## 1.   Central Bank of Colombia’s Intervention Operations and Movements

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---

### Introduction and research questions
- Study period: September 2004 to April 2007.
- Two central questions:
  - How effective was Central Bank’s intervention in stemming domestic currency appreciation in Colombia?
  - What constraints—if any—did the inflation-targeting regime pose on the Central Bank’s ability to influence the currency?
- Context and data:
  - Central Bank: Banco de la República (BdR).
  - BdR engaged in frequent discretionary purchases of foreign exchange intending to depreciate the domestic currency.
  - Novel daily dataset of official discretionary foreign exchange purchases that excludes valuation effects, capitalization of interest gains, portfolio adjustments, and other FX transactions not aimed at influencing the exchange rate.

### Case selection, episodes, and aggregate accumulation
- Two discretionary intervention episodes analyzed:
  - First period: September 20, 2004–March 1, 2006.
  - Second period: January 15, 2007–April 30, 2007.
- Frequency and intensity (Table 1 summary):
  - First Period:
    - Number of trading days = 357
    - Number of intervention days = 251
    - Frequency of central bank intervention = 70.3 percent
    - Average value of intervention (US$ millions) = 29
    - Maximum daily intervention (US$ millions) = 542
    - Average relative value of intervention (in % of mkt. turnover) = 5.1
    - Maximum relative value of intervention (in percent) = 40.9
    - Longest intervention spell (in business days) = 36
  - Second Period:
    - Number of trading days = 73
    - Number of intervention days = 44
    - Frequency of central bank intervention = 60.3 percent
    - Average value of intervention (US$ millions) = 103
    - Maximum daily intervention (US$ millions) = 2,733
    - Average relative value of intervention (in % of mkt. turnover) = 10.7
    - Maximum relative value of intervention (in percent) = 48.6
    - Longest intervention spell (in business days) = 9
- Aggregate accumulation:
  - Over the whole sample period, BdR accumulated approximately US$ 11 billion through discretionary intervention operations.
  - During the first four months of 2007, the BdR accumulated US$4.5 billion by actively intervening in the market.

### Institutional setting and monetary policy stance across episodes
- BdR adopted inflation-targeting with floating exchange rate in October 1999, using overnight repo interest rate as main instrument.
- Intervention characteristics:
  - Discretionary interventions conducted in the spot market only; automatically sterilized to achieve the short-term interest rate operating target.
  - Daily operations were not publicly announced; rules for discretionary intervention were not explicit; no pre-announced exchange rate target.
- Monetary policy stances:
  - First period: constant or falling interest rates; monetary loosening; economy operating below potential.
  - Second period: tightening monetary policy; policy rate increases totaling 175 basis points by January 2007 and continued to rise through April 2007; interest rate differential widened from 125 bps (end-April 2006) to 325 bps (end-April 2007).

### Empirical strategy
- Identification challenges:
  - Counterfactual exchange rate path on days with intervention is unobservable.
  - Potential endogeneity: intervention decisions responsive to past exchange rate movements.
- Two-stage instrumental variable approach:
  - First stage: dynamic censored regression (Tobit) reaction function for BdR intervention (equation (1)), including lagged intervention, exchange rate acceleration (Δ ln s t−1), deviation from a 20-day moving-average target (percentage deviation), and unexpected component of inflation announcements (NewsInf = actual − expected).
  - Second stage: GARCH(1,1) reduced-form model for daily exchange rate returns (Δ ln s), instrumenting intervention with predicted values from first stage; mean equation includes instrumented intervention (TNI), interest rate differential (ri*), EMBI spread (spreadEMBI), AutomINT dummy, day-of-week dummies, post-holiday dummy; volatility equation models conditional variance with standard GARCH terms and absolute inflation surprises.

