## ANNEX I. SINGLE EQUATION REGRESSION OF THE CENTRAL BANK’S REACTION FUNCTION

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---

### Context and objectives
- Capital flows to Peru have grown significantly in recent years, driven by both push (easy money in advanced economies) and pull (strong fundamentals of the Peruvian economy) factors.
- A large share of flows is foreign direct investment (FDI), but portfolio and short-term flows have grown in size and volatility, creating risks and vulnerabilities in the financial system.
- The Central Reserve Bank of Peru (BCRP) uses prudential measures and daily FX intervention to:
  - safeguard the FX market against pressures from large and volatile capital flows, and
  - contain volatility in the FX market (officially stated objective).
- The pattern of interventions suggests that “leaning against the wind” could also be an objective.
- Paper aims:
  - Assess effectiveness against officially stated objectives and against other motives empirically “revealed” by the data.
  - Estimate a reaction function of the BCRP to identify “revealed” motives and address simultaneity between FX interventions and exchange rates.
  - Test for asymmetry in BCRP responses to appreciation versus depreciation pressures, and asymmetry in effectiveness between FX purchases and FX sales.

### Key empirical facts (from introduction and background)
- In 2013, the BCRP intervened with FX purchases of US$5.2 billion through April.
- In 2013, the BCRP intervened with FX sales of a similar amount between July and December in the spot market.
- BCRP intervention decisions are made daily by a committee that meets between 11:30AM and 1:00PM.
- Net capital flows to Peru averaged about 8 percent of GDP a year during 2010–13, compared with about 5 percent of GDP for the regional average and about 6 percent of GDP as Peru’s last-decade average.
- Gross inflows amounted to about 9½ percent of GDP a year during 2010‒13.
- External bond issuance by Peruvian firms doubled to US$6½ billion (3.2 percent of GDP) in 2013, from US$3 billion (1½ percent of GDP) in 2012.
- Net international reserves (NIR) stood at about US$65.7 billion (about 32½ percent of GDP) as of end-2013.
- BCRP securities denominated in local currency have a return of about 4 percent (and a 4 percent fee is charged on transfers of the securities to non-financial entities).
- Financial dollarization: credit and deposit dollarization remain high at around 40 percent.

### Methodological approach and identification
- Main empirical challenge: simultaneity between FX intervention and exchange rate movements.
- Identification strategy:
  - Use timing of BCRP intervention decisions and intra-daily exchange rate data.
  - Use exchange rate movements before 11:30AM to estimate the BCRP’s reaction function.
  - Use predicted likelihoods of FX interventions from the estimated reaction function as instruments for FX intervention in exchange rate equations.
  - Second-stage dependent variables: changes in the level and volatility of the exchange rate between the PM and AM trading sessions.
- Key features of the IV approach:
  - Same-day intra-daily data points at market opening ~9:00AM, 11:00AM, and closing 1:30PM; interventions assumed after 11:30AM.
  - Reaction function estimated using AM session exchange rate movements (average of opening and 11:00AM).
  - Intervention variables used as dummies (1 when BCRP intervenes, 0 otherwise).
  - Assumes interventions are discretionary and unanticipated by markets (except September 2012–April 2013 when preannouncement occurred).
- Reaction function specification:
  - INT (dummy) modeled as function of exchange rate deviation from target and volatility deviation from target.
  - Targets estimated by one-year simple moving average (robustness with 6-month moving average and 1-year rolling HP filtered average).
  - Probit models estimated separately for FX purchases and FX sales to capture asymmetry.
- Operationalization of intervention rules:
  - BCRP tolerable range = target exchange rate ± one standard deviation (primary), with robustness checks at ±1.5*standard deviation.
  - BCRP intervenes to prevent excessive appreciations if AM exchange rate < lower bound; to prevent excessive depreciations if AM exchange rate > upper bound.
  - Volatility trigger: intervene if AM session volatility exceeds historical average weekly standard deviation.
- Exchange rate impact equations:
  - Change in level: dependent variable = closing exchange rate minus 11:00AM rate.
  - Change in volatility: dependent variable = PM session volatility minus AM session volatility.
  - Instruments: predicted likelihoods of FX purchase and FX sale from probit reaction functions.
- Controls:
  - Absolute GDP surprise (Peru monthly GDP release around noon).
  - Change in VIX between opening and closing included in volatility regression.
  - Change in principal component of LA6 exchange rates (Brazil, Chile, Colombia, Mexico, Peru and Uruguay) included in level equation.

