## wpiea2020069-print-pdf - Section IV (concluding section) and Appendix Figure A2

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---

### FXI proxy and measurement
- FXI proxy construction:
  - FXI_iit = ∆BOP_Res_iit − ResIncome_iit + DerivFlows_iit
    - ∆BOP_Res_iit denotes changes in reserves as captured by BOP statistics.
    - ResIncome_iit refers to estimated income on reserves (subtracted to capture only new FX transactions).
    - DerivFlows_iit denotes foreign exchange transactions through derivatives (changes in aggregate short and long positions in forwards, futures, forward leg of swaps, and financial instruments denominated in foreign currency but settled by other means).
  - Nominal US dollar values of FXI are normalized by GDP (FXI/GDP) using a trend measure of nominal GDP in US dollars.
- Data and sample:
  - Quarterly data for the period 2000-17.
  - Sample: 12 AEs and 36 EMDEs (mid-to-large size economies with monetary policy autonomy; excludes currency pegs and monetary unions).
- Reporting threshold:
  - Quarterly FXI proxy values smaller than 0.25 percent of GDP in absolute value are not reported.

### Patterns of foreign exchange intervention — Size
- Frequency and size (full sample):
  - Interventions ≥ 0.25 percent of GDP occurred 74 percent of the time in Non-IT regimes and 60 percent of the time in IT regimes.
  - Interventions ≥ 0.5 percent of GDP occurred about 20 percent of the time in advanced economies and 60-70 percent of the time in EMDEs.
- Cross-group differences:
  - Mean net FX accumulation: AEs accumulate less than 0.1 percent of GDP per quarter on average; EMDEs accumulate 0.3 percent of GDP per quarter on average.
  - Within groups, no meaningful difference between IT and Non-IT regimes in terms of net FXI.
  - IT regimes still display economically sizable average absolute FXI (example cited: 0.8 percent of GDP).
- Time-series patterns:
  - Patterns persist over the last two decades.
  - Clear global waves in FXI use, with a striking increase in the run up to and aftermath of the global financial crisis.

### Patterns of foreign exchange intervention — Symmetry
- Symmetry index:
  - S_iL = 0 if fully symmetric, 1 if one-sided FX purchases, and -1 if one-sided FX sales (computed over L-quarter windows).
- Empirical symmetry findings:
  - EMDEs exhibit marked asymmetry with a bias towards FX purchases.
  - Asymmetry visible in both Non-IT and IT regimes in EMDEs; more pronounced in Non-IT regimes but present in IT regimes as well.
  - AEs show asymmetry too but much less pronounced.
- Formal estimates (selected from Table 2, pooled L = 8 and L = 12 quarters):
  - α_G (All, L=8) = 0.329*** (std. err. 0.0182)
  - β_G (All, L=8) = -0.102*** (std. err. 0.0223)
  - Res/GDP (L-lagged) = -1.500*** (std. err. 0.136) (coefficient negative and significant)
  - Observations and R-squared examples: Observations 2,862; 2,171; 1,753; 2,078. R-squared values 0.007; 0.074; 0.029; 0.105.

### Patterns of foreign exchange intervention — Degree of exchange rate management
- Degree metric:
  - ρ_iL = σ_L,i^FXI / (σ̂_L,i^s + σ_L,i^FXI)
    - σ̂_L,i^s: standard deviation of quarterly changes in the exchange rate (NEER or vis-à-vis the US dollar) over L quarters.
    - σ_L,i^FXI: standard deviation of quarterly FXI/GDP over same window.
  - Index ranges from 0 (free-floating) to 1 (fixed exchange rate).
- Distributional findings:
  - Exchange rates more tightly managed under Non-IT regimes (distribution skewed to right) compared with IT regimes.
  - Difference especially stark for AEs: IT regimes skewed left (more floating), Non-IT skewed right (more managed).
  - EMDEs display a higher degree of exchange rate management than AEs for both IT and Non-IT regimes.
- Formal estimates (Table 3 highlights):
  - Statistically and economically significant difference in ρ between IT and Non-IT regimes in full sample.
  - Within EMDEs, degree of exchange rate management considerably lower in IT regimes compared to Non-IT regimes.
  - Results robust to controlling for Reserves-to-GDP.

### Age of IT regime and dynamics over time
- Specification tested:
  - y_iL = α_G + β_G * IT_iit + γ * IT_iit * IT_Age_iit + ε_iit
    - IT_Age denotes age of the IT regime in years.
- Findings:
  - Statistically significant reduction in the use of FXI over time across size, symmetry, and degree metrics as IT regimes age.
  - Effects are relatively small economically — FXI use remains pervasive even after years of IT regimes.
- Selected coefficient examples from Table 4 (L = 8 and L = 12):
  - αG examples: 0.401***, 0.124***, 0.416***, 0.369***, 0.383***, 0.130***, 0.397***, 0.362*** (with standard errors (0.00857)(0.0142)(0.00877)(0.0126)(0.00832)(0.0127)(0.00854)(0.0126)).
  - βG examples: -0.212***, -0.0166, -0.189***, -0.214***, -0.198***, -0.0208, -0.176***, -0.214*** (with standard errors (0.00931)(0.0146)(0.00997)(0.0107)(0.00898)(0.0131)(0.00959)(0.0107)).
  - Res/GDP (L-lagged) coefficients: 0.453*** and 0.466*** (std. err. (0.0459)(0.0437)).
  - Observations examples: 2,961; 650; 2,311; 2,094; 2,938; 646; 2,292; 1,971.
  - R-squared examples: 0.189, 0.003, 0.148, 0.212, 0.183, 0.006, 0.142, 0.233.

