## Escaping the Financial Dollarization Trap: The Role of Foreign Exchange Intervention — Working Paper No. WP/2024/127

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### Introduction: background, research questions, and key contributions
- Background: financial dollarization and the "financial dollarization trap"
  - Financial dollarization is defined as private sector borrowing denominated in foreign currency.
  - Conventional view: dollarization raises macroeconomic volatility and financial instability because exchange rate depreciation raises the effective cost of foreign-currency borrowing, triggers balance sheet effects, and amplifies contractions in investment and output.
  - Under dollarization:
    - The exchange rate cannot effectively absorb negative external shocks; depreciation can be contractionary.
    - Attempts to fix the exchange rate can require a procyclical monetary stance and result in larger output contractions (Végh et al., 2017).
    - De-dollarization policies (e.g., higher reserve requirements in foreign currency, limits on banks’ FX positions) could lead to financial disintermediation and lower growth (Catao and Terrones, 2016).
  - The policy dilemma for central banks—limited options to mitigate harmful effects—is referred to as the financial dollarization trap.
- Research questions
  - (i) Can foreign exchange intervention lower macroeconomic volatility under dollarization?
  - (ii) How large are the welfare gains from deploying foreign exchange intervention policies in economies with financial dollarization?
- Key contributions
  - Empirical: country-specific VAR models for 45 countries over 2000Q1-2018Q4 (excludes reserve-currency issuers) to estimate macroeconomic effects of foreign exchange intervention (FXI); identification via global capital flow shocks following Blanchard et al. (2015).
  - Theoretical: a small open economy DSGE with liability dollarization, balance sheet effects, and foreign exchange reserves as an additional policy instrument alongside the short-term policy rate.
  - Main theoretical result: dollarization weakens monetary policy transmission, while FX intervention directly affects exchange rate and borrowing costs, enhancing stabilization of capital flows and financial-stability risks.

### Empirical approach (VAR) and main empirical findings
- VAR setup and identification
  - Country-specific recursive VAR with six variables: gkf_i,t (global capital flows series), ∆y_i,t (first difference of log GDP), ∆p_i,t (first difference of log CPI), R_i,t (short-term interest rate), rer_i,t (log real effective exchange rate), and ∆fx_i,t (change in stock of FX reserves divided by trend GDP).
  - Global capital flow series constructed excluding country i to ensure exogeneity.
  - Sample: 45 advanced and emerging economies; period: 2000Q1-2018Q4; excludes United States, United Kingdom, Japan, Euro area countries, Switzerland.
  - Dollarization classification: "dollarized" if deposit dollarization ≥ 20 percent, and "non-dollarized" if < 20 percent (based on Levy-Yeyati (2006)).
  - ∆fx_i,t computed with a Hodrick-Prescott filter with smoothing parameter 1,600.
  - VAR lag length p = 3 (chosen by SBC and AIC); block exogeneity restriction so domestic variables do not affect global capital flows on impact.
- Shock studied and reporting
  - Shock: contraction of global capital flows equal to 2 percent of global GDP.
  - Reporting: median impulse responses for dollarized and non-dollarized economies with 60 percent confidence bands (60% bands computed using bootstrapping).
- Main empirical findings (VAR results)
  - A negative global capital flow shock is contractionary in both dollarized and non-dollarized economies.
  - The negative effect on output is amplified in dollarized economies.
  - Inflation declines following the shock; the decline is larger in dollarized economies (consistent with a standard Phillips curve).
  - Policy responses in dollarized economies:
    - Greater sales of FX reserves.
    - Larger increases in the policy interest rate relative to non-dollarized economies.
    - These responses resemble “leaning against the wind” to contain exchange rate depreciation and adverse balance sheet effects from foreign-currency debt.
  - Real effective exchange rate dynamics:
    - Dollarized economies tend to display a more gradual depreciation in the short run, consistent with policy rate and FX intervention responses.
    - The increase in policy rate in dollarized economies could be associated with unsterilized FX interventions that contract money supply.
- Heterogeneity within dollarized economies (Figure 2 analysis)
  - Dollarized sample split by median interest-rate response to the shock into Group A (above-median interest-rate response) and Group B (below-median interest-rate response).
  - Both groups deploy FX intervention; interpretation:
    - Group B: interpreted as employing sterilized FX interventions (interest rate stable on impact); slower real exchange rate depreciation; more moderate output response; lower inflation.
    - Group A: larger interest-rate reaction; larger depreciation and larger output contraction, consistent with depreciation raising the cost of foreign-currency borrowing and amplifying aggregate demand contraction.
  - Interpretation: Sterilized FX intervention has a stronger transmission mechanism for containing depreciation and mitigating balance-sheet effects than unsterilized intervention coupled with large interest-rate increases.

