## Annex I. Model Calibration to India

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### Model scope and calibration overview
- Annex I calibrates the QIPF model specifically to India and presents calibrated steady states, impulse response functions (IRFs), scenario shock profiles, and the linearized two-country model structure.
- Calibrated steady states are reported in Table A.1 (numerical entries referenced in the source).
- IRFs illustrate transmission for key shocks: foreign investors portfolio outflow (UIP risk premium), domestic demand, interest rate policy, and FX intervention (FXI).
- Scenarios are constructed as unanticipated shocks with values reported as percent deviations from baselines; each period = a quarter.

### Regime-switching results (market depth Γ)
- Estimation setup and interpretation:
  - Market depth parameter Γ modeled as a two-state Markov process (deep vs shallow FX markets).
  - Regimes: R1 = Deep Markets (Low Γ); R2 = Shallow Markets (High Γ).
  - Switching assumed exogenous; estimation implemented with RISE; uninformative priors on transition probabilities.
- Priors used in estimation (reported):
  - R1: Γ — beta mean 0.01, std 0.005; Transition probabilities — beta mean 0.5, std 0.2
  - R2: Γ — beta mean 0.075, std 0.01; Transition probabilities — beta mean 0.5, std 0.2
- Posterior estimation results (regime-switching):
  - Γ — posterior
    - R1: Deep = 0.001
    - R2: Shallow = 0.059
  - Transition probabilities — posterior
    - p(R2|R1) = 0.01
    - p(R1|R2) = 0.55
  - Implied unconditional probability of Deep FX Markets (quarterly) = 0.990
- Historical identification and interpretation:
  - Economy most often characterized by deep FX markets, with episodic switches to shallow-market regime.
  - Shallow-market episodes aligned with: the global financial crisis (GFC), the taper tantrum, and early COVID-19 pandemic periods.
- Caveats relevant to India:
  - Rapid growth of offshore/onshore activity could bias estimated average Γ upward if market depth increased over time.
  - Offshore market stress can spill into onshore markets; offshore market size matters despite model aggregation.
- Policy relevance:
  - Time-varying FX market depth matters for assessing FX intervention effectiveness — FXI may be more effective in shallow regimes (stress episodes) and less effective in deep regimes.

### Impulse response function (IRF) qualitative findings
- Foreign investors portfolio outflow (UIP risk premium) shock:
  - Shock sized to cause the real exchange rate to depreciate by 10 percent on impact.
  - Effects:
    - Domestic demand falls while inflation rises, creating a policy trade-off.
    - A persistent interest rate hike is necessary to bring inflation back to target.
    - A sizable FXI (selling foreign FX reserves) is required to support the exchange rate.
    - Higher policy rate path raises long-term nominal interest rates through expectations theory of the term structure.
- Domestic demand shock:
  - A positive shock raises domestic demand by around 2 percent of GDP and increases inflation.
  - Monetary response: policy rate is raised; long-term interest rate increases.
  - External effects: NFA position worsens as trade balance deteriorates; real exchange rate depreciates.
  - FXI response: small FXI according to the estimated intervention rule.
  - Mechanism: shallow FX market implies UIP premium rises when trade balance and NFA position worsen persistently, causing depreciation despite increased real interest differential.
- Interest rate policy shock:
  - Shock sizing: raises the nominal short-term interest rate by 100 basis points in the first period.
  - Effects:
    - Output gap declines (about a quarter percentage point).
    - Core CPI inflation is reduced somewhat less.
    - Exchange rate appreciates and central bank conducts FXI to accumulate reserves.
- FXI shock:
  - Negative shock to the estimated FXI rule deploys additional FXI through sale of FX reserves.
  - Effects:
    - Currency depreciates notably (reflecting a shallow currency market).
    - Core inflation is reduced and monetary policy cuts the policy rate.
    - Domestic demand is higher, reflecting stimulatory effect of looser monetary policy.
    - Trade balance deteriorates and the output gap becomes negative.

