/month observations have a meaningfully different sign.
- Caveats and interpretation:
  - Analysis premised on official series encompassing all central bank transactions that alter its foreign exchange position; definitional differences cannot be ruled out.
  - Official FXI data were excluded when definitional differences between the proxy and official data were likely.
  - Selection bias: countries that publish official FXI data may be more transparent and provide more granular data, potentially influencing results.
  - Some outliers drive relatively low correlations, where official FXI is reported as zero but proxies assign non-zero values, possibly reflecting narrower official definitions.
- Methodological notes:
  - Country-by-country regressions (described in Appendix Table A1.3) estimate official FXI against either the change in reserves or the spot proxy, both in percent of GDP, over 2000-19, with expectations that α_i = 0 and β_i = 1 under consistency up to measurement error.
  - Users are advised to treat data for excluded countries with caution as proxies and official FXI series may correspond to different FXI definitions.

### Summary statistics and specific numeric points
- Index range: 0 (pure floating) to 1 (peg).
- Period for index computation: 2000-20.
- Officially published FXI coverage in dataset:
  - 43 countries at quarterly frequency.
  - 39 countries at monthly frequency.
  - 14 countries publishing weekly data (subset of the 39 monthly).
- Correlations:
  - Spot estimate vs official FXI: 0.61.
  - Change in reserves vs official FXI: 0.54.
- Frequency of sign mismatch between estimated and official interventions: about 0.5 percent of country/month observations.

_Italic source: wpiea2021047-print-pdf - Appendix 1._

### 0.3 percent of obs

### wpiea2021047-print-pdf - 0.3 percent of obs

### Methodology and validation of FXI proxies
- Regression specification: x*_{i,t} = α_i + β x_{i,t} + ε_{i,t} where x*_{i,t} is official FXI data, x_{i,t} is the FXI proxy, both expressed in percent of GDP, and ε_{i,t} ~ N(0, σ_ε).  
- Interpretation under classical measurement error: α_i ≈ 0, β ≈ 1; if no measurement error then σ_ε ≈ 0.  
- Estimation approach: panel fixed effects estimator for changes in reserves and for the spot estimate; comparisons performed at monthly and quarterly frequency.  
- Comparative performance (Full Sample 2000-19, Table 1):  
  - Monthly regressions (columns 1-3): Official Data coefficients: Change in Reserves 0.927*** (0.054); Spot Estimate 0.940*** (0.031); BOP Flow 0.865*** (0.048).  
  - Quarterly regressions (columns 4-5): Change in Reserves 0.892*** (0.052); Spot Estimate 0.918*** (0.048).  
  - Constants (weighted average country constant): 0.001***, 0.000***, 0.002***, 0.003***, 0.001*** (standard errors all reported as (0.000)).  
  - Observations: 4177 (monthly columns), 1503 (monthly BOP Flow and quarterly columns).  
  - # Countries: 23 (monthly change in reserves and spot), 26 (BOP Flow and quarterly).  
  - R-squared: 0.294 (monthly Change in Reserves), 0.391 (monthly Spot Estimate), 0.500 (monthly BOP Flow), 0.462 (quarterly Change in Reserves), 0.626 (quarterly Spot Estimate).  
  - P-value (β = 1): 0.193, 0.067, 0.009, 0.048, 0.101 (columns as above).  
- Country-by-country median β (running equation (2) country-by-country): median β goes from 0.77 (changes in reserves) to 0.83 (spot) and 0.83 (broad proxy) (see Appendix Table A1.3).  
- Recent-sample advantage: restricting to 2010-19 increases the advantage of the spot estimate (larger differences in β and R-squared), reflecting larger valuation changes with growing stocks of reserves and availability of adjustments after 2002.