### Small open economy DSGE model with FX intervention: structure and mechanisms
- Model overview and key ingredients
  - Two goods: domestic and imported.
  - Domestic production: firms combine capital and labor; entrepreneurs demand capital subject to agency costs (Bernanke et al. (1999)).
  - Liability dollarization: fraction (1 − φ) of corporate borrowing denominated in foreign currency; balance-sheet effects from exchange rate fluctuations.
  - Imperfect asset substitution via transaction/portfolio adjustment cost Θt allows sterilized FX intervention to have real effects through the portfolio balance channel.
  - Monetary authority controls short-term interest rate and stock of FX reserves.
- Households
  - Continuum j ∈ [0,1], expected present value of utility Ut(j) = Et Σ_{i=0}^∞ β^i [ Ct+i(j) − ζL lt+i(j)^{1+σL}/(1+σL) ]^{σC−1)/σC}.
  - Consumption aggregator Ct(j) is CES of home and foreign goods with parameters γC and ηC (equation (4)).
  - Assets: Bt(j), Dt(j), D*_t(j), B*_t(j), and state-contingent domestic bonds dt+1(j); gross return on foreign deposits equals R*_t.
  - Budget constraint includes transaction cost Θt per unit of foreign borrowing; Θt generates a wedge in the UIP condition.
  - Wage setting: Calvo wage rigidity with probability (1 − φL) to re-optimize; labor aggregation as in equations (6)–(7).
- Capital producers and investment
  - Investment It is CES aggregation of home and foreign investment goods (γI, ηI).
  - Capital law of motion: Kt+1 = (1 − δ)Kt + S(It / It−1) It with S(1) = 1, S′(1) = 0, S′′(1) = −μS < 0.
- Entrepreneurs and financial accelerator
  - Entrepreneurs finance Kt+1 with net worth Nt and loans Be,t and E_t B*_e,t: Nt + Be,t + E_t B*_e,t = Qt Kt+1 (equation (8)).
  - Fraction φ domestic loans; (1 − φ) foreign loans; degree of liability dollarization = 1 − φ.
  - Idiosyncratic productivity shock ωt+1 with log-normal distribution; monitoring costs proportional to income with parameter μ.
  - Effective portfolio interest rate R̄_L,t+1 = φ RL,t+1 + (1 − φ) Et+1 / Et R*_L,t+1 (equation (10)).
  - External finance premium sp_t+1 linked to leverage: sp_t+1 = Ψ( Qt Kt+1 / Nt ), Ψ′(·) > 0 (equation (15)).
  - Net worth evolution Nt = γe Λ(ω̄t) RK,t Qt−1 Kt + we (equation (16)).
- Firms and price setting
  - Intermediate producers: YH,t(zH) = AH,t l_t(zH)^{1−α} K_t(zH)^{α}; Calvo price setting for intermediate varieties.
  - Retailers and importers: CES aggregators for home and foreign goods (equations (18)–(19)); importers buy at foreign-currency price P*_F,t and set local-currency prices with Calvo stickiness.
- Monetary and FX policy rules
  - Taylor-type interest rate rule (equation (20)):
    - R_t / R̄ = [ R_{t−1} / R̄ ]^{φR} [ (1 + π_t) / (1 + π̄) ]^{(1−φR) φπ} [ Y_t / Ȳ ]^{(1−φR) φy} [ R*_t / R̄* ]^{(1−φR) φR*}.
    - If φR* > 0, rule stabilizes nominal exchange rate.
  - FX intervention rule that leans against the wind (equation (21)):
    - F*_t / F̄* = [ F*_{t−1} / F̄* ]^{ρfx} [ R*_t / R̄* ]^{θR*},
    - When θR* < 0, central bank offsets capital flows by adjusting FX reserves.
  - Central bank budget constraint for FX reserves (equation (22)) and sterilization via domestic bonds Bt; net profits rebated via lump-sum transfers T_t (costs second-order in simulations).
- Aggregation, balance of payments, and the role of Θt
  - Aggregation identities: Dt = Be,t and D*_t = B*_e,t with Be,t = φ (Qt Kt+1 − Nt) and E_t B*_e,t = (1 − φ) (Qt Kt+1 − Nt) (equation (24)).
  - Balance of payments/net foreign assets: Et( F*_t − B*_t ) = R*_t−1 ( Et F*_{t−1} − Et B*_{t−1} ) + Xt − Mt (equation (30)).
  - Θt determines degree of asset substitution between domestic and foreign bonds and strength of sterilized FX intervention transmission.
    - When Θt = 1 (perfect asset substitution), FX reserve accumulation is fully offset by private sector borrowing from abroad.
    - Θt specified as Θ(B*_t, Bt/Et) with elasticities:
      - ∂Θ / ∂B*_t * B*_t / Θ(B*_t, Bt/Et) = ρ1,
      - ∂Θ / ∂(Bt/Et) * (Bt/Et) / Θ(B*_t, Bt/Et) = ρ2.

