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### I. Introduction — empirical motivation and headline findings
- Many emerging market economies (EMEs) and developing countries shifted from fixed exchange rate regimes toward inflation targeting (IT) since 1990; unlike many advanced economies (AEs), EMEs continued to rely on foreign exchange interventions (FXIs).
- Empirical evidence (Figure 1) for two risk-off episodes (Taper Tantrum June 2013; Covid-19 April 2020):
  - Shares of countries intervening (selling FX reserves, broad measure, month following shock, transaction volume ≥ 0.5% of annual GDP):
    - Advanced Economies: 11% (Taper Tantrum), 6% (Covid-19)
    - Emerging Market Economies: 25% (Taper Tantrum), 29% (Covid-19)
- Model and empirical analysis indicate:
  - FX markets are shallower on average in EMEs than in AEs.
  - Inflation expectations are less well-anchored in EMEs.
  - A subset of EMEs have used FXI systematically and rule-based to respond to exchange rate movements.
  - FX sales that limit exchange rate depreciation reduce the need to raise interest rates to contain inflation, improving policy tradeoffs.
  - Regime-switching evidence: market depth and FXI effectiveness can be time-varying, with greater FXI impact when markets are shallow.

### II. Model purpose, estimation strategy, and identification
- Purpose:
  - Embed theoretical frictions (FX market shallowness, currency mismatches, nominal rigidities, indexation, bounded rationality) in a microfounded DSGE framework to test empirical relevance and quantify when FXI can be useful.
- Estimation strategy:
  - Empirical small open economy DSGE estimated for 12 EMEs and 5 small open AEs pursuing independent monetary policy.
  - Bayesian estimation with identical priors for EMEs and AEs so posterior differences arise from time-series variation.
  - FX intervention proxy (Adler et al., 2019 estimate) is included as an observable to jointly identify FXI policies and FX market depth.
  - Also estimate a regime-switching variant allowing time-variation in market depth and systematic FXI rules.

### III. Key model features and transmission mechanisms
- Behavioral and preference/frictional primitives:
  - Consumption Euler/discounting: 휆_{c,t} = 훿_{c} E_t 휆_{c,t+1} + r_{b,t}. Discounting parameter: 0 < 훿_{c} ≤ 1.
  - Habit persistence: 휆_{c,t} = −1/휎 (c_t − 휔_c c_{t−1} − 휐_{c,t}); 휐_{c,t} = ρ_{휐} 휐_{c,t−1} + ε_{c,t}.
- Financial frictions and UIP distortions:
  - Retail-rate UIP (with Chang wedge set to zero for estimation): q_{p,t} = δ_c E_t q_{p,t+1} + (i_t^* − E_t π_{t+1}^*) − (1+r)/(1+r^*) (i_t − E_t π_{t+1}) + (1+r)/(1+r^*) Γ (b_{F,t} + b_{F} (i_t − E_t π_{t+1})) + (1+r)/(1+r^*) τ_{F,t}.
  - Implication: larger Γ (shallower markets) amplifies depreciation in response to foreign real rate rises and to higher funds intermediated by financiers.
  - Funds intermediated by financiers and central bank intervention: b_{F,t} = − b_t − (1/Γ) b̂_{P,t} + b_{M,t}; central bank FX intervention reduces b_{F,t} when reserves fall (b_{M,t} < 0).
- Price, wage, and trade structure:
  - Modified NK Phillips: π_t − ι_d π_{t−1} = β δ_c E_t(π_{t+1} − ι_d π_t) + κ_p mc_t + ε_{π,t}; κ_p = (1−ξ_p)(1−β ξ_p)/ξ_p.
  - Wage Phillips and indexation: π_{n,t} − π̄_{n,t−1} = β δ_c E_t(π_{n,t+1} − π̄_{n,t}) + κ_n (mrs_t − ζ_{c,t}) + ε_{n,t}; π̄_{n,t} = ι_n π_{n,t} + (1−ι_n) π_{L,t}.
  - Marginal cost and real wage links: mc_t = ζ_t + α/(1−α) y_t; ζ_t = ω_c/(1−ω_c) q_{c,t} + mrs_t (special case).
- FX intervention specifications:
  - Exogenous error-correction: 푓_{fx,t} = ρ_{ΔR} 푓_{fx,t−1} − ρ_R b_{M,t−1} + ε_{fx,t}.
  - Endogenous rule (responds to nominal exchange rate change): 푓_{fx,t} = ρ_{ΔR} 푓_{fx,t−1} − ρ_R b_{M,t−1} − (1 − ρ_{ΔR}) γ_{Δs}/(1 − γ_{Δs}) Δs_t + ε_{fx,t}. γ_{Δs} captures spectrum from non-systematic FX policy (small γ_{Δs}) to very active regimes (γ_{Δs} close to unity).

### IV. Estimation, data, and calibration
- Countries and sample periods:
  - EMEs: Brazil 1998Q1-2022Q1; Chile 2000Q1-2022Q1; Colombia 2005Q1-2022Q1; Indonesia 2003Q4-2022Q1; Kazakhstan 2003Q1-2022Q1; Malaysia 2000Q4-2022Q1; Mexico 2003Q1-2022Q1; Peru 2003Q3-2022Q1; Philippines 2000Q2-2022Q1; South Africa 2002Q2-2022Q1; Thailand 2000Q4-2022Q1; Turkey 2003Q1-2019Q4.
  - AEs: Australia 1994Q1-2022Q1; Canada 1992Q2-2022Q1; New Zealand 1999Q3-2022Q1; Norway 2003Q2-2022Q1; Sweden 1997Q1-2022Q1.
- Observables:
  - Domestic: real GDP, real government expenditure, real imports, real exports, core inflation, wage inflation, policy rate, 10-year government bond yield, real exchange rate, FXI.
  - Foreign approximated by U.S. series: seasonally adjusted real U.S. GDP, real government consumption expenditures and PCE less food & energy, nonfarm business sector hourly compensation, federal funds rate.
- Data treatment:
  - Quantities (logs) detrended using GDP trend approximated by HP filter with smoothing parameter λ = 6400 for quarterly series.
  - FXI from Adler et al. (2021) divided by trend GDP in U.S. dollars (HP filter λ = 6400).
- Calibration and priors:
  - Calibrated steady-state ratios set to country-specific sample averages.
  - Examples: intertemporal elasticity = 1; Frisch elasticity = 0.5; capital share = 0.33; export/import price elasticities = 0.8; ownership share of financial intermediaries = 0.8.
  - Steady-state NFA: EMEs = -22.5 percent of GDP; AEs = nil.
  - 35 parameters estimated; priors identical across economies.

### V. Key estimation results and structural differences (population averages)
- Price/wage rigidities and indexation:
  - EMEs: on average, domestic prices stickier (higher ξ_p), higher wage indexation (higher ι_n), and wages more sensitive to exchange rate (higher ν).
  - Import prices more flexible in EMEs (higher ξ_m), consistent with producer-currency pricing for imports.
- Shock sizes:
  - Shocks hitting EMEs are larger, especially to GDP components, domestic and wage inflation, and domestic risk premium.
- Policy-rule fit:
  - Interest rate reaction coefficients broadly similar, but response to inflation is noticeably lower in EMEs.
  - Average posterior for σ_i in AEs = 0.08; in EMEs = 0.17.
  - Adjusted R2: AEs mean = 0.967; EMEs mean = 0.909.
- FX market depth parameter Γ:
  - Mean inverse market depth Γ is notably higher in EMEs than in AEs when allowing for systematic FX interventions.
  - If endogenous FXI rule is not allowed, EMEs’ FX markets are estimated deeper than AEs on average — implying endogeneity of FXI materially affects Γ estimates.
  - Accounting for endogeneity of FX interventions is critical when assessing market depth.

### VI. Impulse response and policy experiments — main quantitative implications
- Foreign investors portfolio outflow shock (b̂_P,t):
  - Shock sized to induce 10 percent real exchange rate depreciation in all countries (when FXI not deployed).
  - Dispersion: much larger and more persistent output declines and inflation run-ups in EMEs than AEs for similar depreciation.
  - Average increase in core CPI inflation: more than 0.5 percentage points for EMEs and 0.2 percentage points for AEs.
  - Required policy rate hike: more than twice as large in EMEs relative to AEs.
  - Contraction in domestic demand: almost double in EMEs compared with AEs.
- Interest rate tightening shock:
  - Shock: nominal interest rate rises 100 basis points in period 1 in all countries.
  - Average contraction in domestic demand: about 0.7 percentage point for both EMEs and AEs.
  - Average inflation decline: nearly 1/4 percentage point in EMEs versus about 0.15 percentage points in AEs.
  - Mechanism: tighter policy improves NFA; in shallow FX markets (high Γ) this lowers UIP premium strongly and produces larger appreciation in EMEs.
- FX intervention (FXI) effects (subset of 5 EMEs with evidence of systematic FXI):
  - Experiments compare outcomes for risk-off shock with FXI=0 and with γ_{Δs} at each country’s posterior mean.
  - FXIs (sales of reserves) reduce depreciation notably for three of five countries, lowering core CPI inflation increases and the need to hike short-term interest rates.
  - For two countries, interventions have limited impact due to either deep currency markets (Γ < 0.01) or weak systematic response (γ_{Δs}/(1−γ_{Δs}) = 0.48 → γ_{Δs} ≈ 1/3).
  - Intervention magnitudes: 0.5 to 3 percent of GDP, reflecting individually-estimated endogenous FXI rules.
- Interaction summary:
  - FX sales that limit exchange rate depreciation reduce the need for interest rate hikes to contain inflation.
  - FXIs are more effective when markets are shallow; time-variation matters—FXI effectiveness greater in shallow-regime episodes.

### VII. Regime-switching: time variation in market depth and FXI strategy
- Two-state Markov setup for Γ and γ_{Δs}:
  - R1 ("deep"): prior centered on deep FX market (Γ low) and passive FXI policy (γ_{Δs} low).
  - R2 ("shallow"): prior centered on shallower market (Γ high) and more active FXI policy (γ_{Δs} high).
- Findings:
  - Allowing only Γ to vary: limited support (time-varying FX market depth supported in 2 of 5 countries; weak support under conservative criteria).
  - Joint variation (Γ and γ_{Δs} comove): stronger support — hypothesis that γ_{Δs} is bigger when markets are shallower is generally supported.
  - In three of five EMEs, data supports time-varying parameters; in two of those three the data strongly supports occasionally shallow markets combined with more active FXI when markets are shallow.
  - Interpretation nuance: the "shallow" regime may proxy for the joint occurrence of shallow markets and capital outflow shocks, not solely market shallowness.

