## wp1711

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### Introduction and context
- Unconventional monetary policies in advanced economies and volatile capital flows have brought foreign exchange intervention (FXI) back to the forefront of the policy debate.
- Intervention objectives cited:
  - smoothing adjustment,
  - avoiding disorderly market conditions,
  - defending against perceived overshooting.
- Sterilized FXI channels and effectiveness:
  - Sterilized intervention can operate through signaling and coordination channels and when assets are imperfect substitutes.
  - Where reserve-currency assets are near-perfect substitutes for domestic assets, sterilized intervention should be less effective; imperfect asset substitutability or restricted capital mobility can make FXI more effective.
- Literature evolution:
  - Older studies on developed economies: limited evidence of sustained FXI effects except very short term or coordinated interventions.
  - More recent cross-country and emerging market studies: stronger links between spot FXI and exchange rates or volatility (findings not universal).
  - Derivatives-based FXI used in Brazil, Colombia, India, Indonesia, Mexico, South Africa, Thailand; empirical work suggests derivatives-based interventions can be effective.
- Research gap:
  - No prior study directly compares effectiveness of spot and non-spot FXI in a common empirical framework; this paper fills that gap using Brazil as a case.

### Empirical approach and data
- Aim:
  - Compare the Banco Central do Brasil’s (BCB) FXI in spot markets to its intervention using non-deliverable futures contracts (Reverse FX swaps).
- Rationale for Brazil:
  - Long history of futures-based interventions alongside spot interventions.
  - Detailed BCB data on both modes and on instruments for identifying distinct reaction functions.
  - Non-deliverable futures contracts settle in local currency, enabling assessment of convertibility risk effects.
- Estimation method:
  - Instrumental variables regressions using daily data to explain changes in the R$/US$ exchange rate and its implied volatility.
  - Control for conditional heteroscedasticity using the continuously updated GMM estimator (CUE, Hansen et al, 1996).
- Sample:
  - Baseline sample period: 2008‒13; experiments with samples starting as early as 2002.
  - Baseline regression sample period specified: September 3rd 2008 to August 21st, 2013.
- Key explanatory variables (defined exactly as in source):
  - Spot intervention — in billions of U.S. dollars.
  - Futures intervention — in billions of U.S. dollar equivalent of notional principal.
  - Both defined such that positive values imply the BCB takes a long dollar position.
- Important institutional facts:
  - Brazilian FX Swaps and Reverse FX Swaps typically auctioned; settle in local currency (no notional principal exchange); resemble non-deliverable futures.
  - Instrument payoff: at maturity BCB pays observed exchange rate variation plus ex-ante Cupom Cambial and receives ex-ante SELIC rate.
  - Auctions do not directly impact BCB foreign exchange reserves but introduce convertibility risk for counterparties.

### Main empirical findings
- Spot and futures intervention effects on exchange rate level:
  - US$1 billion in net spot market intervention changes the real/dollar exchange rate by about 1 percent.
  - Auctions of non-deliverable futures worth US$1 billion in notional principal change the real/dollar exchange rate by 0.7 percent.
  - Statistical interpretation: the impact of US$1 billion in net spot market intervention (about 1 percent) is statistically indistinguishable from the 0.7 percent change achieved through auctions of non-deliverable futures worth US$1 billion in notional principal.
  - Theoretical concordance: consistent with Eaton and Turnovsky (1984) when convertibility risk is absent.
- Spot and futures intervention effects on implied volatility:
  - Both Spot and Futures intervention enter with positive and significant coefficients when included individually.
  - Example coefficients:
    - Spot intervention (Table 5a, Regression 1): 5.887*** (1.85).
    - Spot intervention (Table A4, Regression 1): 3.793** (1.63).
    - Futures intervention (Table A4, Regression 2–4): 3.647** (1.54); 2.502** (1.21) in alternate specifications.
  - Joint inclusion: coefficients fall but remain in a close range between 2.3 and 3.
  - Interpreted elasticity: US$1 billion in short dollar spot intervention or short dollar futures intervention reduces implied volatility in the real/dollar exchange rate by some 2.5 percent (paper interpretation).
- Symmetry and asymmetry:
  - Spot intervention broadly symmetric in impact (spot interaction coefficient not statistically significant).
  - Futures interventions more effective when BCB takes short dollar positions (Swap positive * Futures intervention coefficient: -0.936 (SE 0.38), negative and statistically significant).

### Reaction functions, instrument choice, and interpretation
- Distinct reaction functions identified:
  - Spot intervention:
    - Reacts more to short-term (daily) exchange rate movements and expected depreciation.
    - Responds to actual outflows / lagged trend FX transactions (spot coefficient on trend FX transactions: 0.000***).
    - Responds to changes in monetary policy rate (policy rate change: spot coefficient 0.616***).
    - Used to offset exchange rate effects of tighter/looser monetary policy.
  - Futures intervention:
    - Responds more to medium-run FX trend (one-year moving average) — used to smooth trend movements.
    - Responds to changes in country risk (5Y sovereign CDS returns) and global risk aversion (VIX) — futures coefficient on 5Y sovereign CDS return, lagged: -0.016*** in reaction function; VIX percent change: futures coefficient -0.004**.
    - Used more to react to changes in global risk aversion and to smooth trend exchange rate movements.
- Market microstructure and balance-sheet implications:
  - Brazil’s derivatives markets around four times larger than its spot market.
  - Derivatives markets appear to lead spot market in price discovery.
  - Auctions of FX swaps do not directly impact BCB’s foreign exchange reserves (advantage), but introduce convertibility risk for counterparties.

