## _wp1311 - appendix contains an extension of the analysis to quantity–based policy transmission and

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### II. EXCHANGERATETARGETING ANDEXCHANGERATEINTERVENTION: TWO UNRELATED LITERATURES

- Exchange Rate targeting literature (summary)
  - Most macro literature assumes a single instrument—the interest rate—omitting direct FX interventions and their transmission channels.
  - Many studies model implicit or "dirty" inflation targeting by adding an exchange rate objective to an interest-rate reaction function.
  - Representative modified Taylor rule used:
    - iT = ̄i + α(π − πT) + δȳ + χΥ,(1)
      - where i denotes the policy rate, π is the rate of inflation, ȳ is the output gap, and superscript T denotes target levels.
    - Real-term specification example:
      - Υ = ˆq − ηˆq−1 = △s − π + π∗ + (1 − η) ˆq−1.
    - Nominal-target form example:
      - Υ = η△s + (1 − η)(s − sT).(2)
  - Findings and limitations highlighted
    - Limited support for including exchange rate terms in interest-rate rules for emerging markets; trade-offs can include reduced volatility in the exchange rate, interest rate, and trade balance at the cost of higher inflation and output volatility under demand and cost-push shocks.
    - Very high degrees of exchange rate targeting can eliminate potential benefits.
    - Major shortcoming: ignoring direct exchange rate interventions and sterilization misrepresents practical use of interventions to expand policy maneuvering.
    - Sterilization cannot be studied with a single instrument; sterilized interventions require two instruments: FX transactions and open-market operations.

- FX Intervention literature (summary)
  - Portfolio–balance approach: sterilized interventions can affect exchange rates via asset composition and risk premia; under perfect asset substitutability this effect vanishes.
  - Backus and Kehoe (1989) critique: some sterilized interventions (holding fiscal and standard monetary policy constant) have no effect on private decisions.
  - For developing countries, imperfect substitutability is plausible due to country-specific default risk, partial capital controls, and incomplete asset markets, opening a channel for sterilized interventions via financial frictions and gross–debt sensitive risk premia.
  - Empirical evidence and practice
    - Identification problems from endogeneity; high-frequency event studies often used.
    - Event studies often find significant but short-lived exchange rate effects; longer-term effects less clear.
    - Mixed cross-country evidence; some emerging-market studies find interventions affect exchange rate levels while others find null results.
    - Adler and Tovar (2011) find interventions can affect pace of appreciation in countries with relatively closed capital accounts (per Chinn and Ito (2008) index).
    - Practitioners in emerging markets and developing countries often consider FX interventions effective where assets are imperfect substitutes and markets are "thin".

### III. KEY CONCEPTS

- Definitions and operational distinctions
  - Final policy objective: price stability.
  - Intermediate targets considered: an exchange rate and a rate of inflation; if both exist they must be set consistently.
  - Operational targets: interbank interest and exchange rates aimed at by central bank operations (transactions changing the central bank’s balance sheet).
  - Exchange rate targeting versus exchange rate interventions:
    - Exchange rate targeting: central bank adjusts policy interest rate to achieve a particular exchange rate level/path set as an intermediate target.
    - Exchange rate interventions: central bank operations in the FX market aimed at affecting the exchange rate as an operational target/instrument.
    - Paper focuses on exchange rate interventions because they introduce the exchange rate as a central bank instrument in addition to the interest rate.
  - Sterilized versus non‑sterilized interventions:
    - Paper’s definition: sterilized interventions keep market interest rates unchanged (all interventions by interest-rate-based central banks are automatically sterilized in this sense).
    - Alternative definition: sterilized interventions do not change the level of reserve (base) money; closely related because changes in free reserves affect market interest rates.
    - Paper main body: stylized IT central bank operating an interest-rate based policy so interventions are automatically sterilized; appendix extends analysis to non-interest based monetary policy where free reserves matter.

- Stochastic behavior of the exchange rate
  - Standard flexible‑exchange‑rate SOE models imply the exchange rate has a stochastic trend (unit root) under UIP, so inflationary shocks result in permanently weaker exchange rates.
  - For the exchange rate level to serve as a nominal anchor it should not have a stochastic trend; interventions must be able to remove the unit root to model pegs, crawling arrangements, managed floats, and IT in a common framework.

### IV. MODEL (overview)

- Core extensions to a new‑Keynesian SOE framework
  - Add FX interventions as a central bank instrument independent of the interest rate, capable of stabilizing exchange rate fluctuations within a stochastic band.
  - Add balance-sheet (liquidity) effects of interventions as a transmission channel working through endogenous spreads derived from optimal behavior of the financial sector.
- Presentation plan: key equations given in main text; rest of equations and calibration in appendix.

### Appendix C — Model structure, calibration, and mechanisms

A. Balance sheets
- Structure (domestic-currency expression; F and B in foreign currency)
  - Central Bank: assets FX reserves F; liabilities central bank securities O (held by financial sector).
  - Financial Sector: assets loans to households L and central bank securities O; refinanced from abroad B.
  - Households: liabilities L; net worth NW.
- Assumptions
  - Economy is cashless and a net debtor: net foreign liabilities (NFL) equal household debt L > 0.
  - F and B denominated in foreign currency and excluded from domestic-currency assets (no financial dollarization modeled).
  - Reserve-money addition and alternative balance‑sheet generalizations discussed qualitatively.