### VIII. Model-fit, comparison across FXI specifications, and selected country metrics
- Model fit:
  - Endogenous FXI rule improves fit (log marginal likelihood) for more than half of EMEs, but not for any AEs.
  - Conservative criterion (difference in LML > 10) identifies EME 3, 4, 5, 6 and 12 as strongly favoring endogenous FXI rule; AE4 strongly favors exogenous FXI rule.
- Selected table excerpt (country-specific posterior and log marginal likelihoods; formatting preserved from source):
  - EME1 -2241.21 -2236.23 0.03 50.029 0.200 0.591 1.35
  - EME2 -2106.46 -2097.06 0.023 0.020 0.200 0.393 3.19
  - EME3 -2541.52 -2565.02 0.008 0.006 2.260 0.425 5.61
  - EME4 -2461.10 -2512.96 0.060 0.007 6.040 0.535 5.86
  - EME5 -2300.37 -2330.63 0.045 0.009 4.800 0.388 8.60
  - EME6 -2565.04 -2579.08 0.042 0.006 12.750 0.402 6.91
  - EME7 -2001.87 -1995.90 0.035 0.028 0.260 0.501 1.96
  - EME8 -2786.25 -2791.23 0.009 0.007 0.580 0.236 6.62
  - EME9 -2076.38 -2078.84 0.027 0.019 0.490 0.313 3.52
  - EME10 -2093.22 -2086.01 0.017 0.008 0.310 0.731 1.83
  - EME11 -2609.22 -2604.50 0.022 0.018 0.350 0.503 3.40
  - EME12 -2920.16 -2934.15 0.038 0.021 0.480 0.453 3.17
  - EMEs mean 0.030 0.015 2.390 0.456 6.00
  - AE1 -2358.92 -2353.14 0.033 0.021 0.260 0.303 3.30
  - AE2 -2506.03 -2506.02 0.015 0.014 0.210 0.152 2.32
  - AE3 -2034.56 -2025.36 0.025 0.022 0.150 0.282 2.47
  - AE4 -2796.33 -2777.12 0.025 0.024 0.040 0.240 0.56
  - AE5 -2791.96 -2784.31 0.024 0.022 0.120 0.301 1.40
  - AEs mean 0.024 0.021 0.160 0.252 2.01

### IX. Policy implications and recommended applications
- FX interventions can be welfare-relevant in economies with:
  - Shallow FX markets (large Γ), strong indexation of wages/prices to exchange rates, rapid pass-through, and significant currency mismatches.
- Operational takeaways:
  - FX sales that limit depreciation reduce the need for interest rate hikes to contain inflation and improve the output-inflation tradeoff in affected EMEs.
  - When market depth varies over time, conditional/state-contingent intervention strategies are more appropriate: FXIs may be ineffective at times but highly effective when liquidity dries up.
  - Accounting for the endogeneity of FX interventions is essential when inferring market depth from observed exchange rate responses.
- Suggested further analysis and model extensions:
  - Study non-sterilized interventions and interventions in derivative markets.
  - Examine whether effective FX intervention strategies require large FX reserves or can rely on fiscal backing and solid public finances.
  - Compare estimated shallowness with external market depth measures while accounting for FX policy endogeneity.
  - Extend model to include supply-side shocks, commodities, more elaborate fiscal sector, and a more developed banking sector to analyze interactions among macroprudential tools, FX, and interest rate policies.

*Italic: wpiea2023135-print-pdf - Appendix B (Table B.5) content extracted from the specified PDF chapter.*

### References .............................................................................................................

### wpiea2023135-print-pdf - References .............................................................................................................

### Appendices (structure and topics)
- Appendix A. Derivations of Linearized Relationships ............................................................................ 49
  - A.1  Resource Constraint ............................................................................................................... 49
  - A.2  UIP and Net Foreign Asset Dynamics ..................................................................................... 53
  - A.3  Wage and Pricing Schedules .................................................................................................. 57
- Appendix B. Calibrated Parameters and Full Estimation Results ......................................................... 61

### Figures listed in the content unit
- 1. FX Interventions during Risk-off Episodes ................................................................................................. 5
- 2. Key Macroeconomic Variables Included in Estimation ............................................................................ 24
- 3. U.S. Variables Included in the Estimation ................................................................................................ 25
- 4.  Prior Distributions .................................................................................................................................... 28
- 5. Difference in Log Marginal Likelihood versus Correlation between FXI and NER ................................... 32
- 6. Country-Specific Impulses to Foreign investors Portfolio Outflow Shocks ............................................... 34
- 7. Average Impulses to Foreign investors Portfolio Outflow Shocks ............................................................ 35
- 8. Impulses to an Unexpected Interest Rate Tightening .............................................................................. 36
- 9. Mean Impulses to an Unexpected Interest Rate Tightening .................................................................... 37
- 10. Impact of FXIs on Transmission of Foreign investors Portfolio Outflow Shocks .................................... 39
- 11. How FXIs Impact Transmission of an Unexpected Interest Rate Tightening ......................................... 40

### Tables listed in the content unit
- 1. Countries and Sample Periods included in Estimation ............................................................................ 22
- 2. All Observables and Shocks Used in Estimation ..................................................................................... 23
- 3. Prior and Posterior ...................................................................................................................................   29
- 4. Comparison of Model Estimates with Different FXI Specifications ........................................................ 31
- 5. Regime-Switching Estimation – Time-Varying FX Market Depth Only .................................................... 42
- 6. Regime-Switching Estimation – Time-Varying FX Market Depth and FXI Rule ....................................... 43

### Appendix Tables
- Appendix B. Table B.1: Parameters Calibrated to Match EME and AE Characteristics .............................. 61
- Appendix B. Table B.2: Parameters Calibrated to Country-Specific Characteristics ...................................   61
- Appendix B. Table B.3: Country-Specific Posterior and Log Marginal Likelihoods with Endogenous                 
  FXI Rule in EMEs ......................................................................................................................................... 62
- Appendix B. Table B.4: Country-Specific Posterior and Log Marginal Likelihoods with Exogenous                   
  FXI Rule in EMEs ......................................................................................................................................... 63

*Source: wpiea2023135-print-pdf - References .............................................................................................................*

### Appendix B. Table B.5: Country-Specific Posterior and Log Marginal Likelihoods for Endogenous and

### Appendix B. Table B.5: Country-Specific Posterior and Log Marginal Likelihoods for Endogenous and Exogenous FXI Rules in AEs

### I. Introduction — empirical motivation and headline findings
- Many emerging market economies (EMEs) and developing countries shifted away from fixed exchange rate regimes toward inflation targeting (IT) since 1990; unlike many advanced economies (AEs), EMEs continued to rely on foreign exchange interventions (FXIs).
- Empirical evidence (Figure 1) for two risk-off episodes:
  - Taper Tantrum (June 2013) and Covid-19 (April 2020).
  - Shares of countries intervening (selling FX reserves, broad measure, month following shock, transaction volume ≥ 0.5% of annual GDP):
    - Advanced Economies: 11% (Taper Tantrum), 6% (Covid-19)
    - Emerging Market Economies: 25% (Taper Tantrum), 29% (Covid-19)
- The paper’s model estimates and empirical analysis indicate:
  - FX markets are shallower on average in EMEs than in AEs.
  - Inflation expectations are less well-anchored in EMEs.
  - A subset of EMEs have used FXI systematically and rule-based to respond to exchange rate movements.
  - FX sales that limit exchange rate depreciation reduce the need to raise interest rates to contain inflation, improving policy tradeoffs.
  - Regime-switching evidence: market depth and FXI effectiveness can be time-varying, with greater FXI impact when markets are shallow.

### II. Model purpose, estimation strategy, and identification
- Purpose:
  - Embed theoretical frictions (FX market shallowness, currency mismatches, nominal rigidities, indexation, bounded rationality) in a microfounded DSGE framework to test empirical relevance and quantify when FXI can be useful.
- Estimation strategy:
  - Empirical small open economy DSGE estimated for 12 EMEs and 5 small open AEs pursuing independent monetary policy.
  - Bayesian estimation with identical priors for EMEs and AEs so posterior differences arise from time-series variation.
  - FX intervention proxy (Adler et al., 2019 estimate) is included as an observable to jointly identify FXI policies and FX market depth.
  - Also estimate a regime-switching variant (Maih, 2015) allowing time-variation in market depth and systematic FXI rules.

