## 2.1 Approach (and related robustness sections)

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### Methodology
- Endogeneity addressed with two-stage least squares (2SLS) using instrumental variables that identify exogenous variations in FXI.
- Estimated panel specification:
  - Second stage (exchange rate equation):
    - log(ER_it) = α + β log(ER_it−1) + γ ̂FXI_it + δ′ X_it + η_i + ε_it
  - First stage (FXI equation / instrumenting FXI):
    - FXI_it = a + b log(ER_it−1) + c′ Z_it + d′ X_it + u_i + v_it
- Definitions and conventions:
  - ER_it: country i’s exchange rate at time t (nominal or real bilateral vs. U.S. dollar, or real effective).
  - An increase in ER represents an appreciation of the domestic currency.
  - FXI_it: proxy for foreign exchange intervention; Z_it: instruments; X_it: control variables.
  - u_i and η_i: country fixed effects.
  - Primary parameter of interest: γ. γ < 0 implies a positive intervention (buying foreign currency) depreciates the domestic currency.
- Benchmark assumes homogeneous parameters across countries; heterogeneity explored subsequently.

### Foreign Exchange Intervention (definition and measurement)
- Conceptual: FXI is any policy-induced financial operation that changes the public sector foreign exchange position (portfolio balance channel).
- Practical proxy: change in the (net) foreign asset position of the central bank (baseline).
- Robustness proxies:
  - Valuation-adjusted measures;
  - Off-balance-sheet operations (swaps, forwards, etc.);
  - Changes in gross international reserves.
- Normalization and controls:
  - FXI normalized by (HP filtered) trend GDP in U.S. dollars.
  - Interest rate (domestic and foreign) included in all specifications to control for monetary policy stance and isolate sterilized interventions.
  - Interest rates included rather than excluding observations classified as unsterilized intervention.

### Exchange rate determinants (controls)
- Parsimonious control set:
  - VIX (level)
  - Three commodity price indices (energy, metals, agriculture) with country-specific coefficients
  - Interest rate differential vis-à-vis the U.S.
- Expanded control set (may restrict sample):
  - GDP per capita and expected GDP growth (both relative to the U.S.)
  - Lagged trade balance
  - Trade openness
  - Additional global financial conditions variable: EPFR net portfolio flows to other countries in the sample
- Rationale: commodity prices capture high-frequency terms-of-trade shocks; interest rate inclusion aids interpreting results as sterilized intervention effects; inflation differential included when using nominal bilateral exchange rate.

### Instruments
- Candidate instruments correlated with FXI but not with contemporaneous exchange rate:
  - Lagged gross (net) international reserves relative to GDP, imports, external debt, or M2 (precautionary motive).
  - Interaction: degree of deposit dollarization × exogenous financial shocks (VIX, Global EMBI, EPFR) for stabilization motive.
  - Lagged trade balance (mercantilist motive).
- Baseline instrument selection criteria:
  i. First-stage coefficients consistent with economic theory.
  ii. Instrument mitigates endogeneity bias (fitted FXI coefficient in 2SLS lower than OLS).
  iii. Joint instrumentation passes overidentification (Hansen/J-test) and weak instrument (Stock and Yogo) tests.
- Stock and Yogo guidance: with the benchmark number of instruments, a test statistic above 18 (11) rejects relative bias above 5% (10%).

### Data
- Monthly observations for 52 countries (13 advanced, 39 emerging), January 1996-October 2013.
- Exclusions: countries using another country’s currency as legal tender; periods with de-facto free falling or dual exchange rate regimes.
- Data sources: IMF IFS, WEO, DOTS; Datastream; Consensus Forecast; World Bank GFDD; Haver Analytics (EPFR); Yeyati (2006) and IMF desks (deposit dollarization); Schindler (2009), Chinn and Ito (2006), Quinn and Toyoda (2008), IMF AREAER (capital controls indices).
- Outlier treatment: benchmark excludes 1% top and bottom observations for each variable (except bounded-by-definition variables); for exchange rates outliers excluded using month-to-month growth rate distribution.
- Stationarity: nominal and real bilateral exchange rates stationary; real effective exchange rates non-stationary in some cases/tests.

### Key descriptive statistics (selected exact figures)
- log RER: 9149 / -3.14 / 2.57 / -10.16 / 0.69
- log NER: 9149 / -3.03 / 2.47 / -9.96 / 0.73
- log REER: 8597 / 4.53 / 0.15 / 3.81 / 5.08
- FXI/GDP: 9149 / 0.19 / 0.71 / -2.70 / 3.77
- FXI/GDP (valuation adj): 9012 / 0.12 / 0.69 / -2.74 / 3.45
- FXI/GDP (valuation adj + off-BS): 9011 / 0.12 / 0.71 / -3.04 / 3.84
- FXI/GDP (∆Reserves): 9103 / 0.18 / 0.66 / -2.40 / 3.50
- FXI/M2 (instrumented): 9053 / 0.53 / 2.20 / -9.09 / 13.21
- FXI/Financial sector size (IFS, instrumented): 8741 / 0.39 / 1.44 / -5.57 / 9.67
- FXI/Financial sector size (WB, instrumented): 8424 / 0.45 / 1.85 / -9.15 / 14.13
- FXI/Market size (instrumented): 8515 / 2.27 / 14.17 / -65.66 / 152.99
- VIX: 9149 / 21.53 / 7.75 / 10.42 / 59.89
- Interest rate (differential): 9149 / 0.39 / 0.51 / -0.39 / 5.12
- Inflation rate (differential): 8723 / 3.09 / 4.99 / -4.71 / 49.75
- Change in M2/GDP: 9149 / 0.49 / 0.83 / -1.90 / 4.47
- Financial dollarization: 9149 / 23.45 / 23.24 / 0.00 / 92.60
- Import coverage: 9141 / 0.52 / 0.49 / -0.44 / 4.31
- Low import coverage: 9149 / 0.22 / 0.42 / 0.00 / 1.00
- Broad money coverage: 9146 / 0.39 / 0.40 / -1.42 / 2.16
- GDP per capita (differential): 9046 / -1.32 / 0.83 / -3.03 / 0.27
- Expected GDP growth (differential): 8571 / 1.08 / 2.54 / -14.36 / 11.02
- Trade Balance: 9039 / -0.29 / 1.01 / -3.70 / 3.57
- Trade Openness: 9046 / 5.43 / 3.04 / 1.41 / 27.68
- EPFR/GDP: 9149 / 0.01 / 0.11 / -0.59 / 0.46
- EMBI spread: 8421 / 4.78 / 2.54 / 1.51 / 14.19