### Data and descriptive statistics
- Sample: daily data January 2010–December 2013, total sample of 982 observations.
  - BCRP purchased FX in 354 days (36 percent).
  - BCRP sold FX in 81 days (8¼ percent).
  - No intervention in 534 days (55½ percent).
- Descriptive associations:
  - About 91 percent of FX purchase days occurred when AM session exchange rate fell below the lower bound of the tolerable range.
  - Less than 5 percent of FX purchases occurred when only volatility breached target while level remained within target.
  - About 75 percent of FX sales occurred when AM session exchange rate exceeded the upper bound.
  - About 20 percent of FX sales occurred when volatility breached target while level remained within range.
- Intervention modalities and sterilization:
  - Interventions mainly in the spot market; occasionally via swaps and sales of dollar-indexed securities (equivalent to selling FX forward).
  - Mostly sterilized through issuance of BCRP securities, Treasury deposits and reserve requirements.
  - FX sales mostly sterilized mainly through swaps and repos.
- FX market features:
  - Interbank spot market with thin trading and a poorly developed derivatives market (very small forwards and options).
  - FX interventions absorb a significant share of pressures from capital flows; interventions since end-2011 appear motivated mainly to ease pressure on the exchange rate rather than solely to accumulate reserves.
  - BCRP’s pattern: concentrated on FX purchases before May 2013 and on FX sales in the second half of 2013; exception: September 2012–April 2013 when BCRP purchased FX almost daily after announcing preannounced policy.

### Reaction function estimation (probit and multinomial logistic results)
- General model performance:
  - Strong goodness of fit: large LR statistics and large Pseudo R2 values.
  - No. of observations reported: 980 (multinomial logistic tables).
  - Pseudo R2 reported around 0.49–0.53 across specifications.
- Dynamics:
  - Two-day lags of dependent variables significant, indicating intervention clustering.
- Asymmetric findings:
  - FX purchases:
    - Strongly and positively associated with deviations below the lower bound (excessive appreciation).
    - Excessive appreciation coefficients reported (examples): 47.200 and 45.548 (z-values (6.31)*** and (5.81)*** in 6-month MA probit).
    - Excessive volatility generally negatively associated with likelihood of FX purchases (e.g., -0.110, -0.217; z-values (-1.13), (-1.94)*).
  - FX sales:
    - Positively and significantly associated with deviations above the upper bound (excessive depreciation).
    - Volatility increases likelihood of FX sales in many specifications (e.g., volatility coefficient 0.220, z-value (2.71)**).
    - Examples of excessive depreciation coefficients: 7.461 (z-value (2.73)**) in 6-month MA; 13.784 (z-value (7.01)**) in 1-year HP.
- Policy change dummy (September 2012–April 2013):
  - Adding a dummy interacted with appreciation and volatility does not substantially change main results.
  - Weak evidence the policy change affected volatility reaction (e.g., excessive appreciation * dummy coefficients and z-values reported in some tables).
  - Some interaction terms dropped where they predicted success perfectly.
- Multinomial logistic specifics (selected reported coefficients):
  - Intervention_1st lag (FX sale): reported values include -1.5312.636-1.5292.439 with z-values (-4.49)*** (11.04)*** (-4.49)*** (10.15)***.
  - Deviation from target (appreciation) reported with large coefficients in some cells: -7151145.131-7383538.394 with z-values including (5.12)*** and (4.09)***.
  - Volatility coefficients in multinomial outputs include 0.285-0.1300.284-0.300 with z-values (1.82)** (-0.68) (1.81)** (-1.39).
- Robustness checks:
  - Reaction functions robust to alternative target definitions: 6-month moving average, 1-year rolling HP filtered average.
  - When tolerable range broadened to ±1.5*standard deviation volatility becomes statistically significant in the FX purchase equation (coefficient remains negative), still supporting asymmetric reaction hypothesis.

