## wp1733

## Source details

**Canonical URL:** [wp1733](https://www.imf.org/-/media/files/publications/wp/wp1733.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/wp1733.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/wp1733.pdf.json)

---

### Box 1 — Monetary Policy Feedback: role, mechanics, and operational implications
- Credibility of the long-run inflation target underpins IFT and requires that policy respond systematically to achieve the objective.
- The nominal anchor is maintained by ensuring over time the rate of inflation and inflation expectations converge to the target via an endogenous, forward-looking policy interest rate.
- Dynamic feedback structure:
  - Policy feedback links expected future inflation to the endogenous short-term interest rate (ensuring the nominal anchor).
  - Expectations about future policy rates influence longer-term interest rates and the exchange rate.
  - Transmission operates through the entire expected Policy Rate Path—the medium-term path—not just the current policy-rate setting.
- Endogenous forward-looking policy vs exogenous interest-rate path:
  - Under endogenous policy, expected future inflation feeds back to the policy instrument.
  - Under an exogenous interest-rate path (e.g., market forward rates), that explicit feedback is absent.
- Policy response trade-offs:
  - When actual inflation differs from the long-run target, policy must choose a response reflecting preferences over the short-run output–inflation trade-off (e.g., asymptotic return to target or planned overshoot).
- Operational example (world oil price shock):
  - Projection Team (PT) assesses external ramifications, simulates domestic impacts, and produces baseline forecast with a model-standard policy response that returns inflation to its long-run target over the medium term while weighing inflation deviations and output-gap costs.
  - Alternative policy responses and scenario forecasts generate full time profiles of short-term interest rates for policymakers.

### Box 2 — Capturing India-specific characteristics in Production‑QPM: model design and calibrations
- Modeling focus and frictions:
  - Weak/slow monetary transmission (interest-rate and exchange-rate channels).
  - Large share of food in CPI and multiple supply shocks to food.
  - Limited historical nominal-anchor/credibility track record (pre-2014) modeled via a time-varying perceived long-run inflation target.
- Monetary transmission and bank-lending channel (empirical features and model treatments):
  - Transmission from policy rates to money markets: “more or less complete.”
  - Transmission from money market rates to lending rates: “sluggish.”
  - Persistence of long-term market interest rates calibrated to reflect slow-moving lending rates.
  - Bank Lending Tightening (BLT) variable included to capture credit-market conditions.
  - Modified risk-adjusted UIP reduces exchange-rate sensitivity to domestic-foreign interest-rate differentials.
  - Weaker transmission implies policy-rate paths need more aggressive adjustment and policies to strengthen transmission are necessary for long-run effectiveness.

- Lending-rate / term-structure calibration:
  - 휌푖푚 = 0.5; 휌푖푅퐼푆퐾 = 0.5; 푖푡 푅퐼푆퐾,푠푠 = 0
  - Term structure: 4-quarter-ahead average of short-term policy rates.
  - Term premium steady-state value set to 0.

- BLT (credit channel) specification and calibration:
  - Deviation equation: 퐵퐿푇푡 − 퐵퐿푇̅푡 = −휅1 · 푦̂푡+4푛푎푔 + 휀푡퐵퐿푇 with 휅1 = 5.0
  - Distributed-lag BLT effects on output:
    - 휂푡퐵퐿푇 = 휃(0.04휀푡−1퐵퐿푇 + 0.08휀푡−2퐵퐿푇 + 0.12휀푡−3퐵퐿푇 + 0.16휀푡−4퐵퐿푇 + 0.20휀푡−5퐵퐿푇 + 0.16휀푡−6퐵퐿푇 + 0.12휀푡−7퐵퐿푇 + 0.08휀푡−8퐵퐿푇 + 0.04휀푡−9퐵퐿푇)
    - Peak weight at 5-quarter lag; 휃 = 1.1

- IS equation (non-agricultural output gap) — calibrated hybrid specification:
  - 푦̂푡푛푎푔 = 훼1·Et(푦̂푡+1푛푎푔) + 훼2·푦̂푡−1푛푎푔 − 훼3·푟̂푡𝑚 + 훼4·푦̂푡𝑓 + 훼5·푧̂푡 − 휂푡𝐵𝐿𝐓 + ε푡푦̂푛푎푔
  - Calibrated coefficients: 훼1 = 0.07; 훼2 = 0.60; 훼3 = 0.08; 훼4 = 0.04; 훼5 = 0.05
  - Rationale: high weight on lagged output (0.60); small lead coefficient (0.07); real lending rate gap coefficient (0.08) within Indian empirical ranges (0.03–0.16).