*Source: _wp15130 - 2.1    Approach (section content).*

### Main robustness checks (summary)
- Normalizations of FXI and link to domestic financial deepening:
  - Alternative normalizations: M2; domestic financial sector size (IFS); broader financial system size (GFDD); domestic financial market size (GFDD).
  - Second-stage (dependent variable: real bilateral exchange rate) key coefficients (instrumented FXI normals):
    - FXI/GDP (instrumented): -1.430 ∗∗∗ (0.326)
    - FXI/M2 (instrumented): -0.468 ∗∗∗ (0.099)
    - FXI/Financial sector size (IFS, instrumented): -0.788 ∗∗∗ (0.172)
    - FXI/Financial sector size (WB, instrumented): -0.586 ∗∗∗ (0.125)
    - FXI/Market size (instrumented): -0.124 ∗∗∗ (0.035)
    - Dependent variable (lagged): 0.966 ∗∗∗ (0.004)
    - VIX: -0.043 ∗∗∗ (0.005)
  - Implied effect of FXI/GDP (evaluated at mean GDPit/NormJit) reported as: -1.40, -1.44, -1.41, -1.61.
  - Formal tests (Table 5) do not indicate a preferred metric; no significant influence of domestic financial depth on FXI effectiveness.
- Instrumentation robustness:
  - Exclude one instrument at a time (Table 6): FXI/GDP (instrumented) varies between -1.395 and -1.771; Stock & Yogo stats include 19.42, 28.00, 24.01, 22.38, 5.07, 6.48.
  - Use only one instrument at a time (Table 8): FXI/GDP (instrumented) examples:
    - Change in M2/GDP: -1.310 ∗∗∗ (0.375), Stock & Yogo 68.86
    - Dep. Dollarization×VIX: -1.995 (1.389), Stock & Yogo 8.48
    - Import coverage: -1.614 ∗∗ (0.803), Stock & Yogo 6.98
    - Broad money: -2.454 ∗ (1.365), Stock & Yogo 5.69
  - First-stage examples (individual instruments, dependent variable: FXI % GDP):
    - Change in M2/GDP: 0.104 ∗∗∗ (0.022), F stat 22.51, F p-value 0.00
    - Financial dollarization×VIX: -0.014 ∗∗∗ (0.005), F stat 8.38, F p-value 0.01
    - Import coverage (lagged): -0.251 ∗∗ (0.116), F stat 4.65, F p-value 0.01
    - Broad money coverage (lagged): -0.227 ∗ (0.125), F stat 3.30, F p-value 0.08
- Exchange rate pegs:
  - Restricting sample by excluding de-jure pegged regimes in three increasingly strict ways yields results very similar to baseline, with FXI coefficients of somewhat larger absolute magnitude.
  - Excluding de-facto peg regimes yields broadly similar results.
- Other simultaneous policy responses:
  - Capital controls: excluding country/year observations with annual changes in Quinn and Toyoda index reduces sample by about 7 percent; coefficients remain similar though slightly smaller in absolute value.
  - Interest rate changes: instrumenting interest rate differential and separating domestic/foreign rates deliver mixed results for interest rate effects, but FXI coefficient remains basically unaltered.
- Proxy and measurement of FXI:
  - Robust to excluding 10% smallest absolute FXI observations; valuation-adjusted proxy; including off-balance-sheet operations; using gross reserves.
  - Different FXI measures highly correlated; results stable (Appendix Tables A8 and A9).

### Numeric robustness highlights
- Baseline second-stage FXI/GDP (instrumented): -1.430 ∗∗∗ (0.326).
- Range under instrument-dropping: -1.395 to -1.771 (Table 6).
- Single-instrument FXI/GDP estimates: -1.310 ∗∗∗; -1.995; -1.614 ∗∗; -2.454 ∗ (Table 8).
- First-stage relevance: Change in M2/GDP single-instrument first-stage coefficient 0.104 ∗∗∗ (0.022), F stat 22.51.
- Sample reduction when excluding annual changes in Quinn and Toyoda capital controls index: about 7 percent.

### Other robustness checks and extensions
- Alternative exogenous financial shock measures: EMBI Global sovereign spread, EPFR flows used as substitutes for VIX (controls and instruments).
- Country-specific coefficients allowed for VIX, interest rate, and both.
- Outlier/sample treatments: drop 2% tails; winsorize 1% and 2%; drop June 2008–May 2009 crisis period; drop Asian crisis period; drop largest 5% and 10% FXI/GDP observations.
- Structural break checks: restrict to 2003-13; restrict to inflation targeting (IT) countries/periods.
- Real effective exchange rate gap added as a control.
- First-differences specification: FXI coefficient negative and significant but smaller in absolute magnitude (baseline permits gradual mean reversion via lagged level).
- Instrumentation note: For interest rate differential instrumentation, Findol×VIX is significant and positive in first stage (in dollarized economies interest rate used to stabilize currency in response to VIX shocks).

### Dynamic effects
- up to three lags of FXI added; contemporaneous FXI instrumented; lags included as controls.
- Immediate impact similar to benchmark; effects persistent, more so for nominal than real exchange rates.
- Lags’ coefficients positive → impact of FXI on exchange rate decreases over time; decay faster than average shock (AR coefficient).
- Half-life estimates:
  - FXI shocks: between 12 and 23 months (highest for nominal bilateral exchange rate; lowest for real effective exchange rate).
  - General shock to exchange rate: between 18 and 29 months (baseline).
- Robustness: Appendix Table A12 confirms dynamics; without outlier treatment FXI effect stronger but less persistent.