### Impacts of FX interventions (IV 2SLS exchange-rate impact results)
- Estimation approach: use predicted likelihoods from reaction-function probits as instruments for intervention dummies in PM–AM change regressions; Table 2 estimated using IV (2SLS) method.
- Sample sizes for IV regressions: No. of obs. reported as 979 / 980 / 960 across specifications.
- Main IV 2SLS findings:
  - FX purchases:
    - No strong statistical evidence that FX purchases prevent appreciation of the exchange rate: likelihood of FX purchase statistically insignificant in regressions (1) and (2); weakly significant in regression (3).
    - Likelihood of FX purchase has a statistically significant and negative impact on exchange rate volatility (i.e., FX purchases reduce volatility).
    - Example reported coefficients in level equations: FX purchase positive coefficients in level equations (e.g., 0.0150.0160.024 across tables).
  - FX sales:
    - Statistically significant negative impact on exchange rate level (i.e., effective in preventing depreciation). Examples: FX sale negative coefficients in level equations (e.g., -0.082 to -0.123).
    - Statistically significant negative impact on exchange rate volatility (i.e., reduce volatility). Examples: volatility coefficients e.g., -0.136 to -0.192.
    - FX sale_1st lag often positive and significant in level equations (e.g., 0.1070.1030.103).
  - Effects timing and persistence:
    - Effects are short-lived; lags of FX intervention generally not significant, with exception of first lag of FX sales.
  - Model fit and explanatory power:
    - Adj. R2 very small in exchange-rate regressions (e.g., values range from 0.004 to 0.027 reported; overall model fit low).
    - Reported F-stat. values for IV regressions include 3.59***, 6.20***, 5.30***, 3.14**, 1.83*, 2.28* across specifications.
  - Controls:
    - Among controls, only common factor (principal component) of LA6 exchange rates is statistically significant in many specifications (coefficient examples: 0.013; significance noted).
    - Change in ER_LA2/... reported as significant in volatility equations in some tables.
    - GDP surprise and Absolute change in VIX included; variable significance varies across specifications.
- Robustness:
  - Results robust to alternative definitions of target and tolerable range (6-month moving average, 1-year HP rolling filtered average, tolerable range ±1.5*standard deviation).
  - When tolerable range broadened to ±1.5*standard deviation, volatility becomes statistically significant in FX purchase equation (coefficient remains negative).

### Concluding remarks and policy implications (from Section V)
- Main empirical conclusions:
  - Asymmetric BCRP reactions: FX purchases driven mainly by excessive appreciation; FX sales respond to both excessive volatility and excessive depreciation.
  - Exchange rate volatility appears to be more of a concern for the BCRP during depreciation pressures than during appreciation pressures.
  - Excessive volatility is negatively associated with likelihood of FX purchases; in some regressions this is weakly significant.
  - FX sales are effective in reducing both the level and volatility of the exchange rate, but effects are short-lived.
  - FX purchases do not have statistically significant impacts on the level of the exchange rate and have an unintended statistically significant negative impact on volatility (they reduce volatility but do not prevent appreciation).
  - BCRP’s preannouncement of interventions in August 2012 did not materially change intervention effectiveness.
- Policy recommendations:
  - Target interventions where they are most effective given sterilization costs (cost of sterilization in 2012 estimated at about ½ percent of GDP).
  - FX sales by the central bank can be warranted during periods of depreciation pressures if there are concerns of excessive volatility and depreciation; however, interventions should not aim at preventing a depreciating trend that ought to be driven by fundamentals because effects are short-lived.
  - FX purchases during appreciation pressures are primarily warranted if reducing volatility is the objective; otherwise, FX purchases could perpetuate appreciation by reducing volatility and encouraging a one-sided bet on the domestic currency.
  - Building international reserves can be another motive for FX purchases during appreciation episodes, although this was less likely to be the case in Peru recently.