### Scenario shock profiles (values are percent deviations from baselines; each row = quarters 1–8)
- Scenario 1: Global fragmentation and domestic shocks without significant risk-off shocks (first block)
  - Domestic
    - UIP Risk-premium shock: -0.3, -0.2, -0.1, 0, 0, 0, 0, 0
    - Domestic price cost-push shock: 0.4, 0.4, 0.4, 0.4, 0.33, 0.27, 0.2, 0.13
    - Wage markup (labor supply) shock: 0.4, 0.4, 0.4, 0.4, 0.33, 0.27, 0.2, 0.13
  - Foreign
    - Foreign price cost-push shock: 0.3, 0.3, 0.3, 0.3, 0.25, 0.2, 0.15, 0.1
    - Foreign wage markup (labor supply shock): 0.3, 0.3, 0.3, 0.3, 0.25, 0.2, 0.15, 0.1
    - Foreign interest rate policy shock: 0.125, 0.125, 0.0625, 0.0625, 0, 0, 0, 0
- Scenario 1: alternate block (second block)
  - Domestic
    - UIP Risk-premium shock: -1.95, -1.2, -0.9, -0.6, -0.3, -0.15, -0.075, 0
    - Domestic risk premium shock: 0.1, 0.1, 0.1, 0, 0, 0, 0, 0
  - Foreign
    - Foreign private domestic demand shock: -0.1, -0.1, -0.1, -0.1, 0, 0, 0, 0
    - Foreign interest rate policy shock: 0.1875, 0.1875, 0.09375, 0.09375, 0, 0, 0, 0
- Scenario 2: Global financial market disruption with significant risk-off shocks
  - The source presents Scenario 2 tables following Scenario 1; Scenario 2 includes foreign shocks and domestic shocks across periods 1–8 as shown under the Scenario 1 blocks.