### Convertibility risk and effectiveness of futures intervention
- Convertibility risk concept:
  - Futures-like instruments settle in local currency; convertibility risk can make hedging incomplete and weaken forward market intervention.
- Empirical testing:
  - Convertibility Risk dummy = 1 on days when the three-month onshore dollar interest rate (cupom cambial) was 1.5 standard deviations above its sample mean.
  - Interaction results:
    - Interaction of Convertibility Risk with Futures intervention: coefficients -2.179 (SE 1.29), -2.269 (SE 1.34) — highly significant and negative.
    - Combined coefficient of Futures intervention plus interaction turns negative, indicating futures intervention can “move the exchange rate with the wind” when convertibility risk is high.
  - Robustness: results robust to alternative thresholds (2 instead of 1 standard deviation) and to using the spread between the cupom cambial and three-month US$ Libor.
- Sample extension to 2002:
  - Main findings persist with somewhat lower coefficients: "0.83‒0.92 for spot intervention and 0.55‒0.58 for futures intervention."
  - Evidence suggests futures intervention is ineffective in the presence of non-negligible convertibility risk in extended sample.

### Quantitative diagnostics, tests, and selected statistics
- Baseline sample size: N = 1,100.
- Selected first-stage and instrument diagnostics:
  - F test (spot column): 12.6 ( 0.00).
  - F test (futures column): 8.6 ( 0.00).
  - Kleibergen-Paap rk Wald F (spot): 12.6.
  - Kleibergen-Paap rk Wald F (futures): 8.6.
  - Sanderson-Windmeijer F test (spot): 7.4 ( 0.00).
  - Sanderson-Windmeijer F test (futures): 13.1 ( 0.00).
  - Kleibergen-Paap rk LM (spot): 71.1 ( 0.00).
  - Kleibergen-Paap rk LM (futures): 47.3 ( 0.00).
- Selected second-stage coefficient examples (Table 2, dependent variable: percent daily change in R$/US$):
  - Spot intervention (selected columns): Column 1: 1.026** (0.49); Column 2: 1.009** (0.49); Column 3: 1.294*** (0.43); Column 4: 0.748* (0.42); Column 5: 0.248 (0.21).
  - Futures intervention (selected columns): Column 1: 0.973** (0.39); Column 2: 0.729** (0.37); Column 3: 0.876** (0.38); Column 4: 0.680* (0.37); Column 5: -0.127** (0.06).
  - Lagged daily pct change in FX (example columns): Column 1: -0.053 (0.06); Column 2: -0.121* (0.07); Column 3: -0.141** (0.07).
  - VIX, percent change (example columns): Column 1: 0.012** (0.01); Column 2: 0.016*** (0.01); Column 3: 0.012** (0.01).
  - 5Y sovereign CDS return, lagged (example columns): Column 1: 0.112*** (0.02); Column 2: 0.118*** (0.02); Column 3: 0.111*** (0.02).
- Goodness-of-fit and specification tests:
  - R2 by column: 0.23, 0.11, 0.15, 0.23, 0.14, 0.18, 0.28.
  - Hansen’s J stat examples: Column 2: 8.4 (0.21); Column 3: 8.8 (0.19); Column 4: 5.2 (0.40).
  - C test for endogeneity: Columns 1–3: 15.0 (0.04); Column 4: 23.4 (0.00); Column 5: 21.4 (0.00).
  - Wald statistic (test of equality of spot and futures coefficients): 0.17 (0.67); 0.01 (0.92) in reported examples (cannot reject equality in main tests).
- Proxy validation:
  - Correlation of constructed daily spot proxy with BCB monthly spot data: 97 percent in baseline sample; 86 percent in extended sample.

### Robustness checks and extensions
- Additional instruments and window variation:
  - Including additional instruments and varying the window for short-term trend variables does not change significance or magnitudes of baseline regressors.
  - Ordered Probit estimates (columns 5 and 6 of Table 1) reduce importance of daily change in exchange rate and FX volatility in spot regressions; overall signs and significance of key variables preserved.
- Dynamic specifications:
  - First five lags included: only first lag of Futures intervention and first two lags of Spot intervention significant.
- Robustness across alternative specifications (Table 4):
  - Adding macro announcement surprises, Citi EM and Citi LATAM Economic Surprise Indexes, additional lags, actual interest rate differentials — findings remain unchanged.
  - Spot and futures based interventions have very similar impacts across robustness checks.
- Volatility regressions robustness:
  - Results robust to extending sample back to 2003, adding macro surprise indices, adding lags, and alternative estimator choices (CUE, OLS, 2SLS).

### Policy implications and recommendations
- Toolkit implications:
  - A broader toolkit including both spot and derivatives-based intervention has advantages; derivatives interventions can be no less effective than spot interventions absent convertibility risk.
- Instrument choice guidance:
  - Use spot intervention when:
    - Responding to price-and-flow pressures contemporaneously,
    - Offsetting exchange rate effects of monetary policy changes,
    - Dealing with observable outflows.
  - Use futures intervention when:
    - Smoothing medium-run trend movements,
    - Reacting to changes in country/global risk perceptions,
    - Providing hedging in cases where private agents face depreciation downside risk.
- Convertibility risk considerations:
  - Where onshore market convertibility risk is negligible and futures maturities are sufficiently long, futures intervention can be as effective as spot intervention at affecting levels and volatility of the exchange rate.
  - Episodes of non-negligible convertibility risk are rare in the sample but when present can render futures intervention ineffective or counterproductive.
- Asymmetry exploitation:
  - Futures auctions that involve short USD positions can be particularly powerful when providing hedging to private agents exposed to depreciation risk.