### Central bank reaction function findings (Table 2)
- First period (Sept 2004–Mar 2006):
  - BdR “leaned against the wind”: statistically significant response to previous-day exchange rate changes.
  - A 1 percent appreciation of the exchange rate was met by a central bank purchase of US$14 million the following day.
  - A 1 percent deviation below the 20-day moving-average target elicited on average US$13 million purchases.
  - Lagged dependence minimal (γ1 ≈ 0.16).
- Second period (Jan 2007–Apr 2007):
  - Weak evidence of reaction to short-term acceleration (γ2 imprecisely estimated).
  - Stronger reaction to deviation from target: a 1 percent negative deviation implied average purchases of US$54 million.
  - Interventions were more persistent (higher autoregressive behavior).

### Effects on exchange rate level and volatility (Tables 3–5 and summary)
- First period (September 2004–March 2006):
  - Mean equation (Table 3): contemporaneous instrumented intervention coefficient β1 = 0.782***.
    - Interpretation: a US$30 million (average daily) sterilized purchase depreciated the domestic currency by approximately 0.23 percent.
    - The intervention required to contemporaneously move the nominal exchange rate by 1 percent represented approximately 2 percent of the country’s reserve money.
  - Volatility equation (Table 4): intervention had a stabilizing effect; intervention coefficient β1 (variance equation) = -0.019***.
  - Dynamic effects (Table 5): contemporaneous effect largest (β1 = 1.000***); about 40 percent of contemporaneous effect mean-reverted within two days (β12 (t-2) = -0.414***).
  - Overall: statistically significant, short-lived, economically small effects; substantial sterilized intervention required for quantitatively important impact.
- Second period (January 2007–April 2007):
  - Mean equation (Table 3): contemporaneous instrumented intervention coefficient β1 = 0.055 (not statistically significant).
  - Interest rate differential effect: β2 = -0.371** (higher interest differentials appreciated the peso).
  - Unexpected inflation effect reversed sign relative to first period: β4 = -0.464*** (a 1 percentage point inflation surprise associated with almost 0.5 percent appreciation of the peso the next day).
  - Volatility equation (Table 4): intervention had no discernible impact on volatility (β1 = -0.009, not significant).
  - Dynamic effects (Table 5): no significant intervention impacts at horizons up to four lags.
  - Overall: sterilized intervention did not influence exchange rate level or volatility; market reactions to inflation surprises and rising interest differentials dominated.

### Key mechanisms, market behavior, and derivatives
- Credibility and consistency:
  - First period: no conflict between intervention and inflation objectives; interventions signaled monetary easing credibly; inflation targets met with precision.
  - Second period: conflict between resisting appreciation and tightening monetary policy to curb inflation; markets perceived inconsistency and expected BdR to prioritize inflation control.
- Role of inflation surprises:
  - First period: unexpected higher inflation associated with depreciation (β4 = 0.286***).
  - Second period: unexpected higher inflation associated with appreciation (β4 = -0.464***).
  - Example magnitude: a 1 percentage point inflation surprise in the second period estimated to appreciate the peso by almost 0.5 percent the next day.
- Derivatives and speculative positions:
  - Offshore entities built leveraged long-peso / short-dollar positions in on-shore forward and derivatives markets.
  - Notable spike on March 30, 2007: off-shore entities bought almost US$600 million in pesos forward that day (seven times the daily average of previous six months).
  - BdR responded with spot purchases of US$740 million on that day, injecting liquidity and moving toward a net debtor position.
  - BdR’s net creditor position vis-à-vis financial sector eroded; BdR reduced its stock of treasury bills and by mid-March 2007 approached a position where it would no longer be a net creditor to the financial system.
  - As BdR approached net debtor status, markets anticipated constrained sterilization, amplifying speculative pressure.
- Operational limits:
  - The central bank’s net creditor/net debtor position vis-à-vis financial system matters for monetary control; becoming a net debtor weakens ability to control interbank rates and hence sterilization capacity.