### Linearized model structure — five building blocks (representative equations preserved as given)
- Overview:
  - Two-country empirical formulation: India (small open economy) and foreign block (proxied by the United States).
  - Endogenous supply side; variables with hats are stationary deviations from permanent technology trend.
- 1. Aggregate demand block (representative equations):
  - ŷt = cy ĉt + gy ĝt + my (m̂t∗ − m̂t)
  - ĉt = δc/(1+δc) ωc ĉt+1|t + ωc/(1+δc) ωc ĉt−1 − σ(1−ωc) /(1+δc) ωc (it + ψt − πc,t+1|t) + 1/(1+δc) ωc ϑc,t − δc ϑc,t+1|t + 1/(1+δc) ωc δc μ̂z,t+1|t − ωc μ̂z,t
  - ĝt = ρg ĝt−1 + εg,t
  - m̂t = (1−ωx) m̂c,t + ωx m̂m,t∗
  - m̂c,t = ĉt − (1−ωc) ηc (pm,t − pt) + ϖm,t
  - m̂m,t∗ = ŷt∗ − zt − (1−ωx) ηx (pm,t − pt) − ηf (px,t − pt∗) + ϖm∗,t
  - m̂d,t∗ = ŷt∗ − zt + ηx ωx (pm,t − pt) − ηf (px,t − pt∗)
  - m̂t∗ = (1−ωx) m̂d,t∗ + ωx m̂m,t∗
- 2. Aggregate supply block (representative equations):
  - πt − ιp πt−1 = β δc πt+1|t − ιp πt−1 + κp mc t + επ,t
  - πm,t − ιm πm,t−1 = β δc πm,t+1|t − ιm πm,t−1 + κm mcm,t + επm,t
  - πx,t − ιx πx,t−1 = β δc πx,t+1|t − ιx πx,t−1 + κx mcx,t
  - πc,t = (1−ωc) πt + ωc πm,t
  - πw,t − πw,t−1 = β δc (πw,t+1|t − πw,t) + κw (mrs t − ζc,t) + εw,t
  - πw,t = ιw πw,t + (1−ιw) πL,t
  - πL,t = (1−ν) πL,t−1 + ν (Δst − Δst|t−1)
  - Additional:
    - yt = 1+φp εt − α μ̂z,t + (1−α) nt
    - ζt = ωc (pm,t − pd,t) + ζc,t
    - ζt = ζt−1 + πw,t − πt − μ̂z,t
- 3. Financial block (representative equations and role of Γ):
  - qp,t = δc qp,t+1|t + i t∗ − πt+1|t∗ − (1+r)/(1+r∗) (it − πt+1|t) + (1+r)/(1+r∗) Γ [bF,t + bF (it − πt+1|t)]
  - bF,t = −bt − 1/Γ b̃P,t + bM,t
  - bt = ĨΠy bt−1 + bΠy [(1−ω) I i t−1 + ω I∗ ΔS (it−1∗ + Δst) − Ĩ πt + μ̂z,t ] − (1−ω) / Πy bM [I i t−1 − I∗ ΔS (it−1∗ + Δst)] − (1−ω) (I − I∗ ΔS) / Πy (bM,t−1 − bM πt + μ̂z,t) + tb t
  - tb t = my (m̂t∗ − m̂t + γt x,∗)
  - iL,t = 1/40 ∑(it+k + ψt+k) (k=0..39)
  - Role of Γ: an agency friction that modifies UIP for the product real exchange rate and motivates FXI; high Γ (shallow FX markets) makes credible FX interventions more effective.
- 4. Central bank policy block (FXI specifications and policy rule):
  - FXI measured by changes in FX reserves fx t = bM,t − bM,t−1
  - Two FXI specifications:
    - FXI Rule 1 (exogenous AR(1) with error correction):
      - fxt = ρfx,1 fxt−1 − ρfx,2 bM,t−1 + εt fx
    - FXI Rule 2 (systematic response to Δs):
      - fxt = ρfx,1 fxt−1 − ρfx,2 bM,t−1 − (1−ρfx,1)/(γΔs/(1−γΔs)) Δst + εt fx
  - Policy rule:
    - it = ρ i t−1 + (1−ρ)[(1+γπ) π̄c,t+4|t + γy ŷt] + γΔy Δÿt + γs Δst + εt i
  - Comment: explicit exchange rate stabilization coefficient γs set to zero in estimation because its value was very small.
  - When exogenous portfolio flow shocks b̃P,t drive exchange rate movements, welfare is enhanced by leaning against exchange rate movements when the FX market is shallow.
- 5. Foreign block:
  - Closed-economy version with seven shocks: μ̂z,t∗, εt∗, ĝt∗, ϑc,t∗, επ,t∗, εw,t∗, εi,t∗.
  - μ̂z,t∗, εt∗, ĝt∗, ϑc,t∗ follow AR(1); cost-push and monetary policy shocks are white noise.
  - Foreign shocks affect the small open economy; small open economy shocks do not affect the foreign block.

### Key policy implications and recommendations
- Allow for time-varying FX market depth in policy analysis: regime-switching evidence supports modeling Γ as time-varying when assessing FX intervention effectiveness.
- FX intervention design:
  - FXI can be effective in shallow regimes (high Γ) typically occurring in major stress episodes; less effective in deep regimes (low Γ).
  - When exogenous portfolio flow shocks drive exchange rate movements, leaning against exchange rate movements can enhance welfare if the FX market is shallow.
- Practical considerations for India:
  - Monitor offshore market size and interaction with onshore markets, since offshore growth and spillovers during stress can affect onshore market depth and the effectiveness of FXI.
  - Scenario-based analysis should consider episodic shallow regimes (e.g., GFC, taper tantrum, early COVID-19) where FXI may play a more prominent role.

*Source: Annex I. Model Calibration to India, from Foreign Exchange Intervention Under the Integrated Policy Framework: The Case of India, Working Paper No. WP/2024/236*

### Annex I. Model Calibration to India ....................................................................................