### Horse-race regressions and decomposition of spot estimate
- Horse-race specification: x*_{i,t} = γ_1 x_{1,i,t} + γ_2 x_{2,i,t} + ξ_{i,t} where x* is official FXI, x_1 is change in reserves, x_2 is spot estimate (all in percent of GDP).  
- Key horse-race results (Table 2, Full Sample 2000-19): monthly and quarterly comparisons show superiority of spot estimate.  
  - Monthly: Change in reserves 0.317*** (0.080) in column (1); when spot estimate added (column 2) Change in reserves 0.132** (0.056) and Spot Estimate 0.316*** (0.059). R-squared rises from 0.294 to 0.420. Observations 4177; # Countries 23.  
  - Quarterly: Change in reserves 0.518*** (0.095) in column (3); when BOP flow added (column 4) Change in reserves 0.150** (0.070) and BOP flow 0.431** (0.157); when spot estimate also added (column 5) Spot Estimate 0.541*** (0.089) and Change in reserves 0.161** (0.077). R-squared rises to 0.649 in column (5). Observations 1503; # Countries 26.  
  - Interpretation: Spot estimate adds significant information beyond changes in reserves; spot often dominates BOP reserve flow when included together.  
- Decomposing the spot estimate (Table 3 and related tables): incremental adjustments to changes in reserves evaluated via intermediate estimates. Main adjustments and their incremental contributions (monthly full sample):  
  - Adjustment: Valuation and income effects — intermediate coefficient sometimes not significant at 10% (but significant at 15% in some specifications) and increases R-squared modestly (column 2). Example coefficient reported as 0.217 (standard error 0.137) in one specification and negative coefficients in others when collinearity present.  
  - Adjustment: CB position relative to IMF — large positive and highly significant contribution (e.g., coefficient 0.447*** (0.074) in column 3) and material increase in R-squared.  
  - Adjustment: Position relative to other non-residents — on its own shows little added value (insignificant coefficient in column 4), but interacts with other adjustments.  
  - Adjustment: Position relative to residents — largest impact when included; coefficient 0.425*** (0.047) in column 5 and major rise in Within R-squared to 0.464.  
  - Across specifications the coefficient on Change in Reserves becomes insignificant in columns (2)-(5), indicating the spot (intermediate or final) estimates subsume the information in change in reserves.  
- Quarterly and recent-sample horse races (Tables A1.5–A1.7) show similar qualitative findings and larger impacts for some adjustments in quarterly or 2010-19 sub-samples (e.g., CB position relative to IMF consistently highly significant).

### Sterilization: classification approaches and empirical findings
- Objective: provide binary classification of FXI estimates into ‘fully sterilized’ and ‘not fully sterilized’.  
- First step: de jure exchange rate regime — interventions under a fixed exchange rate regime are classified as ‘not fully sterilized’. Peg classifications include no legal tender, currency board, conventional peg, pegged exchange rate within horizontal band, crawling peg, crawl-like arrangement, and stabilized arrangements. Free floating, floating, and other managed arrangements classified as non-pegs.  
- Two alternative approaches for non-pegged regimes: contemporaneous behavior of (i) monetary policy rate (interest rate approach) or (ii) monetary base (monetary base approach).  
  - Interest rate approach rule: an FX purchase (sale) is ‘fully sterilized’ when the monetary policy rate remains unchanged or increases (decreases) during the same period. Only changes in policy rates greater or equal than 25 basis points in absolute value are considered. Observations not fulfilling criterion are ‘not fully sterilized’.  
  - Monetary base approach rule: an FX purchase (sale) is ‘fully sterilized’ when the monetary base remains unchanged or decreases (increases) during the same period.  
- Empirical classification (Table 4): cross-tabulation of Interest Rate Approach vs Monetary Base Approach for FXI observations larger than 0.25 percent of GDP in absolute terms for countries with exchange rate regimes other than pegs:  
  - Fully Sterilized under Monetary Base & Interest Rate: 36%  
  - Fully Sterilized under Monetary Base & Not Fully Sterilized under Interest Rate: 6%  
  - Not Fully Sterilized under Monetary Base & Fully Sterilized under Interest Rate: 49%  
  - Not Fully Sterilized under both: 9%  
  - Row/column totals: Interest Rate Approach All = 84% Fully Sterilized, 16% Not Fully Sterilized, All = 100%; Monetary Base Approach All = 42% Fully Sterilized, 58% Not Fully Sterilized, All = 100%.  
- Interpretation and dataset choice: the interest rate approach classifies 84 percent of FXI operations conducted under non-pegged regimes as fully sterilized and 16 percent as not fully sterilized; share of sterilized operations reaches 90 percent for AE and 83 percent for EMDEs (not shown). The monetary base approach yields a lower share of full sterilization (42 percent). Because monetary base can move for demand/seasonal reasons without policy rate changes, the dataset follows the interest rate approach.  
- Distributional findings (Figure 14): large interventions are commonly not fully sterilized (fatter tails for not-fully sterilized distribution). For floating-regime countries only, the two distributions are more similar but not-fully sterilized FXI distribution is tilted right, indicating central banks are less likely to sterilize when leaning against appreciation than when leaning against depreciation; formal test indicates difference is statistically significant.