### Single or Dual Objectives of FXI under IT
- Possible roles of FXI under IT:
  - An additional instrument to achieve inflation objectives via exchange rate pass-through.
  - An instrument aimed at a second objective (the exchange rate) alongside inflation targeting.
- Relevance depends on:
  - Effectiveness of FXI in moving the exchange rate.
  - Extent of pass-through of exchange rate changes to inflation.
- EMDEs: FXI tends to be more powerful in influencing the exchange rate and pass-through tends to be higher than in AEs.

### Measures of inflation expectations (construction)
- Synthetic 12-month horizon expectation Eπ_it_12mm(M):
  - Eπ_it_CY − π_it_TT  plus  Eπ_it_NCY * (12−M)/12
  - First term: expected inflation between time t and end of current year (Eπ_it_CY − π_it_TT).
  - Second term: expected inflation in early months of following year up to 12-month horizon (assumes constant inflation within the following year).

### Joint probabilities of FXI and contemporaneous inflation outcomes (EMDEs, Table 5)
- For FX purchases/sales > 0.25 percent of GDP:
  - Purchase when Above target / Below target / Both (12-month ahead expectations): 0.25, 0.18, 0.43.
  - Sale when Above target / Below target / Both (12-month ahead expectations): 0.15, 0.11, 0.26.
  - Freq (IT-cons. FXI / π) for same: 0.37, 0.62, 0.47.
- For FXI > 0.50 percent of GDP:
  - Purchase Above/Below/Both: 0.17, 0.14, 0.31.
  - Sale: 0.09, 0.08, 0.17.
  - Freq: 0.35, 0.64, 0.48.
- For FXI > 1.0 percent of GDP:
  - Purchase Above/Below/Both: 0.10, 0.07, 0.17.
  - Sale: 0.04, 0.03, 0.08.
  - Freq: 0.30, 0.69, 0.47.
- Interpretation:
  - Less than 1/2 of FX operations were conducted in a manner that would have helped achieve inflation targets (selling FX when inflation above target, or buying FX when inflation below target), holding for actual inflation and measures of inflation expectations, and for larger operations.

### Asymmetry in intervention relative to inflation gaps
- When inflation was running below target, central banks purchased foreign exchange 63 percent of the time.
- When inflation was running above target, central banks sold foreign exchange 35 percent of the time.
- Pattern holds for actual inflation and different inflation expectations measures, and for small and large interventions.
- Indicates greater propensity to attempt to depreciate the domestic currency than to appreciate it.

### FXI and deviations from target bands
- Difference in prevalence of FXI between periods of inflation under- and over-shooting disappears when deviations measured relative to the target range (overshooting upper band or undershooting lower band).
- Propensity to conduct FXI in a manner supportive of inflation objective remains low (30-40 percent) when using target bands.

### FXI reaction function and key coefficient estimates (EMDEs, Table 7)
- Estimated model:
  - FFI_it = ψπ * (Eπ_it_h − π_it_T) + Σ_{l=1}^L ψA_l Δ_l ln(ER)_{it−l+1} + α_it + ε_it
    - FFI_it: period t foreign exchange intervention as share of GDP.
    - (Eπ_it_h − π_it_T): deviation of horizon-h inflation expectation from target.
    - Δ_l ln(ER): l-lagged quarterly change in exchange rate vis-à-vis US dollar (positive = depreciation).
- Key empirical results (selected):
  - ψπ estimates: statistically insignificant across specifications. Examples: 0.01, 0.015, 0.015 (t-stats (0.686)(1.067)(1.062)); E(πNY−πT): 0.019, 0.004, 0.004 (t-stats (0.364)(0.054)(0.062)); E(π12m−πT): 0.035, 0.032, 0.031 (t-stats (0.955)(0.751)(0.750)).
  - ψA (∑Δln(ER)) estimates: sizable and statistically-significant negative coefficients across specifications, e.g., -0.0740***, -0.0638**, -0.0606**, -0.0868***, -0.0872***, -0.0808***, -0.0906**, -0.0889***, -0.0825*** (t-stats (-2.957)(-2.072)(-2.127)(-3.422)(-4.061)(-3.592)(-3.791)(-4.202)(-3.717)).
  - Contemporaneous Δln(ER) coefficients: -0.050***, -0.047***, -0.046***, -0.051***, -0.049**, -0.046**, -0.050***, -0.049**, -0.046** (t-stats (-2.974)(-2.908)(-2.895)(-2.747)(-2.806)(-2.663)(-2.781)(-2.805)(-2.671)).
  - Lags L.Δln(ER) and L2.Δln(ER) show some significance for first two lags in many specifications.
  - Reserves/GDP (l1) in some specs: -0.010, -0.022**, -0.022** (t-stats (-0.887)(-2.302)(-2.315)).
  - Constants reported (examples): 0.003***, 0.003***, 0.005**, 0.003***, 0.003***, 0.007***, 0.003***, 0.003***, 0.006*** (t-stats (5.155)(16.360)(2.280)(4.730)(10.079)(4.285)(4.251)(12.740)(4.131)).
- Interpretation:
  - FXI in IT regimes responds to exchange rate movements—leaning against the wind—rather than to inflation developments.
  - Central banks purchase foreign exchange when the domestic currency is appreciating and sell when it is depreciating.
- Robustness:
  - Similar results using NEER instead of USD exchange rate and using lagged inflation deviations.