### Robustness and endogeneity checks (Appendix II)
- Timing-robustness test using opening exchange rate quotes:
  - Results virtually identical to benchmark estimates in Table 3.
  - Positive impact of intervention during the first discretionary period somewhat lower.
  - For the second period, no significant effect of intervention on exchange rate levels detected.
- Table A.2 (mean returns, opening-quote robustness) — selected coefficients:
  - Intervention Indicator — β1 (t-1):
    - First Period: 0.488 * (0.29)
    - Second Period: 0.067 (0.07)
  - β2 (Overnight Interest Rate Differential) (t-1):
    - First Period: -0.027 (0.01)
    - Second Period: *-0.413 *** (0.14)
  - β3 (Daily Change in EMBI Sovereign Spread) (t-1):
    - First Period: 1.609 *** (0.29)
    - Second Period: 3.868 *** (0.17)
  - Unexpected Component of Inflation Announcement — β4 (t-1):
    - First Period: 0.272 (0.31)
    - Second Period: -0.333 *** (0.12)
  - R-Squared:
    - First Period: 0.088
    - Second Period: 0.585
  - Included observations:
    - First Period: 356
    - Second Period: 73
  - Note: Coefficient on intervention measures percentage change in the exchange rate for a US$ 100 million in foreign currency purchases.
- Unexpected vs. predictable components (Tables A.3 and A.4):
  - Table A.3: unexpected intervention residuals often produced a perverse contemporaneous appreciation effect.
    - β11 (Predicted Amount) (t):
      - First Period: 0.860 ** (0.42)
      - Second Period: 0.024 (0.09)
    - β12 (Unexpected Amount) (t):
      - First Period: -0.039 *** (0.01)
      - Second Period: -0.124 *** (0.04)
  - Table A.4: intervention effects not significantly different on days with predicted probability of intervention below 0.5.
    - β11 (Predicted Amount) (t):
      - First Period: 0.864 ** (0.39)
      - Second Period: 0.085 (0.23)
    - R-Squared:
      - First Period: 0.157
      - Second Period: 0.436
    - Included observations:
      - First Period: 356
      - Second Period: 73
  - Results robust to alternative error distributions (Student’s t, Generalized Error Distribution) for the GARCH model.

### Policy lessons and implications
- Coherence between intervention policy and inflation objectives is critical:
  - Intervention more likely to be effective when no conflict exists between exchange rate and inflation objectives—e.g., when economy operates below potential and monetary easing is consistent with meeting the inflation target.
- Inflation-targeting regimes impose limits on sterilization:
  - Sterilized accumulation of reserves can be constrained when monetary policy needs tightening; the inflation objective can bind and limit scope for reserve accumulation.
- Derivatives markets can blunt intervention:
  - Speculative leveraged positions in derivatives can rapidly offset central bank spot-market interventions.
  - Vulnerability to speculative attacks in inflation-targeting regimes can take the form of attacks that appreciate the currency (short the dollar), exploiting perceived inconsistencies between exchange rate intervention and inflation-targeting.
- Predictability reduces surprise:
  - Highly persistent, one-sided, and predictable interventions reduce their surprise value and effectiveness.
- Operational constraint:
  - The central bank’s net creditor/net debtor status vis-à-vis the financial sector conditions its sterilization capacity and influence over interbank rates.

### Conclusions and recommendations
- Effectiveness varied across episodes:
  - First episode (Sept 2004–Mar 2006): sterilized discretionary intervention had statistically significant but short-lived and economically small effects on exchange rate level; it also reduced volatility.
  - Second episode (Jan–Apr 2007): sterilized intervention had no detectable effect on exchange rate level or volatility; rising interest differentials, inflation surprises, and derivative-based speculative activity dominated market outcomes.
- Main inference: intervention cannot systematically influence exchange rate level when it conflicts with other perceived overriding monetary policy goals (notably inflation control); perceived strong commitment to inflation can undermine central bank ability to influence the exchange rate.
- Recommendation for future work:
  - Improved data availability at daily frequencies and continued research into motives, strategies, and channels for FX intervention in emerging markets to guide appropriateness and effectiveness of intervention strategies.