### III. Key model features and mechanisms (concise technical inventory)
- Behavioral discounting and bounded rationality:
  - Consumption Euler equation (eq. (2)): 휆휆_{c,t} = 훿_{c} E_t 휆_{c,t+1} + r_{b,t}.
  - Discounting parameter: 0 < 훿_{c} ≤ 1. Discounting mutes future short-term rate effects on current consumption.
- Habit persistence and shocks:
  - Marginal utility (eq. (3)): 휆_{c,t} = −1/휎� (c_t − 휔_c c_{t−1} − 휐_{c,t}).
  - Exogenous consumption demand shock (eq. (4)): 휐_{c,t} = ρ_{휐} 휐_{c,t−1} + ε_{c,t}.
- Borrowing spreads and long-term rate:
  - Long-term borrowing rate includes time-varying private borrowing spread Ψ_t (eq. (6)): r_{b,t}^L = r_t^L + Ψ_t.
  - Short-term borrowing spread follows AR(1) (eq. (7)): ψ_t = ρ_ψ ψ_{t−1} + ε_{ψ,t}.
- Exports, imports, and trade structure:
  - Export demand decomposition and use of imported inputs (eqs. (8)–(10)); export demand rises with foreign output y_t^* and falls with relative export price γ_{x,*,t}.
  - Import demand for consumption (eq. (12)): m_{c,t} = c_t − η_c γ_{m,c,t} + ϑ̂_{m,t}, with ϑ_{m,t} following AR(1).
  - Real exchange rates:
    - Product real exchange rate (eq. (11)): q_{p,t} = s_t + p_t^* − p_t.
    - Consumption-based real exchange rate (eq. (13)): q_{c,t} = s_t + p_t^* − p_{c,t}.
- Price and wage setting with indexation and persistence:
  - Modified New Keynesian Phillips Curve (eq. (14)): π_t − ι_d π_{t−1} = β δ_c E_t(π_{t+1} − ι_d π_t) + κ_p mc_t + ε_{π,t}.
  - Phillips-curve slope (eq. (15)): κ_p = (1−ξ_p)(1−β ξ_p)/ξ_p.
  - Wage Phillips curve (eq. (20)): π_{n,t} − π̄_{n,t−1} = β δ_c E_t(π_{n,t+1} − π̄_{n,t}) + κ_n (mrs_t − ζ_{c,t}) + ε_{n,t}.
  - Indexation for non-optimizing wage setters (eqs. (21)–(22)): π̄_{n,t} = ι_n π_{n,t} + (1−ι_n) π_{L,t}; π_{L,t} = (1−ν) π_{L,t−1} + ν/m_y Δs_t.
- Import and export price Phillips curves (eq. (24)): π_{j,t} − ι_j π_{j,t−1} = β δ_c E_t(π_{j,t+1} − ι_j π_{j,t}) + κ_j mc_{j,t} + ε_{j,t}, j ∈ {m,x}.
- Marginal costs in export/import sectors (eqs. (25)–(26)):
  - m c_{x,t} = − q_{p,t} + γ_{x,*,t} + ω_x γ_{m,d,t}.
  - m c_{m,t} = q_{p,t} − γ_{m,d,t}.
- Consumer price inflation aggregation (eq. (29)): π_{c,t} = (1−ω_c) π_t + ω_c π_{m,t}, with ω_c = m_y (1−g_y)(1−ω_x).
- Real wage and marginal cost link (eqs. (16)–(19)):
  - Marginal cost: mc_t = ζ_t − mp l_t.
  - Linearized marginal cost (eq. (17)): mc_t = ζ_t + α/(1−α) y_t.
  - Product real wage special case (eq. (19)): ζ_t = ω_c/(1−ω_c) q_{c,t} + mrs_t.

### IV. International financial markets, UIP distortions, and FXI channel
- Financial frictions and UIP deviations:
  - Retail-rate based UIP with two risk wedges (GM wedge from Gabaix–Maggiori friction and Chang wedge from occasionally binding collateral constraint) presented in compact form (eq. (30)).
  - For estimation, Chang wedge (Θ_t) is set to zero (occasionally binding constraint assumed away).
- Log-linearized UIP (with Θ_t = 0) — eq. (33):
  - q_{p,t} = δ_c E_t q_{p,t+1} + (i_t^* − E_t π_{t+1}^*) − (1+r)/(1+r^*) (i_t − E_t π_{t+1}) + (1+r)/(1+r^*) Γ (b_{F,t} + b_{F} (i_t − E_t π_{t+1})) + (1+r)/(1+r^*) τ_{F,t}.
  - Implications:
    - Real exchange rate depreciates when foreign real rate rises relative to domestic real rate.
    - Greater funds intermediated by financiers (b_F) and larger Γ (shallower markets) amplify depreciation.
    - Presence of discounting δ_c ≤ 1 makes short-run real rates more influential for exchange rate dynamics.
- Funds intermediated by financiers and central bank intervention (eq. (34)):
  - b_{F,t} = − b_t − (1/Γ) b̂_{P,t} + b_{M,t}; b̂_{P,t} = Γ b_{P,t}.
  - Central bank FX intervention reduces funds intermediated by financiers (b_{M,t} < 0 when reserves fall), thereby mitigating depreciation pressures.
- Net foreign assets evolution (log-linearized, eq. (35)):
  - b_t dynamics include debt-service terms, costs of reserves and interventions, capital flow measures, and trade balance.
  - Assumptions for derivation: τ_F = 0 in steady state; ω_B = 1 (banks domestically owned); ω_F = ω_P = ω (same home ownership share).
- Modeling choices to aid identification and interpretation:
  - Rescaling of portfolio investment variable by 1/Γ ensures that shock variances have attenuated effects when markets are deep (low Γ).
  - Inclusion of observed FXI series in estimation helps separate apparent market depth from systematic FXI policy responses.

### V. Quantitative and policy-relevant implications emphasized by the model
- Shallower FX markets (larger Γ) in EMEs imply:
  - Larger exchange rate movements in response to UIP premium shocks.
  - Larger second-round inflation effects via wage indexation and pass-through when inflation expectations are less anchored.
- Systematic FXI (FX sales) can be welfare-relevant in economies with:
  - Shallow FX markets, strong indexation of wages/prices to exchange rates, fast pass-through, and significant currency mismatches.
- Policy tradeoffs and FXI role:
  - FX sales that limit exchange rate depreciation reduce the need for interest rate hikes to contain inflation.
  - Time-variation matters: when market depth is time-varying, FXI effectiveness is greater in shallow-regime episodes.
- Modeling recommendation for applied policy analysis:
  - Use the model for country-specific estimation and scenario analysis to assess policy tradeoffs and the potential role of FX interventions given the estimated market depth, indexation parameters, and shock processes.

*IMF Working Paper — Appendix B (Table B.5) content extracted from the specified PDF chapter.*

### Appendix A.  2 to equal

### Appendix A.  2 to equal

### Trade balance representation
- Equation (36): 푡푡푏푏 / 푡푡 = 푚푚푦푦 (푚푚푡푡∗ − 푚푚푡푡 + 훾훾푡푡푥푥,∗), which is described as a common expression for the trade balance as a share of nominal trend GDP.
- Determinants explicitly identified:
  - real net exports: (푚푚푡푡∗ − 푚푚푡푡)
  - terms of trade: 훾훾푡푡푥푥,∗

### Monetary policy rule (interest rate setting)
- Central bank follows a Taylor-style policy rule (eq. 37):
  - 푖푖푡푡 = max[ −푖푖, (1 − 훾훾푖푖) (1 + 훾훾휋휋) 휋휋̂𝑐,𝑡+4|𝑡 + 훾훾𝑦𝑦 𝑦𝑦𝑡𝑡 ] + 훾훾𝑖𝑖 푖푖𝑡𝑡−1 + 휀휀𝑖𝑖,𝑡𝑡
  - 푖푖 is the steady-state nominal interest rate; 푖푖𝑡𝑡 = −푖푖 implies the policy rate reaches its assumed lower bound of zero.
  - 휋𝑐,𝑡+4|𝑡 = E𝑡[휋𝑐,𝑡+1 + 휋𝑐,𝑡+2 + 휋𝑐,𝑡+3 + 휋𝑐,𝑡+4] / 4 (expected four-quarter change in core CPI inflation).
  - The rule responds to expected core CPI inflation and domestic output gap, allows for interest rate smoothing via 훾훾푖푖, and includes an interest rate shock 휀휀푖푖,푡푡.
  - The rule is characterized as a reasonable approximation (not a full optimal policy) for certain admissible parameterizations.

### FX interventions: definition and conduct
- Definition of FX intervention flow (eq. 38):
  - 푓푓푥푥𝑡𝑡 = 푏푏𝑀𝑀,𝑡𝑡 − 푏푏𝑀𝑀,𝑡𝑡−1
  - 푓푓푥푥𝑡𝑡 > 0 denotes an increase in central bank holdings of foreign reserves.
- Mechanisms:
  - An increase in reserves raises funds 푏푏𝐹𝐹,𝑡𝑡 that financiers intermediate (eq. 34) and tends to raise the UIP risk premium (eq. 33).
  - If portfolio investors pull out of the home currency (푏푏𝑃𝑃,𝑡𝑡 negative in eq. 34), central bank may sell reserves (푓푓푥푥𝑡𝑡 < 0) to defend the currency.
- Two alternative specifications for FX interventions:
  1. Exogenous error-correction specification (eq. 39):
     - 푓푓푥푥𝑡𝑡 = 휌휌∆푅푅 푓푓푥푥𝑡𝑡−1 − 휌휌𝑅𝑅 푏푏𝑀𝑀,𝑡𝑡−1 + 휀휀𝑓푓푥푥,𝑡𝑡
     - In levels: 푏푏𝑀𝑀,𝑡𝑡 = (1 + 휌휌∆푅푅 − 휌휌𝑅𝑅) 푏푏𝑀𝑀,𝑡𝑡−1 − 휌휌∆푅푅 푏푏𝑀𝑀,𝑡𝑡−2 + 휀휀𝑓푓푥푥,𝑡𝑡
     - Imposing 휌휌∆푅푅 > 0 allows for persistent yet stationary deviations of reserves from steady state.
  2. Endogenous FX intervention rule related to nominal exchange rate changes (eq. 40):
     - 푓푓푥푥𝑡𝑡 = 휌휌∆푅푅 푓푓푥푥𝑡𝑡−1 − 휌휌𝑅𝑅 푏푏𝑀𝑀,𝑡𝑡−1 − (1 − 휌휌∆푅푅) 훾훾Δ푠푠 / (1 − 훾훾Δ푠푠) Δ푠푠𝑡𝑡 + 휀휀𝑓푓푥푥,𝑡𝑡
     - If 훾훾Δ푠푠 > 0, a depreciation Δ푠푠𝑡𝑡 > 0 will cause a selloff of reserves (푓푓푥푥𝑡𝑡 < 0), moderating depreciationary pressure.
     - The parameter 훾훾Δ푠푠 / (1 − 훾훾Δ푠푠) captures a spectrum of FX regimes: small 훾훾Δ푠푠 ≈ non-systematic FX policy; 훾훾Δ푠푠 close to unity ≈ very active policy regime.
- Interpretation and normative context:
  - Empirical and normative literature (Basu et al. (2020), Adrian et al. (2021)) suggests FXIs can be used to lean against exogenous UIP risk premium movements driven by risk-off/on shocks (푏푏̂𝑃𝑃,𝑡𝑡), but not against shocks for which exchange rate adjustment is warranted.
  - Estimated model implies 푏푏̂𝑃𝑃,𝑡𝑡 accounts for a sizeable share of exchange rate fluctuations (exchange rate disconnect puzzle references).
  - Both FXI specifications include an i.i.d. shock 휀휀𝑓푓푥푥,𝑡𝑡 to allow for temporary discretionary central bank actions.