### Key empirical magnitudes and robustness notes
- Full sample (2000-19) and recent sample (2010-19) comparisons: spot estimate consistently shows coefficients closer to 1 and higher R-squared relative to change-in-reserves and BOP flows; advantage increases in 2010-19 sample.  
- R-squared examples: monthly Spot Estimate R-squared 0.391 (full sample) and 0.318 (2010-19); quarterly Spot Estimate R-squared 0.626 (full sample) and 0.570 (2010-19).  
- Observations and coverage: monthly observations 4177 (full sample); quarterly observations 1503 (some specifications) and 1503/926/2538 depending on sample and specification (see tables). # Countries vary by specification (23, 26).  
- Diagnostic notes: adjustments for valuation and investment income matter more as stocks of reserves grow and valuation effects increase; availability of central bank FX position adjustments typically only after 2002 improves spot estimate accuracy in recent years.  
- Robustness: alternative regression ordering (regressing official data on proxies) does not overturn conclusions, though variance differences imply smaller beta coefficients under that alternative.

### Conclusions (paper-level)
- The paper constructs a new database of official published FXI data and newly constructed estimates of FXI for spot and derivative markets at monthly and quarterly frequencies.  
- The dataset focuses on any transaction that alters the central bank’s foreign currency position, providing comprehensive and comparable data across many countries and time for cross-country macroeconomic analysis.  
- The dataset distinguishes between sterilized and not sterilized FXI using a binary classification (dataset follows the interest rate approach for classification).

*Source: authors’ estimations as presented in wpiea2021047-print-pdf.*

### References

### wpiea2021047-print-pdf - References and Online Appendix Methodology

### Major themes in References
- Comprehensive literature on foreign exchange intervention effectiveness, channels, and measurement covering studies by Adler, Dominguez, Fratzscher, Gagnon, Sarno & Taylor, Fanelli & Straub, Gabaix & Maggiori, and others.
- Empirical and theoretical contributions cited include:
  - Country-level empirical analyses (e.g., Brazil, Israel, Latin America, 33-country study).
  - Surveys and reviews of intervention effectiveness.
  - Studies on reserve management and international liquidity.
- References list contains many working papers, journal articles, central bank discussion papers, and IMF departmental papers spanning multiple years (examples: NBER Working Paper No. 21427; IMF Departmental Paper No. 2020/002; The Review of Economic Studies 88 (6) 2021: 2857-2885).