*Source: _wp0888 - References (PDF chapter).*

### 1.   Central Bank of Colombia’s Intervention Operations and Movements

### 1.   Central Bank of Colombia’s Intervention Operations and Movements 
in the Nominal Exchange Rate

### Central Bank of Colombia’s Intervention and Movements in the Policy Lending Rate
- Section covers the Central Bank of Colombia’s intervention and movements in the policy lending rate. (page 5)

### Output Gap in Colombia
- Section on the Output Gap in Colombia. (page 21)

### Evolution of Inflation and Inflation Expectations vis-à-vis the Inflation Target
- Section on Evolution of Inflation and Inflation Expectations vis-à-vis the Inflation Target. (page 21)

### Credibility of the Inflation Target
- Section on Credibility of the Inflation Target. (page 25)

### Traded Value in On-Shore Currency Derivatives Market between Local Colombian Banks and Off-Shore Entities
- Section on Traded Value in On-Shore Currency Derivatives Market between Local Colombian Banks and Off-Shore Entities. (page 26)

### Net Creditor Position of the Colombian Central Bank vis-à-vis the Financial Sector and Behavior of Interest Rates
- Section on Net Creditor Position of the Colombian Central Bank vis-à-vis the Financial Sector and Behavior of Interest Rates. (page 27)

### Derivative Markets Can Blunt Central Bank Intervention Operations When Policies Are Inconsistent
- Section on how Derivative Markets Can Blunt Central Bank Intervention Operations When Policies Are Inconsistent. (page 30)

### Tables (listed)
- Table 1: Summary Statistics on Daily Central Bank Intervention in Foreign Exchange Market. (page 11)
- Table 2: Determinants of Colombia Central Bank’s Daily Discretionary Intervention in FX Spot Market. (page 17)
- Table 3: Impact of Central Bank Intervention on Exchange Rate Level. (page 19)
- Table 4: Effect of Central Bank Intervention on Volatility of Exchange Rate. (page 23)
- Table 5: Dynamic Effects of Central Bank Intervention. (page 24)

### Appendixes
- Appendix I: Summary Statistics on the Unconditional Distribution of Daily Exchange Rate Returnes. (page 33)
- Appendix II: Robustness  Tests. (page 34)

*Source: _wp0888 - 1.   Central Bank of Colombia’s Intervention Operations and Movements*

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

### _wp0888 - References..............................................................................................................

### Introduction and research questions
- Study period: September 2004 to April 2007.
- Two central questions:
  - How effective was Central Bank’s intervention in stemming domestic currency appreciation in Colombia?
  - What constraints—if any—did the inflation-targeting regime pose on the Central Bank’s ability to influence the currency?
- Context:
  - Central Bank: Banco de la República (BdR).
  - BdR engaged in frequent discretionary purchases of foreign exchange intending to depreciate the domestic currency.
  - Novel daily dataset of official discretionary foreign exchange purchases that excludes valuation effects, capitalization of interest gains, portfolio adjustments, and other FX transactions not aimed at influencing the exchange rate.

### Case selection and episodes of intervention
- Two discrete discretionary intervention episodes analyzed:
  - First period: September 20, 2004–March 1, 2006.
  - Second period: January 15, 2007–April 30, 2007.
- Frequency and intensity (Table 1 summary):
  - First Period: Number of trading days = 357; Number of intervention days = 251; Frequency of central bank intervention = 70.3 percent; Average value of intervention (US$ millions) = 29; Maximum daily intervention (US$ millions) = 542; Average relative value of intervention (in % of mkt. turnover) = 5.1; Maximum relative value of intervention (in percent) = 40.9; Longest intervention spell (in business days) = 36.
  - Second Period: Number of trading days = 73; Number of intervention days = 44; Frequency of central bank intervention = 60.3 percent; Average value of intervention (US$ millions) = 103; Maximum daily intervention (US$ millions) = 2,733; Average relative value of intervention (in % of mkt. turnover) = 10.7; Maximum relative value of intervention (in percent) = 48.6; Longest intervention spell (in business days) = 9.
- Aggregate accumulation:
  - Over the whole sample period, BdR accumulated approximately US$ 11 billion through discretionary intervention operations.
  - During the first four months of 2007, the BdR accumulated US$4.5 billion by actively intervening in the market.