B. Central bank behavior
- Cash-flow transferred to households:
  - CF_CB = S/S−1 F−1 exp(i∗) − O−1 exp(i) − FX + O.
- Interests and operational targets:
  - Receives interest on FX at constant rate i∗; pays interest i on central bank securities; sets interbank rate i = i_T_t.
  - Two operational targets: exchange rate target S_T and interest rate target i_T.
- FX intervention (quantity) rule:
  - log(F/L) = log(F/L) − ω log(S_T/S) − θ log(S−1/S). (Equation (3))
    - F_L is steady‑state ratio of FX reserves to stock of credit.
    - ω → ∞ implies perfect tracking of S_T; ω = 0 implies no tracking.
    - θ captures exchange smoothing (“leaning–against–the‑wind”).
  - Interest-rate operational target always met; asymmetry: exchange rate implemented via quantities (reserves), interest rate via price instrument.
  - Lower bound on reserves ignored (assumed positive or backstopped by external financing).
- Taylor-type interest-rate operational target:
  - i_T = ρ i_T−1 + (1−ρ)( ī + α(π − π_T) + δ ˆy + χ Υ ). (Equation (5))
  - Exchange-rate operational rule is analogous; for simplicity ρ_s = α_s = δ_s = 0 in analysis.

C. Financial sector behavior
- Arbitrage and spreads (UIP and credit supply):
  - exp(i) = exp(i∗) S+1/S + Ω_O(F/P), with Ω′_O(F/P) > 0. (Equation (6))
  - exp(j) = exp(i∗) S+1/S + Ω_L. (Equation (7))
  - Credit spread between j and i given by Ω_L − Ω_O(F/P).
- Key mechanism
  - UIP spread increases with stock of FX reserves (deflated by price level P); accumulation of central bank paper O (equal to F) raises the premium for banks to hold these bonds.
  - Two real spreads ensure stationarity: ρ(L/P) (credit-sensitive wedge) and Ω_O(F/P) (UIP premium).

D. Households
- Budget constraint with loan-adjustment costs:
  - P C − L = − exp(j−1) L−1 + Π − Ψ(L/P), with Ψ′(L/P) > 0, Ψ′′(L/P) > 0. (Equation (8))
- First‑order conditions:
  - λ/λ+1 (1 − ρ(L/P)) = β exp(j). (Equation (9))
  - P λ = U′(C).
- Adjustment costs Ψ(L/P) determine steady‑state real consumption and NFL via credit-sensitive wedge ρ(L/P).

E. Rest of model
- Two‑sector SOE: exportables and non‑tradables, labor as sole factor, decreasing returns, monopolistic competition, staggered pricing → Phillips curves.
- Imports and exported demand price‑sensitive; households consume domestic non‑tradables and foreign goods with nominal rigidities.

### V. Discussion — steady state and spreads

- Stationarity and role of spreads
  - Model removes unit root from real financial stocks and, depending on regime, from nominal exchange rate level: NFL and FX reserves return to unique steady state after shocks.
  - Two spreads ensure uniqueness:
    - ρ(L/P) pins down real consumption and NFL in steady state.
    - Ω_O(F/P) pins down F/P in steady state; with F/L determined, intervention rule (3) pins S = S_T at steady state.
- Intervention mechanism
  - When S depreciates above target, central bank draws on reserves, F falls → Ω_O(F/P) falls → works toward currency strengthening (ceteris paribus).
- Calibration note (numerical)
  - Baseline calibration implies a one percent increase in reserves—relative to steady state—depreciates the exchange rate by one fourth of a percent.

### VI. Simulations

- Shock studied: foreign interest rate shock.
- Five monetary policy settings compared (regime notation and parameterization χωθ):
  - (i) Pure inflation targeting (IT) / flexible exchange rate (float): 0 0 0
  - (ii) Fixed exchange rate via interest rates: Inf 0 0
  - (iii) Fixed exchange rate via interventions: 0 Inf 0
  - (iv) Exchange rate corridor: 0 5 0
  - (v) Managed float (leaning interventions): 0 0 2 0
- Qualitative simulation findings (foreign interest rate rise)
  - Pure IT (float): exchange rate depreciates → import‑price inflation ↑; domestic policy raises nominal rates → consumption down; real exports up; NFL worsen due to higher interest burden; nominal exchange rate does not return to initial level.
  - Fixed via interest rates: lower inflation but sharper economic decline; policy must raise rates to match foreign rates; export sector loses depreciation boost.
  - Fixed via interventions: allows domestic interest rates to fall, limiting contraction; household debt burden and NFL rise, leading to contraction but smaller than fixed‑via‑interest‑rate case.
  - Exchange rate corridor and managed float: active exchange rate management via interventions keeps interest rates lower than pure float or fixed‑via‑interest‑rates, aiding consumption recovery and allowing some temporary depreciation to support exports.
  - Practical problem: fixing via interest rates forces rates up even when inflation and activity fall.
- Stochastic properties and volatility (high‑level)
  - Structural shocks analyzed: foreign interest rate, non‑tradable consumption, non‑tradable inflation, terms of trade.
  - Main observations:
    - When foreign interest rate shocks dominate, regimes with interventions outperform pure IT and fixed‑via‑interest‑rates in volatility of most variables (except FX reserves).
    - Fixing/managing exchange rate smooths export volatility except for terms‑of‑trade shocks, where real exchange rate flexibility helps reduce volatility of inflation and real variables.
    - Consumption volatility is never higher with interventions than in free float/IT.
    - Except for foreign interest rate shocks, inflation least volatile in floating regimes.
    - Highest FX reserve volatility occurs when domestic inflation and foreign interest rate shocks dominate.
- Limits and risks of interventions
  - Market knowledge of intervention function can invite speculative attacks; interventions often kept opaque.
  - Distinguishing permanent vs temporary shocks is hard; defending a peg against permanent adverse terms‑of‑trade shocks can exhaust reserves and produce larger deflationary adjustments.
  - “Impossible trinity” implications:
    - Fixed exchange rate + free capital account + independent monetary policy incompatible in long run.
    - To fix S either:
      - Interest‑rate targeting collapses monetary independence (χ infinite), or
      - Intervention targeting collapses intervention rule (ω infinite) but preserves interest‑rate rule; sustained peg requires sufficient reserves and that Ω′_O(F/P) be large enough so premia respond to sterilized interventions.
    - Low sensitivity of premia to interventions raises reserve‑loss risk.
  - Managed floats/corridors are more robust to uncertainty about intervention effectiveness.
- Numerical risk example
  - In a variant where the premium is twenty times less sensitive to sterilized interventions, a one percent increase in foreign interest rates results in a loss of one fourth of the country reserves (illustrative risk).