*Source: IMF working paper content (wp1711) excerpt provided.*

### 1. Spot and Brazilian (Reverse) Futures based intervention in Billions of US$ or Notional

### 1. Spot and Brazilian (Reverse) Futures based intervention in Billions of US$ or Notional

### I. Introduction and context
- Unconventional monetary policies in advanced economies and volatile capital flows have brought foreign exchange intervention (FXI) back to the forefront of the policy debate.
- After the global financial crisis, policymakers argued that unconventional policies in developed economies were causing lending booms in developing economies and threatened their competitiveness.
- Net capital flows to emerging markets have slowed and turned negative in some instances amid uncertainty about the pace of policy tightening in major advanced economies (IMF, 2016).
- Intervention has been an important part of the policy response, aimed at smoothing the adjustment, avoiding disorderly market conditions or defending against a perceived overshooting.
- Sterilized FXI can drive exchange rates through signaling and coordination channels as well as when frictions cause agents not to be indifferent between holding assets denominated in different currencies (Mussa, 1981; Vitale, 1999; Taylor, 1995; Taylor and Sarno, 2001; Branson and Henderson, 1985; Kumhoff, 2010; Gabaix and Maggiori, 2015).
- Where reserve currency assets are near-perfect substitutes for domestic assets, sterilized intervention should be less effective because sterilized changes in reserves will be offset by an equal and opposite flow of private money; imperfect asset substitutability or restricted capital mobility can make FXI more effective (Bayoumi and Saborowski, 2014; Bayoumi et al, 2015).
- The literature evolution:
  - Earlier studies on developed economies provided limited evidence of sustained FXI effects except in the very short term or when interventions were coordinated between major central banks.
  - More recent cross-country and emerging market studies (Adler et al 2015; Blanchard et al 2015; Fratzscher et al, 2015; Scalia, 2008; Broto, 2013; Fry and Wanaguru, 2013) find stronger links between spot FXI and exchange rates or volatility, though findings are not universal (Disyatat and Galati, 2007; Broto, 2013; Catalan-Herrera, 2016).
- Derivatives-based FXI has been used in a number of countries (e.g., Brazil, Colombia, India, Indonesia, Mexico, South Africa, Thailand) as markets developed; empirical work suggests derivatives-based intervention can be effective (Kohlscheen and Andrade, 2014; Chamon et al, 2015; Keefe and Rengifo, 2015).
- No prior study directly compares the effectiveness of spot and non-spot FXI in a common empirical framework.

### Empirical approach and data
- Aim: compare the Brazilian Central Bank’s (BCB) FXI in spot markets to its intervention using non-deliverable futures contracts (commonly referred to as FX swaps and Reverse FX swaps).
- Rationale for Brazil as a case:
  - BCB has used futures-based interventions over a long period and often alongside spot interventions, reducing learning bias.
  - BCB provides detailed data on both modes of intervention and on instruments key for identifying distinct reaction functions.
  - The non-deliverable futures contracts settle in local currency, allowing assessment of whether effectiveness depends on the absence of convertibility risk.
- Estimation method:
  - Instrumental variables regressions using daily data to explain changes in the R$-US$ exchange rate and its implied volatility.
  - Control for conditional heteroscedasticity using the continuously updated GMM estimator (CUE, Hansen et al, 1996).
- Sample:
  - Baseline sample period: 2008‒13 (reflects data availability).
  - Experiments with samples starting as early as 2002 by limiting the set of instruments included in the baseline specification.
- Key explanatory variables (defined exactly as in source):
  - Spot intervention—in billions of U.S. dollars.
  - Futures intervention—in billions of U.S. dollar equivalent of notional principal.
  - Both variables are defined such that positive values imply that the BCB takes a long dollar position.

### Main empirical findings
- Both spot and futures intervention have a statistically significant link to changes in the real/dollar exchange rate and enter regressions with the expected signs.
- Point estimates of impact:
  - US$1 billion in net spot market intervention changes the real/dollar exchange rate by about 1 percent.
  - Auctions of non-deliverable futures worth US$1 billion in notional principal change the real/dollar exchange rate by 0.7 percent.
- Statistical interpretation:
  - The impact of US$1 billion in net spot market intervention (about 1 percent) is statistically indistinguishable from the 0.7 percent change achieved through auctions of non-deliverable futures worth US$1 billion in notional principal.
- Theoretical concordance:
  - Result consistent with Eaton and Turnovsky (1984) who show spot and forward market intervention have equivalent effects on the spot exchange rate in the absence of convertibility risk.
- Role of convertibility risk:
  - When convertibility risk rises, hedging local positions through futures contracts becomes incomplete, giving rise to a wedge between covered foreign and domestic interest rates and implying forward market intervention may no longer equally impact the spot rate.
  - In the baseline sample, convertibility risk appears too limited to generate a significant wedge between the relative effectiveness of spot and futures market intervention, though other factors (differences in relative market liquidity, financial intermediary capital constraints, institutional frictions, and global shocks) could generate deviations from covered interest rate parity.
  - In an extended sample, there is some evidence suggesting futures intervention is ineffective in the presence of non-negligible convertibility risk, in line with the contingent local currency claim character of the underlying instrument.