### Stylized facts on inflation outcomes (Section III.A)
- Evaluation metrics:
  - Deviations from inflation target: (π_it_h − π_it_T).
  - Deviations from target range/bands: ΔEπ_it_h defined relative to lower/upper bands.
- Distribution differences AEs vs EMDEs (sample period):
  - EMDEs overshot inflation targets by about 82 basis points on average.
  - AEs undershot targets by 43 basis points on average.
  - EMDEs display greater dispersion:
    - Mass of 15 percent of observations with deviations > 300 basis points above target.
    - Mass of 5 percent of observations with deviations > 300 basis points below target.
  - Inflation within target bands:
    - EMDEs: about 45 percent of the time.
    - AEs: about 65 percent of the time.
  - Inflation expectations:
    - Next-year inflation expectations anchored within target range about 95 percent of the time in AEs.
    - Less than 80 percent for EMDEs.
- Variance:
  - EMDEs show 2-3 times higher variance of inflation and inflation expectation outcomes than AEs (Table 8).

### Linking FXI to Inflation Outcomes (probit and marginal effects)
- Probit specification:
  - Pr(DRD_it) = Φ(β FFI_it_L + Σ δ_l Δ_l ln(ER)_{it−l+1} + Σ ρ_l D_{it−l+1}_r + φ (y_it − ȳ_it) + γ' G_i + α_i)
  - FFI_it_L: average of |FFI|/GDP over L quarters.
  - Controls include exchange rate, real short term interest rate, output gap, global factors, country fixed effects.
- Marginal effects (selected highlights):
  - A 1 percent of GDP quarterly FXI associated with:
    - 16-22 percent higher probability of overshooting the target after controlling for country-specific variables (columns 1-3).
    - Effect reduced when controlling for global factors; becomes statistically insignificant when time fixed effects included (column 5).
  - Controlling for exchange rate movements does not materially change results (columns 6-9).
- Detailed marginal effects (examples from Tables 9 and 10):
  - Overshooting Inflation Target (examples): FXI marginal effects 8.39+, 16.74***, 22.70***, 16.36***, 6.67, 16.94***, 23.09***, 16.83***, 7.93 (std. errors (5.23)(4.60)(6.75)(6.35)(8.40)(4.65)(6.71)(6.24)(8.62)).
  - Output gap marginal effects (examples): 4.92***, 3.96***, 4.53**, 5.31***, 4.08***, 4.05** (std. errors (1.31)(1.30)(1.88)(1.34)(1.37)(1.84)).
  - Expectation-based results (Table 10): Next Year Expectations FXI marginal effects: 7.51, 19.91***, 24.64***, 21.17***, 11.42, 20.13***, 25.11***, 21.44***, 11.16 (std. errors (6.25)(5.46)(6.29)(7.16)(10.06)(5.59)(6.09)(6.96)(9.88)).
- Interpretation:
  - Greater FXI is associated with de-anchoring of inflation expectations, especially at short horizons, and a higher probability of overshooting inflation targets.
  - Part of the link is driven by global factors and the use of FXI in response to those factors (time fixed effects weaken significance).
  - Findings consistent with ‘leaning against the wind’ patterns where FXI aimed at moderating exchange rate movements may have side effects for inflation outcomes under IT in EMDEs.

### Key takeaways and conclusions (Section IV)
- Prevalence and asymmetry:
  - FXI is common across monetary regimes and income groups; only marginally less frequent under IT than Non-IT regimes in the full sample.
  - EMDEs use FXI more frequently and in larger magnitudes than AEs and display a purchase bias (accumulating foreign exchange) in both IT and Non-IT regimes.
- Net accumulation:
  - Net FX accumulation differs markedly: AEs <0.1 percent of GDP per quarter; EMDEs 0.3 percent of GDP per quarter.
  - Within-group differences between IT and Non-IT in net FXI are not meaningful.
- Symmetry and reserves:
  - Symmetry analyses show EMDEs have statistically and economically significant bias toward FX purchases.
  - Lower reserve stocks associated with stronger purchase bias (Res/GDP lagged coefficient negative and significant).
- Degree of exchange rate management:
  - ρ indicates Non-IT regimes and EMDEs manage exchange rates more tightly; in AEs the IT versus Non-IT split is especially pronounced.
- Age of IT regimes:
  - Age of IT regimes associated with statistically significant, but economically modest, declines in FXI across size, symmetry and management metrics — FXI remains pervasive even after many years of IT.
- FXI objectives and effects:
  - FXI use under IT in EMDEs often reflects dual inflation/exchange rate objectives and responds to exchange rate movements rather than inflation developments.
  - More extensive use of FXI associated with de-anchoring of inflation expectations and lower success rates of inflation targeting (higher probability of overshooting targets).
  - Associations partly reflect responses to global factors, highlighting possible side effects of ‘leaning against the wind’ policies under IT.