### Institutional setting and monetary policy stance across episodes
- BdR adopted inflation-targeting with floating exchange rate in October 1999, using overnight repo interest rate as main instrument.
- Intervention characteristics:
  - Discretionary interventions conducted in the spot market only; automatically sterilized to achieve the short-term interest rate operating target.
  - Daily operations were not publicly announced; rules for discretionary intervention were not explicit; no pre-announced exchange rate target.
- Monetary policy stances:
  - First period: constant or falling interest rates; monetary loosening; economy operating below potential.
  - Second period: tightening monetary policy; policy rate increases totaling 175 basis points by January 2007 and continued to rise through April 2007; interest rate differential widened from 125 bps (end-April 2006) to 325 bps (end-April 2007).

### Empirical strategy
- Identification challenges:
  - Counterfactual exchange rate path on days with intervention is unobservable.
  - Potential endogeneity: intervention decisions are responsive to past exchange rate movements.
- Two-stage instrumental variable approach:
  - First stage: dynamic censored regression (Tobit) reaction function for BdR intervention (equation (1)), including lagged intervention, exchange rate acceleration (Δ ln s t−1), deviation from a 20-day moving-average target (percentage deviation), and unexpected component of inflation announcements (NewsInf = actual − expected).
  - Second stage: GARCH(1,1) reduced-form model for daily exchange rate returns (Δ ln s), instrumenting intervention with predicted values from first stage; mean equation includes instrumented intervention (TNI), interest rate differential (ri*), EMBI spread (spreadEMBI), AutomINT dummy, day-of-week dummies, post-holiday dummy; volatility equation models conditional variance with standard GARCH terms and absolute inflation surprises.

### Central bank reaction function findings (Table 2)
- First period (Sept 2004–Mar 2006):
  - BdR “leaned against the wind”: statistically significant response to previous-day exchange rate changes.
  - Interpretation: a 1 percent appreciation of the exchange rate was met by a central bank purchase of US$14 million the following day.
  - Response to deviation from target: a 1 percent deviation below target elicited on average US$13 million purchases.
  - Lagged dependence minimal (γ1 ≈ 0.16).
- Second period (Jan 2007–Apr 2007):
  - Weak evidence of reaction to short-term acceleration (γ2 imprecisely estimated).
  - Stronger reaction to deviation from target: a 1 percent negative deviation implied average purchases of US$54 million.
  - Interventions were more persistent (higher autoregressive behavior).

### Effects on exchange rate level and volatility (Tables 3–5 and summary)
- First period results (September 2004–March 2006):
  - Mean equation (Table 3): contemporaneous instrumented intervention coefficient β1 = 0.782***.
    - Interpretation: a US$30 million (average daily) sterilized purchase depreciated the domestic currency by approximately 0.23 percent.
    - The intervention required to contemporaneously move the nominal exchange rate by 1 percent represented approximately 2 percent of the country’s reserve money.
  - Volatility equation (Table 4): intervention had a stabilizing effect; intervention coefficient β1 (variance equation) = -0.019***.
  - Dynamic effects (Table 5): contemporaneous effect largest (β1 = 1.000***); about 40 percent of contemporaneous effect mean-reverted within two days (β12 (t-2) = -0.414***).
  - Overall: statistically significant, short-lived, economically small effects; substantial sterilized intervention required for quantitatively important impact.
- Second period results (January 2007–April 2007):
  - Mean equation (Table 3): contemporaneous instrumented intervention coefficient β1 = 0.055 (not statistically significant).
  - Interest rate differential effect: β2 = -0.371** (higher interest differentials appreciated the peso).
  - Unexpected inflation effect reversed sign relative to first period: β4 = -0.464*** (a 1 percentage point inflation surprise associated with almost 0.5 percent appreciation of the peso the next day).
  - Volatility equation (Table 4): intervention had no discernible impact on volatility (β1 = -0.009, not significant).
  - Dynamic effects (Table 5): no significant intervention impacts at horizons up to four lags.
  - Overall: sterilized intervention did not influence exchange rate level or volatility; market reactions to inflation surprises and rising interest differentials dominated.