### Asymmetric effects
- Separate instrumentation and estimation for positive interventions (FXI_POS).
- Result: no evidence of asymmetric effect; positive and negative FXI equally effective.

### Key quantitative findings and policy-relevant conclusions
- Impact of a foreign currency purchase of 1 percentage point of GDP:
  - Nominal exchange rate depreciation: in the range of [1.7-2.0] percent.
  - Real exchange rate depreciation: in the range of [1.4-1.7] percent.
- Persistence:
  - FXI half-life: [12-23] months.
  - Half-life of a general shock: [18-29] months.
- Policy implication:
  - Positive and negative interventions appear equally effective; FXI is a useful policy tool for both appreciation and depreciation pressures.
  - FXI should be judged on relative costs and benefits vis-à-vis other instruments, not on effectiveness alone.

*Source: _wp15130 - 2.3 Main Robustness Checks; 2.4 Other robustness checks (excerpt).*

### Annex 1 — Proxies for FXI (valuation and off-BS adjustments)
- Valuation- and income-adjusted net foreign currency asset proxy:
  - FXI_j,t ≡ ∆NFCA_j,t − ∆val_NFCA_j,t − ∆inc_NFCA_j,t (equation (11))
  - ∆NFCA_j,t = Σ_{s∈S} ∆H^s_{j,t} (12)
  - ∆val_NFCA_j,t = Σ_{s∈S} (P^s_t − P^s_{t−1}) H^s_{j,t−1} (13)
  - ∆inc_NFCA_j,t = Σ_{s∈S} i^s_{t−1} H^s_{j,t−1} (14)
  - H^s_{j,t}: net position on security s; P^s_t: market price; i^s_t: monthly interest rate.
  - Price of a (zero coupon) security maturing n months ahead: (1 + i^s_t)^{−n}.
- Data/assumptions:
  - IMF Data Template on International Reserves and Foreign Currency Liquidity used for asset breakdown.
  - Currency composition assumed from COFER: US dollar, Australian dollar, Canadian dollar, British pound, Japanese Yen, Swiss Franc, Euro.
  - Securities assumed mostly 10-year bonds (Dominguez (2012) assumption).
  - 3-month interbank yields proxied returns on foreign currency deposits; valuation effects zero for currency and deposits.
  - IMF reserve position and SDRs valued at SDR rate; gold at market prices.
- Off-balance-sheet extended measure:
  - FXI_j,t ≡ ∆NFCA_j,t − (∆val_NFCA_j,t + ∆inc_NFCA_j,t) + OBS_i,t (equation (15))
  - OBS_i,t includes changes in aggregate short/long positions in forwards and futures in foreign currencies vis-à-vis domestic currency and forward leg of currency swaps, as reported in the Reserve Template.
- Valuation adjustments summary (Table 11 categories):
  - Securities: currency shares from COFER; 10-year sovereign bonds; implicit market value based on 10-year rate; estimated income: 10-year coupon rate.
  - Currency and deposits: currency shares from COFER; 3-month CD; valuation adjustment: none; estimated income: 3-month interbank rate.
  - IMF reserve position: SDR basket; valuation adjustment: SDR valuation changes; estimated income: SDR rate.
  - SDRs: valuation adjustment none indicated; estimated income: SDR rate.
  - Gold: valuation adjustment: Gold Price variations; estimated income: none.

*Source: _wp15130 - Annex 1    Proxies for FXI.*

### Annex 2 — Capital controls (interaction with FXI)
- Model introduces interaction FXI/GDP × KC_it−1 and instruments both FXI/GDP and the interaction term (Equations 16–18).
- Capital controls indices used: Schindler (2009); Quinn and Toyoda (2008); Chinn and Ito (2006).
- Indices introduced in levels or as threshold dummies (absolute or time-varying); lagged values used to mitigate endogeneity.
- Main empirical findings:
  - Overall: results "do not lend support to the hypothesis of complementarity between capital controls and FXI."
  - Some specifications suggest the effect of FXI on the exchange rate may decrease with higher capital controls (counter-intuitive).
- Representative robustness statistics (selected second-stage FXI/GDP coefficients, dependent variable: real bilateral exchange rate):
  - Column (1): -1.231 ∗∗∗ (0.335)
  - Column (2): -1.392 ∗∗∗ (0.405)
  - Column (3): -1.686 ∗∗∗ (0.450)
  - Column (4): -1.650 ∗∗∗ (0.443)
  - Column (5): -2.004 ∗∗∗ (0.543)
  - Column (6): -2.007 ∗∗∗ (0.545)
- Interaction coefficients examples:
  - VIX × Capital controls = -0.048 ∗∗∗ (0.008)
  - VIX × Capital controls = -0.039 ∗∗∗ (0.007)
  - VIX × Capital controls = -0.064 ∗∗∗ (0.009)
  - VIX × Capital controls = -0.065 ∗∗∗ (0.009)
- Sample/fit examples:
  - Observations: examples 8284, 7474, 8020, 8020, 7467, 7467
  - Countries: examples 52, 51, 50, 50, 47, 47
  - R2: 0.98, 0.98, 0.98, 0.98, 0.97, 0.97
  - J p-value examples: 0.20, 0.22, 0.22, 0.45, 0.70, 0.69
  - Stock & Yogo stat examples: 17.24, 13.10, 12.77, 12.90, 10.19, 10.11
- Interpretation and policy implications:
  - Relationship between FXI and capital controls can reflect complementarity (quotas increase FXI effectiveness) or substitution (controls obviate FXI).
  - Empirical ambiguity driven by heterogeneity across countries, instruments, and types of controls; potential instrument validity concerns when capital mobility constrained.
  - Policy implication: analyses of FXI effectiveness should explicitly account for level and nature of capital controls; caution with IV results involving interactions with capital controls.