*Source: Section IV (concluding section) and Appendix Figure A2 of wpiea2020069-print-pdf (quarterly BOP-based FXI analysis, sample period 2000-17).*

### Section IV concludes with key takeaways and brief discussion of further areas of research.

### wpiea2020069-print-pdf - Section IV concludes with key takeaways and brief discussion of further areas of research

### FXI proxy and measurement
- FXI proxy construction:
  - FXI_iit = ∆BOP_Res_iit − ResIncome_iit + DerivFlows_iit
    - ∆BOP_Res_iit denotes changes in reserves as captured by BOP statistics.
    - ResIncome_iit refers to estimated income on reserves (subtracted to capture only new FX transactions).
    - DerivFlows_iit denotes foreign exchange transactions through derivatives (changes in aggregate short and long positions in forwards, futures, forward leg of swaps, and financial instruments denominated in foreign currency but settled by other means).
  - Nominal US dollar values of FXI are normalized by GDP (FXI/GDP) using a trend measure of nominal GDP in US dollars.
- Data and sample:
  - Quarterly data for the period 2000-17.
  - Sample: 12 AEs and 36 EMDEs (mid-to-large size economies with monetary policy autonomy; excludes currency pegs and monetary unions).
- Reporting threshold:
  - Quarterly FXI proxy values smaller than 0.25 percent of GDP in absolute value are not reported to avoid residual measurement error from estimated reserve income flows.

### Patterns of foreign exchange intervention — Size
- Frequency and size findings (full sample):
  - Interventions of 0.25 percent of GDP or more occurred 74 percent of the time in Non-IT regimes and 60 percent of the time in IT regimes.
  - Interventions of 0.5 percent of GDP or larger occurred about 20 percent of the time in advanced economies and 60-70 percent of the time in EMDEs.
- Cross-group differences:
  - Mean net FX accumulation: AEs accumulate less than 0.1 percent of GDP per quarter on average; EMDEs accumulate 0.3 percent of GDP per quarter on average.
  - Within groups, no meaningful difference between IT and Non-IT regimes in terms of net FXI.
  - IT regimes still display economically sizable average absolute FXI (example cited: 0.8 percent of GDP).
- Time-series patterns:
  - Patterns persist over the last two decades.
  - Clear global waves in FXI use, with a striking increase in the run up to and aftermath of the global financial crisis.

### Patterns of foreign exchange intervention — Symmetry
- Symmetry metrics and interpretation:
  - Interventions characterized as symmetric (dampening volatility) or one-sided (leaning against appreciation or depreciation).
  - Symmetry index S_iL constructed so S_iL = 0 if fully symmetric, 1 if one-sided FX purchases, and -1 if one-sided FX sales (computed over L-quarter windows).
- Empirical symmetry findings:
  - EMDEs exhibit a marked asymmetry with a bias towards FX purchases (buying foreign exchange).
  - Asymmetry is visible in both Non-IT and IT regimes in EMDEs; more pronounced in Non-IT regimes but present in IT regimes as well.
  - AEs show asymmetry too but much less pronounced.
- Formal estimates (Table 2 highlights):
  - Full sample α_G = 0.329 (statistically significant) indicating purchase bias in non-IT regimes.
  - For EMDEs, α_G = 0.357 (statistically significant in reported columns), indicating economically and statistically significant purchase bias.
  - Small β_G implies no economically meaningful difference in asymmetry between IT and Non-IT regimes for EMDEs.
  - Controlling for lagged Reserves/GDP: lagged Res/GDP coefficient is negative and significant (Res/GDP (L-lagged) coefficient reported as -1.500*** in the table), indicating economies with lower reserves have a greater bias towards purchasing foreign currency.
  - Selected estimate details from Table 2 (L = 8 and L = 12 quarters, pooled results):
    - α_G (All, L=8) = 0.329*** (std. err. 0.0182)
    - β_G (All, L=8) = -0.102*** (std. err. 0.0223)
    - Res/GDP (L-lagged) = -1.500*** (std. err. 0.136) (column where included)
    - Observations vary by specification (examples: 2,862; 2,171; 1,753; 2,078) and R-squared values reported (examples: 0.007; 0.074; 0.029; 0.105) across columns.

### Patterns of foreign exchange intervention — Degree of exchange rate management
- Degree of exchange rate management metric:
  - ρ_iL = σ_L,i^FXI / (σ̂_L,i^s + σ_L,i^FXI)
    - σ̂_L,i^s is the standard deviation of quarterly changes in the exchange rate (NEER or vis-à-vis the US dollar) over L quarters.
    - σ_L,i^FXI is the standard deviation of quarterly FXI/GDP over the same window.
  - Index ranges from 0 (free-floating) to 1 (fixed exchange rate); captures within-window variation and is largely clean of slow-moving precautionary reserve accumulation motives.
- Distributional findings:
  - Exchange rates are more tightly managed under Non-IT regimes (distribution skewed to the right) compared with IT regimes.
  - Difference is particularly stark for AEs: IT regimes skewed left (more floating), Non-IT skewed right (more managed).
  - EMDEs display a higher degree of exchange rate management than AEs for both IT and Non-IT regimes.
- Formal estimates (Table 3 highlights):
  - For the full sample, statistically and economically significant difference in ρ between IT and Non-IT regimes.
  - Within EMDEs, degree of exchange rate management is considerably lower in IT regimes compared to Non-IT regimes.
  - Results robust to controlling for level of reserves (Reserves-to-GDP).

