## _wp1084

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---

### I. The Context
- Recovery from the global crisis is uneven; Asia is leading a rebound with India and China set to stage a V-shaped turnaround.
- The healing is expected to be "sluggish and hesitant, jobless and credit constrained" in initial stages.
- Major concern: inflation risks are rising, especially in developing countries; monetary policy may need to be tightened sooner than later.
- Inflation developments pose a dilemma: headline inflation appears low in many places while abundant liquidity raises fears of future inflation. Psychology matters: "Expectations shape how economic agents behave. If they fear inflation, they act in ways that bring it about."
- India-specific developments:
  - WPI inflation rose from around 1 percent in October 2009 to 9.9 percent in February 2010.
  - CPI inflation has been running in double digits on the back of high food prices for more than a year.
  - The index of food articles increased 17.8 percent in February 2010 from a year earlier.
  - The index of primary articles prices, with a 22.03 percent weight in the wholesale price basket and comprising mainly of food items, rose 15.5 percent.
- Abundant liquidity linked to policy responses after September 2008; trade-off for policy:
  - Growth concerns argue for a delayed exit from accommodation.
  - Inflation concerns argue for an earlier exit.
  - Growth had accelerated to close to 8 percent in the third quarter of 2009 while consensus expected inflation to rise from current lows to a similar level in early 2010.

### Recent inflation dynamics and drivers (India)
- WPI and CPI movements:
  - WPI inflation: plummeted from 12.9 per cent in August 2008 to 0.8 per cent by end-March 2009; slipped into negative territory for 13 consecutive weeks beginning in June 2009; turned positive again since early September 2009.
  - CPI inflation: increased since June 2008, mainly due to food, fuel and services; reached a range of 16.2 – 17.6 per cent during January 2010.
- Notable item changes:
  - Vegetable prices: increase close to 20 percent year-on-year on February 6, 2010.
  - Pulses: increase of the order of 32 percent on March 13, 2010.
- Supply-side and administered price effects:
  - Upward revision of administered prices of petrol and diesel effective July 2, 2009.
  - Higher administered minimum support prices (MSP) for most agricultural crops contributed to food inflation.
  - Policy supply-side responses included open market sale of wheat from buffer stocks; removal of stock holding limits; restrictions on large sugar consumers; increased releases through public distribution system; removal of import duty on rice, wheat and raw sugar; duty-free import of white/refined sugar by Government agencies and private traders.

### Inflation outlook and commodity prices (global/region)
- "6.2 percent this year." China, a few ASEAN economies and most emerging European economies are likely to experience inflation of less than 5 per cent.
- Commodity price developments:
  - International crude oil prices gradually rose since March 2009; crude oil prices crossed US $ 80 per barrel on October 21, 2009 and remain elevated.
  - Prices of foodgrains (rice, wheat, maize) have been edging up but remain substantially below levels of the first half of 2008.
  - Metal prices have rebounded since April 2009, led by copper, lead and nickel, mainly in response to increased demand from China.
- Risk assessment: Inflation risks have been growing and could threaten currently projected benign conditions.

### Tracking inflation expectations: data and surveys (India)
- No public-domain standard measures of inflation expectations in India.
- RBI household survey (since September 2005): quarterly, internal monitoring, covering 4,000 households using quota sampling across 12 cities; elicits qualitative responses for next three months and next one year, and quantitative current, three-month-ahead and one-year-ahead inflation rates.
- RBI survey of professional forecasters covers domestic forecasters (investment banks, commercial banks, stock exchanges, international brokerage houses, select educational institutions, credit rating agencies, securities firms, asset management companies).
- Break-even inflation from inflation-indexed bonds/swaps is not available in India; only one issuance of capital-indexed bonds met with listless market appetite.
- Survey quality observations:
  - Confidence intervals from RBI household survey narrow (~20 to 30 basis points) for short horizons but widen with horizon.
  - TACS recommended public release of household survey results to improve monetary policy transparency (RBI, September 2009), but longer time series needed for robust analysis.