*Source: _wp15130 - Annex 2 — Capital controls (from _wp15130).*

### 2.1    Approach

### 2.1    Approach

### Methodology
- Endogeneity of interventions to exchange rate movements is addressed using a two-stage least squares approach with instrumental variables that identify exogenous variations in FXI (interventions unrelated to contemporaneous exchange rate movements).
- Estimated panel specification:
  - Second stage (exchange rate equation):
    - log(ER_it) = α + β log(ER_it−1) + γ ̂FXI_it + δ′ X_it + η_i + ε_it
  - First stage (FXI equation / instrumenting FXI):
    - FXI_it = a + b log(ER_it−1) + c′ Z_it + d′ X_it + u_i + v_it
- ER_it denotes country i’s exchange rate at time t (either nominal or real bilateral, vis-a-vis the U.S. dollar, or real effective, depending on the specification).
- Convention: an increase in ER represents an appreciation of the domestic currency in all cases.
- FXI_it is the proxy for foreign exchange intervention; Z_it is the set of instrumental variables; X_it is a set of control variables.
- u_i and η_i denote country fixed effects for the first and second stage regressions, respectively.
- Primary interest: parameter γ. A value of γ < 0 indicates that a positive intervention (buying foreign currency) depreciates the domestic currency.
- Benchmark specification assumes homogeneous parameters across countries; later relaxations consider heterogeneity.

### Foreign Exchange Intervention (definition and measurement)
- From the portfolio balance channel perspective, FXI is any policy-induced financial operation that changes the foreign exchange position of the public sector, implying changes in the relative supply of domestic assets.
- Practical measurement issues:
  - Ideal measure: policy-induced changes in FX position of the consolidated public sector — rarely available at high frequency.
  - Empirical focus: central bank’s balance sheet (consistent with literature).
  - Actual purchases and sales of foreign assets often not reported; study uses several proxies for FXI.
- Baseline proxy: change in the (net) foreign asset position of the central bank.
- Robustness checks include proxies that correct for valuation effects and off-balance sheet operations (swaps, forwards, etc.).
- FXI normalized by (HP filtered) trend GDP in U.S. dollars to:
  - Prevent endogeneity from movements in the U.S. dollar value of nominal GDP;
  - Facilitate interpretation and comparability across countries and time;
  - Help prevent unit root problems.
- Interest rate (domestic and foreign) included in all specifications to control for monetary policy stance and isolate sterilized interventions.
- Interest inclusion approach favored over excluding observations classified as unsterilized intervention.

### Exchange Rate Determinants (Controls)
- Controls classified into two groups:
  - Small set (parsimonious):
    - Level of the Chicago Board Options Exchange Market Volatility Index (VIX)
    - Three indices of commodity prices (energy, metals, agriculture) with country-specific coefficients
    - Interest rate differential vis-à-vis the U.S. (bilateral exchange rate with US Dollar used in most specifications)
  - Expanded set (standard determinants; may restrict sample due to data availability):
    - GDP per capita and expected GDP growth (both relative to the U.S.)
    - Lagged trade balance
    - Trade openness
    - Additional global financial conditions variable: net portfolio flows to other countries in the sample (EPFR)
- Rationale for specific controls:
  - Commodity prices capture high-frequency terms of trade shocks and differential impacts depending on export/import composition.
  - Including interest rate enables interpreting results as pertaining to sterilized intervention by controlling for simultaneous interest rate changes.
  - When using nominal bilateral exchange rate, include inflation differential vis-à-vis the U.S. to control for persistently high inflation effects.
- Robustness checks include introducing domestic and foreign interest rates separately.

### Instruments
- Instruments sought that are strongly correlated with FXI but not with the exchange rate.
- Explored instruments related to motives for FXI:
  - Reserve accumulation for precautionary reasons: lagged gross (net) international reserves relative to GDP, imports, external debt, or M2; evaluated in levels and relative to the average of other countries to capture ‘keeping up with the Joneses’ effects.
  - Exchange rate stabilization motives (new instruments): interaction between degree of deposit dollarization in the domestic financial system and measures of exogenous financial shocks (VIX, Global EMBI, EPFR flows) that exert depreciation pressures on EMEs.
  - Lagged trade balance as a potential mercantilist-motive instrument.
- Baseline instruments chosen according to three criteria:
  i. Each instrument delivers a coefficient sign in the first stage consistent with economic theory (reflecting the intended intervention motive).
  ii. The instrument mitigates endogeneity bias in the second stage: the coefficient for fitted values of FXI in the second stage should be lower than in simple OLS (directional expectation: OLS has an upward bias because central banks tend to react to dampen exchange rate movements when exchange rates are defined as US$/LC).
  iii. Joint instrumentation must pass overidentification (Hansen/J-test) and weak instrument tests (Stock and Yogo (2002) thresholds).
- Stock and Yogo guidance used: given the number of instruments in benchmark, a test statistic above 18 (11) rejects a relative bias above 5% (10%).

### Data
- Monthly observations for 52 countries (13 advanced and 39 emerging market economies), period January 1996-October 2013.
- Sample excludes countries that use other countries’ currencies as legal tender.
- Periods with de-facto exchange rate regimes classified as freely falling or dual exchange rates are excluded (classification follows Ilzetzki et al., 2010).
- Data sources:
  - IMF’s International Financial Statistics, World Economic Outlook, Direction of Trade Statistics
  - Interest rates from Datastream
  - Expected GDP growth from Consensus Forecast
  - Size of domestic financial sector from World Bank’s Global Financial Development Database (GFDD)
  - EPFR flows from Haver Analytics
  - Deposits dollarization from Yeyati (2006) database and IMF country desks
  - Capital control indices from Schindler (2009), Chinn and Ito (2006), Quinn and Toyoda (2008), extended with IMF AREAER where needed
- Benchmark specification excludes the 1% top and bottom observations for each variable (except bounded-by-definition variables) to reduce outlier influence; 1st and 99th percentiles taken over cross-country distribution for whole sample. For exchange rates, outliers excluded using month-to-month growth rate distribution.
- Variables tested for stationarity: both nominal and real bilateral exchange rates are stationary; real effective exchange rates display non-stationarity in some cases and under some tests.