### Age of IT regime and dynamics over time
- Specification to test age effects:
  - y_iL = α_G + β_G * IT_iit + γ * IT_iit * IT_Age_iit + ε_iit
    - IT_Age denotes the age of the IT regime in years; γ is the coefficient of interest.
- Empirical findings:
  - There is evidence of a statistically significant reduction in the use of FXI over time across the three metrics (size, symmetry, degree of exchange rate management) as IT regimes age.
  - Effects are relatively small economically, indicating FXI use remains pervasive even after years of IT regimes.

### Key takeaways
- FXI is common across monetary regimes and income groups; it is only marginally less frequent under IT than Non-IT regimes in the full sample.
- EMDEs use FXI more frequently and in larger magnitudes than AEs; EMDEs also display a purchase bias (accumulating foreign exchange) in both IT and Non-IT regimes.
- Net FX accumulation differs markedly between AEs (<0.1 percent of GDP per quarter) and EMDEs (0.3 percent of GDP per quarter), but within-group differences between IT and Non-IT in net FXI are not meaningful.
- Symmetry analyses show EMDEs have a statistically and economically significant bias toward FX purchases; lower reserve stocks are associated with stronger purchase bias (Res/GDP lagged coefficient negative and significant).
- Degree of exchange rate management (ρ) indicates Non-IT regimes and EMDEs manage exchange rates more tightly; in AEs the IT versus Non-IT split is especially pronounced.
- The age of IT regimes is associated with a statistically significant, but economically modest, decline in FXI use across size, symmetry and management metrics—FXI remains pervasive even after many years of IT.

*Source: Section IV (concluding section) of wpiea2020069-print-pdf (quarterly BOP-based FXI analysis, sample period 2000-17).*

### Appendix Figure A2).

### wpiea2020069-print-pdf - Appendix Figure A2)

### Key findings
- FXI is limited in AEs but pervasive in EMDEs.
- Both IT and Non-IT central banks in EMDEs make extensive use of FXI and largely in an asymmetric manner.
- IT regimes tend to allow for greater exchange rate flexibility; small differences in use of FXI between IT and non-IT regimes indicate significant use of FXI even under IT.
- Evidence points to FXI responding to exchange rate developments rather than contemporaneous inflation developments.

### Age of IT regime and FXI (summary of Table 4 / related estimates)
- Estimated αG coefficients reported (examples): 0.401***, 0.124***, 0.416***, 0.369***, 0.383***, 0.130***, 0.397***, 0.362*** with reported standard errors (0.00857)(0.0142)(0.00877)(0.0126)(0.00832)(0.0127)(0.00854)(0.0126).
- Estimated βG coefficients reported (examples): -0.212***, -0.0166, -0.189***, -0.214***, -0.198***, -0.0208, -0.176***, -0.214*** with reported standard errors (0.00931)(0.0146)(0.00997)(0.0107)(0.00898)(0.0131)(0.00959)(0.0107).
- Res/GDP (L-lagged) coefficients: 0.453*** and 0.466*** with standard errors (0.0459)(0.0437).
- Observations across specifications: 2,961; 650; 2,311; 2,094; 2,938; 646; 2,292; 1,971.
- R square values shown: 0.189, 0.003, 0.148, 0.212, 0.183, 0.006, 0.142, 0.233.
- Windows: L=8 quarters and L=12 quarters.

### Single or Dual Objectives? (FXI objectives under IT)
- FXI under IT can be:
  - An additional instrument to achieve inflation objectives via exchange rate pass-through.
  - An instrument aimed at a second objective (the exchange rate).
- The mechanism’s relevance depends on:
  - Effectiveness of FXI in moving the exchange rate.
  - Extent of pass-through of exchange rate changes to inflation.
- EMDEs: FXI tends to be more powerful in influencing the exchange rate and pass-through tends to be higher than in AEs.

### Measures of inflation expectations (construction)
- Synthetic 12-month horizon inflation expectation measure: Eπ_it_12mm(M) constructed as:
  - Eπ_it_CY − π_it_TT  plus  Eπ_it_NCY * (12−M)/12
  - First term: expected inflation between time t and end of current year (Eπ_it_CY − π_it_TT).
  - Second term: expected inflation in early months of following year up to 12-month horizon (assumes constant inflation within the following year).

### Joint probabilities of FXI and contemporaneous inflation outcomes (Table 5 summary for EMDEs)
- For FX purchases/sales > 0.25 percent of GDP:
  - Purchase when Above target / Below target / Both (12-month ahead expectations): 0.25, 0.18, 0.43.
  - Sale when Above target / Below target / Both (12-month ahead expectations): 0.15, 0.11, 0.26.
  - Freq (IT-cons. FXI / π) for same: 0.37, 0.62, 0.47.
- For FXI > 0.50 percent of GDP:
  - Purchase (12-month ahead expectations) Above/Below/Both: 0.17, 0.14, 0.31.
  - Sale: 0.09, 0.08, 0.17.
  - Freq: 0.35, 0.64, 0.48.
- For FXI > 1.0 percent of GDP:
  - Purchase Above/Below/Both: 0.10, 0.07, 0.17.
  - Sale: 0.04, 0.03, 0.08.
  - Freq: 0.30, 0.69, 0.47.
- Less than 1/2 of FX operations were conducted in a manner that would have helped achieve inflation targets (selling FX when inflation above target, or buying FX when inflation below target), holding for actual inflation and measures of inflation expectations, and for larger operations (e.g., >0.5 or 1.0 percent of GDP).