### Calibration: baseline parameter values and targets
- Model frequency and steady-state targets
  - Quarterly calibration for a representative emerging economy.
  - Discount factor: β = 0.995 (steady state risk-free rate of 2 percent).
  - Share of imported goods in consumption: γC = 0.30; substitution elasticity ηC = 0.5.
  - Share of imported goods in investment: γI = 0.30; substitution elasticity ηI = 0.5.
  - Implied imports-to-GDP broadly coincides with observed value of 27 percent for average of 155 emerging and developing countries (IMF WEO 2000-2018).
  - Net exports chosen to be zero at steady state: (X̄ − M̄)/Ȳ = 0.0.
  - Stock of FX reserves at steady state: F̄∗ = 25 percent of GDP.
- Financial accelerator and dollarization
  - Credit spread in annual terms in steady state: s̄p = 1.035.
  - Default premium in annual terms in steady state: 4×F(ω̄) = 0.03.
  - Capital-net worth ratio Q̄ K̄/N̄ = 2.00.
  - Survival rate of entrepreneurs: γe = 0.975.
  - Annual default rate targeted as 3 percent.
  - Degree of liability dollarization in benchmark: 1 − φ = 0.50 (median emerging economy in Levy-Yeyati (2006)).
  - Capital share α = 0.35.
  - Investment-to-GDP ratio Ī/Ȳ = 0.20.
  - Price elasticity of exports η∗ = 0.5.
- Price, wage, and monetary policy parameters
  - Wage Calvo parameter φL = 0.875 (average wage duration: 8 quarters); indexation ξL = 0.5; εL = 6.0.
  - Price Calvo parameters: φH = 0.75 (average price duration: 4 quarters), ξH = 0.5, εH = 11.0; φF = 0.75, ξF = 0.5, εH (for F varieties) = 11.0.
  - Monetary rule: φR = 0.70, φπ = 1.50, φy = 0.50/4.
  - Persistence of shocks to foreign interest rate: ρR∗ = 0.95.
- Parameters governing the external-risk premium Θt
  - External risk premium elasticity to B∗: ρ1 = 0.001.
  - External risk premium elasticity to Bt/Et: Table 1 entry ρ2 = 0.013; calibration narrative notes ρ2 = 0.030 based on Bayoumi et al. (2015) evidence (the paper reports both figures and lists ρ2 = 0.013 in Table 1).
- Baseline calibration (selected parameter table entries)
  - β: 0.995
  - σC: 1.00
  - σL: 2.00
  - γC: 0.30
  - ηC: 0.5
  - γI: 0.30
  - ηI: 0.5
  - μS: 2.5
  - s̄p: 1.035
  - 4×F(ω̄): 0.03
  - Q̄ K̄/N̄: 2.00
  - γe: 0.975
  - 1 − φ: 0.50
  - α: 0.35
  - Ī/Ȳ: 0.20
  - (X̄ − M̄)/Ȳ: 0.0
  - η∗: 0.5
  - φL: 0.875
  - ξL: 0.5
  - εL: 6.0
  - φH: 0.75
  - ξH: 0.5
  - εH: 11.0
  - φF: 0.75
  - ξF: 0.5
  - εH (for F varieties): 11.0
  - φR: 0.70
  - φπ: 1.50
  - φy: 0.50/4
  - ρR∗: 0.95
  - ρ1: 0.001
  - ρ2: 0.013 (Table 1 entry)

### Model implications and policy conclusions
- Theoretical interpretation of empirical results
  - Monetary policy alone cannot fully stabilize the economy in response to capital outflows under liability dollarization; optimal interest-rate paths can be procyclical as observed in many emerging economies.
  - Including foreign exchange reserves as a second policy instrument:
    - Stabilizes the cost of borrowing in foreign currency.
    - Lowers volatility of consumption, investment, and output.
    - Restores monetary policy autonomy, allowing the central bank to lower the policy rate in bad times.
- Welfare and policy implications
  - Optimal FX intervention can substantially reduce welfare costs of financial dollarization and provide central banks an additional stabilization tool.
  - Sterilized FX intervention can slow depreciation and reduce output volatility in dollarized economies via the portfolio balance channel when imperfect asset substitution (Θt) exists.
  - Prudence required: FXI may be suboptimal in circumstances such as hindering FX market development, creating moral hazard, conflicting monetary-policy signals, or political misuse when the central bank lacks independence (principles referenced in IMF (2023)).

### Empirical sample and figures (select items)
- VAR sample: 45 countries (appendix lists dollarized and non-dollarized country samples with deposit dollarization shares for 1995-2004).
- Key figures described (responses and comparisons across regimes and dollarization levels):
  - Figure 1: Responses to Global Capital Outflow Shocks in Dollarized and Non-dollarized Economies.
  - Figure 2: Role of FXI and Interest Rate Reaction in Transmission in Dollarized Economies.
  - Figures 3–6: Model-based transmission and policy-regime comparisons across Non-dollarization and 50 percent dollarization, and comparisons of Base, Opt MP, Opt FXI, and Joint Optimization, plotting Consumption, Investment, Trade Balance to GDP, GDP, Spread, RER, Real int. rate, Inflation Rate, FX Res to GDP across Quarters 0–25 with deviations from steady state.

*Source: wpiea2024127-print-pdf — Escaping the Financial Dollarization Trap: The Role of Foreign Exchange Intervention — Working Paper No. WP/2024/127*

### 1.    Introduction

### 1.    Introduction

### Background: financial dollarization and the "financial dollarization trap"
- Financial dollarization is defined as private sector borrowing denominated in foreign currency.
- Conventional view: dollarization is a source of macroeconomic volatility and financial instability because exchange rate depreciation raises the effective cost of foreign-currency borrowing, triggers balance sheet effects, and amplifies contractions in investment and output.
- Under dollarization:
  - The exchange rate cannot effectively absorb negative external shocks; depreciation can be contractionary.
  - Attempts to fix the exchange rate can require a procyclical monetary stance and result in larger output contractions (Végh et al., 2017).
  - De-dollarization policies (e.g., higher reserve requirements in foreign currency, limits on banks’ FX positions) could lead to financial disintermediation and lower growth (Catao and Terrones, 2016).
- The resulting policy dilemma for central banks—limited options to mitigate harmful effects— is referred to as the financial dollarization trap.