### Additional outcomes and robustness
- The same qualitative results hold when using the change in implied exchange rate volatility as the dependent variable: both modes of intervention are statistically significant and enter with the expected coefficient sign.
- Definitions, estimation methods, and robustness checks include:
  - Use of instrumental variables regressions and CUE to control for conditional heteroscedasticity.
  - Baseline and extended samples to assess sensitivity to sample period and convertibility risk.

*Source: IMF Working Paper "1. Spot and Brazilian (Reverse) Futures based intervention in Billions of US$ or Notional" (extracted content).*

### 2.5 percent. We also distinguish interventions in which the BCB takes a short dollar position

### wp1711 - 2.5 percent. We also distinguish interventions in which the BCB takes a short dollar position

### Key empirical question and summary conclusion
- The paper compares the relative effectiveness of spot and derivatives (futures-like) foreign exchange intervention (FXI) by the Banco Central do Brasil (BCB) within a common empirical framework.
- Tentative evidence:
  - Auctions of futures in which the BCB takes a long dollar position are less effective in depreciating the exchange rate than spot dollar purchases.
  - Futures intervention is ineffective in the presence of non-negligible convertibility risk, consistent with the contingent local currency claim nature of the instrument.
- The BCB uses spot FXI more in reaction to daily exchange rate movements and to resist capital flow pressures; it uses futures-based intervention more to smooth trend exchange rate movements and to react to changes in global risk aversion.
- Spot intervention tends to offset the exchange rate effects of tighter/looser monetary policy more than derivatives-based intervention.

### Data, instruments, and empirical approach
- Sample period for baseline regression: September 3rd 2008 to August 21st, 2013.
- Spot intervention definition: spot dollar purchases minus spot dollar sales in billions of U.S. dollars.
- Futures intervention definition: notional principal entailed in auctions of Reverse FX swaps minus that entailed in announcements of FX swap auctions in billions of U.S. dollars (auctions for roll-over excluded).
- Spot and futures intervention signs: positive values imply the BCB takes a long dollar position; negative values imply the BCB takes a short dollar position.
- Important institutional facts:
  - Brazilian FX Swaps and Reverse FX Swaps typically auctioned; settle in local currency (no notional principal exchange); resemble non-deliverable futures but settle in local currency.
  - Instrument payoff: at maturity BCB pays observed exchange rate variation plus ex-ante Cupom Cambial and receives ex-ante SELIC rate; BCB makes a positive return if observed exchange rate depreciation falls short of initial expectations and a loss otherwise.
  - Auctions do not directly impact BCB foreign exchange reserves but introduce convertibility risk for counterparties because settlement is in local currency.
- Identification strategy:
  - Main estimation uses continuously updated generalized method of moments estimator (CUE) to address endogeneity of intervention terms; robustness checks use 2SLS.
  - Instruments (Z_t) include: lagged trend exchange rate volatility; lagged exchange rate deviations from trend; lagged one year moving average of the exchange rate; change in the monetary policy rate; trend spot and futures intervention; lagged trend FX flows.
  - Control vector (X_t) benchmark includes: daily percent change in Thomson Reuters Core Commodity (CRB) index (current and lagged), daily percent change in VIX (current and lagged), lagged average change in expected exchange rate depreciation over coming 3 months, lagged daily percent change in five year sovereign CDS spread for Brazil.
- Proxy construction:
  - Daily spot intervention extended back using composite of external sector operations when monthly data indicate non-zero intervention; monthly aggregation of proxy correlates 97 percent with monthly BCB spot data in baseline sample and 86 percent in extended sample.
  - Trend variables reflect short-term trends defined over a two-week window.

### Empirical specification (as presented)
- Exchange rate / volatility regressions:
  - ∆y_t = α_i + Σ_{p_i=1} φ_i ∆y_{t-i} + Σ_{q_i=0} δ_i SWI_{t-i} + Σ_{l_i=0} β_i SPI_{t-i} + X'_t γ + ε_t
  - INT_t = α_i + Σ_{p_i=1} φ_i ∆y_{t-i} + X'_t φ + Z'_t θ + u_t
- Dependent variables:
  - First set: daily percentage change in nominal R$/US$ exchange rate (higher values imply depreciation).
  - Second set: daily percentage change in implied R$/US$ volatility.

### Reaction function estimates — main findings
- General patterns:
  - Both modes of intervention react to short-term exchange rate trends and excessive FX volatility in expected directions: BCB takes short-dollar positions when the real is depreciating or when volatility is elevated; takes long-dollar positions in the opposite case.
  - Significant differences between spot and futures reaction functions across several drivers.
- Specific differential responses:
  - Policy rate change:
    - Lagged change in monetary policy rate is significantly positively associated only with spot intervention → spot intervention used to offset exchange rate effects of monetary policy.
  - Short-term vs medium-term exchange rate dynamics:
    - Spot intervention responds more to short-term (daily) exchange rate movements and expected depreciation.
    - Futures intervention responds more to medium-run FX trend (one-year moving average) → used to smooth trend movements.
  - Country risk and global risk aversion:
    - Futures intervention responds to changes in country risk (5Y sovereign CDS returns) and global risk aversion (VIX); spot reaction has expected sign but often not statistically significant.
  - Actual FX transactions / flow pressures:
    - Lagged trend FX transactions variable enters spot regressions with a positive and significant coefficient; not significant for futures regressions → spot chosen when responding to actual outflows rather than pure price pressures.
  - Persistence and clustering:
    - Both spot and futures interventions cluster; positive and significant coefficients on their own lagged moving averages.
    - Cross-effect between spot and futures lagged terms is generally negative (rarely significant).
- Interpretation:
  - Spot FXI: tool of choice for daily stabilization and reacting to observable flow pressures and monetary policy tightening/loosening.
  - Futures FXI: tool of choice for smoothing trends and reacting to shifts in country/global risk perceptions.