### Methodological approach to measuring inflation expectations
- Two-stage pragmatic approach:
  1. Unbiased parsimonious modeling of actual inflation using monthly annualized WPI data April 1997–December 2008; generate expanding-window one-period-ahead forecasts as proxies for inflation expectations.
  2. Estimate determinants of those model-based expectations using a new-Keynesian-type Phillips curve (Hendry general-to-specific approach) and cross-check with consensus forecasts from financial entities reported to Consensus Economics.
- Time series modeling details:
  - Monthly inflation modeled in ARMA framework with seasonal AR and MA terms identified using X12 and diagnostics.
  - Best-fit ARMA specification indicated as ARMA(1,1) with seasonal AR and MA terms of order 12 to generate next-period (month) unbiased forecasts.
  - Recognized limitations: subjectivity in identification, not embedded in structural priors, potential poor performance predicting turning points; ARMA found robust for short-term forecasts.

### ARMA forecasting equation and model performance
- Forecasting equation:
  - πe = 0.006 + 0.91 πt-1 – 0.22 πt-12 + 0.20 πt-13 + εt + 0.32 εt-2 – 0.85 εt-12 – 0.27 εt-14
- Selected estimates and diagnostics:
  - C coefficient: 0.0509 (Std. Error 0.0025; t-Statistic 20.3436; Prob. 0.0000)
  - AR(1): 0.9100 (Std. Error 0.0429; t-Statistic 21.2210; Prob. 0.0000)
  - SAR(12): -0.2284 (Std. Error 0.1153; t-Statistic -1.9807; Prob. 0.0501)
  - MA(2): 0.3212 (Std. Error 0.1023; t-Statistic 3.1405; Prob. 0.0022)
  - SMA(12): -0.8406 (Std. Error 0.0310; t-Statistic -27.0923; Prob. 0.0000)
  - R-squared 0.9285; Adjusted R-squared 0.9260; S.E. of regression 0.0061; Log likelihood 429.3937; Durbin-Watson stat 1.2447
- Model performance (Table 2):
  - Root Mean Squared Error 0.005972
  - Mean Absolute Error 0.004394
  - Mean Abs. Percent Error 9.244995
  - Theil Inequality Coefficient 0.051917 (Bias Proportion 0.001089; Variance Proportion 0.009193; Covariance Proportion 0.989718)
- Comparison with consensus forecasts: Consensus Economics forecasts tend to average out fluctuations and trace a middle path through actual turning points; consensus data suffer from inconsistent reporting samples and varying horizons.

### Determinants of inflation expectations: empirical findings
- Stationarity: ADF and PP tests indicate most variables are I(0) except changes in REER which are ambiguous.
- Robust determinants and their contributions (model-based and redundant-variable tests):
  - Lagged inflation (especially one-month and twelve-month lags):
    - Sum of coefficients on lagged inflation 0.4609; F-Stat 42.89; p-value 0.00 — indicates high inertia/persistence.
  - Primary articles' prices (food):
    - Sum of coefficients 0.2903; F-Stat 39.11; p-value 0.00 — a little under a third of expected inflation.
  - Fuel price inflation:
    - Sum of coefficients 0.1057; F-Stat 43.32; p-value 0.00.
  - Output gap (y-y*):
    - Sum 0.1381; F-Stat 22.04; p-value 0.00 — close to 14 percent contribution; positive and significant with one-period lag.
  - Real interest rate:
    - Sum -0.0611; F-Stat 2.32; p-value 0.05 — negatively signed and significant; policy rate channel helps anchor expectations.
  - Real Effective Exchange Rate (REER):
    - Sum -0.0293; F-Stat 7.17; p-value 0.00 — negative sign; muted and lagged pass-through.
  - Real fiscal expenditure growth (g(EXPN)):
    - Sum -0.0020; F-Stat 6.16; p-value 0.00 — small and counter-intuitively negative in model-based estimates.
- Engle-Granger residual diagnostic for preferred equation:
  - Augmented Dickey-Fuller test statistic -7.849273; Prob. 0.0000 (reject unit root; residuals stationary).