### Research questions
- The paper focuses on two policy questions:
  - (i) Can foreign exchange intervention lower macroeconomic volatility under dollarization?
  - (ii) How large are the welfare gains from deploying foreign exchange intervention policies in economies with financial dollarization?

### Key contributions
- Empirical contribution:
  - Estimate the macroeconomic effects of foreign exchange intervention (FXI) in dollarized economies using country-specific VAR models rather than standard panel approaches.
  - Address endogeneity by quantifying dynamic effects of FXI in response to a shock in global capital flows (following Blanchard et al. (2015)).
  - Sample: 45 countries over 2000Q1-2018Q4 (excludes reserve-currency issuers).
  - Main empirical findings summarized below.
- Theoretical contribution:
  - Develop a small open economy DSGE model with balance sheet effects where exchange depreciation generates contractionary effects (contrary to Mundell-Fleming).
  - Introduce foreign exchange reserves as an additional policy instrument alongside the short-term policy rate.
  - Show that dollarization weakens monetary policy transmission (policy rate easing induces depreciation and tighter conditions for foreign borrowing), while FX intervention directly affects exchange rate and borrowing costs, increasing its effectiveness for stabilizing capital flows and financial stability risks.
  - Demonstrate that including FX reserves in the central bank toolkit stabilizes the cost of foreign-currency borrowing, lowers volatility of consumption, investment, and output, and restores monetary policy autonomy (allowing lower policy rates in bad times).

### Relation to literature
- Builds on literature that shows monetary policy trade-offs under dollarization (e.g., Céspedes et al. (2004); Gertler et al. (2007); Aghion et al. (2001); Aoki et al. (2021); Braggion et al. (2009); Cavallino and Sandri (2023); Choi and Cook (2004); Hoffman et al. (2022)).
- Relates to studies on optimal use of FXI and portfolio-balance channels (Cavallino (2019); Fanelli and Straub (2021); Davis et al. (2021); Gabaix and Maggiori (2015)).
- Complements lender-of-last-resort FXI literature (Bocola and Lorenzoni, 2020; Céspedes et al., 2017) by evaluating FXI over the business cycle rather than only in crisis episodes.
- Empirical links to VAR-based FXI studies (Blanchard et al. (2015); Kim (2003); Cavallino (2019)).

### Empirical approach: VAR setup and identification
- Country-specific recursive VAR with six variables:
  - global capital flows series (gkf_i,t), ∆y_i,t (first difference of log GDP), ∆p_i,t (first difference of log CPI), R_i,t (short-term interest rate), rer_i,t (log real effective exchange rate), and ∆fx_i,t (change in stock of FX reserves divided by trend GDP).
- Global capital flow series constructed following Blanchard et al. (2015) to ensure exogeneity to each individual economy (country-specific measure excludes country i).
- Sample and data specifics:
  - Sample of 45 advanced and emerging economies.
  - Period: 2000Q1-2018Q4.
  - Excludes reserve-currency issuers (United States, United Kingdom, Japan, Euro area countries, Switzerland).
  - Dollarization classification: economy is "dollarized" if deposit dollarization ≥ 20 percent, and "non-dollarized" if < 20 percent (based on Levy-Yeyati (2006)).
  - ∆fx_i,t computed with a Hodrick-Prescott filter with smoothing parameter 1,600.
- VAR estimation details:
  - VAR lag length p = 3 (chosen by SBC and AIC).
  - Block exogeneity restriction: domestic variables do not affect global capital flows on impact; first equation reduces to gkf_i,t = α_1i + a_11 gkf_i,t−1 + u_1i,t.
  - Matrices A_i,1...A_i,p are 6×6; α_i is 6×1; u_i,t is 6×1 with variance-covariance matrix Ω_i.
  - Estimation by OLS imposing the block exogeneity restriction.

### Empirical findings (VAR results)
- Shock studied: contraction of global capital flows equal to 2 percent of global GDP.
- Reporting: median impulse responses for dollarized and non-dollarized economies with 60 percent confidence bands (60% bands computed using bootstrapping methods).
- Main empirical findings:
  - A negative global capital flow shock is contractionary in both dollarized and non-dollarized economies.
  - The negative effect on output is amplified in dollarized economies.
  - Inflation declines following the shock; the decline is larger in dollarized economies (consistent with a standard Phillips curve).
  - Policy responses in dollarized economies:
    - Greater sales of FX reserves.
    - Larger increases in the policy interest rate relative to non-dollarized economies.
    - These responses resemble a “leaning against the wind” policy to contain exchange rate depreciation and adverse balance sheet effects from foreign-currency debt.
  - Real effective exchange rate dynamics:
    - Dollarized economies tend to display a more gradual depreciation in the short run, consistent with policy rate and FX intervention responses.
    - The increase in policy rate in dollarized economies could also be associated with unsterilized FX interventions that contract money supply.
- Within-dollarized-economy heterogeneity (Figure 2 analysis):
  - Dollarized sample split into two groups based on whether interest rate response to the shock is above or below the median.
  - Both groups deploy FX intervention; Group B (below-median interest rate response) interpreted as employing sterilized FX interventions, Group A as more active interest-rate response.
  - Findings:
    - Group B (sterilized-like): interest rate does not react on impact and is relatively stable; real exchange rate depreciation is slower; output response to capital flows is more moderate; inflation is lower.
    - Group A (larger interest-rate reaction): larger depreciation and larger output contraction, consistent with depreciation raising the cost of foreign-currency borrowing and amplifying aggregate demand contraction.
  - Interpretation: Sterilized FX intervention has a stronger transmission mechanism for containing depreciation and mitigating balance sheet effects than unsterilized intervention coupled with large interest-rate increases.