### VII. CONCLUSIONS AND POLICY IMPLICATIONS

- Framework contribution
  - Provides a framework for hybrid IT regimes with exchange rate management: an FX intervention rule operating alongside a standard interest rate rule, relying on balance‑sheet effects and endogenous spreads.
- Policy lessons (bulleted)
  - Interventions can provide partial insulation of domestic interest rates from foreign shocks and reduce volatility of consumption and some real variables.
  - If inflation control is primary, a free float is robust.
  - For economies dominated by foreign interest rate shocks, fixing via interest rates is uniformly worse in volatility terms than regimes with interventions.
  - Choice of policy depends on shock composition, economic structure, and policymakers’ preferences.
- Suggested research extensions
  - Map the intervention mechanism to micro‑foundations (portfolio choice, bank cost functions).
  - Formal welfare analysis comparing target vs instrument rules.
  - Empirical calibration to specific countries to assess instrument strength needed against particular shocks.

### Appendix A — Sterilized interventions in quantity‑based monetary policy (summary)

- Extension where central bank controls sterilized quantities O rather than perfectly controlling interest rates.
- Introduces free reserves R held by commercial banks and sterilization rule:
  - O/L = O/L − τ(i − i_T). (Equation (10))
  - τ infinite corresponds to main‑text results (perfect control); τ = 0 means central bank uses quantities not interest‑rate targets.
- Free reserves remunerated at i_R = i_T.
- Financial sector supply curve of reserves:
  - exp(i_R) = exp(i∗) S+1/S + Ω_R(R/P), Ω′_R(.) > 0. (Equation (11))

### Appendix B — Microfoundations for UIP spread rising in FX reserves (summary)

- Two rationalizations provided
  1. Portfolio allocation (risk‑averse banks): FOCs yield UIP with a spread linear in stock of FX reserves (O = F) and proportional to foreign exposure (O + L); intuition: larger FX exposure increases required risk premium.
  2. Bank cost‑function approach: with Ω(O, L) linearly homogeneous and concave (example Diewert cost), FOCs produce UIP spread Θ = θ_O − θ √(L/F), increasing in ratio of FX reserves to NFL; credit supply curve arises from second FOC.

### Appendix C — Complete model summary and calibration (selected numeric values preserved)

- Key model elements summarized: household Euler with ρ(L/P) = ρ(L/P − L̄/P̄); consumption aggregator C = C_n^{ω_n} C_m^{1−ω_n}; loan dynamics L = L−1(exp(i∗) + π_S) + (P_m C_m − P_x Y_x); financial intermediaries: exp(i) = exp(i∗ + π_S+1) Ω_O; exp(j) = exp(i∗ + π_S+1) Ω_L; log(Ω_O) = Ω_O(F/P − F̄/P̄) + ε_prem; log(Ω_L) = 0.
- Selected calibration parameters (exact values)
  - ρ = 0.7, α = 3, δ = 0, β = 0.9975, ρ = 0.01, ω_n = 0.5, φ = 0.5, Ω_o = 0.20, γ_n = 0.5, γ_x = 0.5, μ = 1.1
  - ξ_n = 0.01, ξ_x = 0.5, ξ_m = 0.5, ρ_i′ = 0.8, ρ_tot (temporary) = 0.8, ρ_tot (permanent) = 1, s_T = 0, π_T = 0
  - F/L = 1.503, L/P = 0.679
- Simulation outputs referenced (Table 1 and Figures) normalize unconditional standard errors relative to IT pure float (FX reserves absolute variance); baseline one percent reserve increase → exchange rate depreciates by one fourth of a percent.

*Source: _wp1311 - appendix contains an extension of the analysis to quantity–based policy transmission and*

### appendix contains an extension of the analysis to quantity–based policy transmission and

### _wp1311 - appendix contains an extension of the analysis to quantity–based policy transmission and

### II. EXCHANGERATETARGETING ANDEXCHANGERATEINTERVENTION: TWO UNRELATED LITERATURES

- The Exchange Rate targeting Literature
  - Most macroeconomic literature assumes a single central bank instrument—the interest rate—used to target inflation and potentially the exchange rate, omitting direct FX market interventions and their transmission channels.
  - Much literature investigates implicit or "dirty" inflation targeting, adding an exchange rate objective into the interest rate reaction function (examples cited in the source).
  - Typical modified Taylor rule used in literature:
    - iT = ̄i + α(π − πT) + δȳ + χΥ,(1)
      - where i denotes the policy rate, π is the rate of inflation, ȳ is the output gap, and superscript T denotes target levels.
    - Example real-term specification (Roger et al. (2009)):
      - Υ = ˆq − ηˆq−1 = △s − π + π∗ + (1 − η) ˆq−1,
        - where q and s are the natural logarithms of real and nominal exchange rates.
    - Example nominal-target form:
      - Υ = η△s + (1 − η)(s − sT).(2)
  - Literature findings and limitations:
    - Limited support for including exchange rate terms in interest rate rules for emerging markets; potential trade-offs include reduced volatility in exchange rate, interest rate, and trade balance at the cost of higher inflation and output volatility, especially with demand and cost-push shocks.
    - High degrees of exchange rate targeting can eliminate potential benefits.
    - Major shortcomings: ignores direct exchange rate interventions and sterilization; treating exchange rate in the Taylor rule reduces central bank autonomy and misrepresents practical use of interventions to expand policy maneuvering.
    - Sterilization cannot be studied with a single instrument; sterilized interventions require two instruments: FX transactions and open-market operations to neutralize effects on policy interest rates.
  - Some authors specify explicit exchange rate rules (e.g., sT = ρ sT−1 + (1 − ρ)(α ˆπ + δ ȳ)), but these approaches often leave interest rate determination to external elements via UIP and may be ad hoc.