### Key descriptive statistics (selected exact figures from Table 1)
- Obs / Mean / Std Dev / Min / Max for selected variables:
  - log RER: 9149 / -3.14 / 2.57 / -10.16 / 0.69
  - log NER: 9149 / -3.03 / 2.47 / -9.96 / 0.73
  - log REER: 8597 / 4.53 / 0.15 / 3.81 / 5.08
  - FXI/GDP: 9149 / 0.19 / 0.71 / -2.70 / 3.77
  - FXI/GDP (valuation adj): 9012 / 0.12 / 0.69 / -2.74 / 3.45
  - FXI/GDP (valuation adj + off-BS): 9011 / 0.12 / 0.71 / -3.04 / 3.84
  - FXI/GDP (∆Reserves): 9103 / 0.18 / 0.66 / -2.40 / 3.50
  - FXI/M2 (instrumented): 9053 / 0.53 / 2.20 / -9.09 / 13.21
  - FXI/Financial sector size (IFS, instrumented): 8741 / 0.39 / 1.44 / -5.57 / 9.67
  - FXI/Financial sector size (WB, instrumented): 8424 / 0.45 / 1.85 / -9.15 / 14.13
  - FXI/Market size (instrumented): 8515 / 2.27 / 14.17 / -65.66 / 152.99
  - VIX: 9149 / 21.53 / 7.75 / 10.42 / 59.89
  - Interest rate (differential): 9149 / 0.39 / 0.51 / -0.39 / 5.12
  - Inflation rate (differential): 8723 / 3.09 / 4.99 / -4.71 / 49.75
  - Change in M2/GDP: 9149 / 0.49 / 0.83 / -1.90 / 4.47
  - Financial dollarization: 9149 / 23.45 / 23.24 / 0.00 / 92.60
  - Import coverage: 9141 / 0.52 / 0.49 / -0.44 / 4.31
  - Low import coverage: 9149 / 0.22 / 0.42 / 0.00 / 1.00
  - Broad money coverage: 9146 / 0.39 / 0.40 / -1.42 / 2.16
  - GDP per capita (differential): 9046 / -1.32 / 0.83 / -3.03 / 0.27
  - Expected GDP growth (differential): 8571 / 1.08 / 2.54 / -14.36 / 11.02
  - Trade Balance: 9039 / -0.29 / 1.01 / -3.70 / 3.57
  - Trade Openness: 9046 / 5.43 / 3.04 / 1.41 / 27.68
  - EPFR/GDP: 9149 / 0.01 / 0.11 / -0.59 / 0.46
  - EMBI spread: 8421 / 4.78 / 2.54 / 1.51 / 14.19

- Appendix materials referenced: Annex Table A1 (sample details), Appendix Table A2 (variables’ construction and sources), Appendix Figure A2 (distribution of FXI).

Italic: Source: _wp15130 - 2.1    Approach (section content).

### 2.3    Main Robustness Checks

### 2.3    Main Robustness Checks

### Different normalizations of FXI and link to domestic financial deepening
- Motivation: normalizing FXI by GDP is intuitive but theory suggests normalizations relative to domestic asset supply or size of domestic financial markets may be more relevant (portfolio balance channel); signaling channel normalization is less clear.
- Four alternative norms explored:
  - broad money (M2);
  - size of domestic financial sector (total domestic assets held by domestic banks, IFS, excluding central bank and non-depositary financial corporations);
  - broader domestic financial system size (GFDD: domestic assets of domestic banks, non-bank financial institutions, pension funds, mutual funds, insurance companies);
  - domestic financial market size (GFDD: stock market capitalization, value of outstanding domestic private and public debt securities).
- Correlation: In general, the correlation across different measures is high, except for the relationship between FXI/M2 and the other metrics.
- Second-stage results (Table 4, dependent variable: real bilateral exchange rate):
  - FXI/GDP (instrumented): -1.430 ∗∗∗ (0.326)
  - FXI/M2 (instrumented): -0.468 ∗∗∗ (0.099)
  - FXI/Financial sector size (IFS, instrumented): -0.788 ∗∗∗ (0.172)
  - FXI/Financial sector size (WB, instrumented): -0.586 ∗∗∗ (0.125)
  - FXI/Market size (instrumented): -0.124 ∗∗∗ (0.035)
  - Dependent variable (lagged): 0.966 ∗∗∗ (0.004)
  - VIX: -0.043 ∗∗∗ (0.005)
- Implied effect of FXI/GDP (evaluated at mean GDPit/NormJit) reported in Table 4: -1.40, -1.44, -1.41, -1.61 (row labelled "Implied effect of FXI/GDP").
- Formal test for decreasing effects (introducing FXI_GDP and FXI_NormJ simultaneously, instrumenting both):
  - Regression structure given by equations (4)–(6).
  - Marginal effect: ∂log(ERit)/∂(FXI/GDP)it = γ1 + γ2 (GDPit/Norm2it).
  - Results (Table 5) do not point to a preferred metric and indicate the effect of interventions on the exchange rate is not significantly influenced by the depth of the domestic financial system.
  - Selected coefficients from Table 5:
    - Column (3): FXI/GDP (instrumented): -1.851 ∗ (1.116)
    - Column (4): FXI/GDP (instrumented): -1.131 (0.806)
    - Dependent variable (lagged) across columns: 0.964–0.967 ∗∗∗ (0.004)
    - VIX across columns: -0.041 to -0.050 ∗∗∗ (0.005–0.006)