### Annex I. Model Calibration to India

### Content scope
- Annex I is titled "Model Calibration to India".
- Appears in the source document on page 23.

### Related annexes and model material
- Annex II. Scenario Shock Profile — page 26.
- Annex III. The Linearized Model — page 27.
- References — page 30.

### Figures referenced in the surrounding chapter
- Figure 1. OTC FX Turnover: 2022
- Figure 2. India Rupee: Forward Points and Offshore Premium
- Figure 3. EM FX Intervention Proxy
- Figure 4. RBI FX Interventions
- Figure 5. Gross Spot FXI as Share of Onshore Spot Turnover
- Figure 6. Regime Switching Probability
- Figure 7. Scenario 1 - Global Trade Fragmentation
- Figure 8. Adverse Scenario 2, Risk-Off Shock from Global Financial Turbulence

### Tables referenced in the surrounding chapter
- Table 1. Observables and Shocks Used in Estimation — page 12

### Structural focus (as implied by headings and figure/table listings)
- Calibration of a model specifically to India (Annex I).
- Scenario construction and shock profiles (Annex II).
- Presentation of the linearized model equations or system (Annex III).
- Empirical and illustrative material including OTC FX turnover, forward points, offshore premium, EM intervention proxies, RBI interventions, measures of spot FX intervention intensity, regime-switching probabilities, and scenario visualizations.

*Source: wpiea2024236-print-pdf - Annex I. Model Calibration to India*

### 2. Regime Switching Results ............................................................................................

### 2. Regime Switching Results

### Estimation approach and model setup
- Market depth parameter Γ is modeled as a two-state Markov process (deep vs shallow FX markets) following Davig and Leeper (2006, 2007) and Farmer, Waggoner and Zha (2011).
- Switching between regimes is assumed exogenous (not endogenously related to the filtered state of the economy).
- Regime-switching estimation implemented using the toolbox RISE.
- R1 denotes the regime centered on a deep FX market (low Γ); R2 denotes the regime centered on a shallow FX market (high Γ).
- Uninformative priors are used for transition probabilities between regimes.

### Prior distributions used in estimation (as reported)
- R1: Deep Markets (Low Γ)
  - Γ — beta mean 0.01, std 0.005
  - Transition probabilities — beta mean 0.5, std 0.2
- R2: Shallow Markets (High Γ)
  - Γ — beta mean 0.075, std 0.01
  - Transition probabilities — beta mean 0.5, std 0.2

### Posterior estimation results (regime-switching)
- Γ — posterior
  - R1: Deep = 0.001
  - R2: Shallow = 0.059
- Transition probabilities — posterior (reported as R1 to R2 & R2 to R1)
  - p(R2|R1) = 0.01
  - p(R1|R2) = 0.55
- Implied unconditional probability of Deep FX Markets (quarterly) = 0.990

### Model interpretation and historical identification
- The posterior implies the economy is most often best characterized as having deep FX markets but occasionally switches to a shallow-market regime.
- Periods identified by the model as having higher likelihood of being in the shallow-market regime include:
  - the global financial crisis (GFC),
  - the taper tantrum,
  - the early times of the COVID-19 pandemic.
- Figure 6 (in-source) maps the model’s estimated probability of being in the shallow markets state against nominal exchange rate movements and a measure of the UIP risk premium.

### Caveats and implications for India
- India’s large offshore FX markets can be indirectly accounted for in the IPF model by assuming the same ownership structure for financiers and portfolio investors, but two caveats are noted:
  - If off/onshore markets have been growing fast, the estimated average Γ might be upward biased because growing offshore/onshore activity implies a deepening FX market over time.
  - During stress, offshore markets can spill risk into onshore markets, meaning offshore market size matters for IPF considerations despite the model aggregation.
- Empirical implication: India’s FX market is mostly deep (high unconditional probability of deep regime = 0.990) but can become shallow episodically, amplifying UIP premia and exchange rate volatility during large global or domestic shocks.