- The FX Intervention Literature
  - Portfolio–balance approach historically suggested sterilized interventions can affect exchange rates via asset composition and risk premia; fell out of favor under perfect asset substitutability assumptions.
  - Backus and Kehoe (1989) critique: certain sterilized interventions (holding fiscal and standard monetary policy constant) have no effect on private decisions; Kumhof (2010) shows imperfect substitutability can be generated with government spending shocks.
  - For developing countries, country-specific default risk, partial capital controls, and incomplete asset markets make partial asset substitutability plausible, opening theoretical possibility for sterilized interventions to matter through reduced-form financial frictions and gross–debt sensitive risk premia.
  - Empirical evidence:
    - Identification problems are persistent due to endogeneity of interventions; high-frequency event studies often used to mitigate contemporaneous endogeneity.
    - Event studies often find significant but short-lasting effects on exchange rates; fewer clear results on longer-term effects.
    - Mixed evidence across countries; some emerging market studies find interventions affect exchange rate levels, others find null results.
    - Adler and Tovar (2011) find evidence interventions can affect pace of appreciation in countries with relatively closed capital accounts (per Chinn and Ito (2008) index).
  - Practical views: Many practitioners in emerging markets and developing countries consider FX interventions can be effective, especially where assets are imperfect substitutes and markets are "thin".

### III. KEY CONCEPTS

- Definitions and distinctions
  - Policy objective: price stability is the final policy objective.
  - Intermediate targets considered: an exchange rate and a rate of inflation — if both exist they must be set consistently.
  - Operational targets: levels of interbank interest and exchange rates aimed at by central bank operations (transactions changing the central bank’s balance sheet, e.g., open market operations in domestic liquidity/T-bills and foreign exchange operations). Instruments used in practice often refer both to operations and operational targets.
  - Exchange rate targeting versus exchange rate interventions:
    - Exchange rate targeting: central bank adjusts its policy interest rate to achieve a particular level/path of the exchange rate set as an intermediate target.
    - Exchange rate interventions: central bank operations in the FX market aimed at affecting the exchange rate as an operational target/instrument.
    - The paper focuses on exchange rate interventions because they introduce the exchange rate as a central bank instrument (in addition to the interest rate), but also analyzes and compares both cases.
  - Sterilized versus non-sterilized exchange rate interventions:
    - Sterilized interventions (definition used in paper): interventions that keep market interest rates unchanged. All exchange rate interventions of central banks using interest rates as the main instrument (such as IT central banks) are automatically sterilized in this sense.
    - Alternative definition: sterilized interventions do not change the level of reserve (base) money. These definitions are closely related because changes in free reserves affect market interest rates.
    - Paper focus: sterilized interventions that work alongside interest rates as the other central bank instrument. Main body uses a stylized IT central bank operating an interest-rate based monetary policy so interventions are automatically sterilized; appendix extends analysis to non-interest based monetary policy where free reserves matter (important for money-targeting low–income economies).

- Stochastic behavior of the exchange rate
  - Standard flexible–exchange–rate small–open-economy (SOE) models imply the exchange rate has a stochastic trend (unit root) under UIP; inflationary shocks result in permanently weaker exchange rates.
  - For the exchange rate level to serve as a nominal anchor, it should not have a stochastic trend; long-term trajectory should be known ex ante and shocks should cause temporary deviations that revert to the target.
  - Intervention design in the paper should be able to remove the stochastic trend (unit root) from the exchange rate to model pegs, crawling arrangements, managed floats, and IT in a common framework.

### IV. MODEL

- Extensions to a standard new–Keynesian SOE framework (e.g., Gali and Monacelli (2005), Benes et al. (2007)):
  - Add FX interventions as a central bank instrument, independent of the interest rate instrument and capable of stabilizing exchange rate fluctuations within a given stochastic band.
  - Add balance sheet (liquidity) effects of interventions as a new channel of monetary policy transmission, working through endogenous spreads derived from optimal behavior of the financial sector.
- Presentation plan:
  - The section describes the key equations of the model; the rest of the model equations and calibration are presented in the appendix (as noted in the source).

*Source: _wp1311 - appendix contains an extension of the analysis to quantity–based policy transmission and*

### appendix C.

### _wp1311 - appendix C.

### A. Balance sheets
- Structure:
  - Central Bank: assets FX reserves F; liabilities central bank securities O (held by financial sector).
  - Financial Sector: assets loans to households L and central bank securities O; refinanced from abroad B.
  - Households: liabilities L; net worth NW.
- Assumptions:
  - All items expressed in domestic currency; F and B denominated in foreign currency and excluded from domestic-currency assets (no financial dollarization modeled).
  - Economy is cashless and a net debtor: country’s net foreign liabilities (NFL) equal household debt L > 0.
  - Simplifying omissions noted (unhedged FX short positions, households as net borrowers, structural liquidity surplus, etc.).
- Reserve-money addition and alternative balance-sheet generalizations are discussed qualitatively.