*Source: ANNEX I. SINGLE EQUATION REGRESSION OF THE CENTRAL BANK’S REACTION FUNCTION (Content unit: _wp14217)*

### Annex I. Single Equation Regression of the Central Bank’s Reaction Function 22

### Annex I. Single Equation Regression of the Central Bank’s Reaction Function 22

### Context and objectives
- Capital flows to Peru have grown significantly in recent years, driven by both push (easy money in advanced economies) and pull (strong fundamentals of the Peruvian economy) factors.
- A large share of flows is foreign direct investment (FDI), but portfolio and short-term flows have grown in size and volatility, creating risks and vulnerabilities in the financial system.
- The Central Reserve Bank of Peru (BCRP) uses prudential measures and daily FX intervention to:
  - safeguard the FX market against pressures from large and volatile capital flows, and
  - contain volatility in the FX market (officially stated objective).
- The pattern of interventions suggests that “leaning against the wind” could also be an objective.
- This paper aims to assess empirically the motives and effectiveness of FX interventions in Peru:
  - Assess effectiveness against officially stated objectives and against other motives empirically “revealed” by the data.
  - Estimate a reaction function of the BCRP to identify “revealed” motives and address simultaneity between FX interventions and exchange rates.
  - Test for asymmetry in BCRP responses to appreciation versus depreciation pressures, and asymmetry in effectiveness between FX purchases and FX sales.

### Key empirical facts from the introduction
- In 2013, the BCRP intervened with FX purchases of US$5.2 billion through April.
- In 2013, the BCRP intervened with FX sales of a similar amount between July and December in the spot market.
- BCRP intervention decisions are made daily by a committee that meets between 11:30AM and 1:00PM.

### Methodological approach (innovation and identification)
- Main empirical challenge: simultaneity between FX intervention and exchange rate movements.
- Identification strategy:
  - Use an innovative instrumental variables approach leveraging the timing of BCRP intervention decisions and intra-daily exchange rate data.
  - Use exchange rate movements before 11:30AM to estimate the BCRP’s reaction function.
  - Use predicted values of the likelihoods of FX interventions from the estimated reaction function as instruments for FX intervention in the exchange rate equations.
  - Second-stage dependent variables: changes in the level and volatility of the exchange rate between the PM and AM trading sessions.
- Empirical tests included:
  - Estimation of the BCRP reaction function (single-equation regression).
  - Tests for asymmetry in intervention response and in intervention effectiveness (FX purchases vs FX sales).

### Structure of the paper (as stated)
- Section II: highlights capital flows and FX interventions in Peru.
- Section III: discusses methodological issues.
- Section IV: presents data and estimation results.
- Subsequent annexes noted in the table of contents: Annex II, Annex III, Annex IV (titles listed but detailed content not included in this excerpt).

*Source: Annex I. Single Equation Regression of the Central Bank’s Reaction Function 22*

### Section V concludes the study.

### _wp14217 - Section V concludes the study.

### Capital flows and FX interventions
- Net capital flows to Peru averaged about 8 percent of GDP a year during 2010–13, compared with about 5 percent of GDP for the regional average and about 6 percent of GDP as Peru’s last-decade average.
- Gross inflows amounted to about 9½ percent of GDP a year during 2010‒13.
- External bond issuance by Peruvian firms doubled to US$6½ billion (3.2 percent of GDP) in 2013, from US$3 billion (1½ percent of GDP) in 2012.
- Large inflows reflected push factors (easy money and low interest rates in advanced economies) and pull factors (Peru’s record of high economic growth of about 6½ percent a year during the last decade, strong terms of trade, and sound monetary and fiscal policies).
- Early signs of overheating (credit growth of over 20 percent and significant appreciation of stock and housing prices in 2011) moderated towards the end of 2012 despite continued capital inflows.
- Net international reserves (NIR) stood at about US$65.7 billion (about 32½ percent of GDP) as of end-2013.
- BCRP interventions:
  - Conducted mainly in the spot market and occasionally via swaps and sales of dollar-indexed securities (equivalent to selling FX forward).
  - Mostly sterilized through issuance of BCRP securities, Treasury deposits and reserve requirements.
  - BCRP securities denominated in local currency have a return of about 4 percent (and a 4 percent fee is charged on transfers of the securities to non-financial entities).
  - FX sales are mostly sterilized mainly through swaps and repos.
- FX market characteristics:
  - Interbank spot market with thin trading and a poorly developed derivatives market (very small forwards and options).
  - Relatively high financial dollarization: credit and deposit dollarization remain high at around 40 percent.
- FX interventions absorb a significant share of pressures from capital flows; interventions since end-2011 appear motivated mainly to ease pressure on the exchange rate rather than solely to accumulate reserves.
- The BCRP’s pattern of intervention (concentrated on FX purchases before May 2013 and on FX sales in the second half of 2013) suggests motives beyond containing volatility, including leaning against the wind and limiting rates of appreciation/depreciation.
- Exception: between September 2012 and April 2013 the BCRP purchased FX almost on a daily basis after announcing in August 2012 that it would purchase more stable amounts of FX even during days of depreciating pressures.