### Relevance for policy analysis under the IPF
- Regime-switching evidence supports allowing for time-varying FX market depth when assessing the potential effectiveness of FX intervention (FXI).
- The finding that shallow regimes occur during major stress episodes motivates scenario analysis where FXI may be effective in those episodes, while FXI would be less effective when markets are in the deep regime.

*Source: IMF Working Paper — “Foreign Exchange Intervention Under the Integrated Policy Framework: The Case of India”, Section 2 (Regime Switching Results).*

### Annex I. Model Calibration to India

### Annex I. Model Calibration to India

### Calibrated steady states
- Table A.1 contains the calibrated steady states of the model variables, based on their respective sample averages. (Table A.1 referenced in source; numerical entries not reproduced here.)

### Impulse response functions (IRFs) — key qualitative findings
- General:
  - IRFs are presented to key shocks to illustrate transmission mechanisms for India in the QIPF model.

- Transmission of Foreign Investors Portfolio Outflow Shocks:
  - The shock is akin to a UIP risk premium shock and is sized so it causes the real exchange rate to depreciate by 10 percent on impact.
  - Effects and policy responses:
    - Domestic demand falls while inflation rises, creating a policy trade-off.
    - A persistent interest rate hike is necessary to bring inflation back to target.
    - A sizable FXI (selling foreign FX reserves) is required to support the exchange rate.
    - The higher policy rate path translates into higher long-term nominal interest rates through the expectations theory of the term structure.

- Transmission of Domestic Demand Shocks:
  - A positive shock causes domestic demand to increase by around 2 percent of GDP and leads to higher inflation.
  - Monetary policy response:
    - The policy rate is raised, which also increases the long-term interest rate.
  - External and FX effects:
    - Stronger domestic demand worsens the NFA position as the trade balance deteriorates and puts depreciation pressure on the real exchange rate.
    - This leads to a small FXI as dictated by the estimated intervention rule.
  - Mechanism comment:
    - The consumption-based real exchange rate depreciates even though the domestic policy rate is increased relative to the foreign policy rate because the estimated FX market is shallow. A shallow FX market implies the UIP premium rises when the trade balance and net foreign asset position worsen persistently, causing depreciation despite an increased real interest differential.

- Transmission of Interest Rate Policy Shocks:
  - Shock sizing:
    - The shock to the interest rate reaction function is sized to trigger the nominal short-term interest rate to rise 100 basis points in the first period.
  - Effects:
    - The interest rate hike generates a decline in the output gap (about a quarter percentage point) and somewhat less impact on core CPI inflation.
    - As the exchange rate appreciates, the central bank conducts FXI to accumulate reserves.

- Transmission of FXI:
  - Shock:
    - A negative shock to the estimated FXI rule deploys additional FXI through the sale of FX reserves.
  - Effects and policy feedback:
    - The currency depreciates notably, reflecting a shallow currency market.
    - Core inflation is reduced and monetary policy cuts the policy rate.
    - Domestic demand is higher, reflecting the stimulatory effect of a looser monetary policy stance.
    - The trade balance deteriorates and the output gap becomes negative.

### Scenario shock profiles (each period = a quarter)
- Note: Scenarios are constructed using unanticipated shocks whose values are described below. Values are percent deviations from the baselines.

- Scenario 1: Global Fragmentation and Domestic Shocks without Significant Risk-off Shocks
  - (Percent deviations from the baseline)
  - Domestic (first block)
    - UIP Risk-premium shock: -0.3, -0.2, -0.1, 0, 0, 0, 0, 0
    - Domestic price cost-push shock: 0.4, 0.4, 0.4, 0.4, 0.33, 0.27, 0.2, 0.13
    - Wage markup (labor supply) shock: 0.4, 0.4, 0.4, 0.4, 0.33, 0.27, 0.2, 0.13
  - Foreign (first block)
    - Foreign price cost-push shock: 0.3, 0.3, 0.3, 0.3, 0.25, 0.2, 0.15, 0.1
    - Foreign wage markup (labor supply shock): 0.3, 0.3, 0.3, 0.3, 0.25, 0.2, 0.15, 0.1
    - Foreign interest rate policy shock: 0.125, 0.125, 0.0625, 0.0625, 0, 0, 0, 0