### Online Appendix 1 — Conceptual framework for FXI proxies
- Definition focus:
  - FXI captures central bank transactions that alter its net foreign currency position (NFCP).
- Balance-sheet representation (variables described):
  - RES (foreign currency reserves); OFA (other foreign assets); FCDA (foreign currency domestic assets); LCDA (Local-Currency Domestic Assets); FL (foreign liabilities); FCDL (foreign currency domestic liabilities); LCDL (domestic currency domestic liabilities); EQ (equity/net worth).
- Net positions decomposition and key identity:
  - NFCP changes of interest exclude equity valuation effects; proxies isolate changes arising from transactions that have counterparts in net local-currency position (NLCP).
- Practical implication:
  - FXI cannot be proxied solely by changes in reserves (푑푑푅푅푅푅푆푆); must adjust for:
    - Reallocation between reserve and non-reserve foreign assets.
    - Borrowing/repayment of foreign loans affecting reserve levels without changing net positions.
    - Central bank operations on behalf of other domestic entities creating corresponding foreign currency liabilities.
    - Foreign-currency deposits by banks that create reserve holdings with matching liabilities.

### Estimating FXI — data sources and approach
- Data sources:
  - Reserve assets: International Financial Statistics (IFS).
  - Non-reserve foreign assets and liabilities and foreign-currency position vis-à-vis residents: IMF Monetary and Financial Statistics (MFS), some confidential.
  - Asset composition: International Reserves and Foreign Currency Liquidity Template (IRFCLT).
  - Currency composition: COFER and IRFCLT.
- Key estimation identity for FXI:
  - FXI estimate constructed from observed change in NFCP minus estimated investment income and valuation changes (investment income and valuation changes primarily driven by reserve assets).
- Asset composition and weights:
  - Asset-type categories: (i) Currency and Deposits; (ii) Securities; (iii) Position at the IMF; (iv) SDR holdings; (v) Gold; (vi) Other foreign currency assets.
  - Currency weights consider five major currencies: USD, Euro, Yen, Pound, and the SDR.
  - Country-specific currency weights taken from Reserve Template when available; otherwise group averages from COFER are used.
  - Asset-type weights constructed via hierarchy:
    - (i) country-specific IRFCLT when available;
    - (ii) splice backwards using median weights observed for other countries if only recent periods available;
    - (iii) MFS for gold and SDR plus median IRFCLT breakdown for other assets if no IRFCLT;
    - (iv) median of weights observed for all IRFCLT countries if no IRFCLT or MFS information.
- Coverage notes:
  - Asset-structure data available for about 50 percent of countries in sample from IRFCLT.
  - For most AEs and some EMDEs ample information exists since early 2000s; smaller EMDEs and LICs have limited data.

### Investment income and valuation change estimation
- Investment income on reserves decomposed by currency c and asset type a using shares w_ac and coupon/interest rates i_ac.
- Interest rate assumptions (Online Appendix 1 Table 2):
  - Currency & Deposits: short-term market rates (e.g., 3-month interbank rates).
  - Securities: effective rate (synthetic portfolio) approximated by a weighted combination of 10-year and 2-year bonds:
    - synthetic effective rate formula uses weights 0.7 for 10-year series and 0.3 for 2-year series:
      - 횤횤̿푡푡푐푐 = (0.7)*[ (1/10) Σ_{l=1}^{10} i_{t-l,c,10y} ] + (0.3)*[ (1/2) Σ_{l=1}^{2} i_{t-l,c,2y} ]
- Asset price / valuation assumptions (Online Appendix 1 Table 3):
  - Currency & Deposits, SDR, IMF position: nominal value -> valuation changes arise only from exchange rate movements.
  - Securities: market price estimated from weighted average of 2- and 10-year government bond prices acquired over prior 2 and 10 years respectively.
  - Gold valued at end-of-period market rates.
  - Exchange rates: end-of-period nominal rates vis-à-vis US dollar from IFS.
- Use of yield curve information to estimate bond price changes and valuation effects.

### Frequency-specific adjustments for FXI proxies
- Quarterly frequency:
  - Balance-of-payments (BOP) statistics report changes in reserves on a transaction basis (flows) and thus require adjustment mainly for investment income flows.
- Monthly frequency:
  - Monthly proxies rely on changes in stocks (not transaction flows) and therefore require adjustments for both investment income and valuation changes.
- Online Appendix 1 Tables 4 and 5 provide country-by-period details on which basis (flows vs stocks) and which adjustments (reported income, estimated income, valuation changes) are applied.