### Methodology
- Objective: empirically investigate the motives and effectiveness of FX interventions in Peru via two steps:
  1. Estimate BCRP’s reaction functions separately for FX purchases and FX sales to shed light on motives that may vary between appreciation and depreciation episodes.
  2. Use predicted likelihoods of intervention from the first stage regressions as instrumental variables (IV) for FX interventions in exchange rate equations to overcome potential simultaneity biases.
- Theoretical channels for sterilized intervention effects: portfolio balance and signaling effects.
- Simultaneity issue:
  - Intervention decisions depend on exchange rate movements; common solutions include lagged intervention variables, event studies with high-frequency data, and IV methods based on reaction functions.
- This paper’s IV approach innovations:
  - Uses same-day exchange rates (intra-daily data points at market opening ~9:00AM, 11:00AM, and closing 1:30PM) and approximate timing of FX interventions (committee meets between 11:30AM and 1:00PM; interventions assumed after 11:30AM).
  - Estimates BCRP reaction function using AM session exchange rate movements (average of opening and 11:00AM) and uses predicted likelihoods as instruments for PM–AM changes.
  - Intervention variables used as dummies (1 when BCRP intervenes, 0 otherwise) to avoid simultaneity from intervention amounts that may depend on market reaction.
  - Assumes interventions are discretionary and unanticipated by markets (consistent with BCRP practice except September 2012–April 2013).
- Reaction function specification:
  - INT (dummy) modeled as function of exchange rate deviation from target and volatility deviation from target.
  - Targets estimated by one-year simple moving average (robustness with 6-month moving average and 1-year rolling HP filtered average).
  - Probit models estimated separately for FX purchases and FX sales to capture asymmetry.
- Intervention rules operationalized:
  - BCRP tolerable range = target exchange rate ± one standard deviation (primary), with alternative ±1.5*standard deviation robustness checks.
  - BCRP intervenes to prevent excessive appreciations if AM exchange rate < lower bound; to prevent excessive depreciations if AM exchange rate > upper bound.
  - Volatility trigger: intervene if AM session volatility exceeds historical average weekly standard deviation.
- Exchange rate impact equations (PM vs AM differences):
  - Change in level: dependent variable = closing exchange rate minus 11:00AM rate.
  - Change in volatility: dependent variable = PM session volatility minus AM session volatility.
  - Instruments: predicted likelihoods of FX purchase and FX sale from probit reaction functions.
- Controls:
  - Absolute GDP surprise (Peru monthly GDP release around noon) included.
  - Change in VIX between opening and closing included in volatility regression.
  - Change in principal component of LA6 exchange rates (Brazil, Chile, Colombia, Mexico, Peru and Uruguay) included in level equation.