### Instrumentation robustness
- Two exercises:
  1. Exclude one instrument at a time (Tables 6 and 7): results robust to dropping any single instrument; coefficient of FXI in second stage remains close to baseline and statistically significant. Strength of instrumentation partly driven by change in M2 (Stock and Yogo test weakens when dropping M2-related instruments).
     - Second-stage FXI/GDP (instrumented) across drops (Table 6):
       - Baseline: -1.430 ∗∗∗ (0.326)
       - Dropping Import coverage: -1.468 ∗∗∗ (0.349)
       - Dropping Broad money coverage: -1.424 ∗∗∗ (0.326)
       - Dropping Dep. Dollarization×VIX: -1.395 ∗∗∗ (0.334)
       - Dropping Change in M2/GDP: -1.771 ∗∗ (0.721)
       - Dropping Change in M2 & Broad money coverage: -1.753 ∗∗ (0.718)
     - Stock & Yogo stat examples: 19.42, 28.00, 24.01, 22.38, 5.07, 6.48 (Table 6).
  2. Use only one instrument at a time (Table 8): significance of second-stage FXI coefficient falls in some cases, but magnitude remains close to baseline.
     - FXI/GDP (instrumented) when instrumenting only with:
       - Change in M2/GDP: -1.310 ∗∗∗ (0.375)
       - Dep. Dollarization×VIX: -1.995 (1.389)
       - Import coverage: -1.614 ∗∗ (0.803)
       - Broad money: -2.454 ∗ (1.365)
     - Stock & Yogo stat examples (Table 8): 68.86, 8.48, 6.98, 5.69
- First-stage strength (Table 9, individual instruments, dependent variable: foreign exchange intervention (% GDP)):
  - Change in M2/GDP (as single instrument) first-stage: Change in M2/GDP 0.104 ∗∗∗ (0.022), F stat 22.51, F p-value 0.00
  - Financial dollarization×VIX: coefficient -0.014 ∗∗∗ (0.005), F stat 8.38, F p-value 0.01
  - Import coverage (lagged): -0.251 ∗∗ (0.116), F stat 4.65, F p-value 0.01
  - Broad money coverage (lagged): -0.227 ∗ (0.125), F stat 3.30, F p-value 0.08

### Exchange rate pegs
- Baseline includes all exchange rate regimes except de facto free falling/dual exchange rates and countries without their own currency.
- Robustness: restrict sample by excluding de-jure pegged regimes in three increasingly strict ways:
  1. excluding de-jure pegs and crawling pegs;
  2. excluding the latter and ‘narrow crawling band’ regimes (<= +/-2%);
  3. excluding the latter two and ‘wide crawling band’ regimes (<= +/-5%).
- Results (Appendix Table A5): very similar to baseline, with FXI coefficients of somewhat larger absolute magnitude.
- Excluding de-facto peg regimes: results broadly similar to baseline (Appendix Table A5).

### Other simultaneous policy responses
- Capital controls:
  - Problem: contemporaneous changes in capital flow restrictions could cause omitted variable bias; available indices at annual frequency only.
  - Approach: exclude country/year observations where Quinn and Toyoda index of capital controls changes at annual frequency; sample reduces by about 7 percent.
  - Results (Appendix Table A6, columns 1 and 2): coefficients do not change significantly; coefficient of interest slightly smaller in absolute value, suggesting some contemporaneous use of capital flow measures with FXI.
  - Allowing heterogeneity: include interactions of key external financial variables with lagged capital controls index; results similar to baseline (Appendix Table A6, columns 3 and 4).
- Interest rate changes:
  - Baseline surprising result: interest rate differential coefficient in second stage is small and non-significant.
  - Two concerns:
    1. Endogeneity of interest rate to exchange rate (countries may use interest rate to defend the exchange rate). Remedy: instrument interest rate differential by adding an extra first-stage equation for interest rate.
    2. Asymmetric effects of domestic and foreign interest rates. Remedy: introduce domestic and foreign interest rates separately.
  - Variations deliver mixed results for interest rate effects (Appendix Table A7), but in all cases the FXI coefficient in second stage remains basically unaltered.

### Proxy and measurement of FXI
- Main proxy used: change in central bank NFA position (consistent with other studies) but contaminated by valuation effects and income flows.
- Robustness checks performed:
  - Excluding observations with small absolute values (10% smallest) of FXI to reduce valuation/income flow contamination.
  - Using a refined proxy adjusting for estimated valuation effects and income flows (methodology described in Annex 1).
  - Including off-balance sheet operations to capture non-spot instruments (FX derivatives) (Annex 1).
  - Using changes in gross international reserves instead of net concept.
- Findings: results are very stable across these alternative measures; different measures of FXI are highly correlated (see Appendix Tables A8 and A9).

### Summary of key numeric robustness findings
- Baseline second-stage FXI/GDP (instrumented): -1.430 ∗∗∗ (0.326).
- Range of FXI/GDP second-stage coefficients under instrument-dropping robustness: -1.395 to -1.771 (Table 6).
- When instrumenting with single instruments, FXI/GDP estimates: -1.310 ∗∗∗; -1.995; -1.614 ∗∗; -2.454 ∗ (Table 8).
- First-stage relevance example: Change in M2/GDP single-instrument first-stage coefficient 0.104 ∗∗∗ (0.022), F stat 22.51.
- Sample reduction when excluding annual changes in Quinn and Toyoda capital controls index: about 7 percent.

*Italic: Source: _wp15130 - 2.3    Main Robustness Checks*

### 2.4    Other robustness checks

### 2.4    Other robustness checks

### Robustness checks undertaken
- Explored alternative measures of exogenous financial shocks:
  - Substituted the VIX by the EMBI Global sovereign spread or the measure of EPFR flows to other countries.
  - Used these alternative variables both as controls and as instruments interacted with deposits dollarization.
- Allowed for country-specific coefficients for VIX, interest rate, and both.
- Changed treatment of outliers and sample period:
  - Dropped 2% top and bottom outliers.
  - Winsorized the data (1% and 2%).
  - Dropped the crisis period (from June 2008 to May 2009).
  - Dropped the Asian crisis period.
  - Dropped the largest 5% and 10% FXI/GDP observations.
- Considered possible structural breaks related to changes in monetary policy regimes:
  - Restricted the sample period to 2003-13.
  - Restricted the sample only to inflation targeting (IT) countries/periods.
- Added a measure of the real effective exchange rate gap, defined by deviations from an HP filter.
- Estimated a model in first differences to address stationarity concerns:
  - The estimated coefficient for FXI remained negative and statistically significant, although smaller in absolute magnitude.
  - Explanation: baseline permits gradual mean reversion via lagged exchange rate level; first-differences specification imposes permanent effects of shocks.

- Instrumentation note:
  - For the instrumentation of the interest rate differential, Findol×VIX is significant and positive in the first stage, suggesting that in dollarized economies the interest rate is used to stabilize the domestic currency in response to external financial (VIX) shocks.

- Overall conclusion from robustness checks:
  - Results display very stable estimates for the effect of FXI on the exchange rate, with magnitudes consistent with those of the baseline specification.