### Key mechanisms and market behavior
- Credibility and consistency:
  - First period: no conflict between intervention and inflation objectives; interventions signaled monetary easing credibly; inflation targets met with precision.
  - Second period: conflict between resisting appreciation and tightening monetary policy to curb inflation; markets perceived inconsistency and expected BdR to prioritize inflation control.
- Role of inflation surprises:
  - First period: unexpected higher inflation associated with depreciation (β4 = 0.286***).
  - Second period: unexpected higher inflation associated with appreciation (β4 = -0.464***).
  - Magnitude example: a 1 percentage point inflation surprise in the second period estimated to appreciate the peso by almost 0.5 percent the next day.
- Derivatives and speculative positions:
  - Offshore entities built leveraged long-peso / short-dollar positions in on-shore forward and derivatives markets.
  - Traded value in on-shore currency derivatives (off-shore entities buying pesos forward) surged, with a notable spike on March 30, 2007: off-shore entities bought almost US$600 million in pesos forward that day (seven times the daily average of previous six months).
  - BdR responded with spot purchases of US$740 million on that day, injecting liquidity and moving toward a net debtor position.
  - BdR’s net creditor position vis-à-vis financial sector eroded; BdR reduced its stock of treasury bills and by mid-March 2007 approached a position where it would no longer be a net creditor to the financial system.
  - As BdR approached net debtor status, markets anticipated constrained sterilization, amplifying speculative pressure.

### Policy lessons and implications
- Coherence between intervention policy and inflation objectives is critical:
  - Intervention is more likely to be effective when no conflict exists between exchange rate and inflation objectives—e.g., when economy operates below potential and monetary easing is consistent with meeting the inflation target.
- Inflation-targeting regimes impose limits on sterilization:
  - Sterilized accumulation of reserves can be constrained when monetary policy needs tightening; the inflation objective can bind and limit scope for reserve accumulation.
- Derivatives markets can blunt intervention:
  - Speculative leveraged positions in derivatives can rapidly offset central bank spot-market interventions.
  - Vulnerability to speculative attacks in inflation-targeting regimes can take the form of attacks that appreciate the currency (short the dollar), exploiting perceived inconsistencies between exchange rate intervention and inflation-targeting.
- Predictability of intervention reduces surprise element:
  - Highly persistent, one-sided, and predictable interventions reduce their surprise value and effectiveness.
- Operational limits:
  - The central bank’s net creditor/net debtor position vis-à-vis financial system matters for monetary control; becoming a net debtor weakens ability to control interbank rates and hence sterilization capacity.

### Robustness and sensitivity
- Sensitivity tests (Appendix II) probing endogeneity treatment and role of surprise element yield results virtually identical to main findings.
- Results robust to alternative error distributions (Student’s t, Generalized Error Distribution) for the GARCH model.

### Conclusions
- Effectiveness varied sharply across episodes:
  - First episode (Sept 2004–Mar 2006): sterilized discretionary intervention had statistically significant but short-lived and economically small effects on exchange rate level; it also reduced volatility.
  - Second episode (Jan–Apr 2007): sterilized intervention had no detectable effect on exchange rate level or volatility; rising interest differentials, inflation surprises, and derivative-based speculative activity dominated market outcomes.
- Main inference: intervention cannot systematically influence exchange rate level when it conflicts with other perceived overriding monetary policy goals (notably inflation control); perceived strong commitment to inflation can undermine central bank ability to influence the exchange rate.
- Recommendation for future work: improved data availability at daily frequencies and continued research into motives, strategies, and channels for FX intervention in emerging markets to guide appropriateness and effectiveness of intervention strategies.