- Phillips curve for core inflation — specification and calibration:
  - Hybrid NKPC with forward- and backward-looking elements.
  - Core inflation equation includes forward-looking Etℎ(휋4푡+1𝑐표푟푒), lagged inflation, output gap, and pass-through terms from headline, energy, and food.
  - Calibrated coefficients: 훽1 = 0.33; 훽2 = 0.10; 훽3 = 0.05; 훽4 = 0.05; 훽5 = 0.01; 훽6 = 0.02
  - Interpretation: lagged core-inflation persistence is high (empirical range 0.5–0.8); low output-gap coefficient (0.10); pass-through from food and fuel collectively ~10 percent.

- Inflation expectations and endogenous credibility:
  - Expectations formation: Etℎ(휋4푡+1𝑐표푟푒) = (1 − c푡)·휋4푡−1𝑐표푟푒 + c푡·휋4푡+1𝑐표푟푒 + η푡𝐸(휋4𝑐표푟푒)
  - η푡𝐸 follows AR with ρηE(휋4𝑐표푟푒) = 0.4
  - Credibility stock: c푡 = ρc·c푡−1 + (1 − ρc)·ξ푡 with ρc = 0.95
  - Credibility signal ξ푡 constructed from forecasting errors under “good” and “bad” regimes:
    - ρ휖 = 0.5; 휋푏푎푑 = 8.0; 휋푔표표푑 = 4.0
    - Boundary rules: ξ푡 = 0 if 휖푡푏푎푑 > 0 and ξ푡 = 1 if 휖푡푔표표푑 < 0
  - Historical decomposition uses low credibility value c = 0.25 for pre-FIT period; forecasts use endogenous credibility.

- Food inflation block — structure and calibrations:
  - Food inflation equation includes lagged food inflation, deviation between headline and food, future relative food-core prices, and short-run shocks.
  - Calibrated: 휑1 = 0.1; 휑2 = 1.0
  - Short-run shocks:
    - Monsoon shocks (ε푡몬ᴀ): longer-lived (~1 year), peak in harvest quarter.
    - MSP shocks (ε푡MSP): more long-lasting; alter relative food-price trends.
    - Vegetable shocks (ε푡veg): transitory, large, rapid reversal (e.g., onion spikes).
  - Equilibrium relative food-price dynamics: 푟𝑝̅푡𝑓표표𝑑 AR coefficient ρη푟𝑝̅𝑓 = 0.9; θ = 0.3

- Energy price dynamics — market and administered components:
  - Market fuel (deregulated petrol/diesel): 훽1em = 0.5; 훽2em = 0.9; pass-through assumed within 2 quarters.
  - Administered fuel (judgmental): 훽1ea = 0.1 (slow adjustment to core inflation).
  - Real price of energy trend: ρ푟𝑝̅푒𝑚 = 0.85

- Monetary policy rule — inflation‑forecast‑based reaction function and calibration:
  - Rule: 푖푡 = 휆1·푖푡−1 + (1 − 휆1){푟̅푡 + 휋4푡∗ + 휆2[Et(휋4푡+3𝑐표푟푒) − 휋4푡∗] + 휆3[Et(휋4푡+3ℎ𝑒𝑎𝑑𝑙𝑖𝑛𝑒) − 휋4푡∗] + 휆4·푦̂푡} + ε푡𝑖
  - Calibrated parameters: 휆1 = 0.85; 휆2 = 2.5; 휆3 = 0.5; 휆4 = 0.5
  - Notes: higher weight on core inflation (2.5); three-quarter-ahead forecast used; perceived inflation target follows unit-root 휋4푡∗ = 휋4푡−1∗ + ε휋4∗ (allowing drift).

- Modified risk-adjusted UIP (exchange-rate equation) and calibration:
  - Expectations modeled as a mix of forward-looking and past/Purchasing-Power-Parity elements.
  - Calibrated coefficients: γ1 = 0.7; δ1 = 0.6
  - Purpose: reduce exchange-rate sensitivity to interest-rate differentials reflecting low pass-through and rigidities.

- Calibrated parameter summary (selected key values):
  - IS: 훼1 = 0.07; 훼2 = 0.60; 훼3 = 0.08; 훼4 = 0.04; 훼5 = 0.05
  - BLT: 휅1 = 5.0; 휃 = 1.1
  - Phillips Curve: 훽1 = 0.33; 훽2 = 0.10; 훽3 = 0.05; 훽4 = 0.05; 훽5 = 0.01; 훽6 = 0.02
  - Credibility stock: ρc = 0.95; ρ휖 = 0.5; 휋푏푎푑 = 8.0; 휋푔표표푑 = 4.0
  - Food: 휑1 = 0.1; 휑2 = 1.0
  - Market fuel: 훽1em = 0.5; 훽2em = 0.9
  - Administered fuel: 훽1ea = 0.1
  - Monetary policy: 휆1 = 0.85; 휆2 = 2.5; 휆3 = 0.5; 휆4 = 0.5
  - Modified UIP: γ1 = 0.7; δ1 = 0.6