### Channels and interactions between FX interventions and monetary policy
- Portfolio balance channel: FX interventions affect the currency via changes in the composition of assets.
- Signalling channel: Interactions with interest rate policy; e.g., an interest rate tightening that appreciates the currency may prompt FXIs (when 훾훾Δ푠푠 > 0) to build reserves, which undoes some appreciation pressure.
- Empirical note: Correlation between smoothed innovations in the interest rate policy rule (eq. 37) and the endogenous FXI rule (eq. 40) was studied; average correlation found to be close to 0 in both EMEs and AEs.

### Contribution of reserves to net foreign assets (NFA)
- Expression for NFA contribution when 휔휔𝐹 = 휔휔𝑃 = 휔휔 (eq. 41):
  - 퐵퐵𝑡𝑡 = [ (1 − 휔휔) 𝐼𝐼𝑡𝑡−1 + 휔휔 𝐼𝐼𝑡𝑡−1∗ (𝑆𝑆𝑡𝑡 / 𝑆𝑆𝑡𝑡−1) ] 𝐵𝐵𝑡𝑡−1 − (1 − 휔휔) [ 𝐼𝐼𝑡𝑡−1 − 𝐼𝐼𝑡𝑡−1∗ (𝑆𝑆𝑡𝑡 / 𝑆𝑆𝑡𝑡−1) ] 𝐵𝐵𝑀𝑀,𝑡𝑡−1
- Log-linearized variant (eq. 42) decomposes impact of reserves on NFA into:
  - Revaluation effect (first group of terms): captures valuation changes when reserves are kept constant and exchange rate moves.
  - Intervention effect (second group of terms): captures effects of changes in 푏푏𝑀𝑀,𝑡𝑡 (FX reserve sell-offs or purchases) that bring domestic capital back and strengthen NFA.
- When a negative risk-off 푏푏𝑃𝑃,𝑡𝑡 shock causes depreciation:
  - Revaluation effect is typically benign if reserves 푏푏𝑀𝑀,𝑡𝑡 are constant.
  - If central bank sells reserves (Δ푏푏𝑀𝑀,𝑡𝑡 < 0) to lean against depreciation, the less beneficial revaluation effect may offset positive interaction/intervention effect.
- Dominance between effects depends on calibration:
  - Steady state stock of reserves 푏푏𝑀𝑀 and the term (𝐼𝐼 − 𝐼𝐼∗ Δ𝑆𝑆) are decisive.
- Use of eq. (42):
  - Dynamically assess contribution of reserves to NFA following shocks.
  - Measure cost of an FX intervention as evolution of 푏푏𝑡𝑡 when 푏푏𝑀𝑀,𝑡𝑡 changes, compared to a counterfactual with 푏푏𝑀𝑀,𝑡𝑡 = 0 for all t (movements then reflect only revaluation effects driven by 푏푏𝑀𝑀 > 0).

### Fiscal policy specification
- Government expenditure (eq. 43):
  - 푔푔𝑡𝑡 = 휌휌𝑔𝑔 푔푔𝑡𝑡−1 + 휀휀𝑔𝑔,𝑡𝑡 (exogenous AR(1) process).
- Financing and assumptions:
  - Steady-state level of 푔푔 financed by labor income taxes.
  - Variations around steady state financed by lump-sum taxes.
  - Ricardian equivalence holds, allowing abstraction from dynamic aspects of fiscal policy.

### Foreign economy block (closed-economy variant)
- Key equations for foreign economy (eqs. 44–50 and parameter definitions):
  - Output composition (eq. 44): 푦푦𝑡𝑡∗ = (1 − 푔푔𝑦𝑦∗) 푐𝑐𝑡𝑡∗ + 푔푔𝑦𝑦∗ 𝑔𝑔𝑡𝑡∗
  - Euler/discount relations and marginal utilities (eqs. 45–46): 휆𝑐,𝑡𝑡∗ = 훿𝑐∗ 휆𝑐,𝑡𝑡+1∗ + 푟푟𝑡𝑡∗ ; 휆𝑐,𝑡𝑡∗ = −1/휎휎∗ (푐𝑐𝑡𝑡∗ − 휂𝑐∗ 푐𝑐𝑡𝑡−1∗ − 휐휐𝑐𝑐,𝑡𝑡∗)
  - Phillips-curve style price equation (eq. 47): 휋𝑡𝑡∗ − 휄𝑝∗ 휋𝑡𝑡−1∗ = 훽∗ 훿𝑐∗ (휋𝑡𝑡+1|𝑡𝑡∗ − 휄𝑝∗ 휋𝑡𝑡∗) + 휅𝑝∗ (휁𝑡𝑡∗ + (훼∗/(1 − 훼∗)) 𝑦𝑦𝑡𝑡∗) + 휀휀𝜋,𝑡𝑡∗
  - Real marginal cost/wage dynamics (eq. 48–49): 휁𝑡𝑡∗ = 휁𝑡𝑡−1∗ + 휋𝑛,𝑡𝑡∗ − 휋𝑡𝑡∗ ; 휋𝑛,𝑡𝑡∗ − 휄𝑛𝑛∗ 휋𝑛,𝑡𝑡−1∗ = 훽∗ 훿𝑐∗(휋𝑛,𝑡𝑡+1|𝑡𝑡∗ − 휄𝑛𝑛∗ 휋𝑛,𝑡𝑡∗) + 휅𝑛∗(휆𝑚𝑟𝑠∗ 𝑦𝑦𝑡𝑡∗ − 휆𝑐,𝑡𝑡∗ − 휁𝑡𝑡∗) + 휀휀𝑛,𝑡𝑡∗
  - Foreign monetary policy rule (eq. 50): 푖푖𝑡𝑡∗ = max[ −푖푖∗, (1 − 훾훾𝑖𝑖∗) (1 + 훾훾𝜋𝜋∗) 휋𝜋𝑡𝑡∗ + 훾훾𝑦𝑦∗ 𝑦𝑦𝑡𝑡∗ ] + 훾훾𝑖𝑖∗ 푖푖𝑡𝑡−1∗ + 휀휀𝑖𝑖,𝑡𝑡∗
- Composite parameter definitions (eqs. 51–55):
  - 휎휎�∗ = 휎휎∗ (1 − 휂𝑐∗)
  - 휆푚𝑟𝑠∗ = 휒휒∗ / (1 − 훼훼∗)
  - 휅𝑝∗ = (1 − 휉𝑝∗) (1 − 훽∗ 휉𝑝∗) / 휉𝑝∗
  - 휅𝑛∗ = (1 − 휉𝑤∗) (1 − 훽∗ 휉𝑤∗) 휙𝑤∗ 휉𝑤∗ ( 휒∗ (1 + 휙𝑤∗) + 휙𝑤∗ )
  - Note duplicate listing: 휆푚𝑟𝑠∗ = 휒휒∗ / (1 − 훼훼∗) (eq. 55).
- Shocks and measurement:
  - All variables measured as percent or percentage point deviations from steady state levels.
  - Foreign shocks: 푔𝑡𝑡∗ (government spending), 휐𝑐,𝑡𝑡∗ (consumption demand), white-noise cost-push shocks 휀휀휋,𝑡𝑡∗ and 휀휀𝑛,𝑡𝑡∗, and monetary policy shock 휀휀𝑖𝑖,𝑡𝑡∗.
  - 휋𝜋∗ denotes the inflation target.
  - 푔𝑡𝑡∗ and 휐𝑐,𝑡𝑡∗ follow stochastic AR(1) processes.

### Model estimation: data, countries, and procedure
- Estimation approach:
  - Model estimated on quarterly data for 17 small open economies individually: 12 emerging market economies (EMEs) and 5 small open advanced economies (AEs).
  - All countries have adopted flexible inflation targeting with interest rates as the primary monetary policy tool.
  - Bayesian techniques following Smets and Wouters (2003, 2007) used to estimate parameters.
  - Bayesian inference: prior distribution updated by observed data to obtain posterior distribution of parameters (summarized by mode/mean, standard deviation, probability intervals).
- Countries and sample periods included (as listed):
  - Emerging Market Economies:
    - Bra zil 1998Q1-2022Q1
    - Ch ile 2000Q1-2022Q1
    - Colombia 2005Q1-2022Q1
    - Indonesia 2003Q4-2022Q1
    - Kazakhstan 2003Q1-2022Q1
    - M alay s ia 2000Q4-2022Q1
    - Mexico 2003Q1-2022Q1
    - Peru 2003Q3-2022Q1
    - Ph ilip p in es 2000Q2-2022Q1
    - South Africa 2002Q2-2022Q1
    - Th ailan d 2000Q4-2022Q1
    - Tu rkey 2003Q1-2019Q4
  - Advanced Economies:
    - Au s t ralia 1994Q1-2022Q1
    - Canada 1992Q2-2022Q1
    - New Zealand 1999Q3-2022Q1
    - Norway 2003Q2-2022Q1
    - Sweden 1997Q1-2022Q1
- Estimation steps:
  1. Pre-estimate foreign bloc (closed economy with 5 observables and shocks) using U.S. data; keep foreign parameters fixed for each domestic estimation.
  2. Conditional on posterior mean parameters for the foreign economy, estimate domestic economy bloc comprising 10 observables and 11 structural shocks.
  - Rationale: domestic economy assumed small relative to large foreign economy; pre-estimation without loss of efficiency.
- Domestic observables included (Panel A, summarized in text):
  - real GDP, real government expenditure, real imports, real exports, core inflation, wage inflation, policy rate, 10-year government bond yield (long-term interest rate), real exchange rate, and a measure of FXI.
  - Core inflation data taken from WEO database; quarterly FX intervention data based on Adler et al. (2021); remaining domestic observables from Haver Analytics.
  - Foreign observables approximated by U.S. series: seasonally adjusted real U.S. GDP, real government consumption expenditures and PCE less food & energy, nonfarm business sector hourly compensation, and the federal funds rate (% p.a.).
- Data treatment:
  - Quantities (logs) detrended using GDP trend approximated by HP filter with a smoothing parameter of [text truncated in source].