### Data and estimation results
- Sample: daily data January 2010–December 2013, total sample of 982 observations.
  - Of 982 observations: BCRP purchased FX in 354 days (36 percent), sold FX in 81 days (8¼ percent), and did not intervene in 534 days (55½ percent).
- Descriptive findings:
  - FX purchases: about 91 percent of FX purchase days occurred when AM session exchange rate fell below the lower bound of the tolerable range; less than 5 percent of FX purchases occurred when only volatility breached target while level remained within target.
  - FX sales: about 75 percent of FX sales occurred when AM session exchange rate exceeded the upper bound, and about 20 percent occurred when volatility breached target while level remained within range.
- Reaction function (probit) estimation results:
  - Strong goodness of fit: large LR statistics and large Pseudo R2 values.
  - Two-day lags of dependent variables significant, indicating intervention clustering.
  - FX purchases are strongly and positively associated with deviations below the lower bound (excessive appreciation).
  - FX sales are positively and significantly associated with deviations above the upper bound (excessive depreciation) and with excessive volatility.
  - Evidence of asymmetric reaction: volatility increases likelihood of FX sales but not FX purchases (in some specifications volatility is negatively associated with FX purchases and in some regressions weakly significant).
  - Adding a dummy for intervention policy change (September 2012–April 2013) interacted with appreciation and volatility does not substantially change main results; weak evidence the policy change affected volatility reaction.
  - Multinomial logistic regression robustness: odds of FX purchases affected only by excessive appreciations; odds of FX sales affected by both excessive depreciations and volatility.
- Impacts of FX interventions (IV 2SLS estimates for PM–AM changes):
  - FX purchases:
    - No strong statistical evidence that FX purchases prevent appreciation of the exchange rate (likelihood of FX purchase statistically insignificant in regressions (1) and (2); weakly significant in regression (3)).
    - Likelihood of FX purchase has a statistically significant and negative impact on exchange rate volatility (i.e., FX purchases reduce volatility).
  - FX sales:
    - Statistically significant negative impact on exchange rate level (i.e., effective in preventing depreciation).
    - Statistically significant negative impact on exchange rate volatility (i.e., reduce volatility).
    - Effects are short-lived; lags of FX intervention generally not significant, with exception of first lag of FX sales.
  - Model fit for exchange rate regressions is low (Adj. R2 very small), reflecting difficulty of explaining exchange rate variability and data limitations.
  - Among controls, only common factor (principal component) of LA6 exchange rates is statistically significant, underscoring regional factors like commodity prices.
- Robustness:
  - Results robust to alternative definitions of target and tolerable range (6-month moving average, 1-year HP rolling filtered average, tolerable range ±1.5*standard deviation).
  - Exception: when tolerable range is broadened to ±1.5*standard deviation volatility becomes statistically significant in the FX purchase equation (coefficient remains negative), still supporting asymmetric reaction hypothesis.

### Concluding remarks and policy implications
- Main empirical findings:
  - Asymmetric BCRP reactions: FX purchases driven mainly by excessive appreciation; FX sales respond to both excessive volatility and excessive depreciation.
  - Exchange rate volatility appears to be more of a concern for the BCRP during depreciation pressures than during appreciation pressures.
  - Excessive volatility is negatively associated with likelihood of FX purchases; in some regressions this is weakly significant, suggesting occasional intervention against very low volatility during appreciation episodes (consistent with BCRP statements in August 2012).
  - FX sales are effective in reducing both the level and volatility of the exchange rate, but effects are short-lived.
  - FX purchases do not have statistically significant impacts on the level of the exchange rate and have an unintended statistically significant negative impact on volatility (they reduce volatility but do not prevent appreciation).
  - BCRP’s preannouncement of interventions in August 2012 did not materially change intervention effectiveness.
- Policy recommendations:
  - Target interventions where they are most effective given sterilization costs (cost of sterilization in 2012 estimated at about ½ percent of GDP).
  - FX sales by the central bank can be warranted during periods of depreciation pressures if there are concerns of excessive volatility and depreciation; however, interventions should not aim at preventing a depreciating trend that ought to be driven by fundamentals because effects are short-lived.
  - FX purchases during appreciation pressures are primarily warranted if reducing volatility is the objective; otherwise, FX purchases could perpetuate appreciation by reducing volatility and encouraging a one-sided bet on the domestic currency.
- Additional note:
  - Building international reserves can be another motive for FX purchases during appreciation episodes, although this was less likely to be the case in Peru recently.

*Source: _wp14217 - Section V concludes the study.*

### ANNEX I. SINGLE EQUATION REGRESSION OF THE CENTRAL BANK’S REACTION FUNCTION

### ANNEX I. SINGLE EQUATION REGRESSION OF THE CENTRAL BANK’S REACTION FUNCTION

### Regression coefficients (multinomial logistic regression of FX intervention)
- Dependent variable: dummy taking values of 1 for FX purchase, -1 for FX sale, and 0 otherwise. The base outcome is no-intervention.
- Two specifications: (1) without intervention policy change dummy interaction; (2) with intervention policy change dummy interaction.