### Dynamic effects (extensions)
- Method:
  - Added up to three lags of FXI to the benchmark specification (further lags were not significant).
  - Contemporaneous FXI instrumented as before; lags included in both stages as controls.
  - Figure 3 displays implied dynamics for an FXI (FX purchase) of 1 percent of GDP for different exchange rate measures.
- Findings:
  - Immediate impact of FXI on the exchange rate remains similar to benchmark.
  - Effects are relatively persistent, more so for nominal than for real exchange rates.
  - Coefficients of the three FXI lags are positive, implying the impact of FXI on the exchange rate decreases over time and the decay is faster than that of an average shock (captured by the autoregressive coefficient).
- Half-life estimates:
  - Half-life of FXI shocks ranges between 12 and 23 months, with highest values for the nominal bilateral exchange rate and lowest for the real effective exchange rate.
  - These FXI half-life estimates remain below those of a general shock to the exchange rate, which lie between 18 and 29 months according to baseline estimates.
  - Context: previous studies reported half-lives ranging between 2 and 7 years depending on approach; referenced studies obtained estimates of 4 years, 2-5 years, below 3 years, or 1-2 years under alternative definitions.
- Robustness:
  - A number of additional robustness checks (see Appendix Table A12) confirm these dynamics.
  - Without outlier treatment, FXI effect is generally stronger but less persistent due to smaller autoregressive coefficients and higher coefficients for lagged FXI regressors.

### Asymmetric effects
- Hypothesized channels for asymmetry:
  - FX sales may be constrained by a lower bound on reserves, limiting central bank ability to defend exchange rate levels; anticipation could mute FX sales effects.
  - FX purchases can be expanded but larger FX positions entail quasi fiscal costs and may not be sustained indefinitely; expectations about such costs could render FXI ineffective.
- Empirical specification:
  - Enriched the baseline to instrument positive interventions (FXI_POS) separately and to estimate γ2, where γ2<0 implies positive interventions are more effective and γ2>0 implies they are less effective than negative ones.
- Finding:
  - No evidence of an asymmetric effect in either direction; positive and negative FXI are equally effective.

### Key quantitative findings and policy-relevant conclusions
- Impact of FXI on exchange rate level:
  - A purchase of foreign currency of 1 percentage point of GDP causes a depreciation of:
    - Nominal exchange rate in the range of [1.7-2.0] percent.
    - Real exchange rate in the range of [1.4-1.7] percent.
- Persistence:
  - FXI half-life in the range of [12-23] months depending on specification.
  - Half-life of a general shock to the exchange rate between 18 and 29 months.
- Policy implication:
  - Positive and negative interventions appear equally effective, indicating FXI is a useful policy tool both when facing appreciation and depreciation pressures.
  - FXI should be judged on its relative costs and benefits vis-à-vis other instruments, rather than on effectiveness alone.

*Source: 2.4 Other robustness checks (excerpt).*

### Annex 1    Proxies for FXI

### Annex 1    Proxies for FXI

### Adjusting NFA for valuation and income flows
- Purpose: construct a more precise proxy for foreign exchange intervention (FXI) by adjusting reserve series for valuation effects and income flows.
- Core net concept and definitions:
  - FXI_j,t ≡ ∆NFCA_j,t − ∆val_NFCA_j,t − ∆inc_NFCA_j,t (11)
  - ∆NFCA_j,t = Σ_{s∈S} ∆H^s_{j,t} (12)
  - ∆val_NFCA_j,t = Σ_{s∈S} (P^s_t − P^s_{t−1}) H^s_{j,t−1} (13)
  - ∆inc_NFCA_j,t = Σ_{s∈S} i^s_{t−1} H^s_{j,t−1} (14)
  - H^s_{j,t} is the net position on security s at time t; P^s_t denotes market price of foreign assets at time t; i^s_t denotes the monthly interest rate on those securities.
  - Price of a (zero coupon) security maturing n months ahead is estimated by (1 + i^s_t)^{−n}.
- Data and assumptions:
  - Breakdown of foreign currency assets follows the IMF’s Data Template on International Reserves and Foreign Currency Liquidity.
  - Currency composition of asset classes is assumed uniform and broken down into 7 major currencies per COFER: US dollar, the Australian dollar, Canadian dollar, British pound, Japanese Yen, Swiss Franc and Euro.
  - Central bank foreign liabilities are taken from IMF’s International Financial Statistics to complement asset-focused reserve template.
  - Securities are assumed mostly composed of 10-year bonds (as in Dominguez (2012)).
  - 3-month interbank yields are used as proxies for returns on holdings of foreign currency and deposits; valuation effects are zero for currency and deposits.
  - IMF reserve position and holdings of SDR are valued at the SDR rate and generate income according to the SDR interest rate.
  - Gold holdings are valued at market prices.
- Implementation note: Table 11 summarizes the information used to make the valuation and income flow adjustments.

### Off Balance Sheet FX Interventions
- Extended measure including off-balance sheet operations:
  - FXI_j,t ≡ ∆NFCA_j,t − (∆val_NFCA_j,t + ∆inc_NFCA_j,t) + OBS_i,t (15)
  - OBS_i,t includes changes in aggregate short and long positions in forwards and futures in foreign currencies vis-a-vis the domestic currency (including the forward leg of currency swaps), and financial instruments denominated in foreign currency but settled by other means (e.g., in domestic currency), as reported in the International Reserves and Foreign Currency Liquidity Template.