### Policy implications and operational recommendations
- Central policy dilemma: act against inflation (risk undermining recovery) vs. accommodate growth (risk unanchoring inflation expectations).
- Key empirical inferences for policy:
  - Considerable inertia in inflation expectations; past inflation and food prices explain a large share of expected inflation.
  - Food price shocks revert slowly; supply-side inflation alone cannot be relied on to contain expectations.
  - Real interest rate has a significant negative effect on inflation expectations, outweighing effects of fiscal policy and exchange rate changes; calibrated increases in policy rates can help anchor expectations.
  - Timing matters: output gap significance with one-period lag highlights speed at which demand translates into expected inflation.
- Operational recommendations:
  - Step up exit from extraordinary liquidity provision facilities instituted during the global crisis; follow up with more active liquidity drainage, including aggressive use of reserve requirements.
  - Distinguish liquidity policy operations (regular) from monetary policy operations (quarterly review cycle); use rate channel to signal and achieve real policy tightening.
  - Monetary policy should act in measured steps to indicate firm intent and stay ahead of the inflation curve rather than waiting for a cold-turkey intervention.
- Recent RBI projections and actions (as cited):
  - April 2009 APS projected WPI inflation around 4.0 per cent by end-March 2010; First Quarter Review raised projection to 5.0 per cent.
  - RBI October 2009 baseline projection raised to 6.5 per cent "with an upside bias".
  - RBI January 2010 quarterly review raised baseline projection for WPI inflation for end-March 2010 to 8.5 per cent.
  - RBI actions: in review for October–December 2009 announced on January 29, 2010, RBI raised the cash reserve ratio by 75 basis points but kept key policy rates unchanged; on March 19, 2010 the RBI increased key policy repo and reverse repo rates by 25 basis points each.
- Liquidity context: abundant liquidity with absorptions through RBI’s absorption window averaging Rs 1.1 trillion daily; effectiveness of policy rate increases may be weakened without liquidity drainage.

### ANNEX I — Model-based forecasts: selected coefficients and diagnostics (Table 7)
- Selected coefficients (exact values):
  - Model constant: Coefficient 0.009680  Std. Error 0.002842  t-Statistic 3.406411  Prob. 0.0011
  - Lagged Inflation(-1): Coefficient 0.467190  Std. Error 0.043458  t-Statistic 10.75035  Prob. 0.0000
  - Lagged Inflation (-11): Coefficient -0.347933  Std. Error 0.064165  t-Statistic -5.422460  Prob. 0.0000
  - Lagged Inflation (-12): Coefficient 0.341650  Std. Error 0.068878  t-Statistic 4.960187  Prob. 0.0000
  - GDPGAP(-1): Coefficient 0.138062  Std. Error 0.029408  t-Statistic 4.694740  Prob. 0.0000
  - G(EXPN)(-1): Coefficient -0.000253  Std. Error 0.000199  t-Statistic -1.272781  Prob. 0.2071
  - G(EXPN) (-4): Coefficient -0.000502  Std. Error 0.000200  t-Statistic -2.507965  Prob. 0.0143
  - G(REER)(-10): Coefficient -0.089328  Std. Error 0.024469  t-Statistic -3.650673  Prob. 0.0005
  - Real Interest Rate (-12): Coefficient -0.016666  Std. Error 0.008233  t-Statistic -2.024344  Prob. 0.0465
  - πPR: Coefficient 0.174784  Std. Error 0.026323  t-Statistic 6.639931  Prob. 0.0000
  - πFL: Coefficient 0.068762  Std. Error 0.022961  t-Statistic 2.994748  Prob. 0.0037
- Key model statistics:
  - R-squared 0.977566; Adjusted R-squared 0.971503
  - Mean dependent var 0.054068; S.D. dependent var 0.022268
  - S.E. of regression 0.003759; Sum squared resid 0.001046; Log likelihood 407.5067
  - Akaike info criterion -8.136982; Schwarz criterion -7.572441; Hannan-Quinn criter. -7.908865
  - F-statistic 161.2296; Prob(F-statistic) 0.000000; Durbin-Watson stat 1.859746
- Diagnostic tests (reported values and p-values):
  - ARCH 1-6 test: 1.3248 [0.2597]
  - AR 1-6 test: 1.0565 [0.33]
  - Normality test: 9.0155 [0.0110]
  - Hetero test: 0.50548 [0.9799]
  - RESET test: 0.41338 [0.5223]