### Selected quantitative diagnostics and statistics (from first-stage regressions and tests)
- Baseline sample size in Table 1: N = 1,100.
- Selected test statistics (reported p-values in parentheses):
  - F test (spot column): 12.6 ( 0.00)
  - F test (futures column): 8.6 ( 0.00)
  - Kleibergen-Paap rk Wald F (spot): 12.6
  - Kleibergen-Paap rk Wald F (futures): 8.6
  - Sanderson-Windmeijer F test (spot): 7.4 ( 0.00)
  - Sanderson-Windmeijer F test (futures): 13.1 ( 0.00)
  - Kleibergen-Paap rk LM (spot): 71.1 ( 0.00)
  - Kleibergen-Paap rk LM (futures): 47.3 ( 0.00)
- Selected estimated coefficients and significance patterns (as reported in Table 1; standard errors omitted here but retained in original table):
  - Lagged daily percent change in FX: spot coefficient -0.019*; futures coefficient 0.012 (spot significant at 10%).
  - VIX percent change: futures coefficient -0.004** (significant at 5%).
  - Trend spot forward differential: spot coefficient -0.047***; futures coefficient 0.008.
  - 5Y sovereign CDS return, lagged: spot coefficient -0.002; futures coefficient -0.016*** (futures significant at 1%).
  - Lagged pct FX deviation from trend: spot coefficient -1.115*; futures coefficient -2.741***.
  - Lagged trend FX volatility: spot coefficient -0.009***; futures coefficient -0.014***.
  - Lagged trend FX transactions: spot coefficient 0.000***; futures coefficient 0.00 (significant in spot).
  - Policy rate change: spot coefficient 0.616***; futures coefficient -0.012 (spot significant at 1%).
  - Trend spot intervention, lagged: spot coefficient 0.168**; futures coefficient -0.126*.
  - Trend futures intervention, lagged: spot coefficient -0.022; futures coefficient 0.399***.
  - McFadden’s R^2 reported: spot 0.485; futures 0.407 (in ordered probit columns).
- Robustness and validity:
  - Instruments pass identification and weak instrument tests; Sanderson and Windmeijer conditional F-test strongly rejects weak instrument hypothesis.
  - Correlation of the constructed spot proxy with BCB monthly spot data: 97 percent in baseline sample; 86 percent in extended sample.

### Mechanisms and interpretation related to instrument nature
- Convertibility risk matters:
  - Futures-like instruments settle in local currency; if convertibility risk is non-negligible investors may not buy the derivative because proceeds may not be convertible into dollars at maturity → futures intervention likely ineffective under convertibility risk.
- Balance sheet and reserve implications:
  - Auctions of FX swaps do not directly impact BCB’s stock of foreign exchange reserves (advantage for central bank), whereas spot sales/purchases change reserves.
- Market microstructure:
  - Brazil’s derivatives markets are around four times larger than its spot market for foreign exchange (cited literature).
  - Derivatives markets appear to lead spot market in price discovery.

### Policy implications emphasized by the analysis
- A broader toolkit that includes both spot and derivatives-based intervention has advantages; derivatives interventions can be no less effective than spot interventions absent convertibility risk.
- Choice of instrument should consider:
  - Nature of pressure (price-based vs flow-based): spot preferred for flow pressures and daily stabilization.
  - Time horizon of exchange rate movement: futures preferred for smoothing medium-run trends and reacting to shifts in global risk sentiment.
  - Convertibility risk and market willingness to hold local-currency-settling instruments at maturity.
- Empirical identification of distinct reaction functions for spot and futures intervention helps understand which factors incentivize FXI generally and the mode selection between instruments.

*Source: IMF working paper content (wp1711) excerpt provided.*

### Appendix  presents  the  estimates  of  the  reaction  functions when  additional  instruments  are

### Appendix presents the estimates of the reaction functions when additional instruments are included and when the window over which the short term trend variables are calculated varies.

### Robustness of instruments and specification checks
- Including additional instruments and varying the window for short-term trend variables:
  - "Although some of the additional instruments are significant in the first stage regressions, this does not change the significance or the magnitudes of the coefficients of the baseline regressors."
  - Table A3 shows changes in the instrument set do not impact the second stage results.
- Concern about multiple zeros in dependent variables:
  - Columns 5 and 6 of Table 1 report Ordered Probit estimates (Ito and Yabu, 2007) to assess bias from mass points at zero.
  - "Neither the significance of the key variables nor their signs change much."
  - The Ordered Probit reduces the importance of the daily change in the exchange rate and FX volatility in the spot intervention regressions.