### Theoretical interpretation and policy implications
- In the DSGE model with liability dollarization:
  - Monetary policy alone cannot fully stabilize the economy in response to capital outflows; optimal interest-rate paths can be procyclical as observed in many emerging economies.
  - Inclusion of foreign exchange reserves as a second instrument:
    - Stabilizes the cost of borrowing in foreign currency.
    - Lowers volatility of consumption, investment, and output.
    - Restores monetary policy autonomy, allowing the central bank to lower the policy rate in bad times.
- Policy implications:
  - Optimal FX intervention can substantially reduce welfare costs of financial dollarization and provide central banks an additional stabilization tool.
  - Sterilized FX intervention can play a macroeconomic stabilization role in dollarized economies by slowing depreciation and reducing output volatility.
  - Prudence is required: the paper notes circumstances where FXI may be suboptimal (e.g., hindering FX market development, creating moral hazard, conflicting monetary policy signals, or political misuse when central bank lacks independence, as discussed in the Principles for the Use of Foreign Exchange Intervention (IMF, 2023)).

### Structure of the paper (outline)
- Section 2: VAR analysis of macroeconomic effects of global capital flow shocks.
- Section 3: Small open economy model with balance sheet effects and liability dollarization.
- Section 4: Model calibration strategy.
- Section 5: Model responses to a capital outflow, comparing economies with and without liability dollarization.
- Section 6: Welfare evaluation of optimal FX intervention and monetary policy.
- Section 7: Conclusion.

*Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024127-print-pdf.pdf*

### 3.    A  Small  Open  Economy  Model  with  Foreign

### 3.    A Small Open Economy Model with Foreign Exchange Intervention

### Model overview
- Two goods: domestic and imported.
- Domestic good produced by firms combining capital and labor with constant-returns-to-scale technology; entrepreneurs demand capital subject to agency costs as in Bernanke et al. (1999).
- A fraction of corporate borrowing is denominated in foreign currency, capturing liability dollarization and balance-sheet effects of exchange rate fluctuations.
- Imperfect asset substitution (portfolio adjustment/transaction cost Θt) allows sterilized FX intervention to have real effects via the portfolio balance channel.
- The model evaluates welfare gains from relying on FX intervention in response to capital outflows under liability dollarization.

### Households (Section 3.1)
- Continuum of households indexed by j ∈ [0,1].
- Expected present value of utility:
  - Ut(j) = Et Σ_{i=0}^∞ β^i [ Ct+i(j) − ζL lt+i(j)^{1+σL}/(1+σL) ]^{σC−1)/σC} (as in original expression (3)).
- Consumption aggregator (CES of home and foreign goods):
  - Ct(j) = [ γC^{1/ηC} CH,t(j)^{(ηC−1)/ηC} + (1−γC)^{1/ηC} CF,t(j)^{(ηC−1)/ηC} ]^{ηC/(ηC−1)} (equation (4)).
- Assets available: non-contingent domestic bonds Bt(j), domestic deposits Dt(j), foreign currency deposits D*_t(j), non-contingent foreign debt B*_t(j), and state-contingent domestic bonds dt+1(j).
- Gross return on foreign deposits equals risk-free foreign interest rate R*_t.
- Household nominal budget constraint (equation (5)) includes transaction cost Θt per unit of foreign borrowing; Θt generates imperfect asset substitution and a wedge in the UIP condition.
- Θt functional form specified in section 3.6; follows literature introducing portfolio adjustment/transaction costs to generate imperfect substitution and stationarity.

#### Wage setting and labor supply (3.1.1)
- Each household j supplies a differentiated labor service lt(j); aggregate labor:
  - lt = [ ∫_0^1 lt(j)^{(εL−1)/εL} dj ]^{εL/(εL−1)} (equation (6)).
- Labor demand for household j:
  - lt(j) = [ Wt(j) / Wt ]^{−εL} lt (equation (7)).
- Wage setting follows Calvo (1983)-style staggered nominal wage rigidity: each period a household can re-optimize with probability (1−φL).

### Capital producers (Section 3.2)
- Aggregate investment It is a CES aggregation of home (IH,t) and foreign (IF,t) investment goods with elasticity ηI and domestic investment share γI.
- Capital law of motion:
  - Kt+1 = (1−δ)Kt + S(It / It−1) It,
  - where S(.) is the investment adjustment cost satisfying: S(1) = 1, S′(1) = 0, S′′(1) = −μS < 0 (see footnote referencing Altig et al. (2011)).
- Capital goods sold at price Qt to entrepreneurs.