### Selected model properties and impulse-response scenarios (principal findings)
- (1) Inflation-target shock: 1 Percentage Point increase in the inflation target
  - Passive policy response with imperfect credibility → short-run real rate decline larger than nominal; real depreciation larger than nominal; positive non-agriculture cumulative output gap until return to equilibrium is 2 percent → implied sacrifice ratio “approximately 2.”
  - Long run: nominal interest rate rises by amount equal to increased long-run inflation; real variables return to original long-run values.
- (2) Policy-rate shock: 0.5 Percentage Point increase in policy rate (active IT, stable expectations)
  - Short run: negative output gap, appreciation of nominal and real exchange rate, core and headline inflation fall.
  - Medium run: policy unwound to return inflation to target; exchange rate cycles and returns to equilibrium.
- (3) Demand shock: 0.4 Percentage Point increase in output gap
  - Positive demand shock raises non-agriculture output gap and inflation; central bank raises real/nominal rate by more than inflation increase; currency appreciates; output and inflation return to potential/target over medium term.
- (4) Cost-push shock: 1 Percentage Point increase in core inflation
  - Central bank raises interest rate to return inflation to target, generating negative output gap; nominal and real exchange rates appreciate; output gap closes as inflation returns to target.
- (5) Monsoon disappointment: 2 Percentage Point increase in food inflation due to monsoon
  - Anticipated rise in inflation expectations; policymakers raise interest rates to stabilize expectations, opening negative output gap; food-price cycle with spike then drop as rains normalize.
- (6) MSP shock: 1 Percentage Point increase in food inflation due to MSP
  - MSP increases have longer-lasting impacts on food inflation and relative food prices; policy rate must rise to anchor expectations, opening negative output gap and appreciating exchange rate.
- (7) Transitory food shock (vegetable prices): 4 Percentage Point increase in food inflation due to vegetable-price shock
  - Sharp but short-lived increase; self-correcting market and administrative responses imply negligible need for monetary policy response (small macro movements).

- Simulation, calibration, and solution notes:
  - Calibration grounded in Indian empirical literature and historical behavior; validated via simulation and historical decomposition.
  - Implemented in IRIS toolbox in Matlab; linearized around steady state; first-order approximate solution; steady states computed via nonlinear Newton-type algorithm; generalized Schur decomposition used to integrate out expectations.

### Phase 3 (2014–present) — Flexible inflation targeting and implications
- Central bank adopted a regime of flexible inflation targeting.
- The policy rate has followed the inflation‑forecast‑based reaction function closely—i.e., no large interest-rate shocks.
- Inflation dropped faster than expected because of falling commodity prices, especially crude oil.
- Going forward, the new regime should provide a firmer anchor for inflation expectations.
- Given the large weight of food in the CPI basket and the high volatility of food prices, food-price shocks will continue to have a large impact on the rate of inflation.
- Simulations (5), (6) and (7) illustrate the persistent influence of food-price shocks on inflation dynamics.

### Data, variable definitions, and historical decompositions (key points)
- Headline CPI: MoSPI, GoI; latest data based on 2012=100, available from Jan-2013; All India CPI available from 2011; Jan-2011 to Dec-2012 spliced with old base; pre-2011 back-cast using CPI-Industrial workers.
- Food CPI, Fuel CPI, CPI excl Food and Fuel: MoSPI, GoI (same construction notes as Headline CPI).
- Fuel CPI Market (non-admn) and Administered (admn): constructed series based on Petrol and Diesel price indices; New Synthetic Series: weighted average of administered and non-administered fuel.
- Real GDP at Factor Cost (and non‑agricultural/agricultural splits): MoSPI, GoI; base-2004-05 =100 up to 2014Q3; for 2014Q4, 2015Q1 and Q2, y‑o‑y quarterly growth rates of new series (base 2011‑12 =100) applied to old series.
- Policy Rate and Rupee/USD Exchange Rate: RBI Quarterly Average.
- Indian Basket Crude Price in USD: Ministry of Petroleum and Natural Gas, GoI; compositions by year provided for 2005‑06 through 2014‑15.
- Variable decompositions (authors’ findings):
  - Output gap: opened sharply during crisis, narrowed and became positive with accommodative policy; credit conditions benign then tightened causing negative output gap; post-2014 policy accommodative helping output gap move closer to zero; large positive shocks to aggregate demand during 2007–12 partly due to non-monetary measures (MGNREGA, fiscal stimulus).
  - Food inflation: driven by relative food-price trend and shocks (MSP increases in 2008‑09 and 2012; deficient monsoon in 2009; repeated transitory onion-price spikes).

### Model framework, use cases, and policy relevance
- Framework based on FPAS to generate forecasts, risk assessment, and policy analysis in a FIT regime.
- Satellite models (DSGE or traditional econometrics) may complement FPAS for parameterization, forecast assumptions, and disaggregated sectoral dynamics.
- QPM incorporates:
  - Importance of agriculture and food prices in inflation.
  - India-specific monetary policy transmission.
  - Building policy credibility and nonlinearity.
- Model simulations illustrate central bank responses to demand and supply shocks to return inflation to the announced target over the medium term.
- The paper provides historical decompositions attributing causal contributions to key macroeconomic variables.