### B. Central bank behavior
- Central bank cash-flow transferred to households:
  - CF_CB = S/S−1 F−1 exp(i∗) − O−1 exp(i) − FX + O.
- Interest/funding and operational targets:
  - Receives interest on FX stock at constant rate i∗.
  - Pays interest i on central bank securities; sets interbank rate i = i_T_t.
  - Two operational targets: exchange rate target S_T and interest rate target i_T.
- FX intervention rule (quantity adjustment to influence nominal exchange rate):
  - log(F/L) = log(F/L) − ω log(S_T/S) − θ log(S−1/S). (Equation (3))
  - F_L is steady-state ratio of FX reserves to stock of credit (NFL).
  - ω → ∞ implies perfect tracking of exchange rate target; ω = 0 implies no tracking.
  - θ captures exchange smoothing (“leaning–against–the–wind”).
- Interest-rate operational target is always met; asymmetry: exchange rate implemented via quantities (reserves), interest rate via price instrument.
- Lower bound on reserves ignored (assumed positive or backstopped by external financing).

- Taylor-type interest-rate operational target (general form):
  - i_T = ρ i_T−1 + (1−ρ)( ī + α(π − π_T) + δ ˆy + χ Υ ). (Equation (5))
  - Exchange-rate operational rule analogous; for simplicity ρ_s = α_s = δ_s = 0 in analysis.

### C. Financial sector behavior
- Arbitrage (UIP and credit supply):
  - exp(i) = exp(i∗) S+1/S + Ω_O(F/P), with Ω′_O(F/P) > 0. (Equation (6))
  - exp(j) = exp(i∗) S+1/S + Ω_L. (Equation (7))
  - Credit spread between j and i given by Ω_L − Ω_O(F/P).
- Key mechanism:
  - UIP spread increases with stock of FX reserves (deflated by price level P); accumulation of central bank paper O (equal to F) raises the premium required for banks to hold these bonds.
  - Two real spreads ensure stationarity: ρ(L/P) (credit-sensitive wedge) and Ω_O(F/P) (UIP premium).

### D. Households behavior
- Budget constraint with loan-adjustment costs:
  - P C − L = − exp(j−1) L−1 + Π − Ψ(L/P), with Ψ′(L/P) > 0, Ψ′′(L/P) > 0. (Equation (8))
- FOCs:
  - λ/λ+1 (1 − ρ(L/P)) = β exp(j). (Equation (9))
  - P λ = U′(C).
- Adjustment costs Ψ(L/P) provide mechanism to determine steady-state real consumption and NFL via the credit-sensitive wedge ρ(L/P).

### E. Rest of the model
- Two-sector small-open-economy structure: exportables and non-tradables, labor as sole factor, decreasing returns, monopolistic competition, staggered pricing → Phillips curves.
- Imports and exported demand price-sensitive; labor mobile across sectors; households consume domestic non-tradables and foreign goods (imports) with nominal rigidities.

### V. Discussion — steady state and spreads
- Model removes unit root from real financial stocks and, depending on regime, from nominal exchange rate level: NFL and FX reserves return to unique steady state after shocks.
- Two spreads ensure uniqueness:
  - ρ(L/P) pins down real consumption and NFL in steady state.
  - Ω_O(F/P) pins down F/P in steady state; with F/L determined, intervention rule (3) pins S = S_T at steady state.
- Intervention rule (3) plays role analogous to Taylor rule for exchange rate level (determines S, not F).
- Intervention mechanism: when S depreciates above target, CB draws on reserves, F falls → Ω_O(F/P) falls → works toward currency strengthening (ceteris paribus).
- Calibration note: baseline calibration implies a one percent increase in reserves—relative to steady state—depreciates the exchange rate by one fourth of a percent.

### VI. Simulations
- Shock examined: foreign interest rate shock. Compare five monetary policy settings:
  - (i) Pure inflation targeting (IT) / flexible exchange rate (float).
  - (ii) Fixed exchange rate via interest rates.
  - (iii) Fixed exchange rate via interventions.
  - (iv) Exchange rate corridor.
  - (v) Managed float (leaning interventions).
- Parameterization (Regime/parameter χωθ):
  - IT pure float: 0 0 0
  - Fixed via interest rate: Inf 0 0
  - Fixed via interventions: 0 Inf 0
  - Exchange rate corridor: 0 5 0
  - Managed float: 0 0 2 0
- Qualitative simulation findings:
  - Pure IT: foreign rate rise → exchange rate depreciates → import-price inflation ↑; domestic policy raises nominal rates → consumption down; real exports up; NFL worsen due to higher interest burden. Nominal exchange rate does not return to initial level.
  - Fixed via interest rates: lower inflation but sharper economic decline; policy must raise rates to match foreign rates; export sector loses depreciation boost.
  - Fixed via interventions: allows domestic interest rates to fall, limiting contraction; household debt burden and NFL rise, leading to contraction but smaller than fixed-via-interest-rate case.
  - Exchange rate corridor and managed float: active exchange rate management via interventions keeps interest rates lower than pure float or fixed-via-interest-rates, aiding consumption recovery and allowing some temporary depreciation to support exports.
  - Practical problem highlighted: fixing via interest rates forces rates up even when inflation and activity fall.
- Stochastic properties / volatility under dominant shocks:
  - Structural shocks analyzed: foreign interest rate, non-tradable consumption, non-tradable inflation, terms of trade.
  - Table 1 normalized unconditional standard errors relative to pure IT case (FX reserves absolute variance).
  - Main observations:
    - When foreign interest rate shocks dominate, regimes with interventions outperform pure IT and fixed-via-interest-rates in volatility of most variables (except FX reserves).
    - Fixing/managing exchange rate smooths export volatility except for terms-of-trade shocks, where real exchange rate flexibility helps reduce volatility of inflation and real variables.
    - Consumption volatility is never higher with interventions than in free float/IT.
    - Except for foreign interest rate shocks, inflation least volatile in floating regimes.
    - Highest FX reserve volatility occurs when domestic inflation and foreign interest rate shocks dominate.
- Limits and risks of interventions:
  - Market knowledge of CB intervention function can invite speculative attacks; interventions often kept opaque.
  - Distinguishing permanent vs temporary shocks is hard; defending a peg against permanent adverse terms-of-trade shocks can exhaust reserves and produce larger deflationary adjustments.
  - “Impossible trinity”: fixed exchange rate + free capital account + independent monetary policy incompatible in long-run. Two ways to fix S:
    - Interest-rate targeting collapses monetary independence (χ infinite).
    - Intervention targeting collapses intervention rule (ω infinite) but preserves interest-rate rule; sustained peg requires sufficient reserves and that Ω′_O(F/P) be large enough so premia respond to sterilized interventions. Low sensitivity of premia to interventions raises reserve-loss risk.
  - Managed floats/corridors more robust to uncertainty about intervention effectiveness.