### Asymmetry in intervention relative to inflation gaps
- When inflation was running below target, central banks purchased foreign exchange 63 percent of the time.
- When inflation was running above target, central banks sold foreign exchange 35 percent of the time.
- Pattern holds for actual inflation and different inflation expectations measures, and for small and large interventions.
- Indicates greater propensity to attempt to depreciate the domestic currency than to appreciate it.

### FXI and deviations from target bands (Table 6 summary)
- Difference in prevalence of FXI between periods of inflation under- and over-shooting disappears when deviations measured relative to the target range (overshooting upper band or undershooting lower band).
- Propensity to conduct FXI in a manner supportive of inflation objective remains low (30-40 percent) when using target bands.

### FXI reaction function (specification and interpretation)
- Estimated model:
  - FFI_it = ψπ * (Eπ_it_h − π_it_T) + Σ_{l=1}^L ψA_l Δ_l ln(ER)_{it−l+1} + α_it + ε_it
  - FFI_it: period t foreign exchange intervention as share of GDP.
  - (Eπ_it_h − π_it_T): deviation of horizon-h inflation expectation from target.
  - Δ_l ln(ER) terms: l-lagged quarterly change in exchange rate vis-à-vis US dollar (positive = depreciation).
  - Contemporaneous and 7 lags considered for exchange rate variables.
- Key coefficients of interest: ψπ (inflation response) and ψA (exchange rate response).
- Table 7 results (EMDEs) summary:
  - ψπ estimates: statistically insignificant across specifications. Example coefficients: π-πT: 0.01, 0.015, 0.015 (t-stats (0.686)(1.067)(1.062)); E(πNY−πT): 0.019, 0.004, 0.004 (t-stats (0.364)(0.054)(0.062)); E(π12m−πT): 0.035, 0.032, 0.031 (t-stats (0.955)(0.751)(0.750)).
  - ψA (∑Δln(ER)) estimates: sizable and statistically-significant negative coefficients across specifications, e.g., -0.0740***, -0.0638**, -0.0606**, -0.0868***, -0.0872***, -0.0808***, -0.0906**, -0.0889***, -0.0825*** with t-stats (-2.957)(-2.072)(-2.127)(-3.422)(-4.061)(-3.592)(-3.791)(-4.202)(-3.717).
  - Contemporaneous Δln(ER) coefficients: -0.050***, -0.047***, -0.046***, -0.051***, -0.049**, -0.046**, -0.050***, -0.049**, -0.046** with t-stats (-2.974)(-2.908)(-2.895)(-2.747)(-2.806)(-2.663)(-2.781)(-2.805)(-2.671).
  - Lags L.Δln(ER) and L2.Δln(ER) show some significance for first two lags in many specifications.
  - Reserves/GDP (l1) in some specs: -0.010, -0.022**, -0.022** (t-stats (-0.887)(-2.302)(-2.315)).
  - Constants reported (examples): 0.003***, 0.003***, 0.005**, 0.003***, 0.003***, 0.007***, 0.003***, 0.003***, 0.006*** (t-stats (5.155)(16.360)(2.280)(4.730)(10.079)(4.285)(4.251)(12.740)(4.131)).
- Interpretation: FXI in IT regimes responds to exchange rate movements—leaning against the wind—rather than to inflation developments. Central banks purchase foreign exchange when the domestic currency is appreciating and sell when it is depreciating.
- Robustness: Similar results using NEER instead of USD exchange rate and using lagged inflation deviations.

### Stylized facts on inflation outcomes (Section III.A)
- Evaluation metrics: deviations from inflation target (π_it_h − π_it_T) and deviations from target range/bands (ΔEπ_it_h defined relative to lower/upper bands).
- Distribution differences AEs vs EMDEs:
  - During sample period:
    - EMDEs overshot inflation targets by about 82 basis points on average.
    - AEs undershot targets by 43 basis points on average.
  - EMDEs display greater dispersion:
    - Mass of 15 percent of observations with deviations > 300 basis points above target.
    - Mass of 5 percent of observations with deviations > 300 basis points below target.
  - Inflation within target bands:
    - EMDEs: about 45 percent of the time.
    - AEs: about 65 percent of the time.
  - Inflation expectations:
    - Next-year inflation expectations anchored within target range about 95 percent of the time in AEs.
    - Less than 80 percent for EMDEs.
- Table 8: EMDEs show 2-3 times higher variance of inflation and inflation expectation outcomes than AEs.

### Linking FXI to Inflation Outcomes (probit specification)
- Probit specification for probability of missing inflation target:
  - Pr(DRD_it) = Φ(β FFI_it_L + Σ δ_l Δ_l ln(ER)_{it−l+1} + Σ ρ_l D_{it−l+1}_r + φ (y_it − ȳ_it) + γ' G_i + α_i)
  - FFI_it_L: metric of FXI averaging interventions over current and L-1 previous quarters, defined as average of |FFI|/GDP over L quarters.
  - D_{RD} indicates overshooting (π−πT > 0) or undershooting (π−πT < 0); analogous definitions for target bands.
  - Controls: exchange rate (US$ or NEER), real short term interest rate, output gap, global factors (VIX, World GDP growth, World CPI inflation, US 10-year Treasury yield), country fixed effects.