### Entrepreneurs and financial accelerator (Section 3.3)
- Continuum of risk-neutral entrepreneurs finance Kt+1 with net worth Nt and loans Be,t (domestic) and E_t B*_e,t (foreign):
  - Nt + Be,t + E_t B*_e,t = Qt Kt+1 (equation (8)).
- Fraction φ of loans denominated in domestic currency, and (1−φ) in foreign currency; degree of liability dollarization = 1−φ.
- Entrepreneurs face idiosyncratic shock ωt+1 to effective capital ωt+1 Kt+1; log(ωt+1) ~ Normal(mean = −σ_ω^2/2, sd = σ_ω) so Et ωt+1 = 1.
- Ex-post return for entrepreneur (equation (9)):
  - ωt+1 RK,t+1 = ωt+1 Zt+1 + (1−δ) Qt+1 / Qt.
- Monitoring costs proportional to investment income: μ ωt+1 RK,t+1 Qt Kt+1 with μ ∈ (0,1).
- Debt contracts: interest rates RL,t+1 (domestic) and R*_L,t+1 (foreign); effective interest rate for loan portfolio:
  - R̄_L,t+1 = φ RL,t+1 + (1−φ) Et+1 / Et R*_L,t+1 (equation (10)).
- Cutoff realization of ω, ω̄t+1, defined by incentive compatibility (equation (11)):
  - ω̄t+1 RK,t+1 Qt Kt+1 = R̄_L,t+1 B̄_e,t = R̄_L,t+1 (Qt Kt+1 − Nt).
- Net expected benefits for entrepreneurs expressed via Λ(ω̄t+1)R K,t+1 Qt Kt+1 (equation (12)).
- Zero-profit condition for financial intermediaries leading to Γ(ω̄t+1)R K,t+1 Qt Kt+1 (equation (13)).
- External finance premium (credit spread) sp_t+1 satisfies (equation (14)):
  - sp_t+1 = RK,t+1 Qt ( φ Rt + (1−φ) Et+1 / Et R*_t ) = ρ(ω̄t+1),
  - ρ(ω̄t+1) = ( Γ(ω̄t+1) − Λ(ω̄t+1) / Γ′(ω̄t+1) / Γ(ω̄t+1) )^{−1}.
- Log-normal ω implies increasing relationship between credit spread sp_t+1 and leverage (Qt Kt+1 / Nt):
  - sp_t+1 = Ψ( Qt Kt+1 / Nt ), Ψ′(·) > 0 (equation (15)).
- Entrepreneur turnover: fraction γe survives each period; entrants (and exiting survivors) receive initial wealth we.
- Net worth evolution (equation (16)):
  - Nt = γe Λ(ω̄t) RK,t Qt−1 Kt + we.
- Aggregate entrepreneur consumption (equation (17)):
  - Ce,t = (1−γe) Λ(ω̄t) RK,t Qt−1 Kt / PC,t.

### Firms (Section 3.4)
- Three firm types: intermediate good producers (monopolistic, Calvo price setting), perfectly competitive retailers of home goods assembling differentiated intermediate goods, and importers who purchase homogeneous foreign goods and differentiate them with local-currency price stickiness.

#### Intermediate home good producers (3.4.1)
- Production for variety zH:
  - YH,t(zH) = AH,t l_t(zH)^{1−α} K_t(zH)^{α},
  - α is capital share. Intermediate producers set prices à la Calvo.

#### Retailers of intermediate home goods (3.4.2)
- Aggregate home good from intermediate varieties:
  - YH,t = [ ∫_0^1 YH,t(zH)^{(εH−1)/εH} dzH ]^{εH/(εH−1)} (equation (18)).

#### Importers (3.4.3)
- Assemblers form final import good:
  - YF,t = [ ∫_0^1 YF,t(zF)^{(εF−1)/εF} dzF ]^{εF/(εF−1)} (equation (19)).
- Importers buy at foreign currency price P*_F,t and set local-currency prices with Calvo stickiness.

### Monetary and foreign exchange policy (Section 3.5)
- Monetary authority controls short-term interest rate and stock of FX reserves.
- Interest rate follows a Taylor-type rule with interest rate smoothing (equation (20)):
  - R_t / R̄ = [ R_{t−1} / R̄ ]^{φR} [ (1 + π_t) / (1 + π̄) ]^{(1−φR) φπ} [ Y_t / Ȳ ]^{(1−φR) φy} [ R*_t / R̄* ]^{(1−φR) φR*},
  - where φR, φπ, φy, and φR* are weights on smoothing, inflation, GDP, and foreign interest rate. If φR* > 0, rule stabilizes nominal exchange rate.
- Central bank FX intervention rule that leans against the wind (equation (21)):
  - F*_t / F̄* = [ F*_{t−1} / F̄* ]^{ρfx} [ R*_t / R̄* ]^{θR*},
  - where F*_t is stock of FX reserves, F̄* steady state, θR* governs responsiveness to foreign interest rate, ρfx persistence. When θR* < 0, central bank offsets capital flows by adjusting FX reserves.
- Central bank budget constraint for FX reserves (equation (22)):
  - Et(F*_t − Bt) = Et( F*_{t−1} R*_t−1 − B_{t−1} R_{t−1} ) − T_t.
- Sterilized FX interventions conducted via issuance of domestic bonds Bt and accumulation of foreign reserves F*_t. Net profits from FX operations rebated to households via lump-sum transfers T_t (costs summarized as second-order in simulations).