*Source: Authors’ calculations; Box 1 and Box 2, wp1733.*

### Box 1. Monetary Policy Feedback ........................................................................................

### Box 1. Monetary Policy Feedback

### Role of credibility and IFT mechanics
- The credibility of the long-run inflation target underpins IFT and requires that policy respond systematically to achieve the objective (references in source: Laxton and N’Diaye, 2002; Goretti and Laxton, 2005; Levin, Natalucci, and Piger, 2004; Gurkaynak and others, 2007; Gurkaynak, Levin, and Swanson, 2010).
- The nominal anchor is maintained by ensuring that over time the rate of inflation and inflation expectations converge to the target via an endogenous, forward-looking policy interest rate.

### Dynamic feedback structure (as depicted in Box Figure 1)
- Policy feedback is represented by red dashed arrows linking expected future inflation to the endogenous short-term interest rate; this ensures the nominal anchor holds.
- Expectations about future policy rates influence longer-term interest rates and the exchange rate (blue hollow arrows pointing to “Longer Term Interest Rates” and “Exchange Rate”).
- The transmission operates through the entire expected Policy Rate Path—the medium-term path—not just the current policy rate setting.

### Contrast: endogenous forward-looking policy vs exogenous interest-rate path
- Under an endogenous, forward-looking policy, expected future inflation feeds back to the policy instrument (red dashed arrows present).
- If the model is modified to represent an exogenous interest rate path (including one derived from market forward rates), there is no explicit feedback from expected future inflation to the policy instrument; in the flowchart the red dashed feedback arrows would be erased.

### Policy response choices and trade-offs
- When actual inflation differs from the long-run target, monetary policy must choose an appropriate response; the speed and form of the response reflect policymakers’ preferences over the short-run output–inflation trade-off.
- Possible approaches include an asymptotic return to target or a planned overshoot; the central bank will typically select the approach that reflects its judgment as to the best outcome.

### Operational example: world oil price shock
- Following a sudden drop in the world price of oil:
  - The Projection Team (PT) assesses ramifications on external variables (e.g., demand in trading partners).
  - Using the model, the PT simulates the impact on the domestic economy.
  - The baseline forecast, using the model’s standard policy response, implies an interest rate path that returns inflation to its long-run target over the medium term while accounting for the trade-off between inflation deviations and output gap costs.
  - Alternative policy responses and scenario forecasts (e.g., differing assumptions on the oil price) may be simulated to provide policymakers with a menu of options.
  - Each simulated response produces a full time profile of short-term interest rates.

*Source: Box 1. Monetary Policy Feedback, from the provided IMF content.*

### Box 2. Capturing India-Specific Characteristics in Production-QPM

### Box 2. Capturing India-Specific Characteristics in Production-QPM

### Overview and modeling focus
- The Production-QPM incorporates India-specific frictions to reflect:
  - Weak/slow monetary transmission (interest-rate and exchange-rate channels).
  - Large share of food in CPI and multiple supply shocks to food.
  - A limited historical nominal-anchor/credibility track record (pre-2014), modeled via a time-varying perceived long-run inflation target.

### Monetary transmission and bank-lending channel
- Empirical features:
  - Transmission from policy rates to money markets: “more or less complete.”
  - Transmission from money market rates to lending rates: “sluggish.”
- Model treatments and implications:
  - Persistence of long-term market interest rates is calibrated to reflect slow-moving lending rates.
  - Bank Lending Tightening (BLT) variable included to capture credit-market conditions and their effect on output.
  - Modified risk-adjusted UIP reduces exchange-rate sensitivity to domestic-foreign interest-rate differentials, moderating the exchange-rate channel.
  - Weakened transmission implies policy-rate paths need more aggressive adjustment and policies to strengthen transmission are necessary for long-run effectiveness.

- Long-run market/lending rate relations and calibration:
  - Lending rate equation parameters:
    - 휌푖푚 = 0.5
    - 휌푖푅퐼푆퐾 = 0.5
    - 푖푡 푅퐼푆퐾,푠푠 = 0
  - Term structure: 4-quarter-ahead average of short-term policy rates.
  - Term premium steady-state value set to 0.