### ANNEX I — Consensus expectations: selected coefficients and diagnostics (Table 8)
- Selected coefficients (exact values):
  - C (constant): Coefficient 0.017022  Std. Error 0.001845  t-Statistic 9.225329  Prob. 0.0000
  - Lagged Inflation(-1): Coefficient 0.347068  Std. Error 0.058696  t-Statistic 5.912935  Prob. 0.0000
  - Lagged Inflation (-12): Coefficient 0.203359  Std. Error 0.041968  t-Statistic 4.845585  Prob. 0.0000
  - GDPGAP coefficients include lags with mixed signs and significance (e.g., GDPGAP: -0.017869; GDPGAP(-6): -0.126999; GDPGAP(-7): 0.125718; GDPGAP(-9): -0.142886; GDPGAP(-10): 0.115813; GDPGAP(-12): -0.072185).
  - g(REER): Coefficient -0.029892  Std. Error 0.005689  t-Statistic -5.254570  Prob. 0.0000
  - Real Interest Rate (-12): Coefficient -0.011026  Std. Error 0.002303  t-Statistic -4.787435  Prob. 0.0000
  - πPR and πFL include multiple lagged coefficients with statistical significance.
- Key model statistics:
  - R-squared 0.992581; Adjusted R-squared 0.987160
  - Mean dependent var 0.050639; S.D. dependent var 0.006763
  - S.E. of regression 0.000766; Sum squared resid 3.05E-05; Log likelihood 549.1639
  - Akaike info criterion -11.21239; Schwarz criterion -10.13631; Hannan-Quinn criter. -10.77826
  - F-statistic 183.0916; Prob(F-statistic) 0.000000; Durbin-Watson stat 2.602310

### Cointegration and long-run relationships (ANNEX II)
- Variables included in cointegrating vector: Inflation, GDP Gap, Real Expenditure Growth (Centre), Change in Real Effective Exchange Rate, Real Interest Rate, Changes in Primary Articles Prices and Changes in Fuel Prices.
- Cointegration LR Test Based on Maximal Eigenvalue:
  - r = 0 vs r = 1: Statistic 142.6694  95% Critical Value 42.3  90% Critical Value 39.39
  - r <= 1 vs r = 2: Statistic 107.0166  95% Critical Value 36.27  90% Critical Value 33.48
  - r <= 2 vs r = 3: Statistic 34.7275  95% Critical Value 29.95  90% Critical Value 27.57
  - r <= 3 vs r = 4: Statistic 23.0125  95% Critical Value 23.92  90% Critical Value 21.58
  - r <= 4 vs r = 5: Statistic 14.8864  95% Critical Value 17.68  90% Critical Value 15.57
  - r <= 5 vs r = 6: Statistic 7.1997  95% Critical Value 11.03  90% Critical Value 9.28
  - r <= 6 vs r = 7: Statistic 0.09874  95% Critical Value 14.16  90% Critical Value 3.04
- Trace test statistics:
  - r = 0 vs r >= 1: Statistic 329.6105  95% Critical Value 110.1  90% Critical Value 105.44
  - r <= 1 vs r >= 2: Statistic 186.9415  95% Critical Value 83.18  90% Critical Value 78.47
  - r <= 2 vs r >= 3: Statistic 79.9249  95% Critical Value 59.33  90% Critical Value 55.42
  - r <= 3 vs r >= 4: Statistic 45.1973  95% Critical Value 39.81  90% Critical Value 36.69
  - r <= 4 vs r >= 5: Statistic 22.1849  95% Critical Value 24.05  90% Critical Value 21.46
  - r <= 5 vs r >= 6: Statistic 7.2985  95% Critical Value 12.36  90% Critical Value 10.25
  - r <= 6 vs r = 7: Statistic 0.09874  95% Critical Value 14.16  90% Critical Value 3.04
- Estimated cointegrated vectors (selected normalization; Vector 1 shown):
  - Inflation 14.1422  (-1.0000)
  - GDPGAP -0.2597  (.018364)
  - g(LEXPN) -0.0050098  (.3542E-3)
  - g(REER) (0.25451  (-.017996))
  - Interest Rate 6.0158  (-.42537)
  - πPR -6.9023  (.48807)
  - πFL -3.9656  (.28040)

### Concluding framing
- Inflation expectations centrally influence monetary policy effectiveness; anchoring expectations is crucial to prevent medium-term inflation entrenchment.
- Given evidence of persistence and the prominent role of food and fuel, recommended policy mix:
  - Use calibrated real rate increases to signal anti-inflation intent and anchor expectations.
  - Complement rate action with decisive liquidity management (exit from extraordinary facilities, aggressive reserve requirement use).
  - Improve measurement and public availability of inflation-expectation indicators (RBI household survey release and development of systematic series) to reduce imperfect information and better align policy with public perceptions.