### Marginal effects: FXI and probability of overshooting the target (Table 9 summary)
- A 1 percent of GDP quarterly FXI associated with:
  - 16-22 percent higher probability of overshooting the target after controlling for country-specific variables (columns 1-3).
- Controlling for global factors reduces estimated effect; effect becomes statistically insignificant when time fixed effects included (column 5).
- Controlling for exchange rate movements (columns 6-9) does not materially change results.
- Results for probability of undershooting mirror overshooting regressions (probability of exactly hitting target is virtually zero).

### Detailed marginal effects reported (selected values from Tables 9/10)
- Overshooting Inflation Target (examples):
  - FXI marginal effects across specs: 8.39+, 16.74***, 22.70***, 16.36***, 6.67, 16.94***, 23.09***, 16.83***, 7.93 (standard errors shown in table: (5.23)(4.60)(6.75)(6.35)(8.40)(4.65)(6.71)(6.24)(8.62)).
  - Output gap marginal effects: 4.92***, 3.96***, 4.53**, 5.31***, 4.08***, 4.05** (standard errors (1.31)(1.30)(1.88)(1.34)(1.37)(1.84)).
- Overshooting Upper Band (examples without exchange rate controls and with):
  - FXI marginal effects across specs: 7.49, 6.90, 14.90***, 9.63+, 11.04+, 7.54, 18.05***, 13.16**, 12.47* (standard errors (6.37)(5.77)(5.49)(6.07)(6.83)(5.78)(4.69)(5.30)(6.58)).
  - Output gap marginal effects: 2.37*, 1.73, 2.88*, 3.85***, 2.56**, 2.69* (standard errors (1.25)(1.27)(1.65)(1.33)(1.25)(1.53)).
- Probability of inflation expectation overshooting target (Table 10 examples):
  - Target, Current Year Expectations: FXI marginal effects: 8.32+, 17.30***, 17.73**, 13.28*, 4.98, 17.71***, 17.67***, 13.68**, 6.32 (standard errors (5.38)(5.32)(6.90)(7.05)(9.62)(5.52)(6.81)(6.87)(9.83)).
  - Target, Next Year Expectations: FXI marginal effects: 7.51, 19.91***, 24.64***, 21.17***, 11.42, 20.13***, 25.11***, 21.44***, 11.16 (standard errors (6.25)(5.46)(6.29)(7.16)(10.06)(5.59)(6.09)(6.96)(9.88)).
  - Target Range (upper band), Current Year Expectations: FXI marginal effects: 11.05*, 7.98+, 15.14***, 10.29**, 12.88**, 8.61*, 17.56***, 13.05***, 12.44** (standard errors (5.97)(5.10)(3.92)(4.42)(5.89)(5.11)(3.66)(4.11)(5.67)).
  - Target Range (upper band), Next Year Expectations: FXI marginal effects: 9.37*, 0.56, 3.82, 4.09, 5.53, 1.86, 4.70, 4.51, 6.06 (standard errors (5.37)(6.60)(5.96)(5.40)(5.58)(6.71)(5.87)(5.29)(5.63)).

### Interpretation of empirical results (summary)
- Greater FXI is associated with:
  - De-anchoring of inflation expectations, especially at short horizons (current year expectations).
  - Higher probability of overshooting inflation targets.
- Part of the link between FXI and inflation outcomes is driven by global factors and the use of FXI in response to those factors (time fixed effects weaken statistical significance).
- Findings are consistent with ‘leaning against the wind’ patterns: FXI aimed at moderating exchange rate movements may have detrimental side effects for inflation outcomes under IT in EMDEs.

### Conclusions (section IV)
- FXI is limited in advanced economies across regimes but pervasive and one-sided (bias towards buying reserves) in emerging and developing economies even after accounting for precautionary motives.
- FXI use under IT in EMDEs often reflects dual inflation/exchange rate objectives; FXI responds to exchange rate movements rather than inflation developments.
- A more extensive use of FXI is associated with:
  - More frequent de-anchoring of inflation expectations.
  - Lower success rates of inflation targeting (higher probability of overshooting targets).
  - These associations partly reflect responses to global factors, pointing to possible side effects of ‘leaning against the wind’ policies under IT.

*Source: Authors’ estimations and calculations as presented in the supplied content.*

### References

### References

### Key topics covered in the referenced literature
- Foreign exchange intervention and its effectiveness: "Unveiling the Effects of Foreign Exchange Intervention: A Panel Approach"; "When Is Foreign Exchange Intervention Effective? Evidence from 33 Countries"; "On the effectiveness of exchange rate interventions in emerging markets"; "Foreign Exchange Intervention in Inflation Targeting: The Role of Credibility"; "Optimal Foreign Exchange Intervention in an Inflation Targeting Regime: Some Cautionary Tales".
- Inflation targeting and exchange rate management: "Inflation Targeting and exchange rate management in less developed economies"; "Inflation Targeting at 20: Achievements and Challenges"; "Did the Exchange Rate Floor Prevent Deflation in the Czech Republic?"; "How much should inflation targeters care about the exchange rate".
- Capital flows, capital controls, and policy responses: "Official Financial Flows, Capital Mobility, and Global Imbalances"; "Managing Large Capital Inflows"; "Managing Capital Inflows; What Tools to Use?"; "Managing Capital Inflows: The Role of Capital Controls and Prudential Policies"; "Capital Inflows; The Role of Controls".
- Reserve accumulation and motives: "Financial versus Monetary Mercantilism: Long-run View of Large International Reserve Hoarding"; "Shifting Motives: Explaining the Buildup in Official Reserves in Emerging Markets since the 1980’s".
- Theoretical and modeling foundations: New-Keynesian frameworks, real wage rigidities, imperfect credibility, time series methods: "Real Wage Rigidities and the New Keynesian Model"; "Imperfect Credibility and Inflation Persistence"; "Time Series Analysis"; Tinbergen’s "On the Theory of Economic Policy".
- Surveys and reviews of empirical evidence: "Foreign Exchange Intervention in Emerging Markets: A Survey of Empirical Studies"; country- and region-specific studies and working papers.