_Italic: wpiea2023135-print-pdf - Appendix A.  2 to equal_

### 6400. By deducting the same trend based on GDP for all quantities, we ensure that the relative

### wpiea2023135-print-pdf - 6400. By deducting the same trend based on GDP for all quantities, we ensure that the relative

### Data treatment and observables
- GDP is detrended using a common trend based on GDP; detrended GDP is referred to as the output gap (output as deviation from trend).
- All nominal variables (interest rates, price and wage inflation) are left untouched; their sample means are matched by model-consistent (calibrated) steady state levels.
- Real exchange rate is measured as a percent deviation from its sample mean, consistent with the model’s stationarity assumption for the real exchange rate.
- The U.S. is chosen as the representative foreign economy; U.S. variables are included as observables and the real exchange rate is calculated vis-à-vis the U.S. dollar.
- FXI is taken from quarterly broad estimates from Adler et al. (2021) and divided by trend GDP measured in U.S. dollars (calculated using an HP filter with the smoothing parameter λ set to 6400).
- Observable lists (domestic and foreign) included in estimation: Output gap; Domestic demand; Core inflation; Import demand; Real exports; Export demand; Real imports; Domestic price mark-up; Real government expenditure; Import price mark-up; Nominal wage growth; Wage mark-up; Real exchange rate; Policy rate; Long-term interest rate; Foreign exchange intervention (FXI); Global risk appetite; Domestic term premium; Interest rate policy; Government spending. (Structure preserved from source.)

### FX intervention (FXI) specifications in the model
- Two alternative FXI specifications estimated for each country:
  - Exogenous FXI rule: FXI is characterized by an exogenous AR(1) process with a small error correction term to ensure stationarity of central bank FX reserves; approximates a unit root specification as a special case.
  - Endogenous FXI rule: FXI responds systematically to the current state of the economy; the current change in the nominal exchange rate provided the best explanation of variations in FX interventions when estimating the full model.
- Both exogenous and endogenous FXI rule specifications in eqs. (39) and (40) include an error correction term where coefficient 휌휌
푓푓푥푥,2
>0 ensures FX reserves return to steady state in the long run.
- FXI data limitations: many countries do not publish official FXI data; Adler et al. (2021) construct quarterly proxies based on BOP data or changes in stock of reserves adjusted for valuation effects.

### Priors, calibration, and estimation setup
- Calibrated steady-state ratios: government expenditure, exports, imports, and central bank FX reserves to GDP are set to country-specific sample averages.
- Steady states of price and wage inflation and interest rates are consistent with countries’ official inflation targets and sample averages.
- Calibrated behavioral parameter examples:
  - Intertemporal elasticity of substitution in consumption = 1.
  - Frisch elasticity of labor supply = 0.5.
  - Capital income share in Cobb-Douglas production = 0.33.
  - Export and import relative price elasticities = 0.8.
  - Ownership share of financial intermediaries = 0.8 for all countries.
  - Steady-state NFA position for EMEs = -22.5 percent of GDP; for AEs = nil.
- Priors:
  - 35 parameters estimated: nominal and real frictions (12), policy rule parameters (6), exogenous shock persistence parameters (6), and 11 standard deviations of innovations.
  - Beta distribution used for parameters bounded between 0 and 1; inverse gamma for parameters assumed positive.
  - Priors are identical across economies; differences in posteriors are driven by data and calibrated country-specific steady states.
- Prior analysis:
  - 10,000 draws sampled from the prior for all estimated parameters; impulses to a risk-off foreign portfolio investors shock computed.
  - Percentiles (90th, 95th, 99th) and median impulse responses plotted for t=1,2,...,20 in Figure 4.
  - Prior results indicate priors do not impose that depreciations have contractionary effects in EMEs and expansionary effects in AEs; prior may even suggest sharper contractionary effects in AEs.

### Estimation approach and computational details
- Two-step estimation:
  1. Obtain posterior mode and approximate covariance matrix via numerical optimization on log posterior density for each country (inverse Hessian at mode).
  2. Explore posterior using Metropolis-Hastings algorithm in separate chains; proposal distribution is multivariate normal centered at previous draw with covariance proportional to inverse Hessian at the posterior mode.
- Results in Table 3 show averages of all EMEs’ and AEs’ posterior means for estimated parameters; standard deviations measure dispersion among the 12 EMEs and 5 AEs.
- Reporting: posterior means and dispersion for each estimated parameter are presented (see Table 3 structure preserved in source).

### Key estimation results and structural differences (population averages)
- Price and wage rigidities and indexation:
  - EMEs: on average, domestic prices are stickier (higher 휉휉
푝푝), wages have higher indexation (higher 휄휄
푛푛), and wages are more sensitive to the exchange rate (higher 휈휈), increasing likelihood/severity of wage-price spiral after depreciations.
  - Import prices are more flexible (higher 휉휉
푚푚) in EMEs, consistent with dominant (producer) currency pricing in imports.
- Shock sizes:
  - Shocks hitting EMEs are larger, particularly shocks to components of GDP, domestic and wage inflation, and the domestic risk premium.
- Policy rule fit and coefficients:
  - Interest rate reaction coefficients largely similar across EMEs and AEs, except response to inflation is noticeably lower in EMEs (suggesting use of other instruments or lower priority to fight inflation).
  - Average posterior for 휎휎
푖푖 in AEs = 0.08; in EMEs = 0.17.
  - Adjusted R2: AEs average = 0.967; EMEs average = 0.909. (Fit of simple policy rule is somewhat better in AEs.)
  - Notable dispersion: in five AEs adjusted R2 is never lower than 0.93; lowest among 12 EMEs is about 0.75.
- FX market depth parameter Γ:
  - Mean value of inverse market depth parameters Γ is notably higher in EMEs than in AEs when allowing for systematic FX interventions.
  - Standard deviation indicates noticeable dispersion in Γ across EMEs; AEs show similar values across five included countries.
  - In the model variant without an endogenous FXI rule, EMEs’ FX markets are estimated to be deeper than AEs on average.
  - Allowing for a systematic FX intervention rule can substantially affect estimated Γ; evidence of systematic interventions typically implies estimated FX markets are shallower.
  - Implication: accounting for endogeneity of FX interventions is critical when assessing market depth; past interventions may have kept market spreads small and thus bias simple inferences about depth.

### Model comparison and model-fit implications
- Model fit under the two FXI specifications:
  - Table 4 compares model fit (log marginal likelihood, LML) under exogenous versus endogenous FXI rules.
  - The model with systematic FX interventions (endogenous FXI rule) fits the data better for more than half of the EMEs, but not for any of the AEs in the sample.
  - Using a conservative criterion (difference in LML exceeding 10 as strong evidence), countries EME 3, 4, 5, 6 and 12 strongly favor an endogenous FXI rule; AE4 strongly favors an exogenous FXI rule.
  - Allowing for systematic FX interventions can lead to large LML gains and materially different estimates of market depth Γ.
- Prior-driven insights:
  - Prior for FX market depth parameter Γ centered around 0.05 implies FX interventions can have sizeable impact; deep markets would imply a notably lower estimated Γ and correspondingly lower effectiveness of FX intervention.
  - Prior impulse simulations showed that interventions that lean against depreciation (selling FX reserves) improve the output-inflation trade-offs following an adverse outflow shock.

*IMF WORKING PAPERS — An Estimated DSGE Model for Integrated Analysis (excerpt from provided content)*

### 1. Rather, Γ is identified as it shapes the transmission of all shocks in the model. For instance,

### An Estimated DSGE Model for Integrated Analysis

### Identification of Γ and FX market depth
- Γ is identified as it shapes the transmission of all shocks in the model.
- When Γ is low (FX markets are “deep”):
  - A consumption demand shock 휐휐ᶜ,ᵗ that drives up domestic absorption tends to increase inflation and put upward pressure on real rates.
  - Higher real rates in the small open economy relative to the rest of the world will appreciate the real producer exchange rate 푞푞ᵖ,ᵗ via the UIP condition (eq. 33), and also the consumption-based RER 푞푞ᶜ,ᵗ.
- When Γ is higher (FX markets are “shallow”):
  - Stronger domestic consumption demand worsens the NFA position as the trade balance deteriorates and puts depreciationary pressure on the RER.
- Empirical patterns:
  - The correlation between FXI and nominal exchange rate change is a good predictor for the best-fitting model: countries where LML favors an endogenous FXI rule tend to have FXI more strongly correlated with nominal exchange rate change.
  - Exceptions exist: AE2 has correlation almost -0.4 but no evidence for an endogenous FXI rule, whereas EME6 with correlation about -0.3 shows strong evidence in favor.
- Cross-country summary:
  - More EMEs—but by far not all—have shallower FX markets than the five small open AEs used as a control group.
  - Estimation results suggest many EMEs use FXIs systematically, more forcefully (larger response coefficient), and more persistently (higher autocorrelation coefficient).
  - The unexplained component (standard error of FXI shocks) still accounts for a large share in EMEs—and an even larger one in AEs.