*Source: _wp1084 - ANNEX I: DETERMINANTS OF INFLATION EXPECTATIONS*

### 1.  Inflation Expectations Equation ............................................................    13

### 1.  Inflation Expectations Equation ............................................................    13

### I. The Context
- Recovery from the global crisis is uneven; Asia is leading a rebound with India and China set to stage a V-shaped turnaround.
- The healing is expected to be "sluggish and hesitant, jobless and credit constrained" in initial stages.
- Major concern: inflation risks are rising, especially in developing countries; monetary policy may need to be tightened sooner than later.
- Inflation developments pose a dilemma to monetary policy authorities: headline inflation appears low in many places while abundant liquidity raises fears of future inflation.
- Psychology matters: "Expectations shape how economic agents behave. If they fear inflation, they act in ways that bring it about."
- In India the dilemma is acute:
  - WPI inflation rose from around 1 percent in October 2009 to 9.9 percent in February 2010.
  - CPI inflation has been running in double digits on the back of high food prices for more than a year.
  - The index of food articles increased 17.8 percent in February 2010 from a year earlier.
  - The index of primary articles prices, with a 22.03 percent weight in the wholesale price basket and comprising mainly of food items, rose 15.5 percent.
- These developments occur in an environment of abundant liquidity linked to policy responses after September 2008 when domestic financial markets seized up and liquidity froze.
- Higher food prices reflect both structural and cyclical factors; persistent price pressures have implications for inflation expectations and could force monetary policy to react, creating a trade-off:
  - Growth concerns argue for a delayed exit from accommodation.
  - Inflation concerns argue for an earlier exit.
  - Growth had accelerated to close to 8 percent in the third quarter of 2009 while consensus expected inflation to rise from current lows to a similar level in early 2010.

### II. Recent Inflation Dynamics in India
- The WPI is monitored as the main indicator of inflation in India because of broader coverage (447 items with a weight of 57 percent for manufactures) and frequent, timely availability (until recently weekly; since October 2009, headline WPI is monthly).
- CPI is calculated for four sections of society and is important for indexation; CPI series are heavily weighted towards food (40-70 percent of the total index) and primary articles.
- Concerns about coverage and base years:
  - CPI for industrial workers covers only 260 items relative to the WPI.
  - The Reserve Bank of India (RBI) notes available price indices fail to adequately capture underlying inflationary conditions due to inadequate coverage and outdated base years.
  - RBI has underscored the need to expedite revision of coverage and updating of the base year for the WPI series and two proposed consumer price indices (CPI-Urban and CPI-Rural).
- GDP deflator is the most comprehensive indicator but is available only on an annual basis with long lags.
- Measures of core and underlying inflation have been developed (exclusion and trimmed mean principles), especially in the RBI, but have limited public traction because food and fuel dominate the consumption basket.
- Since 2008 two distinct phases in inflation evolution are discernible:
  - Decline in WPI inflation after its peak in August 2008 coincided with easing global inflation, reflecting India’s integration into the global cycle.
  - Year-on-year consumer price inflation in OECD countries declined from a peak of 4.9 per cent to (-) 0.3 per cent in August 2009; headline inflation in the US, Japan and Euro Area turned negative.
  - Core inflation and producer price inflation moderated in major economies and EMEs.
  - In emerging economies, inflation eased significantly since July 2008 in line with decreases in international commodity prices and general slowdown.
  - Among major emerging economies, consumer price inflation in China and Thailand turned negative in early 2009; Malaysia in June 2009; others also eased.
- IMF (January 2010) projection cited: global inflation expected to remain subdued due to "still-low levels of capacity utilization and well-anchored inflation expectations".
  - Inflation in advanced economies projected to pick up from close to zero in 2009 to 1.3 per cent in 2010.
  - Inflation in emerging economies expected to go up from 5.2 percent in 2009 to (text truncated in source).