### Notable empirical approaches and data sources cited
- Empirical methods: panel approaches; analyses distinguishing spot vs derivatives-based interventions; New-Keynesian modeling of sterilized interventions and balance-sheet effects.
- Data sources and institutional reports: IMF Balance of Payment Statistics, World Economic Outlook, AREAER, Haver Analytics, International Financial Statistics, IRFCL, BOP, INS, central banks’ websites.
- Policy-oriented analyses and staff/working papers from IMF, NBER, Peterson Institute, BIS, CEMLA.

### Appendix figures and their content
- Appendix Figure A1. Index of exchange rate management, 2000-18
  - Sources: IRFCL, BOP, INS and Authors’ calculations
  - Notes: Reports the distribution of indexes 휌휌
푖푖 = 휎휎
푖푖
푓푓푓푓푖푖/(휎휎
푖푖
푠푠
̂
+휎휎
푖푖
푓푓푓푓푖푖), computed over 12-quarter windows using nominal effective exchange rate. Includes all available observations for 2000Q1 through 2018Q1. Vertical lines indicate IT and non-IT group averages.
- Appendix Figure A2. Exchange rate management by group and regime (3-year moving window)
  - Sources: IMF Balance of Payment Statistics, World Economic Outlook, and authors’ calculations.
  - Visual elements include series spanning 2000q1, 2006q1, 2012q1, 2018q1 and plotted values from 0 to .6 for groups AE vs EMDEs and EMDEs: IT vs Non-IT.
- Appendix Figure A3. Frequency of IT misses
  - Sources: AREAER, Haver Analytics, International Financial Statistics, and authors’ calculations.
  - Notes: Figures display the frequency of actual inflation missing the targets, based on monthly observations. Large over- and under-shooting refer to deviations of 2 percentage points or more.
- Appendix Figure A4. Frequency of unanchored expectations
  - Sources: AREAER, Consensus Forecasts, Haver Analytics, International Financial Statistics, and authors’ calculations.
  - Notes: Figures display the frequency of unanchored inflation expectations, based on monthly observations. Large over- and under-shooting refer to deviations of 2 percentage points or more.

### Appendix Table A1: Sample of countries (high-level)
- Sources: AREAER database; central banks’ websites; Roger (2009); Ebeke and Azangue (2015).
- The table lists Advanced Economies and Emerging Markets and Developing Economies with columns including:
  - Country
  - Inflation Targeting Adoption Date
  - Point Target (in percent)
  - Target Range (in percent)
  - Target Change
- Examples from the table (preserving exact strings as in source):
  - Australia 04/1993 No None 2.0-3.0
  - Canada 02/1991 Yes Various +/-1.0
  - Chile 09/1999 No 3 +/-1.0
  - Egypt 05/2017 No 13 +/-3.0
  - Moldova 01/2010 No 5 +/-1.5
  - South Africa 02/2000 No None 3.0-6.0
  - Uruguay 09/2007 No None 4.0-6.0

### Appendix Table A2: Probability of undershooting inflation target — Marginal effects (selected entries)
- Source: Authors’ estimations.
- Footnote: 1/ Standard errors are reported in parentheses. *** p<0.01, ** p<0.05, *p< 0.1, + p<0.15.
- FXI row (coefficients across specifications (1)–(9)):
  - -8.39
  - -16.74***
  - -22.70***
  - -16.36***
  - -6.67
  - -16.94***
  - -23.09***
  - -16.83***
  - -7.93
- FXI standard errors (corresponding to the above columns):
  - (5.23)
  - (4.60)
  - (6.75)
  - (6.35)
  - (8.40)
  - (4.65)
  - (6.71)
  - (6.24)
  - (8.62)
- Output gap row (selected coefficients and significance):
  - -4.92***
  - -3.96***
  - -4.53**
  - -5.31***
  - -4.08***
  - -4.05**
- Output gap standard errors:
  - (1.31)
  - (1.30)
  - (1.88)
  - (1.34)
  - (1.37)
  - (1.84)
- Model controls and design elements (as reported in table):
  - Country Fixed Effects: reported as present in specified columns.
  - Output gap: included in specified columns.
  - Real Interest Rate: included in specified columns.
  - Exchange Rate: included in specified columns.
  - Global variables: included in specified columns.
  - Time Fixed Effects: included in specified columns.
- Observations by column:
  - 1,541
  - 1,523
  - 1,089
  - 1,089
  - 1,041
  - 1,498
  - 1,067
  - 1,067
  - 1,019

*Source: wpiea2020069-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020069-print-pdf.pdf_