### Valuation adjustments (summary of Table 11)
- Official Reserve Assets — Foreign currency reserves:
  - Securities:
    - Currency shares from COFER (US$, AC, £, U, A$, C$, and SFranc)
    - Asset/Maturity: 10-year sovereign bonds
    - Valuation Structure: Implicit market value based on 10-year rate
    - Estimated Income Structure: 10-year coupon rate
  - Total currency and deposits:
    - Currency shares from COFER (US$, AC, £, U, A$, C$, and SFranc)
    - Asset/Maturity: 3-month CD
    - Valuation adjustment: None
    - Estimated Income Structure: 3-month interbank rate
  - IMF reserve position:
    - Currency: SDR basket
    - Asset/Maturity: SDR basket
    - Valuation adjustment: SDR valuation changes
    - Estimated Income Structure: SDR rate
  - SDRs:
    - Valuation adjustment: None indicated in table
    - Estimated Income Structure: SDR rate (implied above)
  - Gold:
    - Asset/Maturity: None
    - Valuation adjustment: Gold Price variations
    - Estimated Income Structure: None
- Other reserve assets:
  - Currency shares from COFER (US$, AC, £, U, A$, C$, and SFranc)
  - Asset/Maturity: 10-year sovereign bonds
  - Valuation Structure: Implicit market value based on 10-year rate
  - Estimated Income Structure: 10-year coupon rate
- Source notes from table:
  - Source: IMF COFER and Data Template on International Reserves /Foreign Currency Liquidity.
  - Footnote 1: Using annual aggregate statistics for the groups of emerging market economies. Weights are adjusted proportionally to add to 1.
  - Footnote 2: As in Dominguez (2012), assumes 10-year maturity holdings.
  - Footnote 3: Computed from the market interest rate.

*Source: _wp15130 - Annex 1    Proxies for FXI*

### Annex 2    Capital controls

### Annex 2 — Capital controls

### Methodology: interaction between FXI and capital controls
- Model specification introduces an interaction term between FXI and capital controls, estimated via instrumental variables:
  - log(ER_it) = α + β log(ER_it−1) + γ3 ̂FXI/GDP_it + γ4 ̂(FXI/GDP_it × KC_it−1) + δ′X_it + η_i + ε_it  (Equation 16)
  - FXI/GDP_it is instrumented: FXI/GDP_it = a3 + b3 log(ER_it−1) + c′3 Z_it + e′3 (Z_it × KC_it−1) + d′3 X_it + u_i + v_it  (Equation 17)
  - FXI/GDP_it × KC_it−1 is instrumented separately: FXI/GDP_it × KC_it−1 = a4 + b4 log(ER_it−1) + c′4 Z_it + e′4 (Z_it × KC_it−1) + d′4 X_it + w_i + z_it  (Equation 18)
- Capital controls (KC_it) measures used:
  - Schindler (2009)
  - Quinn and Toyoda (2008)
  - Chinn and Ito (2006)
- Each index introduced either in levels or as threshold dummies for “high capital controls” using different threshold values.
- Both absolute (time-invariant) and time-varying thresholds (based on the period cross-country distribution) are explored.
- Lagged values of capital controls are used to mitigate endogeneity concerns; the level of capital controls is also included as a control variable.
- The set of instruments includes the baseline instruments both alone and interacted with capital controls.

### Main empirical findings
- Overall result: the authors report that their results "do not lend support to the hypothesis of complementarity between capital controls and FXI."
- In some specifications the results are counter-intuitive:
  - Evidence sometimes suggests that the effect of FXI on the exchange rate may decrease with higher levels of capital controls.
- Possible interpretations and mechanisms noted:
  - Complementarity channel: restrictions on capital flows in the form of “quotas” could increase the effectiveness of FXI by reducing substitutability between domestic and foreign assets.
  - Substitution channel: imposing capital controls could render FXI unnecessary if controls suffice to maintain exchange rate stability — in this case one would observe high capital controls and very low levels of intervention.
  - Instrument validity concerns: the set of instruments used in the baseline specification may not be appropriate when exploring the interaction between capital controls and FXI, because reserve accumulation and exchange rate stabilization motives are likely to change in the presence of significant restrictions on capital mobility.

### Representative robustness statistics (selected results from tables)
- Robustness to capital controls — second stage (Dependent variable: real bilateral exchange rate), FXI/GDP coefficient estimates:
  - Column (1): FXI/GDP = -1.231 ∗∗∗  (standard error: 0.335)
  - Column (2): FXI/GDP = -1.392 ∗∗∗  (standard error: 0.405)
  - Column (3): FXI/GDP = -1.686 ∗∗∗  (standard error: 0.450)
  - Column (4): FXI/GDP = -1.650 ∗∗∗  (standard error: 0.443)
  - Column (5): FXI/GDP = -2.004 ∗∗∗  (standard error: 0.543)
  - Column (6): FXI/GDP = -2.007 ∗∗∗  (standard error: 0.545)
- Interaction effects and related coefficients reported:
  - VIX × Capital controls = -0.048 ∗∗∗  (standard error: 0.008)
  - VIX × Capital controls = -0.039 ∗∗∗  (standard error: 0.007)
  - VIX × Capital controls = -0.064 ∗∗∗  (standard error: 0.009)
  - VIX × Capital controls = -0.065 ∗∗∗  (standard error: 0.009)
- Sample and fit statistics in the robustness table:
  - Observations range across columns (examples): 8284, 7474, 8020, 8020, 7467, 7467
  - Countries included across specifications: 52, 51, 50, 50, 47, 47
  - R2 values reported: 0.98, 0.98, 0.98, 0.98, 0.97, 0.97
  - J p-value examples: 0.20, 0.22, 0.22, 0.45, 0.70, 0.69
  - Stock & Yogo stat examples: 17.24, 13.10, 12.77, 12.90, 10.19, 10.11

### Interpretation and policy implications (as discussed in the text)
- The relationship between FXI and restrictions on capital mobility is complex and can reflect either complementarity or substitution:
  - Complementarity: capital controls (especially quotas) can enhance FXI effectiveness by limiting asset substitutability.
  - Substitution: strong capital controls can obviate the need for FXI to stabilize exchange rates; observed high controls may coincide with low intervention.
- Empirical ambiguity and counter-intuitive findings point to:
  - Heterogeneity across countries, instruments, and types of capital controls.
  - Potential issues with instrument validity when capital controls materially alter motives for reserve accumulation and exchange rate stabilization.
- Implication for empirical work and policy evaluation:
  - Analyses of FXI effectiveness should explicitly account for the level and nature of capital controls.
  - Caution is warranted when interpreting IV results involving interactions with capital controls because traditional instruments for FXI may not remain exogenous once capital mobility is constrained.

*Source: Annex 2 — Capital controls (from _wp15130 - Annex 2    Capital controls)*

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