- Intervention_1st lag
  - FX sale: -1.5312.636-1.5292.439
  - z-values: (-4.49)*** (11.04)*** (-4.49)*** (10.15)***

- Intervention_2nd lag
  - FX sale: -0.7980.853-0.7970.634
  - z-values: (-2.30)** (3.57)*** (-2.30)** (2.63)***

- Deviation from target (appreciation)
  - Coefficients: -7151145.131-7383538.394
  - z-values: (-0.02) (5.12)*** (-0.01) (4.09)***

- Deviation from target (depreciation)
  - Coefficients: 14.940-940614.850-9170
  - z-values: (4.08)*** (-0.00) (4.06)*** (-0.00)

- Volatility
  - Coefficients: 0.285-0.1300.284-0.300
  - z-values: (1.82)** (-0.68) (1.81)** (-1.39)

- Deviation from target (appreciation) * dummy for intervention policy change
  - Coefficient (when included): ......56546519.424
  - z-values: ......(0.01) (2.39)**

- Volatility * dummy for intervention policy change
  - Coefficients: ......-1.783-1.453
  - z-values: ......(-0.42) (-1.39)

- Constant
  - Coefficients: -2.703-2.668-2.693-2.516
  - z-values: (-9.22)*** (-12.63)*** (-9.19)*** (-11.78)***

### Model statistics (multinomial logistic regression table)
- No. of observations: 980
- LR-chi2 (10)
- Pseudo R2: 0.50 / 0.52 (values shown adjacent to model outputs)
- Additional reported values in table: 877.12***, 909.20*** (presented next to observation counts)

### Annex II — Exchange rate target estimated by six months moving average exchange rate (Probit regressions)
- FX purchase_1st lag: 1.6351.548
  - z-values: (11.75)*** (11.05)***

- FX sale_1st lag: 1.430
  - z-value: (7.48)***

- FX purchase_2nd lag: 0.5690.464
  - z-values: (4.07)*** (3.28)**

- FX sale_2nd lag: 1.010
  - z-value: (5.11)***

- Excessive appreciation: 47.20045.548
  - z-values: (6.31)*** (5.81)***

- Excessive depreciation: 7.461
  - z-value: (2.73)**

- Excessive volatility: -0.110-0.217
  - z-values: (-1.13) (-1.94)*

- Volatility: 0.220
  - z-value: (2.71)**

- Excessive appreciation * dummy for intervention policy change
  - Dropped from equation 2 as it predicts success perfectly (noted in table)

- Excessive volatility * dummy for intervention policy change
  - Coefficient: ...0.630
  - z-value: ...(1.59)

- Constant (models): -2.022; -1.669-1.639
  - z-values: (-21.12)***, (-17.76)*** (-17.29)***

- Model statistics:
  - No. of observations: 980 / 898 / 980 (as reported per column)
  - LR-chi2: 642.5*** / 484.87***
  - F-stat.: 217.62***
  - Pseudo R2: 0.50 / 0.44
  - Adj. R2: 0.39

- Notes for Table 1 and Table 2:
  - Purchase and sale of FX are represented by dummy variables with values of 1 when there was purchase (sale) and 0 otherwise.
  - Equations (1) and (2) are without and with intervention policy change dummy interaction, respectively.
  - Table 2 estimated using IV (2SLS) method. Statistically significant variables in regressions (1) and (2) of Table IIa are used as instruments for likelihood of FX sales and purchases, respectively.
  - Change in ER_LA 2/... denotes change in the principal component of exchange rates in LA6 (Brazil, Chile, Colombia, Mexico, Peru and Uruguay) economies.
  - GDP surprise is the difference between actual real GDP growth and conSensus estimates prior to data release; entered in absolute value in the volatility equations.