### Bank-Lending-Tightening (BLT) condition (credit channel)
- BLT deviation from equilibrium:
  - 퐵퐿푇푡 − 퐵퐿푇̅푡 = −휅1 · 푦̂푡+4푛푎푔 + 휀푡퐵퐿푇
  - Calibration: 휅1 = 5.0
- BLT effects on output via distributed lag of past BLT shocks:
  - 휂푡퐵퐿푇 = 휃(0.04휀푡−1퐵퐿푇 + 0.08휀푡−2퐵퐿푇 + 0.12휀푡−3퐵퐿푇 + 0.16휀푡−4퐵퐿푇 + 0.20휀푡−5퐵퐿푇 + 0.16휀푡−6퐵퐿푇 + 0.12휀푡−7퐵퐿푇 + 0.08휀푡−8퐵퐿푇 + 0.04휀푡−9퐵퐿푇)
  - Peak weight at 5-quarter lag; 휃 = 1.1

### IS equation (non-agricultural output gap) — calibration
- Forward-looking hybrid IS specification (non-agricultural output gap 푦̂푡푛푎푔):
  - 푦̂푡푛푎푔 = 훼1·Et(푦̂푡+1푛푎푔) + 훼2·푦̂푡−1푛푎푔 − 훼3·푟̂푡𝑚 + 훼4·푦̂푡𝑓 + 훼5·푧̂푡 − 휂푡𝐵𝐿𝐓 + ε푡푦̂푛푎푔
- Calibrated coefficients:
  - 훼1 = 0.07
  - 훼2 = 0.60
  - 훼3 = 0.08
  - 훼4 = 0.04
  - 훼5 = 0.05
- Rationale:
  - High weight on lagged output (0.60) consistent with Indian estimates and FPAS-like calibrations.
  - Small lead coefficient (0.07) reflects need for confidence to promote activity.
  - Real lending rate gap coefficient (0.08) lies within Indian empirical ranges (Patra and Kapur, 0.03–0.16).

### Phillips curve for core inflation — specification and calibration
- Core inflation equation (annualized quarterly changes in seasonally-adjusted log of core CPI):
  - 휋푡𝑐표푟푒 = 훽1·Etℎ(휋4푡+1𝑐표푟푒) + (1 − 훽1)·휋푡−1𝑐표푟푒 + 훽2(푦̂푡 + 훽3푧̂푡) + 훽4(휋4푡ℎ𝑒𝑎𝑑𝑙𝑖𝑛𝑒 − 휋4푡𝑐표푟푒) + 훽5(푝푡𝑒𝑛𝑒𝑟𝑔𝑦,𝑚𝑘𝑡 − 푝푡𝑐표푟푒 − 푟𝑝̅푡𝑒𝑛𝑒𝑟𝑔𝑦,𝑚𝑘𝑡) + 훽6(푝푡+4𝑓𝑜𝑜𝑑 − 푝푡+4𝑐표푟푒 − 𝑟𝑝̅푡+4𝑓𝑜𝑜𝑑) + ε푡휋𝑐표푟푒
- Calibrated coefficients:
  - 훽1 = 0.33
  - 훽2 = 0.10
  - 훽3 = 0.05
  - 훽4 = 0.05
  - 훽5 = 0.01
  - 훽6 = 0.02
- Interpretation:
  - Hybrid NKPC with both forward- and backward-looking elements; lagged core inflation persistence is high (empirical range 0.5–0.8).
  - Low output-gap coefficient (0.10) reflects Indian empirical estimates.
  - Pass-through from food and fuel captured via 훽4, 훽5, 훽6, collectively reflecting a pass-through of around 10 percent in line with alternate estimates.

### Inflation expectations and endogenous credibility
- Inflation expectations formation:
  - Etℎ(휋4푡+1𝑐표푟푒) = (1 − c푡)·휋4푡−1𝑐표푟푒 + c푡·휋4푡+1𝑐표푟푒 + η푡𝐸(휋4𝑐표푟푒)
  - η푡𝐸 evolves as AR with ρηE(휋4𝑐표푟푒) = 0.4
- Credibility stock (c푡) dynamics:
  - c푡 = ρc·c푡−1 + (1 − ρc)·ξ푡
  - ρc = 0.95
- Credibility signal ξ푡 constructed from forecasting errors under “good” and “bad” regimes:
  - ρ휖 = 0.5; 휋푏푎푑 = 8.0; 휋푔표표푑 = 4.0
  - Boundary rules: set ξ푡 = 0 if 휖푡푏푎푑 > 0 and ξ푡 = 1 if 휖푡푔표표푑 < 0
- Historical and forecasting practice:
  - Historical decomposition uses low credibility value c = 0.25 to capture pre-FIT absence of nominal anchor.
  - Forecasts use an endogenous credibility specification capturing interaction among announced target, outcomes, and expectations.