### Key Implications and Analytical Focus
- The paper focuses on what people think about inflation and determinants of those beliefs, with India as a laboratory but with generalized relevance to other emerging economies.
- Organization of the paper: stylized facts about inflation dynamics in India; measurement of inflation expectations and exploration of their determinants; monetary policy perspectives drawn from modeling inflation expectations; concluding observations.
- Emphasis on recent contributions in the literature and on developing survey-based measures of inflation expectations (including professional forecasters) by the RBI.

*Source: _wp1084 - 1.  Inflation Expectations Equation ............................................................    13*

### 6.2 percent this year. China, a few ASEAN economies and most emerging European economies

### _wp1084 - 6.2 percent this year. China, a few ASEAN economies and most emerging European economies

### Inflation outlook and commodity prices
- Global/region summary
  - "6.2 percent this year." China, a few ASEAN economies and most emerging European economies are likely to experience inflation of less than 5 per cent.
- Commodity price developments
  - International crude oil prices gradually rose since March 2009; crude oil prices crossed US $ 80 per barrel on October 21, 2009 and remain elevated.
  - Prices of foodgrains (rice, wheat, maize) have been edging up but remain substantially below levels of the first half of 2008.
  - Metal prices have rebounded since April 2009, led by copper, lead and nickel, mainly in response to increased demand from China.
- Risk assessment
  - Inflation risks have been growing and could threaten currently projected benign conditions.

### India: recent inflation dynamics and drivers
- WPI and CPI movements
  - WPI inflation: plummeted from 12.9 per cent in August 2008 to 0.8 per cent by end-March 2009; slipped into negative territory for 13 consecutive weeks beginning in June 2009; turned positive again since early September 2009.
  - CPI inflation: increased since June 2008, mainly due to food, fuel and services; reached a range of 16.2 – 17.6 per cent during January 2010.
- Notable price changes (selected items)
  - Vegetable prices: increase close to 20 percent year-on-year on February 6, 2010.
  - Pulses: increase of the order of 32 percent on March 13, 2010.
- Supply-side and administered price effects
  - Upward revision of administered prices of petrol and diesel effective July 2, 2009.
  - Higher administered minimum support prices (MSP) for most agricultural crops contributed to food inflation.
  - Policy supply-side responses included open market sale of wheat from buffer stocks; removal of stock holding limits; restrictions on large sugar consumers; increased releases through public distribution system; removal of import duty on rice, wheat and raw sugar; duty-free import of white/refined sugar by Government agencies and private traders.

### Tracking inflation expectations: data and surveys
- Data availability and survey practice
  - No public-domain standard measures of inflation expectations in India.
  - Since September 2005, the RBI conducts a quarterly inflation expectations survey of households for internal monitoring covering 4,000 households using quota sampling across 12 cities.
  - The RBI’s household survey elicits qualitative responses for the next three months and next one year, and quantitative current, three-month-ahead and one-year-ahead inflation rates.
  - RBI’s survey of professional forecasters covers domestic forecasters (investment banks, commercial banks, stock exchanges, international brokerage houses, select educational institutions, credit rating agencies, securities firms, asset management companies).
  - Break-even inflation from inflation-indexed bonds/swaps is not available in India; only one issuance of capital-indexed bonds met with listless market appetite.
- Survey quality observations
  - Confidence intervals from RBI household survey narrow (~20 to 30 basis points) for short horizons but widen with horizon.
  - TACS recommended public release of household survey results to improve monetary policy transparency (RBI, September 2009), but longer time series needed for robust analysis.

### Methodological approach to measuring inflation expectations
- Two-stage pragmatic approach (in absence of standard market-based measures)
  1. Unbiased parsimonious modeling of actual inflation process using monthly annualized WPI data April 1997–December 2008; generate expanding-window one-period-ahead forecasts as proxies for inflation expectations.
  2. Estimate determinants of those model-based expectations using a new-Keynesian-type Phillips curve (Hendry general-to-specific approach) and cross-check with consensus forecasts from financial entities reported to Consensus Economics.
- Time series modeling details
  - Monthly inflation modeled in ARMA framework with seasonal AR and MA terms identified using X12 and diagnostics.
  - Best-fit ARMA specification indicated as ARMA(1,1) with seasonal AR and MA terms of order 12: form used to generate next-period (month) unbiased forecasts.
  - Recognized model limitations: subjectivity in identification, not embedded in structural priors, potential poor performance predicting turning points; ARMA found robust for short-term inflation forecasts.