### Aggregation and equilibrium conditions (Section 3.6)
- Aggregate holdings:
  - Dt = ∫_0^1 Dt(j) dj, D*_t = ∫_0^1 D*_t(j) dj, Bt = ∫_0^1 Bt(j) dj, B*_t = ∫_0^1 B*_t(j) dj (equation (23)).
- Financial intermediation aggregate identities (equation (24)):
  - Dt = Be,t and D*_t = B*_e,t,
  - with Be,t = φ B̄_e,t = φ (Qt Kt+1 − Nt) and E_t B*_e,t = (1−φ) B̄_e,t = (1−φ) (Qt Kt+1 − Nt).
- Labor and capital market equilibria (equations (25) and (26)):
  - lt = [ ∫_0^1 lt(j)^{(εL−1)/εL} dj ]^{εL/(εL−1)} = ∫_0^1 lt(zH) dzH,
  - Kt = ∫_0^1 Kt(zH) dzH.
- Final home good equilibrium (equation (27)):
  - YH,t = CH,t + Ce,H,t + IH,t + C*_H,t + μ [ ∫_0^{ω̄t+1} f(ω) dω ] RK,t+1 Qt Kt+1.
- Exports volume (equation (28)):
  - C*_H,t = ζ* [ PH,t Et / P*_t ]^{−η*} C*_t, where ζ* is share of domestic goods in rest-of-world consumption and η* is price elasticity.
- Foreign goods market equilibrium (equation (29)):
  - YF,t = [ ∫_0^1 YF,t(zF)^{(εF−1)/εF} dzF ]^{εF/(εF−1)} = CF,t + Ce,F,t + IF,t.
- Balance of payments / net foreign assets dynamics (equation (30)):
  - Et( F*_t − B*_t ) = R*_t−1 ( Et F*_{t−1} − Et B*_{t−1} ) + Xt − Mt,
  - with Xt = PH,t C*_H,t and Mt = Et P*_F,t ∫_0^1 YF,t(zF) dzF.
- Role of transaction cost Θt:
  - Θt determines degree of asset substitution between domestic and foreign bonds and strength of sterilized FX intervention transmission.
  - When Θt = 1 (perfect asset substitution), FX reserve accumulation is fully offset by private sector borrowing from abroad.
  - Θt specified as Θ(B*_t, Bt/Et). Two elasticities defined:
    - ∂Θ / ∂B*_t * B*_t / Θ(B*_t, Bt/Et) = ρ1,
    - ∂Θ / ∂(Bt/Et) * (Bt/Et) / Θ(B*_t, Bt/Et) = ρ2.

*Source: IMF working paper chapter "3.    A Small Open Economy Model with Foreign Exchange Intervention" (content unit: wpiea2024127-print-pdf).*

### 4.    Calibration

### 4.    Calibration

### Model setup and steady state targets
- Quarterly frequency calibration for a representative emerging economy.
- Discount factor: β = 0.995, consistent with a steady state risk-free rate of 2 percent.
- Household preferences:
  - Intertemporal substitution elasticity: σC = 1.00
  - Frisch elasticity of labor supply inverse: σL = 2.00 (i.e., labor supply Frisch elasticity = 1/2)
- Shares and elasticities for traded goods:
  - Share of imported goods in consumption: γC = 0.30
  - Substitution elasticity between domestic and imported consumption goods: ηC = 0.5
  - Share of imported goods in investment: γI = 0.30
  - Substitution elasticity between domestic and imported investment goods: ηI = 0.5
- Implied ratio of imports to GDP in calibration broadly coincides with the observed value of 27 percent for an average of 155 emerging and developing countries in the IMF WEO database for 2000-2018.
- Net exports chosen to be zero at steady state by selecting ζ∗ accordingly: (X̄ − M̄)/Ȳ = 0.0
- Stock of FX reserves at steady state: F̄∗ = 25 percent of GDP.

### Financial accelerator and dollarization parameters
- Financial accelerator calibrated following Bernanke et al. (1999) and Gertler et al. (2007):
  - Credit spread in annual terms in steady state: s̄p = 1.035
  - Default premium in annual terms in steady state: 4×F(ω̄) = 0.03
  - Capital-net worth ratio of entrepreneurs in steady state: Q̄ K̄/N̄ = 2.00
  - Survival rate of entrepreneurs: γe = 0.975
- Annual default rate targeted as 3 percent (calibration consistent with this).
- Degree of liability dollarization in benchmark calibration: 1 − φ = 0.50, matching the median emerging economy in Levy-Yeyati (2006).
- Capital share in domestic production: α = 0.35
- Investment-to-GDP ratio in steady state: Ī/Ȳ = 0.20
- Price elasticity of exports: η∗ = 0.5

### Price, wage, and monetary policy parameters
- Price and wage rigidities (Calvo-style):
  - Calvo parameter in wages: φL = 0.875 (average wage duration: 8 quarters)
  - Indexation to past inflation in wages: ξL = 0.5
  - Substitution elasticity across labor varieties: εL = 6.0
  - Calvo parameter in prices of H goods: φH = 0.75 (average price duration: 4 quarters)
  - Indexation to past inflation in prices of H goods: ξH = 0.5
  - Substitution elasticity across H varieties: εH = 11.0
  - Calvo parameter in prices of F goods: φF = 0.75
  - Indexation to past inflation in prices of F goods: ξF = 0.5
  - Substitution elasticity across F varieties: εH = 11.0
- Monetary policy rule (standard values):
  - Smoothing of the monetary policy rule: φR = 0.70
  - Reaction to inflation: φπ = 1.50
  - Reaction to output: φy = 0.50/4
- Persistence of shocks to the foreign interest rate: ρR∗ = 0.95

### Parameters governing the risk premium Θt
- External risk premium elasticity to B∗: ρ1 = 0.001 (calibrated close to zero to ensure stationarity, following Schmitt-Grohè and Uribe (2003))
- External risk premium elasticity to Bt/Et: ρ2 = 0.013 in Table 1; however, calibration narrative sets ρ2 = 0.030 based on Bayoumi et al. (2015) evidence that a 1 percent of GDP increase in foreign reserves improves the current account balance by around 0.4 percent of GDP. Table 1 summarizes parameter values and lists ρ2 = 0.013 as a parameter value.