*Source: _wp0888 - References (PDF chapter).*

### Appendix II: R

### Appendix II: R

### Endogeneity: identification and timing strategy
- Fundamental identifying assumption: the amount of dollars bought by the BdR on a given day depends on past exchange rate returns, but is independent of movements in the exchange rate within that day.
- Concern: if BdR acted strategically using intraday exchange rate evolution, aggregate daily interventions and exchange rate changes could be simultaneously determined, biasing estimates of the effect of central bank intervention downwards.
- Data limitation: exact timing and magnitudes of BdR’s intervention are not available at an intra-daily frequency.
- Empirical strategy used to attenuate simultaneity:
  - Use opening exchange rate quotes from SET-FX (quoted at the beginning of the trading day) and intervention data reported at the close of the day.
  - Exchange rate returns at time t (percentage change in opening prices between t and t-1) are treated as predetermined with respect to the amount of intervention at t.
  - Re-estimate the impact of BdR’s intervention on exchange rate returns using opening exchange rate quotes to measure daily exchange rate returns (Table A.2).
- Main result from timing-robustness test:
  - Results are virtually identical to the benchmark estimates presented in Table 3 (text).
  - The positive impact of central bank intervention on exchange rate returns during the first discretionary period is somewhat lower.
  - For the second period, no significant effect of intervention on exchange rate levels is detected, confirming the baseline result that intervention was not a useful short-term policy instrument for exchange rate management during 2007.

### Table A.2 — Effects of Central Bank Intervention: Robustness Test for Endogeneity Concerns (Mean Returns Equation)
- Sample periods:
  - First Period: September 2004-March 2006
  - Second Period: January 2007-April 2007
- Estimated coefficients and statistics (standard errors in parentheses):
  - β0 (Lagged Dependent Variable) (t-1):
    - First Period: -0.095 (0.07)
    - Second Period: -0.130 (0.10)
  - Intervention Indicator — β1 (Instrumented Amount of Dollar Purchases by Central Bank) (t-1):
    - First Period: 0.488 * (0.29)
    - Second Period: 0.067 (0.07)
  - β2 (Overnight Interest Rate Differential) (t-1):
    - First Period: -0.027 (0.01)
    - Second Period: *-0.413 *** (0.14)
  - β3 (Daily Change in EMBI Sovereign Spread) (t-1):
    - First Period: 1.609 *** (0.29)
    - Second Period: 3.868 *** (0.17)
  - Unexpected Component of Inflation Announcement — β4 (Actual minus Expected Value of Inflation) (t-1):
    - First Period: 0.272 (0.31)
    - Second Period: -0.333 *** (0.12)
  - Dummy for Days with Automatic FX Intervention: Yes (both periods)
  - Log L:
    - First Period: -28.001
    - Second Period: -7.581068
  - R-Squared:
    - First Period: 0.088
    - Second Period: 0.585
  - Included observations:
    - First Period: 356
    - Second Period: 73
- Note: The coefficient on the intervention variable measures the pecentage change in the exchange rate for a US$ 100 million in foreign currency purchases. Asterisks denote significance with ***, ** and * indicating 1%, 5% and 10% significance levels, respectively.

### Unexpected intervention: predictable vs. surprise components
- Question: does the “surprise” element of intervention (unexpected component) have a significant effect on exchange rates, beyond the predictable component?
- Two alternative specifications tested:
  1. Decompose actual intervention into expected and unexpected components (unexpected given by residuals from the Tobit first-stage). Include both in the exchange rate equation.
     - Main findings (Table A.3):
       - Predictable component of discretionary intervention is significant during the first period and has no significant measurable impact during the second period.
       - Unexpected amount of intervention has a consistently perverse effect in both periods: higher unexpected intervention led to a contemporaneous appreciation of the currency.
  2. Use a Probit model to estimate ex-ante likelihood of intervention; define days with predicted probability below 0.5 as low-likelihood days and include an interaction between the instrumented level of intervention and the low-likelihood dummy.
     - Main finding (Table A.4):
       - Effects of BdR intervention were not significantly different on days with low perceived likelihood of central bank intervention.