### Second-stage regression results for exchange rate changes (Table 2)
- Estimators and columns:
  - Columns 1–3 use the CUE estimator, Columns 4–6 use the 2SLS estimator, Column 7 uses simple OLS.
  - Dependent variable: "the percent daily change in the R$/US$ rate."
  - Explanatory variables defined in Table A1.
- Key coefficient estimates (point estimate and heteroscedasticity-robust standard error in parentheses, significance stars preserved):
  - Lagged daily pct change in FX:
    - Column 1: -0.053 (0.06)
    - Column 2: -0.121* (0.07)
    - Column 3: -0.141** (0.07)
    - Column 4: -0.148* (0.08)
    - Column 5: -0.171** (0.08)
    - Column 6: -0.158** (0.07)
    - Column 7: -0.167** (0.07)
  - CRB index, percent change:
    - Column 1: -0.161* (0.10)
    - Column 2: -0.1 (0.10)
    - Column 3: -0.138 (0.10)
    - Column 4: -0.112 (0.08)
    - Column 5: -0.097 (0.11)
    - Column 6: -0.119 (0.11)
    - Column 7: -0.064 (0.10)
  - CRB index, lagged percent change:
    - Column 1: -0.406*** (0.08)
    - Column 2: -0.435*** (0.08)
    - Column 3: -0.420*** (0.08)
    - Column 4: -0.413*** (0.10)
    - Column 5: -0.421*** (0.08)
    - Column 6: -0.415*** (0.08)
    - Column 7: -0.423*** (0.08)
  - VIX, percent change:
    - Column 1: 0.012** (0.01)
    - Column 2: 0.016*** (0.01)
    - Column 3: 0.012** (0.01)
    - Column 4: 0.012* (0.01)
    - Column 5: 0.015** (0.01)
    - Column 6: 0.014** (0.01)
    - Column 7: 0.013** (0.01)
  - VIX, lagged percent change:
    - Column 1: -0.009 (0.01)
    - Column 2: -0.006 (0.01)
    - Column 3: -0.009 (0.01)
    - Column 4: -0.009* (0.01)
    - Column 5: -0.008 (0.01)
    - Column 6: -0.009* (0.01)
    - Column 7: -0.006 (0.01)
  - Trend FX forward differential:
    - Column 1: 0.147*** (0.05)
    - Column 2: 0.087** (0.04)
    - Column 3: 0.164*** (0.05)
    - Column 4: 0.146*** (0.04)
    - Column 5: 0.073* (0.04)
    - Column 6: 0.130*** (0.05)
    - Column 7: 0.047 (0.04)
  - 5Y sovereign CDS return, lagged:
    - Column 1: 0.112*** (0.02)
    - Column 2: 0.118*** (0.02)
    - Column 3: 0.111*** (0.02)
    - Column 4: 0.106*** (0.01)
    - Column 5: 0.118*** (0.02)
    - Column 6: 0.116*** (0.02)
    - Column 7: 0.104*** (0.02)
  - Spot intervention:
    - Column 1: 1.026** (0.49)
    - Column 2: 1.009** (0.49)
    - Column 3: 1.294*** (0.43)
    - Column 4: 0.748* (0.42)
    - Column 5: 0.248 (0.21)
    - Columns 6–7: not reported in table excerpt for spot in those columns
  - Futures intervention:
    - Column 1: 0.973** (0.39)
    - Column 2: 0.729** (0.37)
    - Column 3: 0.876** (0.38)
    - Column 4: 0.680* (0.37)
    - Column 5: -0.127** (0.06)
    - Columns 6–7: not reported in table excerpt for futures in those columns
- Goodness-of-fit and sample:
  - R2 by column: 0.23, 0.11, 0.15, 0.23, 0.14, 0.18, 0.28
  - N = 1,100 (for all reported regressions)
- Specification and instrument diagnostics (bottom of Table 2):
  - Hansen’s J stat:
    - Column 2: 8.4 (0.21)
    - Column 3: 8.8 (0.19)
    - Column 4: 5.2 (0.40)
    - Column 5: 8.5 (0.20)
    - Column 6: 12.1 (0.06)
    - Column 7: 9.3 (0.10)
  - Kl.-Paap rk Wald F stat: 12.6, 8.6, 7.8, 11.7, 8.5, 6.1 (by column where reported)
  - Kl.-Paap rk LM stat:
    - Column 1: 71.1 (0.00)
    - Column 2: 47.3 (0.00)
    - Column 3: 49.2 (0.00)
    - Column 4: 17.8 (0.01)
    - Column 5: 24.7 (0.00)
    - Column 6: 22.7 (0.00)
  - Stock-Wright LM S stat: 21.4 (0.00) repeated across columns as reported
  - C test for endogeneity:
    - Column 1–3: 15.0 (0.04)
    - Column 4: 23.4 (0.00)
    - Column 5: 21.4 (0.00)
    - Column 6: 24.1 (0.00)
  - Wald statistic (test of equality of spot and futures coefficients):
    - 0.17 (0.67)
    - 0.01 (0.92)