### Food inflation block — structure and calibrated values
- Food inflation equation:
  - 휋푡𝑓표표𝑑 = 휋푡−1𝑓표표𝑑 + 휑1(휋4푡ℎ𝑒𝑎𝑑𝑙𝑖𝑛𝑒 − 휋4푡𝑓표표𝑑) − 휑2(푝푡+4𝑓표표𝑑 − 푝푡+4𝑐표푟푒 − 𝑟𝑝̅푡+4𝑓표표𝑑) + Γ몬ᴀ(L)ε푡몬ᴀ + ΓMSP(L)ε푡MSP + Γveg(L)ε푡veg + ε푡휋𝑓표표𝑑
- Calibrated coefficients:
  - 휑1 = 0.1
  - 휑2 = 1.0
- Short-run shocks to food inflation:
  - Monsoon shocks (ε푡몬ᴀ): longer-lived effects (~1 year), price pressures build up and peak in harvest quarter; partial moderation afterwards.
  - MSP shocks (ε푡MSP): more long-lasting, can alter relative food-price trends and equilibrium relative prices.
  - Vegetable shocks (ε푡veg, e.g., onions): transitory, large, rapid reversal; sharp rise followed by quick undershoot.
- Equilibrium relative food price dynamics:
  - 푟𝑝̅푡𝑓표표𝑑 = 푟𝑝̅푡−1𝑓표표𝑑 + η푡𝑟𝑝̅𝑓 + θ·ε푡MSP + ε1,푡𝑟𝑝̅𝑓
  - η푡𝑟𝑝̅𝑓 follows AR with ρη푟𝑝̅𝑓 = 0.9
  - θ = 0.3

### Energy price dynamics — market and administered components
- Market fuel inflation (deregulated petrol/diesel):
  - 휋푡𝑒𝑛𝑒𝑟𝑔𝑦,𝑚𝑘𝑡 = 훽1em·휋푡−1𝑒𝑚 + (1 − 훽1em)·4(∆St + ∆p푡표푖𝑙 − ∆Z̅𝑡) − 훽2em·ε푡−1휋𝑒𝑚 + ε푡휋𝑒𝑚
  - 훽1em = 0.5; 훽2em = 0.9
  - Pass-through assumed to occur within 2 quarters; 훽1em = 0.5
- Administered fuel inflation (exogenous/judgmental):
  - 휋푡𝑒𝑛𝑒𝑟𝑔𝑦,𝑎𝑑𝑚 = 휋푡−1𝑎𝑑𝑚 + 훽1ea·(휋푡−1𝑐표푟푒 − 휋푡−1𝑒𝑛𝑒𝑟𝑔𝑦,𝑎𝑑𝑚) + ε푡휋𝑒𝑎
  - 훽1ea = 0.1 (slow adjustment to core inflation)
- Real price of energy trend:
  - 푟𝑝̅푡𝑒𝑚 = ρ푟𝑝̅𝑒𝑚 · 푟𝑝̅푡−1𝑒𝑚 + (1 − ρ푟𝑝̅𝑒𝑚)·(푝푡+4𝑒𝑚 − 푝푡+4𝑐표푟푒)
  - ρ푟𝑝̅𝑒𝑚 = 0.85

### Monetary policy rule — inflation-forecast-based reaction function and calibration
- Policy rule:
  - 푖푡 = 휆1·푖푡−1 + (1 − 휆1){푟̅푡 + 휋4푡∗ + 휆2[Et(휋4푡+3𝑐표푟푒) − 휋4푡∗] + 휆3[Et(휋4푡+3ℎ𝑒𝑎𝑑𝑙𝑖𝑛𝑒) − 휋4푡∗] + 휆4·푦̂푡} + ε푡𝑖
- Calibrated reaction-function parameters:
  - 휆1 = 0.85 (interest-rate smoothing)
  - 휆2 = 2.5 (weight on core inflation forecast)
  - 휆3 = 0.5 (weight on headline inflation forecast)
  - 휆4 = 0.5 (weight on output gap)
- Notes:
  - Higher weight on core inflation (2.5) than some historical Indian estimates to account for hybrid Phillips-curve features and the need for active policy when inflation process is backward-looking.
  - Three-quarter-ahead forecast used to combine current data and model projections.
- Perceived inflation target dynamics:
  - 휋4푡∗ = 휋4푡−1∗ + ε휋4∗ (unit-root specification allowing drift; model calibration allows upward drift 2009–14 to capture perceived target drift).

### Modified risk-adjusted UIP (exchange rate equation)
- Exchange rate and expectations:
  - γ1[푖푡 − (푖푡𝑓 + σ푡)] + (1 − γ1)[4∆Z̅푡−1 + (휋4푡−1𝑐표푟푒 − 휋4푡−1𝑓)] = 4(EtSt+1 − St) + ε푡𝑆
  - EtSt+1 = δ1·S t+1 + (1 − δ1){St−1 + 2/4[∆Z̅t + (휋4푡∗ − 휋4𝑓)]}
- Calibrated coefficients:
  - γ1 = 0.7
  - δ1 = 0.6
- Purpose:
  - Reduce sensitivity of exchange rate to interest-rate differentials reflecting low pass-through and rigidities in India.
  - Expectations on future exchange rates modeled as mix of forward-looking and past/purchasing-power-parity elements.