### VII. Conclusions and policy implications
- The paper provides a framework for hybrid IT regimes with exchange rate management: an FX intervention rule operating alongside a standard interest rate rule, relying on balance-sheet effects and endogenous spreads.
- Policy lessons:
  - Interventions can provide partial insulation of domestic interest rates from foreign shocks and reduce volatility of consumption and some real variables.
  - If inflation control is primary, free float is robust.
  - For economies dominated by foreign interest rate shocks, fixing via interest rates is uniformly worse in volatility terms than regimes with interventions.
  - Choice of policy depends on shock composition, economic structure, and policymakers’ preferences.
- Research extensions suggested:
  - Map intervention mechanism to micro-foundations (portfolio choice, bank cost functions).
  - Formal welfare analysis comparing target vs instrument rules.
  - Empirical calibration to specific countries to assess instrument strength needed against particular shocks.

### Appendix A — Sterilized interventions in quantity-based monetary policy
- Extension where CB controls sterilized quantities O rather than perfectly controlling interest rates.
- Introduces free reserves R held by commercial banks and sterilization rule:
  - O/L = O/L − τ(i − i_T). (Equation (10))
  - τ infinite corresponds to main-text results (perfect control); τ = 0 means CB uses quantities not interest-rate targets.
- Free reserves remunerated at i_R = i_T for simplicity.
- Financial sector supply curve of reserves:
  - exp(i_R) = exp(i∗) S+1/S + Ω_R(R/P), Ω′_R(.) > 0. (Equation (11))

### Appendix B — Microfoundations for UIP spread rising in FX reserves
- Two rationalizations:
  1. Portfolio allocation (risk-averse banks):
     - Banks maximize expected real revenue minus c/2 var(revenue) subject to L + O = B.
     - FOCs yield UIP with a spread linear in stock of FX reserves (O = F) and proportional to foreign exposure (O + L).
     - Intuition: larger FX exposure increases risk premium required.
  2. Bank cost-function approach:
     - Banks maximize cash flow subject to cost function Ω(O, L), linearly homogeneous and concave with Ω_i > 0, Ω_ii > 0, Ω_ij < 0.
     - Example Diewert cost: Ω(O, L) = θ_O O + θ_L L − 2 θ √(OL).
     - FOCs produce UIP spread Θ = θ_O − θ √(L/F), increasing in ratio of FX reserves to NFL.
     - Credit supply curve arises from second FOC; spreads functions fall in FX-to-loan ratio due to homogeneity.

### Appendix C — Complete model (summary and calibration)
- Households: utility, labor supply N^φ and Euler with ρ(L/P) = ρ(L/P − L̄/P̄).
- Consumption aggregator: C = C_n^{ω_n} C_m^{1−ω_n}; CPI inflation π = ω_n π_n + (1−ω_n) π_m.
- Household loan stock: L = L−1(exp(i∗) + π_S) + (P_m C_m − P_x Y_x), with π_S = log(S) − log(S−1).
- Financial intermediaries: exp(i) = exp(i∗ + π_S+1) Ω_O; exp(j) = exp(i∗ + π_S+1) Ω_L; log(Ω_O) = Ω_O(F/P − F̄/P̄) + ε_prem; log(Ω_L) = 0.
- Non-traded producers, exporters, importers: marginal cost conditions, Phillips curves with ξ_n, ξ_x, ξ_m.
- Rest of world: P_x Y_x = P∗_x Y_w exp(ε_yw); terms of trade AR(1), foreign interest rate AR(1).
- Calibration (selected parameters):
  - ρ = 0.7, α = 3, δ = 0, β = 0.9975, ρ = 0.01, ω_n = 0.5, φ = 0.5, Ω_o = 0.20, γ_n = 0.5, γ_x = 0.5, μ = 1.1
  - ξ_n = 0.01, ξ_x = 0.5, ξ_m = 0.5, ρ_i′ = 0.8, ρ_tot (temporary) = 0.8, ρ_tot (permanent) = 1, s_T = 0, π_T = 0
  - F/L = 1.503, L/P = 0.679
- Table 1 (normalized unconditional standard errors relative to IT pure float) and Figures illustrate simulation results (foreign interest rate shock, temporary and permanent terms-of-trade shocks, reserve-sensitivity cases).
- Notable numeric outcomes in text:
  - Baseline: one percent increase in reserves (relative to steady state) → exchange rate depreciates by one fourth of a percent.
  - In a variant with premium twenty times less sensitive to sterilized interventions, a one percent increase in foreign interest rates results in a loss of one fourth of the country reserves (illustrative risk).