*Selected table excerpt (preserve formatting and numeric values as in source):*
- EME1 -2241.21 -2236.23 0.03 50.029 0.200 0.591 1.35
- EME2 -2106.46 -2097.06 0.023 0.020 0.200 0.393 3.19
- EME3 -2541.52 -2565.02 0.008 0.006 2.260 0.425 5.61
- EME4 -2461.10 -2512.96 0.060 0.007 6.040 0.535 5.86
- EME5 -2300.37 -2330.63 0.045 0.009 4.800 0.388 8.60
- EME6 -2565.04 -2579.08 0.042 0.006 12.750 0.402 6.91
- EME7 -2001.87 -1995.90 0.035 0.028 0.260 0.501 1.96
- EME8 -2786.25 -2791.23 0.009 0.007 0.580 0.236 6.62
- EME9 -2076.38 -2078.84 0.027 0.019 0.490 0.313 3.52
- EME10 -2093.22 -2086.01 0.017 0.008 0.310 0.731 1.83
- EME11 -2609.22 -2604.50 0.022 0.018 0.350 0.503 3.40
- EME12 -2920.16 -2934.15 0.038 0.021 0.480 0.453 3.17
- EMEs mean 0.030 0.015 2.390 0.456 6.00
- AE1 -2358.92 -2353.14 0.033 0.021 0.260 0.303 3.30
- AE2 -2506.03 -2506.02 0.015 0.014 0.210 0.152 2.32
- AE3 -2034.56 -2025.36 0.025 0.022 0.150 0.282 2.47
- AE4 -2796.33 -2777.12 0.025 0.024 0.040 0.240 0.56
- AE5 -2791.96 -2784.31 0.024 0.022 0.120 0.301 1.40
- AEs mean 0.024 0.021 0.160 0.252 2.01

### IV. Posterior Predictive Analysis — overview
- Focus: impulse response function (IRF) analysis to understand shock transmission channels and policy tradeoffs.
- Emphasis on shocks that drive unexpected large depreciations of the currency and necessitate monetary policy interventions (short-term interest rate changes and FX interventions).
- For each country, IRFs use the best-fitting model specification.
- When best-fitting model features an endogenous FXI rule, the coefficient 훾훾Δ푠 = 0 is set in rule eq. (40) for certain exercises to isolate interest rate effects (i.e., FXI=0 in those experiments).

### IV.1 Transmission of Foreign Investors Portfolio Outflow Shocks
- Shock studied: negative realization of 푏푏̂ᴾ,ᵗ (a portfolio investors’ outflow shock akin to a UIP risk premium shock).
- Shock sized to induce the real exchange rate to depreciate by 10 percent in all countries.
- Experimental setup: use posterior parameters that maximize LML; set 훾훾Δ푠 = 0 when best-fitting model features an endogenous FXI rule so FXI=0 in Figure 6.
- Key findings:
  - Much more dispersion in impulses among EMEs than in AEs for a roughly same-sized real exchange rate depreciation.
  - Some EMEs face sizeable and persistent declines in output and large persistent run-ups in core CPI inflation, necessitating marked interest rate hikes when FX interventions are not available.
  - In AEs, similar qualitative effects (output contracts, inflation rises) but quantitatively smaller and associated with more muted interest rate hikes.
- Average responses (Figure 7):
  - Average increase in core CPI inflation: more than 0.5 percentage points for EMEs and 0.2 percentage points for AEs.
  - Larger run-up in inflation in EMEs necessitates a policy rate hike of more than twice the magnitude (relative to AEs).
  - Contraction in domestic demand in EMEs is almost double that experienced in Advanced Economies.

### IV.2 Transmission of Interest Rate Policy Shocks
- Shock: unexpected tightening of the short-term interest rate in period 1 (shock 휀휀ᵢ,1 in eq. 37).
- Experiment: shock causes the nominal interest rate to rise 100 basis points in period 1 in all countries; thereafter the systematic part of the policy rule dictates outcomes.
- Setup: posterior parameters that maximize LML; set 훾훾Δ푠 = 0 when best-fitting model features an endogenous FXI rule to study tightening without FX interventions.
- Key findings:
  - Interest rate hike generates a more powerful response of output gap and core CPI inflation in some EMEs compared to AEs.
  - For two EMEs, appreciation of the exchange rate following policy tightening is substantial due to shallow currency markets (high Γ) and normally offset swings via systematic FX interventions (high 훾훾Δ푠/(1−훾훾Δ푠) coefficients). When interventions are counterfactually restricted, very substantial appreciation occurs with noticeable effects on output gap and core CPI inflation.
  - Mechanism: tighter monetary policy improves the NFA position (via reduced import demand); when FX markets are shallow this leads to a larger decline in the UIP risk premium which strengthens the currency appreciation.
  - For other countries, effects in EMEs and AEs are more similar, except interest rate tightening tends to have a larger impact on core CPI inflation in EMEs.
- Mean effects (Figure 9, t=1,2,...,20):
  - Monetary tightening contracts domestic demand by about 0.7 percentage point for both EMEs and AEs on average.
  - Lowers inflation slightly more in EMEs: nearly ¼ percentage points versus about 0.15 percentage points in AEs.
  - Drivers: stronger real exchange rate appreciation in EMEs due to lower import price stickiness (휉휉ₘ lower in EMEs than in AEs) and higher wage indexation to exchange rate movements (휈 higher in EMEs than in AEs).

### IV.3 Transmission of FX Interventions
- Motivation: For some EMEs an endogenous FXI specification is strongly preferred by the data (Table 4); more realistic to assume central bank uses FX interventions when facing large risk-off shocks that put depreciationary pressure on the exchange rate.
- Focus: subset of countries for which evidence points to systematic use of FXIs (a subset of 5 economies).
- Important caveats for the subset:
  - One of the 5 countries is estimated to have rather deep currency markets (posterior mean for Γ below 0.01), implying FX interventions will have limited traction.
  - Another country responds weakly to exchange rate movements (훾훾Δ푠/(1−훾훾Δ푠) = 0.48, translating into a 훾훾Δ푠 of around 1/3), which biases downwards the overall impact of FX interventions.
  - Both countries are included in the set for analysis despite these features.
- Experiment (Figure 10):
  - Compare outcomes for the foreign investor risk-off shock for these 5 economies without FXI (훾훾Δ푠 = 0) and with 훾훾Δ푠 kept at the posterior mean in each country.
  - All other parameters set to country-specific posterior means (currency market depth varies by country).
  - Risk-off shock sized to cause the real exchange rate to depreciate by 10 percent when FXI is not deployed.
- Findings:
  - When FXI is deployed through sale of FX reserves, the currency depreciates notably less for three countries, reducing the increase in core CPI inflation and the need to hike the short-term interest rate.
  - In the remaining two countries, impulses with and without FXI are similar, explained by either deep currency markets or weak systematic interventions in response to exchange rate movements.
  - The size of FXI ranges from (text truncated in source).

*Italic source attribution line as provided in the source.*

### 0.5 to 3 percent of GDP, reflecting the individually-estimated endogenous FXI rules. All told, the

### wpiea2023135-print-pdf - 0.5 to 3 percent of GDP, reflecting the individually-estimated endogenous FXI rules. All told, the

### Impact of FX interventions (FXIs) on transmission of shocks
- FXIs reduce the depreciation (or appreciation) of the exchange rate by amounts varying across countries according to FX market depth and intervention size; intervention magnitudes referenced in the text are "0.5 to 3 percent of GDP, reflecting the individually-estimated endogenous FXI rules."
- In simulations of a 100 basis point interest rate hike:
  - An endogenous FXI rule can translate the 100 basis point interest rate hike into a much smaller appreciation in the exchange rate when currency markets are shallow and the FXI rule is aggressive.
  - When the central bank increases FX reserves in response to appreciationary pressure from the policy rate hike, movements in the exchange rate can be offset, which in some cases implies a weakened interest rate transmission, especially to core CPI inflation.
  - The decline in output is similar with and without FXI, but the reduction in core CPI inflation is notably lower when FXIs are active and effective.
- FXIs can be more effective when markets are shallow; under shallow market conditions an aggressive FXI can substantially dampen exchange rate movements and thus alter the interest-rate-to-inflation transmission channel.
- These results underline important interactions between interest rate policy and FX policy and raise the question of when central banks would prefer to lean against appreciation induced by a nominal policy rate hike versus using FXIs as a substitute for interest rate policy in risk-off capital outflow episodes.

### Regime-switching estimation: time variation in market depth and FXI strategy
- Two parameters are allowed to vary via a two-state Markov process: the market depth parameter Γ and the FX intervention response coefficient γΔS.
- Economic interpretation of regimes:
  - R1 ("deep"): prior centered on a deep FX market (Γ low) and a fairly passive FX intervention policy (γΔS low).
  - R2 ("shallow"): prior centered on shallower markets (Γ high) and a more active systematic FX intervention policy (γΔS high).
- Estimation approach and caveats:
  - Regime switching implemented following Leeper and Zha (2006, 2007) and Farmer, Waggoner and Zha (2011) using the RISE toolbox.
  - Transition probabilities between regimes are treated as exogenous and not a function of the filtered state of the economy; reasonable for empirical detection of time-variation but a drawback for policy simulations.
- Findings when only Γ is time-varying:
  - Data supports time-varying FX market depth for two out of five countries (log marginal likelihood improves relative to the no-switching model), but support is limited and weak for one country under a conservative posterior odds ratio criterion.
  - Overall limited support for the specification with only Γ time-varying.
- Findings when Γ and γΔS comove (joint regime-switching):
  - Model fit (change in log marginal likelihood relative to constant-parameter model) is notably more supportive of time variation when both Γ and γΔS vary.
  - The hypothesis that the FXI response coefficient γΔS is bigger when markets are shallower is generally supported.
  - In three of the five EMEs considered, the data supports time-varying parameters; in two of those three the data strongly supports occasionally shallow FX markets combined with a more active FXI response when markets are shallow.
  - Posterior transition probabilities indicate a majority (three) of the economies often have deep markets, while two economies predominantly have shallow FX markets.
- Interpretation nuance:
  - The "shallow" regime may proxy for the joint occurrence of shallow FX markets and capital outflow shocks, rather than simply FX market shallowness.
  - FXI is not necessarily desirable when markets are shallow in isolation, but may be desirable when shallow markets coincide with risk-off capital outflow shocks.

### Key empirical and model conclusions
- Model and sample:
  - Estimated New Keynesian small open economy DSGE with FX market frictions and a role for FXI, calibrated/estimated for a set of EMEs and AEs; empirical formulation embeds Gabaix and Maggiori (2015) FX market frictions.
- Cross-country empirical findings:
  - Currency markets are fairly deep in the control group of five small open advanced economies.
  - Evidence of shallower currency markets found in 6 of the 12 studied emerging market economies.
  - Risk appetite shocks generate a sizeable tradeoff between output and inflation stabilization for some EMEs; differences reflect structural differences in price and wage formation and FX market depth.
- Policy implications:
  - Under the assumption that currency market depth is not affected by FX interventions, frequent and systematic use of FXIs is justified in EMEs with shallow markets because interventions help stabilize the exchange rate and improve policy tradeoffs.
  - When market depth varies over time, FX interventions can be non-effective sometimes but occasionally very effective when market liquidity dries up (supporting conditional or state-contingent intervention strategies).
- Research extensions suggested:
  - Study non-sterilized interventions and interventions in derivative markets.
  - Examine whether effective FX intervention strategies require large FX reserves or whether fiscal backing and solid public finances suffice.
  - Compare estimated shallowness with empirical, externally-validated market depth measures across countries while accounting for the endogeneity of FX policy.
  - Extend the model to include supply-side shocks, commodities and a more elaborate fiscal sector, and a more developed banking sector with durable goods to analyze interactions between macroprudential tools, FX, and interest rate policies.

*Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023135-print-pdf.pdf*

### chapter 22, pages 1237-1302, Elsevier

### Appendix A. Derivations of Linearized Relationships

### A.1 Resource Constraint
- Equilibrium resource constraint (small open economy, ignoring price and wage dispersion terms):
  - Y_t = C_{D,t} + G_t + M_{D,t}^*  (eq. A.1)
  - Aggregate foreign total export demand: M_t^* = m_y (P_{t}^x / P_{t}^*)^{-η_x} Y_t^*  (eq. A.2)
- Aggregate consumption CES index and first-order conditions yield:
  - C_t = [ (1−ω_c)^{1/η_c} C_{D,t}^{(η_c−1)/η_c} + ω_c^{1/η_c} (M_{C,t} ϑ_{m,t})^{(η_c−1)/η_c} ]^{η_c/(η_c−1)}  (eq. A.3)
  - C_{D,t} = (1−ω_c) (P_t / P_{C,t})^{-η_c} C_t  (eq. A.4)
  - M_{C,t} ϑ_{m,t} = ω_c (P_{M,t} / P_{C,t})^{-η_c} C_t  (eq. A.5)
  - CPI price index: P_{C,t} = [ (1−ω_c) (P_t)^{1−η_c} + ω_c (P_{M,t})^{1−η_c} ]^{1/(1−η_c)}  (eq. A.6)
- Rewriting GDP identity by adding/subtracting imports used in exports:
  - Y_t = C_{D,t} + M_{C,t} + G_t + M_{D,t}^* + M_{M,t}^* − (M_{C,t} + M_{M,t}^*)  (eq. A.7)
  - M_t^* = M_{D,t}^* + M_{M,t}^*  (eq. A.8); M_t = M_{C,t} + M_{M,t}^*  (eq. A.9)
- Relative price notations:
  - Γ_{t}^{C,D} ≡ P_{C,t} / P_t  (A.10)
  - Γ_{t}^{x,*} ≡ P_{X,t} / P_t^*  (A.11)
  - Γ_{t}^{M,D} ≡ P_{M,t} / P_t  (A.12)
- Log-linearized resource constraint (after total differentiation and assuming relative prices = 1 in steady state, balanced trade M+M^* = 0):
  - y_t = c_y c_t + c_y η_c (γ_{t}^{c,d} − ω_c γ_{t}^{m,d}) + (1−c_y) g_t + m_y (m_t^* − m_t)  (A.14, intermediate)
  - Using Γ_{M,D} = 1 and relations between γ terms, final simplified log-linearized resource constraint:
    - y_t = c_y c_t + (1−c_y) g_t + m_y (m_t^* − m_t)  (eq. 1 in main text; derived at end of A.1)
- Relations between price deviation terms (assuming Γ_{M,D} = 1):
  - γ_{t}^{c,d} = ω_c γ_{t}^{m,d}  (A.17)
  - γ_{t}^{c,m} = −(1−ω_c) γ_{t}^{m,d}
  - γ_{t}^{m,c} = (1−ω_c) γ_{t}^{m,d}  (A.18)
- Import aggregates decomposition:
  - m_t^* = (1−ω_x) m_{d,t}^* + ω_x m_{m,t}^*  (after differentiating A.8)
  - m_t = (1−ω_x) m_{c,t} + ω_x m_{m,t}^*  (after differentiating A.9)
- Steady-state note and assumption:
  - Derivation rests on assumption that all relative prices equal unity in the non-stochastic steady state; strictly true only if substitution elasticities and markups are parameterized symmetrically for imported and domestically produced goods.

### A.2 UIP and Net Foreign Asset Dynamics

A.2.1 Linearized UIP condition
- Starting UIP (eq. 30) rewritten in gross nominal rates and steady-state evaluation leads to:
  - (1−τ_{F,t}) (1 + r_{t}^{bb}) = (1 + r_t^*) Q_{PP,t+1|t} / Q_{PP,t} + Γ_t (1 + r_t) B_{F,t} / (P_t Y_t) + (1−τ_{F,t}) Θ_t / (1+π_{t+1|t})  (A.19)
- In steady state (Γ_t = Γ > 0, Q_{PP} constant, Θ = 0, r^{bb} = r, τ_F = 0), obtain:
  - (1 + r) = (1 + r^*) + Γ (1 + r) b^{bb}_F  (A.20)
  - Hence b^{bb}_F = (r − r^*) / [ Γ (1 + r) ]  (A.21)
- Solving for ΔS from eq. (30) in steady state:
  - I = I^* ΔS + Γ I b^{bb}_F  ⇔  ΔS = (I − Γ I b^{bb}_F) / I^* = (I / I^*) = (1+π)/(1+π^*)  (A.22)
- Totally differentiating real UIP, ignoring non-smooth term, yields expression convenient for discounting:
  - q_t = q_{t+1|t} − (1 + r)/(1 + r^*) r_t + (1 + r)/(1 + r^*) τ_{F,t} + r_t^* + (1 + r)/(1 + r^*) Γ b_{F,t} + (1 + r)/(1 + r^*) Γ b_F r_t  (intermediate from A.19 derivation)

A.2.2 Linearized financial flow equations
- Aggregate net foreign assets decomposition (eq. 31): B_t = −B_{F,t} − B_{P,t} + B_{M,t}
  - Positive B_{P,t} = currency outflow; positive B_{M,t} = central bank stock of foreign reserves.
- Log-linearized after scaling with 1/(P_t Y_t):
  - b_{F,t} = −b_t − b_{P,t} + b_{M,t}  (A.23)

A.2.3 Linearized net foreign asset and trade balance equations
- Assumptions for simplifying eq. (32):
  1. ω_B = 1 (all banks domestically owned)
  2. ω_F = ω_P = ω (same degree of home ownership of profits of financial intermediaries and exogenous financial investors)
- Simplified net foreign asset accumulation (scaled by P_t Y_t):
  - b_t = [ (1−ω) I_{t−1} + ω I_{t−1}^* (S_t / S_{t−1}) ] / (1+π_t) b_{t−1} − (1−ω) [ I_{t−1} − I_{t−1}^* (S_t / S_{t−1}) ] / (1+π_t) b_{M,t−1}
    + (1−ω) τ_{F,t−1} I_{t−1} / (1+π_t) [ b_{F,t−1} ] + b_{P,t−1} + ttb_t  (A.24, scaled)
- After total differentiation and notation Ĩ = (1−ω) I + ω I^* ΔS, the linearized expression (variables denoted as percent deviations where appropriate) yields:
  - Full expression in (A.25); when b̄ = 0 and τ_F = 0, simplifies to (A.26):
    - b_t = Ĩ / (1+π) b_{t−1} − (1−ω)/(1+π) b_M [ I i_{t−1} − I^* ΔS (i_{t−1}^* + Δs_t) ] − (1−ω) (I − I^* ΔS)/(1+π) [ b_{M,t−1} − b_M π_t ] + (1−ω) τ_F I /(1+π) [ (b_F + b_P) (i_{t−1} − π_t) + b_{F,t−1} + b_{P,t−1} ] + (1−ω) I /(1+π) [ b_F + b_P ] τ_{F,t−1} + ttb_t  (A.26, simplified case)
- Trade balance in levels and log-linearized trade balance:
  - TB_t = S_t P_t X_t^M* − S_t P_t^* M_t  (A.27)
  - Scaled and linearized trade balance: tt b_t = Q_{PP} m_y ( γ_{t}^{x,d} + m_t^* − q_{p,t} − m_t )  (intermediate)
  - Using γ_{t}^{x,d} − q_{p,t} = p_{t}^x − p_t^* = γ_{t}^{x,*}, the log-linearized trade balance equation matches equation (36) in the main text.
- Steady-state considerations and calibration choices:
  - From A.24 steady state (τ_F = 0): b = [ (1−ω) I + ω I^* ΔS ] / (1+π) b − (1−ω) (I − I^* ΔS)/(1+π) b_M + ttb_b  (intermediate)
  - Define I_{eff}/(1+π) −1 = 1.06^{1/4} 1/ 1.03^{1/4} −1 = 0.0072 (exact expression preserved)
  - Compute (1−ω)(r − r^*) factor example:
    - (1−ω) (r − r^*) = (1−0.8) [ 1.04^{1/4} −1 − 1.02^{1/4} + 1 ] = 9.7809ee−04  (exact as in text)
  - Example computation of required trade balance surplus:
    - ttb_b = (0.0072 + 9.7809ee−04) × 1.2 = 0.0098  (explicit arithmetic as given)
    - Interpretation: country would need to run a surplus of approximately one percent (as share of quarterly GDP) to balance debt service costs under these assumptions.
  - Reserve and portfolio flow steady-state setting:
    - Set b_M = 1.2 (which corresponds to 30 percent of annualized GDP) to match CB average currency reserves (as share of GDP) for many EMEs.
    - Alternative steady-state setup (used in the model): start from eq. (31) and impose shares of steady-state quarterly GDP to obtain b_P = −b + b_M − b_F, leading under assumptions to b_P = − (r − r^*)/Γ(1+r) + 2 b_M (A.28 and surrounding discussion).
  - Special case when b = 0: b_P = b_M − b_F  (A.28)