### Calibrated parameter summary (selected key values from Table 1)
- IS Equation: 훼1 = 0.07; 훼2 = 0.60; 훼3 = 0.08; 훼4 = 0.04; 훼5 = 0.05
- BLT: 휅1 = 5.0; 휃 = 1.1
- Phillips Curve: 훽1 = 0.33; 훽2 = 0.10; 훽3 = 0.05; 훽4 = 0.05; 훽5 = 0.01; 훽6 = 0.02
- Credibility stock: ρc = 0.95; ρ휖 = 0.5; 휋푏푎푑 = 8.0; 휋푔표표푑 = 4.0
- Food: 휑1 = 0.1; 휑2 = 1.0
- Market fuel: 훽1em = 0.5; 훽2em = 0.9
- Administered fuel: 훽1ea = 0.1
- Monetary policy: 휆1 = 0.85; 휆2 = 2.5; 휆3 = 0.5; 휆4 = 0.5
- Modified UIP: γ1 = 0.7; δ1 = 0.6

### Model properties and impulse-response scenarios (selected findings)
- (1) Inflation-target shock: 1 Percentage Point increase in the inflation target
  - Passive policy response with imperfect credibility → short-run real rate decline larger than nominal; real depreciation larger than nominal; positive non-agriculture cumulative output gap until return to equilibrium is 2 percent → implied sacrifice ratio “approximately 2.”
  - Long-run: nominal interest rate rises by amount equal to increased long-run inflation; real variables return to original long-run values.
- (2) Policy-rate shock: 0.5 Percentage Point increase in policy rate (active IT, stable expectations)
  - Short-run: negative output gap, appreciation of nominal and real exchange rate, core and headline inflation fall.
  - Medium run: policy unwound to return inflation to target; exchange rate cycles and returns to equilibrium.
- (3) Demand shock: 0.4 Percentage Point increase in output gap
  - Positive demand shock raises non-agriculture output gap and inflation; central bank raises real/nominal rate by more than inflation increase; currency appreciates; output and inflation return to potential/target over medium term.
- (4) Cost-push shock: 1 Percentage Point increase in core inflation
  - Trade-off: central bank must raise interest rate to return inflation to target, generating negative output gap; nominal and real exchange rates appreciate; output gap closes as inflation returns to target.
- (5) Monsoon disappointment: 2 Percentage Point increase in food inflation due to monsoon
  - Anticipated rise in inflation expectations; policymakers raise interest rates to stabilize expectations, opening negative output gap; food-price cycle with spike then drop as rains normalize.
- (6) MSP shock: 1 Percentage Point increase in food inflation due to MSP
  - MSP increases have longer-lasting impacts on food inflation and relative food prices; policy rate must rise to anchor expectations, opening negative output gap and appreciating exchange rate.
- (7) Transitory food shock (vegetable prices): 4 Percentage Point increase in food inflation due to vegetable-price shock
  - Sharp but short-lived increase; self-correcting market and administrative responses imply negligible need for monetary policy response (small macro movements).

### Simulation, calibration, and estimation notes
- Calibration grounded in Indian empirical literature and historical behavior; combined parameter effects are validated via simulation and historical decomposition.
- Model solution and simulation methods:
  - Implemented in IRIS toolbox in Matlab.
  - Linearized around steady state; first-order approximate solution; steady states computed via nonlinear Newton-type algorithm; generalized Schur decomposition used to integrate out expectations.

*Source: Authors’ calculations, Box 2. Capturing India-Specific Characteristics in Production-QPM (wp1733).*

### 2. As inflation rose, in the absence of a well-defined nominal anchor, the implicit policy

### 2. As inflation rose, in the absence of a well-defined nominal anchor, the implicit policy objective of the central bank for inflation, as perceived by the public rose with it.

### Phase 3: 2014-present — Flexible inflation targeting and implications
- The central bank adopted a regime of flexible inflation targeting.
- The policy rate has followed the inflation-forecast-based reaction function quite closely—i.e., there have been no large interest rate shocks.
- Inflation did drop faster than expected because of falling commodity prices, especially crude oil.
- Going forward, the new regime should provide a firmer anchor for inflation expectations.
- Given the large weight of food in the CPI basket, and the high volatility of food prices, food price shocks will continue to have large impact on the rate of inflation.
- Simulations (5), (6) and (7) illustrate the persistent influence of food price shocks on inflation dynamics.