- Scenario 1: (alternate block presented in source)
  - (Percent deviations from the baseline)
  - Domestic (second block)
    - UIP Risk-premium shock: -1.95, -1.2, -0.9, -0.6, -0.3, -0.15, -0.075, 0
    - Domestic risk premium shock: 0.1, 0.1, 0.1, 0, 0, 0, 0, 0
  - Foreign (second block)
    - Foreign private domestic demand shock: -0.1, -0.1, -0.1, -0.1, 0, 0, 0, 0
    - Foreign interest rate policy shock: 0.1875, 0.1875, 0.09375, 0.09375, 0, 0, 0, 0

- Scenario 2: Global Financial Market Disruption with Significant Risk-off Shocks
  - (Percent deviations from the baseline)
  - [Scenario 2 tables are presented in the source; values above include foreign shocks and domestic shocks across periods 1–8 as shown under the first Scenario 1 block and second Scenario 1 block. The source presents Scenario 2 heading following Scenario 1 tables.]

### Linearized model — five building blocks and key equations
- Overview:
  - The linearized two-country empirical formulation of the QIPF model consists of India and a foreign block (proxied by the United States). The model features an endogenous supply side and five building blocks. Variables with hats are stationary deviations from the permanent technology trend.

- 1. Aggregate demand block:
  - Domestic production used for private consumption ĉt (endogenous), government spending ĝt (exogenous), exports m̂t∗ and imports m̂t (endogenous).
  - Consumption Euler equation includes the exogenous domestic risk-premium spread ψt in addition to the inflation-adjusted policy interest rate it − πc,t+1|t, and features an exogenous consumption demand shock ϑc,t.
  - Representative equations (as given):
    - ŷt = cy ĉt + gy ĝt + my (m̂t∗ − m̂t)
    - ĉt = δc/(1+δc) ωc ĉt+1|t + ωc/(1+δc) ωc ĉt−1 − σ(1−ωc) /(1+δc) ωc (it + ψt − πc,t+1|t) + 1/(1+δc) ωc ϑc,t − δc ϑc,t+1|t + 1/(1+δc) ωc δc μ̂z,t+1|t − ωc μ̂z,t
    - ĝt = ρg ĝt−1 + εg,t
    - m̂t = (1−ωx) m̂c,t + ωx m̂m,t∗
    - m̂c,t = ĉt − (1−ωc) ηc (pm,t − pt) + ϖm,t
    - m̂m,t∗ = ŷt∗ − zt − (1−ωx) ηx (pm,t − pt) − ηf (px,t − pt∗) + ϖm∗,t
    - m̂d,t∗ = ŷt∗ − zt + ηx ωx (pm,t − pt) − ηf (px,t − pt∗)
    - m̂t∗ = (1−ωx) m̂d,t∗ + ωx m̂m,t∗

- 2. Aggregate supply block:
  - Domestic price inflation πt follows a Phillips curve with slope κp. Export πx,t and import πm,t pricing allow for gradual pass-through of exchange rate movements Δst.
  - CPI inflation πc,t is the weighted average of domestic price inflation and import price inflation πm,t.
  - Wage setting follows Erceg, Henderson and Levin (2000) and can include an exchange-rate-influenced wage growth channel πL,t if ν>0.
  - Representative equations (as given):
    - πt − ιp πt−1 = β δc πt+1|t − ιp πt−1 + κp mc t + επ,t
    - πm,t − ιm πm,t−1 = β δc πm,t+1|t − ιm πm,t−1 + κm mcm,t + επm,t
    - πx,t − ιx πx,t−1 = β δc πx,t+1|t − ιx πx,t−1 + κx mcx,t
    - πc,t = (1−ωc) πt + ωc πm,t
    - πw,t − πw,t−1 = β δc (πw,t+1|t − πw,t) + κw (mrs t − ζc,t) + εw,t
    - πw,t = ιw πw,t + (1−ιw) πL,t
    - πL,t = (1−ν) πL,t−1 + ν (Δst − Δst|t−1)
    - Additional equations for output and labor wedge:
      - yt = 1+φp εt − α μ̂z,t + (1−α) nt
      - ζt = ωc (pm,t − pd,t) + ζc,t
      - ζt = ζt−1 + πw,t − πt − μ̂z,t