### A.3 Wage and Pricing Schedules

A.3.1 Marginal Costs
- Production function:
  - Y_t = e^{z_t} K^{α} N_t^{1−α}  (A.29)
- Marginal cost expression:
  - MC_t / P_t = W_t / r_{MP_L,t} = W_t / [ r (1−α) n_z_t K^{α} N_t^{−α} ]  (A.30, structure preserved)
- Total differentiation and steady-state normalization yield linearized marginal cost:
  - m c_t = ζ_t + α n_t − z_t  (A.31)  where ζ_t ≡ dW_t^{r} / W^{r}
- Using log-linearized production function:
  - y_t = z_t + (1−α) n_t  ⇔  n_t = (1/(1−α)) (y_t − z_t)  (A.32)
- Inserting into (A.31) gives:
  - m c_t = ζ_t + α/(1−α) y_t − 1/(1−α) z_t  (linearized marginal cost equation corresponding to eq. (17) with z_t = 0)

A.3.2 Labour Wedge
- Household first-order conditions and definitions:
  - χ_0 N_t / χ Λ_{C,t} = (1−τ_{N,t}) W_t / P_{C,t}  (A.33)
  - Λ_{C,t} = (C_t − φ C_{t−1} − C_t ν_{c,t})^{-1/σ} (1 + τ_{C,t})  (A.34)
  - Marginal rate of substitution: MRS_t ≡ MU_{L,t} / MU_{C,t} = χ_0 N_t / χ [ C_t − φ C_{t−1} − C_t ν_{c,t} ]^{-1/σ}  (A.35)
- Optimal wage-setting schedule (labor wedge form):
  - MRS_t = (1−τ_{N,t})/(1+τ_{C,t}) W̄_t / P̄_{C,t}  (A.36)
- Total differentiation yields linearized relationships; defining small letters as percent deviations and τ_{C,t} in percentage points:
  - mrs_t = χ n_t − (1 + τ_{C,t})^{-1} τ_{C,t} − λ_C,t  (A.37 simplified form leading to eq. (18))
  - Also: mrs_t = ζ_{c,t} − τ_{N,t}/(1−τ_{N}) − τ_{C,t}/(1+τ_{C})  (A.38 intermediate)
- Model labor wedge that drives nominal wage inflation (defining lledge_t as labor wedge):
  - lledge_t = mrs_t − ζ_{c,t} + τ_{N,t}/(1−τ_{N}) + τ_{C,t}/(1+τ_{C})
  - Substituting mrs expression and simplifying (with z_t = 0 and τ_{N,t} = 0 in the model) yields:
    - lledge_t = χ [ 1/(1−α) y_t − z_t ] − λ_{C,t} − ζ_{c,t} + τ_{N,t}/(1−τ_{N})  (final labor wedge expression, reduces to eq. (18) in main text when z_t = 0 and τ_{N,t} = 0)

*Appendix A, "Derivations of Linearized Relationships", chapter 22, pages 1237–1302.*

### Appendix B. Calibrated Parameters and Full

### Appendix B. Calibrated Parameters and Full Estimation Results

### Common calibrated parameters (Table B.1)
- Labor elasticity in Cobb-Douglas production function: 0.3 (EMEs) / 0.3 (AEs)
- Frisch elasticity of substitution (FELS): 22
- Import price elasticity: 0.8 / 0.8
- Export price elasticity: 0.8 / 0.8
- Marginal rate of consumption/leisure substitution: 2.8571 / 2.8571
- Coefficient of relative risk aversion: 1 / 1
- Wage mark-up: 0.333 / 0.333
- Ownership share of financial intermediaries/investors: 0.8 / 0.8
- NFA relative to Quarterly GDP: -1.012 (EMEs) / 0 (AEs)
- gmarkup: 21.5
- Kimball curvature: 50
- (Other parameter symbols listed in the table: 훼, 휒, η, 푐, 휃, 푥, 휔, 휎, 휒/(1−훼), η, 푥, 푏, �, 휖, 1+휙)

### Country-specific calibrated parameters (Table B.2)
- Table B.2 reports country-specific calibrated parameters set to match country characteristics (values shown for a suite of EMEs and small open AEs). Selected rows and values as presented:
  - Reserves relative to Quarterly GDP (sample EMEs/AEs entries): 0.496 0.608 0.492 0.464 0.680 0.460 1.500 1.076 0.916 1.476 0.464 0.464
  - Household subjective discount factor (sample EMEs/AEs entries): 0.9867 0.9975 0.9975 0.9950 0.9902 0.9963 0.9970 0.9963 0.9950 0.9975 0.9902 0.9926
  - Steady-State Inflation (ann. perc. points) (sample entries): 4.5 3.0 4.0 3.0 4.0 3.0 2.5 2.0 3.0 2.0 5.0 4.5
  - Steady-State Real Rate (ann perc points) (sample entries): 5.39 1.00 1.00 2.01 3.96 1.49 1.20 1.49 2.01 1.00 3.96 2.98
  - Share of Government Expenditure in GDP (sample entries): 0.190 0.130 0.143 0.080 0.090 0.120 0.110 0.160 0.109 0.145 0.138 0.050
  - Share of Import in Export (sample entries): 0.107 0.160 0.095 0.150 0.130 0.270 0.400 0.130 0.240 0.370 0.180 0.214
  - Share of Exports & Imports in GDP (sample entries): 0.120 0.290 0.184 0.200 0.520 0.310 0.610 0.230 0.290 0.690 0.238 0.290
  - Share of Import Goods in Consumption (sample entries): 0.13 0.28 0.19 0.18 0.50 0.26 0.41 0.24 0.25 0.51 0.23 0.24
  - Term Premium (ann. perc. points) (sample entries): 1.0 1.5 2.5 1.0 1.0 1.5 1.0 2.0 2.0 1.0 1.5 1.0
  - Gross Steady-State Nominal Interest Rate (sample entries): 1.025 1.010 1.013 1.013 1.020 1.011 1.009 1.009 1.013 1.008 1.023 1.019
- For the small open advanced economies (AUS, CAN, NOR, NZL, SWE, For. Economy (US)), sample calibrated rows:
  - Reserves relative to Quarterly GDP: 0.168 0.148 0.564 0.368 0.352 N/A
  - Household subjective discount factor: 0.9975 0.9975 0.9975 0.9975 0.9975 0.9962
  - Steady-State Inflation (ann. perc. points): 2.5 2.0 2.0 2.0 2.0 2.0
  - Steady-State Real Rate (ann perc points): 1.00 1.00 1.00 1.00 1.00 1.5
  - Share of Government Expenditure in GDP: 0.180 0.230 0.230 0.190 0.290 0.216
  - Share of Import in Export: 0.110 0.210 0.180 0.150 0.300 N/A
  - Share of Exports & Imports in GDP: 0.215 0.320 0.340 0.310 0.370 N/A
  - Share of Import Goods in Consumption: 0.23 0.33 0.36 0.33 0.36 N/A
  - Term Premium (ann. perc. points): 0.5 1.5 1.0 1.0 1.0 N/A
  - Gross Steady-State Nominal Interest Rate: 1.009 1.008 1.008 1.008 1.008 N/A

### Country-specific posterior distributions (Tables B.3–B.5)
- Tables B.3 and B.4: country-specific posterior distributions and log marginal likelihoods for EMEs under:
  - endogenous FXI rule (Table B.3)
  - exogenous FXI rule (Table B.4)
- Table B.5: country-specific posterior distributions and log marginal likelihoods for AEs under endogenous and exogenous FXI rules.
- Parameter categories reported (examples of parameter names appearing across posterior tables):
  - Calvo parameters: import prices, export prices, domestic prices, wages
  - Price indexation: imported goods price indexation, domestic price indexation, exported goods price indexation, wage indexation
  - Wage sensitivity to exchange rate
  - Habit formation (norm)
  - Discount factor
  - FX market friction
  - Shock persistences: domestic riskpremium, domestic demand, government expenditure, import demand, export demand, exchange riskpremium
  - Shock variances / innovation distributions: consumption demand shock (inv gamma), import markup shock (inv gamma), domestic markup shock (inv gamma), wage markup shock (inv gamma), domestic riskpremium shock (inv gamma), govt. expenditure shock (inv gamma), import demand shock (inv gamma), export demand shock (inv gamma), exchange riskpremium shock (inv gamma), interest rate policy shock (inv gamma), FXI policy shock (inv gamma)
  - Monetary policy coefficients: interest rate reaction to CPI inflation (norm), interest rate reaction to output gap (beta), interest rate smoothing (beta)
  - FX intervention (FXI) parameters: FXI response to change in exchange rate (beta), FXI persistence (beta), FXI rule error correction (beta)
- Examples of reported posterior statistics and model fit metrics (as presented in the tables):
  - Posterior reporting format: typ e (prior distribution), mean, std. dev. (and in some columns LML - Laplace Approximation and LML - Modified Harmonic Mean)
  - Sample LML values shown in the EMEs endogenous FXI table (sequence as reported): -2540.95 -2106.02 -2241.50 -2920.16 -2609.22 -2093.22 -2076.38 -2786.25 -2001.87 -2565.04 -2300.37 -2461.10 -2541.52 -2106.46 -2241.21 -2920.11 -2607.77 -2093.65 -2077.55 -2785.91 -2001.86 -2565.05 -2299.98 -2464.01
  - Sample LML values shown in the EMEs exogenous FXI table (sequence as reported): -2573.78 -2096.76 -2236.57 -2934.15 -2604.50 -2086.01 -2078.84 -2791.23 -1995.90 -2579.08 -2330.63 -2512.96 -2565.02 -2097.06 -2236.23 -2933.78 -2605.65 -2085.41 -2081.77 -2789.97 -1996.57 -2576.77 -2330.68 -2511.58
  - Sample LML values shown in the AEs table (endogenous/exogenous FXI rules) (sequence as reported): -2354.12 -2791.96 -2796.33 -2034.56 -2506.03 -2358.92 -2784.31 -2777.12 -2025.36 -2506.02 -2353.14 -2791.62 -2798.13 -2035.57 -2506.22 -2360.06 -2784.08 -2777.73 -2026.19 -2506.13
- The posterior tables provide mean and standard deviation estimates for the full set of structural, policy-rule, shock-persistence, and shock-variance parameters for each country under each FXI rule specification.

*Appendix B, Tables B.1–B.5, "Calibrated Parameters and Full Estimation Results."*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023135-print-pdf.pdf_