*Source: _wp1311 - appendix C.*

### REFERENCES

### REFERENCES

### Foreign exchange market intervention (motives, techniques, effectiveness)
- Adler, Gustavo, and Camilo Tovar, 2011, “Foreign Exchange Market Intervention: How Good a Defense Against Appreciation Winds?” IMF Working Paper 11/165.
- BIS, 2005, “Foreign Exchange Market Intervention in Emerging Markets: Motives, Techniques and Implications,” BIS Papers No. 24.
- Canales-Kriljenko, Jorge Ivan, 2003, “Foreign exchange intervention in developing and transition economies: results of a survey, IMF Working Paper 03/95.
- Disyatat, Piti and Gabriele Galati, 2007, “The Effectiveness of Foreign Exchange Intervention in Emerging Market Countries: Evidence from the Czech Koruna,” Journal of International Money and Finance, Vol. 27 (April), pp. 383–402.
- Dominguez, Kathryn M., and Jeffrey A. Frankel, 1993, “Does foreign-exchange intervention matter? The portfolio effect,” The American Economic Review, Vol. 83 (5), pp. 1356–1369.
- Ersek, Zsolt, 2005, “Defending the Strong Side of the Band: The Hungarian Experience,” in BIS, Foreign Exchange Market Intervention in Emerging Markets: Motives, Techniques and Implications, BIS Papers No. 24.
- Fatum, Rasmus, 2010, “Foreign Exchange Intervention When Interest Rates Are Zero: Does the Portfolio Balance Channel Matter After All?,” EPRU Working Paper Series No. 2010-07.
- Fatum, Rasmus and Michael M. Hutchison, 2003, “Is Sterilized Foreign Exchange Intervention Effective After All? An event study approach,” The Economic Journal, Vol. 113 (April) pp. 390–411.
- Fatum, Rasmus and Michael M. Hutchison, 2010, “Evaluating foreign exchange market intervention: Self-selection, counterfactuals and average treatment effects,” Journal of International Money and Finance, Vol. 29 (3), pp. 570–584.
- Ho, Wai-Ming, 2004, “The Liquidity Effects of Foreign Exchange Intervention,” Journal of International Economics, 63, pp. 179–208.
- Kamil, Herman, 2008, “Is Central Bank Intervention Effective Under Inflation Targeting Regimes? The Case of Colombia,” IMF Working Paper 08/88.
- Loiseau-Aslanidi, Olga, 2011, “Determinants and Effectiveness of Foreign Exchange Market Intervention in Georgia,” Emerging Markets Finance and Trade, Vol. 47(4), pp. 75-95.
- Menkhoff, Lukas, 2010, “High–Frequency Analysis of Foreign Exchange Interventions: What do we Learn?” Journal of Economic Surveys, Vol. 24 (1), pp. 85-112.
- Neely, Christopher J., 2011, “A Foreign Exchange Intervention in an Era of Restraint,” Federal Reserve Bank of St. Louis Review, Vol. 93(5), pp. 303-24.
- Sarno, Lucio and Mark P. Taylor, 2001, “Official intervention in the foreign exchange market: Is it Effective and, if so, How Does it Work?,” Journal of Economic Literature, Vol. 39 (September), pp. 839–868.
- Sarno, Lucio and Mark Taylor, 2001, “Official Intervention in the Foreign Exchange Market: Is It Effective and, If So, How Does It Work?” Journal of Economic Literature, Vol. 39, No. 3 (September), pp. 839–868.
- Taylor, Mark P., 2004, “Is Official Exchange Rate Intervention Effective?” Economica, vol. 71 (281), pp. 1–11.
- Tuna, Gulcay, 2011, “The effectiveness of Central Bank intervention: evidence from Turkey,” Applied Economics, Vol. 43(14), pp. 1801–1815.

### Inflation targeting, exchange rate rules, and hybrid regimes
- Batini, Nicoletta, Paul Levine, and Joseph Pearlman, 2007, “Monetary Rules in Emerging Economies with Financial Market Imperfections,” in Jordi Gali and Mark J. Gertler, eds., International Dimensions of Monetary Policy.
- Benes, Jaromir, Jaromir Hurnik, and David Vavra, 2008, “Exchange Rate Management and Inflation Targeting: Modeling the Exchange Rate in Reduced-Form New Keynesian Models,” Czech Journal of Economics and Finance, Vol. 58, No. 3–4, pp. 166–194.
- Benes, Jaromir, Marta de Castello Branco, and David Vavra, 2007, “A Simple DGE Model for Inflation Targeting,” IMF Working Paper 07/197.
- Berganza, Juan Carlos and Carmen Broto, 2011, “Flexible inflation targets, forex interventions and exchange rate volatility in emerging countries,” Banco de Espaa Working Papers No. 1105.
- Carare, Alina and Mark Stone, 2003, “Inflation Targeting Regimes,” IMF Working Paper 03/09.
- Gersl, Adam and Thomas Holub, 2006, “Foreign Exchange Interventions Under Inflation Targeting: The Czech Experience,” Contemporary Economic Policy, Vol. 24, No. 4 (October), pp. 475–491.
- Kamil, Herman, 2008, “Is Central Bank Intervention Effective Under Inflation Targeting Regimes? The Case of Colombia,” IMF Working Paper 08/88.
- Morn, Eduardo, and Diego Winkelried, 2005, “Monetary Policy Rules for Financially Vulnerable Economies,” Journal of Development Economics, Vol. 76, pp. 25-51.
- Parrado, Eric, 2004a, “Inflation Targeting and Exchange Rate Rules in an Open Economy,” IMF Working Paper 04/21.
- Parrado, Eric, 2004b, “Singapore’s Unique Monetary Policy: How Does it Work?”, IMF Working Paper 04/10.
- Roger, Scott, Jorge Restrepo, and Carlos Garcia, 2009, “Hybrid Inflation Targeting Regimes,” IMF Working Paper 09/324.
- IMF, 2009, “The Role of the Exchange Rate in Inflation-Targeting Emerging Economies,” IMF Occasional Paper No. 267.
- IMF, 2011(c), “Foreign Exchange Market Intervention: How Good a Defense Against Appreciation Winds?” Regional Economic Outlook: Western Hemisphere, Chapter 3.