- 3. Financial block:
  - Includes banks and financiers; introduces an “agency friction” Γ that generates a modified UIP condition for the product real exchange rate qp,t and motivates FXI (change in central bank reserves bM,t) to lean against capital outflow shocks bP,t.
  - When Γ is high (shallow FX markets), credible FX interventions can be effective.
  - Representative equations (as given):
    - qp,t = δc qp,t+1|t + i t∗ − πt+1|t∗ − (1+r)/(1+r∗) (it − πt+1|t) + (1+r)/(1+r∗) Γ [bF,t + bF (it − πt+1|t)]
    - bF,t = −bt − 1/Γ b̃P,t + bM,t
    - bt = ĨΠy bt−1 + bΠy [(1−ω) I i t−1 + ω I∗ ΔS (it−1∗ + Δst) − Ĩ πt + μ̂z,t ] − (1−ω) / Πy bM [I i t−1 − I∗ ΔS (it−1∗ + Δst)] − (1−ω) (I − I∗ ΔS) / Πy (bM,t−1 − bM πt + μ̂z,t) + tb t
    - tb t = my (m̂t∗ − m̂t + γt x,∗)
    - iL,t = 1/40 ∑(it+k + ψt+k) (k=0..39)

- 4. Central bank policy block:
  - Standard forward-looking interest rate reaction function with interest rate smoothing and responses to expected inflation. The explicit exchange rate stabilization coefficient γs is set to zero in estimation because its value was very small.
  - The central bank can also use FXIs measured by changes in FX reserves fx t = bM,t − bM,t−1.
  - Two FXI specifications studied:
    - FXI Rule 1 (exogenous AR(1) with error correction):
      - fxt = ρfx,1 fxt−1 − ρfx,2 bM,t−1 + εt fx
    - FXI Rule 2 (systematic response to Δs):
      - fxt = ρfx,1 fxt−1 − ρfx,2 bM,t−1 − (1−ρfx,1)/(γΔs/(1−γΔs)) Δst + εt fx
  - Policy rule (as given):
    - it = ρ i t−1 + (1−ρ)[(1+γπ) π̄c,t+4|t + γy ŷt] + γΔy Δÿt + γs Δst + εt i
  - Comment:
    - When exogenous portfolio flow shocks b̃P,t drive a significant portion of exchange rate movements, welfare is enhanced by leaning against exchange rate movements when the FX market is shallow.

- 5. Foreign block:
  - Closed economy version of the model with output, hours, private consumption, price and wage inflation, and the policy rate.
  - Seven shocks: permanent technology μ̂z,t∗, stationary technology εt∗, government spending ĝt∗, consumption demand shock ϑc,t∗, cost-push shocks επ,t∗ and εw,t∗, and monetary policy shock εi,t∗.
  - μ̂z,t∗, εt∗, ĝt∗, and ϑc,t∗ follow AR(1); cost-push and monetary policy shocks are white noise.
  - Shocks in the foreign economy affect the small open economy; shocks from the small open economy do not affect the foreign block.

*Source: Annex I. Model Calibration to India, from Foreign Exchange Intervention Under the Integrated Policy Framework: The Case of India, Working Paper No. WP/2024/236*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024236-print-pdf.pdf_