### Annex III — Exchange rate target estimated by one year average rolling HP filtered exchange rate (Probit regressions)
- FX purchase_1st lag: 1.6201.519
  - z-values: (11.65)*** (10.80)***

- FX sale_1st lag: 1.072
  - z-value: (5.34)***

- FX purchase_2nd lag: 0.5310.405
  - z-values: (3.80)** (2.85)**

- FX sale_2nd lag: 0.660
  - z-value: (3.16)**

- Excessive appreciation: 31.93529.668
  - z-values: (6.73)*** (5.88)***

- Excessive depreciation: 13.784
  - z-value: (7.01)***

- Excessive volatility: -0.115-0.220
  - z-values: (-1.16) (-1.94)*

- Volatility: 0.283
  - z-value: (3.52)**

- Excessive appreciation * dummy for intervention policy change
  - Coefficient: ...323.227
  - z-value: ...(2.39)**

- Excessive volatility * dummy for intervention policy change
  - Coefficient: ...-0.675
  - z-value: ...(-1.14)

- Constants: -2.254; -1.773-1.720
  - z-values: ( -19.14)***, (-17.31)*** (-16.52)***

- Model statistics:
  - No. of observations: 980 (across reported columns)
  - LR-chi2 (4): 648.38*** / 6678.62*** (values as presented)
  - Pseudo R2: 0.51 / 0.53
  - Adj. R2: 0.47

- Table 2 (impact of FX intervention on level and volatility of exchange rate) summary items:
  - Explanatory variables include FX purchase, FX sale, FX sale_1st lag, Change in ER_LA2/..., GDP surprise, Absolute value of change in VIX, Likelihood of FX purchase interacted with dummy for intervention policy change, and constants.
  - Sample sizes: No. of obs. 979/980 as reported per specification.
  - Reported F-stat.: ranges (e.g., 3.59***, 6.20***, 5.30***, 3.14**, 1.83*, 2.28*)
  - Adj. R2 in these regressions: values range from 0.004 to 0.027 as shown.

### Annex IV — Tolerable range defined as 1-year historical average exchange rate ±1.5 times standard deviation (Probit regressions)
- FX purchase_1st lag: 1.6911.625
  - z-values: (12.27)*** (11.75)***

- FX sale_1st lag: 1.391
  - z-value: (7.21)***

- FX purchase_2nd lag: 0.6060.524
  - z-values: (4.39)*** (3.75)***

- FX sale_2nd lag: 0.972
  - z-value: (4.91)***

- Excessive appreciation: 41.36734.138
  - z-values: (5.01)*** (3.81)***

- Excessive depreciation: 9.592
  - z-value: (3.44)***

- Excessive volatility: -0.170-0.246
  - z-values: (-1.75)* (-2.26)**

- Volatility: 0.244
  - z-value: (3.12)***

- Excessive appreciation * dummy for intervention policy change
  - Not shown in equation (1); constant reported as -2.034 with z-value (-21.04)***

- Excessive volatility * dummy for intervention policy change
  - Coefficient: ...0.375
  - z-value: ...(0.87)

- Constants: -1.544-1.500
  - z-values: (-18.25)*** (-17.61)***

- Model statistics:
  - No. of observations: 980 / 896 / 980 (as reported per column)
  - LR-chi2 (4): 627.7*** / 461.24***
  - F-stat.: 222.06***
  - Pseudo R2: 0.49 / 0.42
  - Adj. R2: 0.40

- Table 2 (impacts on level and volatility of the exchange rate) summary items:
  - Explanatory variables and signs reported consistently across Tables II–IV: FX purchase positive coefficients in level equations (e.g., 0.0150.0160.024), FX sale negative coefficients in level equations (e.g., -0.082 to -0.123), and FX sale negative and significant in volatility equations (e.g., -0.136 to -0.192).
  - FX sale_1st lag positive and significant in many specifications (e.g., 0.1070.1030.103).
  - Change in ER_LA2/... coefficient reported as 0.013 (significant in volatility equations).
  - Likelihood of FX purchase interacted with dummy for intervention policy change shows coefficients such as -0.017 (t-value -0.96) and 0.078 (t-value 1.68)* depending on specification.
  - Constants in these IV (2SLS) specifications: e.g., 0.1210.1340.137 with t-values (6.53)***, (6.09)***, (6.17)***.
  - No. of obs. for these regressions reported as 979/980/960 across columns; F-stat. values and Adj. R2 values presented per column.

*Source: _wp14217 - ANNEX I. SINGLE EQUATION REGRESSION OF THE CENTRAL BANK’S REACTION FUNCTION*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14217.pdf_