### Interpretation of intervention coefficients and endogeneity
- Interpretation from text and coefficients:
  - "The first regression in Table 2 shows that the spot intervention term is highly significant and carries the expected positive coefficient."
  - "Taken at face value, the coefficient of 1.03 suggests that US$1 billion of spot purchases (sells) would depreciate (appreciate) the exchange rate by 1.03 percent."
  - "Regression 2 would suggest that futures intervention is a highly significant determinant ... with futures intervention worth US$1 billion in notional equivalent moving the exchange rate by some 0.97 percent."
  - When both intervention terms are included jointly (Column 3), coefficients remain similar (about 1 and 0.7 respectively) and highly significant; the Wald-test cannot reject equality of the two coefficients.
- Controls and signs:
  - Lagged dependent variable is significant with a negative coefficient.
  - Commodity price index and its lag carry expected negative coefficients; the lagged term is consistently significant.
  - VIX term is positive and highly significant, suggesting risk aversion is associated with depreciating exchange rates contemporaneously.
  - Lagged depreciation expectations and a rise in country risk are associated with real depreciation.
- Endogeneity and estimator comparison:
  - Baseline specification passes the J-test of overidentifying restrictions, underidentification and weak identification tests in the reported columns.
  - Stock and Wright LM statistic confirms intervention impacts are significant even allowing for weak instruments.
  - C-test confirms both intervention types are endogenous to contemporaneous exchange rate movements.
  - Replacing CUE with 2SLS (Columns 4–6) barely affects results; intervention coefficients slightly smaller when included jointly.
  - OLS without instruments (Column 7) yields substantially smaller coefficients and futures coefficient turns negative, consistent with expected negative bias from endogeneity.

### Extensions and sensitivity (preview of Table 3 discussion)
- Extending sample to 2002 (when futures intervention data begin):
  - This extension loses the FX transactions instrument and the implied volatility term due to data availability.
  - Replace lagged trend exchange rate volatility with a lagged trend difference between onshore and offshore forward rates (sample correlation 0.47 over the period with the volatility series).
  - Main findings persist with somewhat lower coefficients: "0.83‒0.92 for spot intervention and 0.55‒0.58 for futures intervention."
  - Column 1 in Table 3 fails the J-test; Column 2 excluding the long-run trend instrument does not change results.
- Testing convertibility risk:
  - Extending back to 2002 allows testing whether futures intervention loses effectiveness with non-negligible convertibility risk.
  - Define a "Convertibility Risk" dummy that takes value 1 on days when the three-month onshore dollar interest rate (cupom cambial) was ... (text ends here in the provided excerpt).

*Source: wp1711 — Appendix (excerpt).*

### 1.5  standard  deviations above  its  sample mean.

### wp1711 - 1.5  standard  deviations above  its  sample mean.

### Impact of convertibility risk on futures intervention
- Interaction of Convertibility Risk with Futures intervention:
  - Interaction term coefficients: -2.179 (SE 1.29), -2.269 (SE 1.34) — highly significant and negative.
  - Combined coefficient of Futures intervention plus interaction turns negative, indicating futures intervention can “move the exchange rate with the wind” when convertibility risk is high.
- Convertibility Risk definition and threshold:
  - Convertibility Risk variable = 1 on days on which the three month local interest rate (cupom cambial) was 1.5 standard deviations above its sample mean.
  - Results robust to alternative thresholds (2 instead of 1 standard deviation) and to using the spread between the cupom cambial and the three month US$ Libor rate in place of the cupom cambial.

### Asymmetry in intervention effects (Spot vs Futures)
- Spot intervention interaction:
  - Spot positive * Spot intervention coefficient: -1.188 (SE 1.11) — negative but not statistically significant → spot FXI broadly symmetric in its impact.
- Futures intervention interaction:
  - Swap positive * Futures intervention coefficient: -0.936 (SE 0.38) — negative and statistically significant → futures interventions are more effective when the BCB takes short dollar positions.
- Interpretation:
  - Futures-based interventions may fill hedging gaps in an underdeveloped FX-hedging market (limited long-maturity instruments), yielding larger impacts when providing hedging (short USD positions).
  - In Brazil, private foreign liabilities in local currency grossly exceed private domestic assets in foreign currency, making depreciations the more salient downside risk for private investors and increasing the relevance of short USD central bank positions.

### Dynamic and cumulative impacts (Table 3 highlights)
- Dynamic specification (first five lags added):
  - Only the first lag of Futures intervention and the first two lags of Spot intervention are significant.
- Selected second-stage coefficient snapshots from Table 3 (percent daily change in R$/US$ is dependent variable):
  - Lagged daily pct change in FX: -0.082 (0.05), -0.077 (0.05), -0.079 (0.04), -0.066 (0.04), -0.120** (0.06), -0.197** (0.08)
  - CRB index, percent change: -0.177** (0.07), -0.166** (0.07), -0.179*** (0.07), -0.182*** (0.07), -0.142 (0.09), -0.111 (0.11)
  - VIX, percent change: 0.006 (0.00), 0.007 (0.00), 0.006 (0.00), 0.007* (0.00), 0.011* (0.01), 0.015** (0.01)
  - Trend spot forward differential: 0.164*** (0.05), 0.180*** (0.05), 0.163*** (0.05), 0.175*** (0.05), 0.159*** (0.05), 0.093 (0.06)
  - 5Y sovereign CDS return, lagged: 0.091*** (0.01), 0.096*** (0.01), 0.090*** (0.01), 0.093*** (0.01), 0.103*** (0.02), 0.121*** (0.02)
  - Spot intervention coefficients (columns 1–6): 0.927* (0.48), 0.831* (0.48), 0.892* (0.46), 0.781* (0.46), 2.140** (1.01), 0.839** (0.35)
  - Futures intervention coefficients (columns 1–6): 0.582* (0.34), 0.556* (0.34), 0.651** (0.32), 0.512* (0.32), 0.693* (0.36), 0.926** (0.46)
- Statistical tests and diagnostics from Table 3:
  - Hansen’s J stat. examples: 13.9 (0.01), 4.4 (0.23), 17.3 (0.04), 7.7 (0.36), 8.0 (0.33), 4.6 (0.47)
  - Kl.-Paap rk Wald F stat examples: 9.6, 11.4, 5.7, 6.7, 7.3, 3.7
  - Wald statistic – long USD: 6.01 (0.01) — rejects equality in some tests.