### Sterilization, central bank balance sheets, and unconventional monetary policy
- Obstfeld, Maurice, 1982, “Can we sterilize? Theory and Evidence,” NBER Working Paper No. 833.
- Kumhof, Michael, 2010, “On the Theory of Sterilized Foreign Exchange Intervention,” Journal of Economic Dynamics and Control, Vol. 34(8), pp. 1403-1420.
- Ouyang, Alice Y. and Ramkishen S. Rajan, 2011, “Reserve accumulation and monetary sterilization in Singapore and Taiwan,” Applied Economics, Vol. 43(16), pp. 2015-2031.
- Curdia, Vasco and Michael Woodford, 2011, “The Central–Bank Balance Sheet as an Instrument of Monetary Policy,” Journal of Monetary Economics, Vol. 58, pp. 54–79.
- Gertler, Mark and Peter Karadi, 2011, “A Model of Unconventional Monetary Policy,” Journal of Monetary Economics, Vol. 58, pp. 17–34.
- Woodford, Michael, 2005, “Comment on ’Using a Long-Term Interest Rate as the Monetary Policy Instrument,’” Journal of Monetary Economics, Vol. 52, pp. 881–887.
- Fatum, Rasmus, 2010, “Foreign Exchange Intervention When Interest Rates Are Zero: Does the Portfolio Balance Channel Matter After All?,” EPRU Working Paper Series No. 2010-07.

### Exchange rate regimes, trilemma, and real exchange rate issues
- Calvo, Guillermo, Carmen Reinhart and Carlos Vegh, 1995, “Targeting the Real Exchange Rate: Theory and Evidence,” Journal of Development Economics, Vol. 47, pp. 97–133.
- Edwards, Sebastian, and Carlos Vegh, 1997, “Banks and Macroeconomic Disturbances under Predetermined Exchange Rates,” Journal of Monetary Economics, Vol. 40, No. 2 (October), pp. 239–278.
- Gali, Jordi and Tommasso Monacelli, 2005, “Monetary Policy and Exchange Rate Volatility in a Small Open Economy,” Review of Economic Studies, Vol. 72, pp. 707–734.
- Monacelli, Tommasso, 2004, “Into the Mussa Puzzle: Monetary Policy Regimes and the Real Exchange Rate in a Small Open Economy,” Journal of International Economics, 62, pp. 191–217.
- Obstfeld, Maurice, Jay Shambaugh and Alan Taylor, 2004, “The Trilemma in History: Tradeoffs among Exchange Rates, Monetary Policies and Capital Mobility,” NBER Working Paper 10396.
- Obstfeld, Maurice, Jay Shambaugh and Alan Taylor, 2004, “Financial Stability, The Trilemma, and International Reserves,” American Economic Journal: Macroeconomics Vol. 2(2), pp. 57–94.
- Kraay, Aart and Jaume Venture, 2000, “Current Accounts in Debtor and Creditor Countries,” The Quarterly Journal of Economics, Vol. 115 (4), pp. 1137–1166.

### Empirical country studies, reports, and institutional publications
- Bank of Israel, 2009, “Inflation Report” January–March.
- Reserve Bank of Australia, 2008, “Statement on Monetary Policy” November.
- Swiss nationalBank, 2008, “Quarterly Bulletin” Fourth Quarter.
- IMF, 2008, “Republic of Serbia—Request for a Stand–By Arrangement,” IMF Country Report No. 08/162.
- IMF, 2011(a), “Foreign Exchange Market Intervention: How Good a Defense Against Appreciation Winds?,” in Regional Economic Outlook, Western Hemisphere, Chapter 3.
- IMF, 2011(b), “Hungary: Ex–Post Evaluation of Exceptional Access Under the 2008 Stand–By Arrangement,” IMF Country Report No. 11/145.
- Klyuev, Vladimir and Stephen Snudden, 2011, “Effects of Fiscal Consolidation in the Czech Republic,” IMF Working Paper 11/65.
- Sorezcky, Avihay, 2010, “Did the Bank of Israel Influence the Exchange Rate?,” Research Department Discussion Paper No. 2010.10.

### Modeling, monetary rules, and small-economy frameworks
- Batini, Nicoletta, Paul Levine, and Joseph Pearlman, 2007, “Monetary Rules in Emerging Economies with Financial Market Imperfections,” in International Dimensions of Monetary Policy.
- Leitemo, Kai, and Ulf Sderstrm, 2005, “Simple Monetary Policy Rules and Exchange Rate Uncertainty,” Journal of International Money and Finance, Vol. 24, pp. 481–507.
- Schmitt-Groh, Stephanie and Martin Uribe, 2003, “Closing Small Economy Models,” Journal of International Economics, Vol. 61, pp. 163–185.
- Morn, Eduardo, and Diego Winkelried, 2005, “Monetary Policy Rules for Financially Vulnerable Economies,” Journal of Development Economics, Vol. 76, pp. 25-51.
- Natalucci, Fabio, and Federico Ravenna, 2002, “The Road to Adopting the Euro: Monetary Policy and Exchange Rate Regimes in EU Candidate Countries,” International Finance Discussion Papers 741.

*Source: _wp1311 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp1311.pdf_