### Coverage tables and categorical adjustment codes
- Online Appendix 1 Table 1 lists country coverage (examples):
  - Denmark (IFS code 128), Norway (142), Sweden (144), Switzerland (146), Canada (156), ... through many country entries up to Macao SAR (546).
- Online Appendix 1 Table 4 and Table 5:
  - Provide per-country, per-period categorical codes indicating basis for valuation and income adjustments at quarterly and monthly frequencies, using categories labelled 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 with definitions such as:
    - 1: Based on BOP changes in reserves (flows).
    - 2: Based on change in reserve stocks — Unadjusted.
    - 3: Adjusted for estimated reserve income and valuation changes, based on country-specific currency and asset-type weights.
    - 6: Adjusted for reported reserve income.
    - 7, 8, 9, 10: Other hybrid or extended-weight adjustment categories (see table legend).
- Online Appendix 1 Table 6 (Ad-hoc adjustments):
  - Lists manual or proxy-not-reported adjustments by country, period, and comments (examples include Argentina 2017-2022 manual adjustment due to large change from accounting standards; Sri Lanka All — source replaced: use MFS central bank gross reserves instead of IFS because IFS includes government reserves; Euro Area All — proxy not reported: major reserve-currency economies excluded).

### Foreign exchange derivatives and swap considerations
- FX derivatives in IRFCLT include aggregate short and long positions in forwards and futures, forward leg of currency swaps, and other instruments; notional amounts may not equal balance-sheet market values.
- Notional changes capture new FXI operations via derivatives (e.g., sale of FX forward) but also capture unwinding when contracts come due; unwinding normally mirrored elsewhere in balance sheet.
- FX swaps used for liquidity management may not alter NFCP; spot and forward legs captured separately in spot and derivative FXI proxies. For frequent FX-swap users, a combined spot+derivative FXI measure provides a more accurate read of FXI operations.
- Central bank swap lines generally provide foreign currency liquidity without altering net foreign currency positions (contingent credit lines until drawn); when drawn, increase both foreign assets and liabilities but do not change NFCP.

### Online Appendix 2 — Summary metadata for officially published FXI
- Country-level metadata examples (fields: Country Name; Coverage; Agency; Types of operations; Frequency; Reported format; Link; Notes):
  - Angola: Coverage 2000M1 – 2020M9; Agency Central Bank; Types Spot; Frequency Monthly; Reported format Millions of U.S. Dollars and Euros.
  - Argentina: Coverage 2003M1 – 2020M9; Agency Central Bank; Types Spot; Frequency Daily, Monthly; Reported format Millions of U.S. Dollars.
  - Australia: Coverage 1989M1 – 2020M6; Agency Central Bank; Types Spot; Frequency Daily; Reported format Millions of Local Currency.
  - Bangladesh: Coverage 2005Q1 – 2020Q2; Agency Central Bank; Types Spot; Frequency Quarterly; Reported format Millions of U.S. Dollars. Note: Partial data via various central bank reports.
  - Brazil: Coverage 2000M1 – 2020M9; Agency Central Bank; Types Spot, forward and forward like (Swap), and other derivatives (Options); Frequency Monthly, daily (from 2009); Reported format Millions of U.S. Dollars.
  - United States: Coverage 1973M3 - 2020M6; Agency Central Bank; Types Spot; Frequency Daily from 1973M3 - 2011Q1, Quarterly from 2011Q2-2020Q2; Reported format Millions of U.S. Dollars.
  - United Kingdom: Coverage 2010M6 – 2020M9; Agency Government; Types Spot; Frequency Monthly; Reported format Millions of Local Currency.
  - (Many other country metadata entries follow a similar template covering sample periods, agencies, types, frequency, formats, and links.)
- Frequency notation examples preserved exactly as in source: e.g., 2000M1 – 2020M9; 2005Q1 – 2020Q2; 1989M1 – 2020M6; 1973M3 - 2020M6.

*Source: wpiea2021047-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021047-print-pdf.pdf_