### Robustness checks (Table 4 highlights)
- Baseline repetition and additional regressors:
  - Regression 1 repeats baseline. Regression 2 adds Brazilian macro announcement surprises. Regressions 3 and 4 add Citi EM and Citi LATAM Economic Surprise Indexes and lags. Regression 5 adds additional lags of dependent variable. Regression 6 adds actual interest rate differential. Regression 7 drops insignificant variables.
  - Findings remain unchanged across these checks.
- Representative coefficients from Table 4:
  - Lagged daily pct change in FX (Regressions 1–7): -0.141** (0.07), -0.140** (0.07), -0.139** (0.07), -0.138** (0.06), -0.152** (0.06), -0.163** (0.06), -0.142** (0.06)
  - CRB index, lagged percent change: -0.420*** (0.08) ... -0.416*** (0.08)
  - VIX, percent change: 0.012** (0.01) ... 0.017*** (0.01)
  - Trend spot forward differential: 0.164*** (0.05) ... 0.161*** (0.05)
  - Spot intervention (Regressions 1–7): 1.009** (0.49), 1.005** (0.49), 1.090** (0.52), 1.223** (0.56), 1.072** (0.49), 0.900* (0.51), 0.934* (0.48)
  - Futures intervention (Regressions 1–7): 0.729** (0.37), 0.729* (0.37), 0.711* (0.39), 0.670* (0.38), 0.733** (0.35), 0.944*** (0.36), 0.660* (0.37)
- Robustness conclusion:
  - Spot and futures based interventions have very similar impacts on the exchange rate across robustness checks.
  - Evidence suggests episodes of non-negligible convertibility risk are rare and have limited impact on regression coefficients.
  - The finite nature of futures contracts does not significantly weaken the relative effectiveness of futures intervention in Brazil; maturities appear sufficiently long to limit roll-over risk.

### Interventions and implied exchange rate volatility (Tables 5, A4)
- Dependent variable: percent daily change in R$/US$ implied volatility.
- Key findings:
  - Both Spot and Futures intervention enter with positive and significant coefficients when included individually.
  - Coefficient magnitudes (examples):
    - Table 5a, Regression 1 (Spot intervention individually): Spot intervention = 5.887*** (1.85)
    - Table A4, Regression 1 (CUE, excluded insignificants): Spot intervention = 3.793** (1.63)
    - Table A4, Regression 2–4 (2SLS/CUE variants): Spot intervention = 6.426*** (1.94); Futures intervention = 3.647** (1.54); other specifications show Spot 4.200** (2.09) and Futures 2.502** (1.21)
  - When both interventions included jointly (Regression 3, Table 5a), coefficients fall but remain in a close range between 2.3 and 3.
  - Interpreted elasticity:
    - US$1 billion in short dollar spot intervention or short dollar futures intervention reduces implied volatility in the real/dollar exchange rate by some 2.5 percent (interpretation taken from the paper’s summary of coefficients).
- Persistence and controls:
  - Lagged dependent variable often positive and significant, indicating small persistency in volatility movements.
  - CRB index contemporaneous change negatively associated with implied volatility; VIX positively and highly significantly associated with implied volatility.
- Asymmetry and dynamics:
  - Interaction terms between intervention and “positive” dummies carry negative signs but are not statistically significant → both modes appear symmetric in effect on volatility.
  - Dynamic specification shows only the first lag of futures intervention significant.
- Robustness:
  - Results robust to extending sample back to 2003, adding macro surprise indices, adding lags, and alternative estimator choices (CUE, OLS, 2SLS).
  - Instrument validity and endogeneity tests confirm instruments’ importance in attenuating negative bias.

### Central bank reaction functions and policy-relevant inferences
- Distinct reaction functions identified:
  - BCB uses spot intervention more in reaction to daily exchange rate movements and capital flow pressures.
  - BCB uses futures intervention more to smooth trend movements in the exchange rate and when price pressures dominate.
  - Spot intervention more often used to offset exchange rate effects of tighter/looser monetary policy compared to derivatives-based intervention.
- Policy implications:
  - Derivatives-based intervention can be no less effective than spot intervention, supporting a broader central bank toolkit that includes futures/non-deliverable instruments.
  - Where onshore market convertibility risk is generally negligible and futures maturities are sufficiently long, futures intervention can be as effective as spot intervention at affecting levels and volatility of the exchange rate.
  - Asymmetries in futures effectiveness when the central bank takes short USD positions imply targeted use of futures auctions can be particularly powerful when providing hedging to private agents exposed to depreciation risk.

### Instrumentation and data definitions (selected)
- Instruments used (examples from Table A1):
  - FX deviation from trend: difference between exchange rate and two week moving average (log terms).
  - Trend FX volatility: two week moving average of implied volatility.
  - Medium-run FX trend: one year moving average of log exchange rate.
  - Trend FX transactions, Trend spot intervention, Trend futures intervention: one-week averages.
  - Policy rate change: one week change in the Selic target rate.
- Convertibility Risk and cupom cambial:
  - Cupom cambial = three-month onshore dollar interest rate; served as proxy for onshore dollar interest rate and convertibility risk measure.

*Italic: Source — wp1711 - 1.5  standard  deviations above  its  sample mean.*

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*Source: wp1711 - REFERENCES (PDF chapter).*

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