### Data and variable definitions (Table 2)
- Headline CPI: MoSPI, GoI. The latest data is based on 2012=100, available from Jan-2013. All India CPI is only available from 2011. Data for Jan-2011 to Dec-2012 has been obtained by splicing with the old base. Before 2011 the series has been back casted using CPI-Industrial workers.
- Food CPI: MoSPI, GoI. CPI (Food and beverages): Explanation as above.
- Fuel CPI: MoSPI, GoI. CPI (Fuel and Light): Explanation as above.
- CPI excl Food and Fuel: MoSPI, GoI. CPI (Ex Food and Fuel): Explanation as above.
- Fuel CPI Market (non-admn): MoSPI, GoI. Constructed series based on Petrol and Diesel price indices in the ‘Transport and communication’ sub group in the CPI (Ex Food and Fuel). The other explanations are the same.
- Fuel CPI Excl-Market (admn): MoSPI, GoI. Same as CPI (Fuel and Light). The other explanations are the same.
- Fuel CPI New Synthetic Series: MoSPI, GoI. Weighted average of administered and non-administered fuel. The other explanations are the same.
- CPI ex Food and Fuel New Synthetic Series: MoSPI, GoI. CPI (Ex Food and Fuel) after removing Petrol and Diesel indices.
- Real GDP at Factor Cost: MoSPI, GoI. National Accounts data (base-2004-05 =100) up to 2014Q3. For 2014Q4, 2015Q1 and Q2, y-o-y quarterly growth rates of new series (base 2011-12 =100) have been applied on the old series).
- Non Agricultural Real GDP at Factor Cost: MoSPI, GoI. National Accounts data (base-2004-05 =100) up to 2014Q3. For 2014Q4, 2015Q1 and Q2, y-o-y quarterly growth rates of new series (base 2011-12 =100) have been applied on the old series).
- Agricultural Real GDP at Factor Cost: MoSPI, GoI. National Accounts data (base-2004-05 =100) up to 2014Q3. For 2014Q4, 2015Q1 and Q2, y-o-y quarterly growth rates of new series (base 2011-12 =100) have been applied on the old series).
- Policy Rate: RBI Quarterly Average.
- Rupee/USD Exchange Rate: RBI Quarterly Average.
- Indian Basket Crude Price in USD: Ministry of Petroleum and Natural Gas, GoI. The composition of Indian Basket of Crude represents Average of Oman & Dubai for sour grades and Brent (Dated) for sweet grade in the ratio of 72.04:27.96 for 2014-15; 69.9:30.1 for 2013-14; 68.2:31.8 for 2012-13; 65.2:34.8 for 2011-12, 67.6:32.4 for 2010-11, 63.5:36.5 for 2009-10, 62.3:37.7 for 2008-09 ,61.4:38.6 for 2007-08, 59.8:40.2 for the year 2006-07 and 58:42 for the year 2005-06. (The historical data are as available from the source)
- Note: MoSPI stands for Ministry of Statistics and Program Implementation. GoI stands for Government of India.
- Source: RBI.

### Variable decomposition — Output gap
- The output gap opened up sharply during the crisis period and narrowed quickly and became positive, supported by an accommodative monetary policy stance.
- Credit conditions then remained somewhat benign, even though an overvalued Rupee continued to hurt demand.
- Subsequently, credit conditions became tight on account of strict credit standards set out by banks leading to negative output gap.
- Post-2014 policy rate became accommodative helping output gap to move closer to zero.
- Large positive shocks to aggregate demand during 2007-12 could be attributed to non-monetary measures like MGNREGA and other post-crisis fiscal stimulus which provided a boost to aggregate demand during those periods.
- Figure 12: Historical Variable Decomposition for the Output Gap (Authors’ calculations).

### Variable decomposition — Food inflation
- Food inflation dynamics are characterized by the relative food price trend and various shocks affecting food prices.
- Positive slope in the relative food price trend contributed to food inflation during 2004-08.
- Large MSP increases contributed to food inflation in 2008-09 and 2012.
- Deficient monsoon contributed to inflation in 2009.
- Large unexpected shocks in the form of onion price spikes affected food inflation many times but were transitory.
- Figure 13: Historical Variable Decomposition for Food Inflation (Authors’ calculations).

### Model framework, simulations, and key features
- The paper outlines a coherent framework based on the FPAS for generating forecasts and risk assessment as well as conducting policy analysis, useful to policymakers in a FIT regime.
- Models based on the DSGE methodology, or traditional econometrics, may be used as satellite models to complement the FPAS.
- Satellite models may be used in the parameterization of QPM, or to shape judgments about forecast assumptions, and to provide disaggregated sectoral dynamics and projections of key macro-variables considered in the QPM.
- QPM incorporates key features of the Indian economy:
  - Importance of the agricultural sector and food prices in the inflation process;
  - India-specific monetary policy transmission;
  - Building policy credibility and nonlinearity.
- Model simulations illustrate how the central bank might respond to demand and supply shocks to return inflation over the medium term to the announced target.
- The paper provides a decomposition of contributions of causal factors to the historical evolution of some key macroeconomic variables.

*Source: Authors’ calculations; RBI; MoSPI, GoI (as provided in the content unit).*

---


_Source: https://www.imf.org/-/media/files/publications/wp/wp1733.pdf_