### Table A.3 — The Impact of the Unexpected component of Central Bank Intervention (Mean Returns Equation)
- Sample periods:
  - First Period: September 2004-March 2006
  - Second Period: January 2007-April 2007
- Estimated coefficients and statistics (standard errors in parentheses):
  - β0 (Lagged Dependent Variable) (t-1):
    - First Period: 0.251 *** (0.08)
    - Second Period: 0.102 (0.09)
  - Intervention Indicators:
    - β11 (Predicted Amount of Dollar Purchases by Central Bank) (t):
      - First Period: 0.860 ** (0.42)
      - Second Period: 0.024 (0.09)
    - β12 (Unexpected Amount of Dollar Purchases by Central Bank) (t):
      - First Period: -0.039 *** (0.01)
      - Second Period: -0.124 *** (0.04)
  - β2 (Overnight Interest Rate Differential) (t):
    - First Period: -0.031 *** (0.01)
    - Second Period: -0.587 *** (0.17)
  - β3 (Daily Change in EMBI Sovereign Spread) (t):
    - First Period: 1.472 *** (0.21)
    - Second Period: 1.835 ** (0.84)
  - Unexpected Component of Inflation Announcement — β4 (Actual minus Expected Value of Inflation) (t-1):
    - First Period: 0.432 ** (0.21)
    - Second Period: -0.461 *** (0.10)
  - Dummy for Days with Automatic FX Intervention: Yes (both periods)
  - Log L:
    - First Period: -28.001
    - Second Period: -3.251016
  - R-Squared:
    - First Period: 0.157
    - Second Period: 0.512
  - Included observations:
    - First Period: 356
    - Second Period: 73
- Note: The unexpected amount of intervention corresponds to estimated residuals from the foreign exchange intervention policy reaction model fitted in the first stage. The coefficient on the intervention variable measures the pecentage change in the exchange rate for a US$ 100 million in foreign currency purchases.

### Table A.4 — The Impact of Intervention in Days when the Central Bank was Less Likely to Have Intervened (Mean Returns Equation)
- Sample periods:
  - First Period: September 2004-March 2006
  - Second Period: January 2007-April 2007
- Estimated coefficients and statistics (standard errors in parentheses):
  - β0 (Lagged Dependent Variable) (t-1):
    - First Period: 0.261 *** (0.08)
    - Second Period: 0.132 (0.22)
  - Intervention Indicators:
    - β11 (Predicted Amount CB Intervention) (t):
      - First Period: 0.864 ** (0.39)
      - Second Period: 0.085 (0.23)
    - β12 (Dummy for Days in Which CB was Less Likely to Have Intervened) (t):
      - First Period: -0.116 (0.16)
      - Second Period: 0.083 (0.25)
    - β13 (Predicted Amount CB Intervention) X (Dummy for Less Likely CB Intervention) (t):
      - First Period: 0.845 (0.66)
      - Second Period: -0.187 (0.42)
  - β2 (Overnight Interest Rate Differential) (t):
    - First Period: -0.018 (0.01)
    - Second Period: -0.377 (0.25)
  - β3 (Daily Change in EMBI Sovereign Spread) (t):
    - First Period: 1.479 *** (0.25)
    - Second Period: 2.114 ** (0.91)
  - Unexpected Component of Inflation Announcement — β4 (Actual minus Expected Value of Inflation) (t-1):
    - First Period: 0.469 ** (0.19)
    - Second Period: -0.454 *** (0.12)
  - Dummy for Days with Automatic FX Intervention: Yes (both periods)
  - Log L:
    - First Period: -108.442
    - Second Period: -5.81293
  - R-Squared:
    - First Period: 0.157
    - Second Period: 0.436
  - Included observations:
    - First Period: 356
    - Second Period: 73
- Note: The dummy variable takes the value of 1 in those days when the predicted probability of intervention was less than 0.5. The coefficient on the intervention variable measures the pecentage change in the exchange rate for a US$ 100 million in foreign currency purchases.

*Source: Author's calculations.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0888.pdf_