### Baseline Calibration (selected parameter values from Table 1)
- β: 0.995
- σC: 1.00
- σL: 2.00
- γC: 0.30
- ηC: 0.5
- γI: 0.30
- ηI: 0.5
- μS: 2.5 (parameter for adjustment cost in investment)
- s̄p: 1.035 (credit spread in annual terms in the steady state)
- 4×F(ω̄): 0.03 (default premium in annual terms in the steady state)
- Q̄ K̄/N̄: 2.00
- γe: 0.975
- 1 − φ: 0.50 (degree of financial dollarization)
- α: 0.35
- Ī/Ȳ: 0.20
- (X̄ − M̄)/Ȳ: 0.0
- η∗: 0.5
- φL: 0.875
- ξL: 0.5
- εL: 6.0
- φH: 0.75
- ξH: 0.5
- εH: 11.0
- φF: 0.75
- ξF: 0.5
- εH (for F varieties): 11.0
- φR: 0.70
- φπ: 1.50
- φy: 0.50/4
- ρR∗: 0.95
- ρ1: 0.001
- ρ2: 0.013 (Table 1 entry)

*Source: wpiea2024127-print-pdf — 4. Calibration*

### References

### References

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### Appendix: Sample of Countries used in the VAR estimation
- Dollarized (Financial dollarization, Country 1995-2004 (%)):
  - Azerbaijan 69.1
  - Bolivia 90.1
  - Bulgaria 50.0
  - Costa Rica 42.5
  - Chile 7.9
  - Croatia 68.6
  - Egypt 26.4
  - Estonia 27.2
  - Georgia 70.1
  - Hungary 21.3
  - Jamaica 25.4
  - Kazakhstan 48.6
  - Latvia 44.9
  - Lithuania 36.7
  - Korea, Republic of 2.7
  - Moldova 39.4
  - Paraguay 54.5
  - Peru 67.2
  - Philippines 30.8
  - Qatar 25.3
  - Romania 39.9
  - Russia 32.8
  - Turkey 48.8
  - Ukraine 34.7
  - Uruguay 82.5
- Non-dollarized (Financial dollarization, Country 1995-2004 (%)):
  - Australia 0.0
  - Brazil 0.0
  - Canada 0.0
  - China 7.9
  - Colombia 0.4
  - Czech Republic 11.0
  - Denmark 3.8
  - India 0.0
  - Indonesia 19.8
  - Israel 18.4
  - Guatemala 0.8
  - Malaysia 2.7
  - Mexico 8.3
  - New Zealand 3.5
  - Norway 3.7
  - Poland 19.3
  - Sri Lanka 20.0
  - Sweden 1.4
  - Thailand 1.0
  - South Africa 3.2

### Figures and captions included in the source
- Figure 1: Responses to Global Capital Outflow Shocks in Dollarized and Non-dollarized Economies — panels show Responses of Global flows, DLog of GDP, DLog of CPI, Interbank int. rate, log of RER, Change in FX/GDP across Quarters 5, 10, 15 with percentage deviation scales.
- Figure 2: Role of FXI and Interest Rate Reaction in the Transmission of Global Capital Outflow Shocks in Dollarized Economies — panels contrast FXI with more reaction in interest rate (group A) and FXI with a more stable interest rate (group B); responses plotted for Global flows, DLog of GDP, DLog of CPI, Interbank int. rate, log of RER, Change in FX/GDP across Quarters 5, 10, 15 with percentage deviation scales.
- Figure 3: Transmission of Monetary Policy Rate and FX Intervention — panels A. Rise in the MP rate and B. Rise in FX Reserves; series include Spread, RER, Real int. rate, FX/GDP for Non-dollarization and 50% dollarization across Quarters 0–25 with exact plotted scales.
- Figure 4: Amplification Role of Dollarization with Constant FX reserves — panels for Consumption, Investment, Trade Balance to GDP, GDP, Spread, RER, Real int. rate, Inflation Rate, FX Res to GDP comparing Non-dollarization and 50% dollarization across Quarters 0–25 with exact plotted scales and deviations from SS.
- Figure 5: Comparison of Policy Regimes with 50 percent of Dollarization — panels show Base, Opt MP, Opt FXI for Consumption, Investment, Trade Balance to GDP, GDP, Spread, RER, Real int. rate, Inflation Rate, FX Res to GDP across Quarters 0–25 with deviations from SS and exact plotted scales.
- Figure 6: Comparison of Policy Regimes with 50 percent of Dollarization: Joint Optimization — panels compare Non-Opt MP & Opt FXI, Opt FXI, Opt MP and FXI for Consumption, Investment, Trade Balance to GDP, GDP, Spread, RER, Real int. rate, Inflation Rate, FX Res to GDP across Quarters 0–25 with deviations from SS and exact plotted scales.

*Escaping the Financial Dollarization Trap: The Role of Foreign Exchange Intervention — Working Paper No. WP/2024/127*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024127-print-pdf.pdf_