### ARMA forecasting equation and model performance
- Forecasting equation (model yields):
  - πe = 0.006 + 0.91 πt-1 – 0.22 πt-12 + 0.20 πt-13 + εt + 0.32 εt-2 – 0.85 εt-12 – 0.27 εt-14
- Table 1 (selected estimates and diagnostics)
  - C coefficient: 0.0509 (Std. Error 0.0025; t-Statistic 20.3436; Prob. 0.0000)
  - AR(1): 0.9100 (Std. Error 0.0429; t-Statistic 21.2210; Prob. 0.0000)
  - SAR(12): -0.2284 (Std. Error 0.1153; t-Statistic -1.9807; Prob. 0.0501)
  - MA(2): 0.3212 (Std. Error 0.1023; t-Statistic 3.1405; Prob. 0.0022)
  - SMA(12): -0.8406 (Std. Error 0.0310; t-Statistic -27.0923; Prob. 0.0000)
  - R-squared 0.9285; Adjusted R-squared 0.9260; S.E. of regression 0.0061; Log likelihood 429.3937; Durbin-Watson stat 1.2447
- Model performance (Table 2)
  - Root Mean Squared Error 0.005972
  - Mean Absolute Error 0.004394
  - Mean Abs. Percent Error 9.244995
  - Theil Inequality Coefficient 0.051917 (Bias Proportion 0.001089; Variance Proportion 0.009193; Covariance Proportion 0.989718)
- Comparison with consensus forecasts
  - Consensus Economics forecasts tend to average out fluctuations and trace a middle path through actual turning points; consensus data suffer from inconsistent reporting samples and varying horizons.

### Determinants of inflation expectations: estimation findings
- Stationarity tests (ADF and PP): most variables I(0) except changes in REER which are ambiguous; variables used include inflation, output gap, real interest rate, real fiscal expenditure growth, REER change, primary article prices (% change), fuel prices (% change).
- Main determinants (robust results)
  - Lagged inflation (especially one-month and twelve-month lags): sum of coefficients on lagged inflation contributes nearly 0.4609 (nearly 50 percent) to explaining formation of inflation expectations; indicates high inertia/persistence.
  - Primary articles' prices (food): sum of coefficients 0.2903 — a little under a third of expected inflation; food and fuel price changes together account for 40 percent of variations in inflation expectations.
  - Output gap (y-y*): positive sign; accounts close to 0.1381 (close to 14 percent) of expected inflation; significant with one-period lag.
  - Real interest rate: negatively signed and significant (sum of coefficients -0.0611 in model-based estimation; also significant in consensus estimates); indicates monetary policy stance via the rate channel helps anchor expectations. The 12-month lagged real interest rate significant with relatively low coefficient, indicating lagged transmission.
  - Real Effective Exchange Rate (REER): negative sign; appreciation expected to lower inflation expectations; coefficient low, indicating muted and lagged pass-through.
  - Real fiscal expenditure growth (g(EXPN)): small and counter-intuitively negative in model-based estimates (sum -0.0020 in redundant test), possibly reflecting period-specific fiscal consolidation and credible monetary offset.
- Redundant-variable tests (selected sums and F-stats)
  - Lagged Inflation: Sum of Coeffts 0.4609; F-Stat 42.89; p-value 0.00
  - GDPGAP: Sum 0.1381; F-Stat 22.04; p-value 0.00
  - g(EXPN): Sum -0.0020; F-Stat 6.16; p-value 0.00
  - g(REER): Sum -0.0293; F-Stat 7.17; p-value 0.00
  - Real Interest Rate: Sum -0.0611; F-Stat 2.32; p-value 0.05
  - Primary Articles' Prices Inflation: Sum 0.2903; F-Stat 39.11; p-value 0.00
  - Fuel Prices Inflation: Sum 0.1057; F-Stat 43.32; p-value 0.00

### Cointegration and residual diagnostics
- Johansen-Juselius procedure finds cointegrating vectors among variables; preferred new-Keynesian Phillips curve specification is one of them.
- Engle-Granger two-step test on residuals from the preferred equation:
  - Augmented Dickey-Fuller test statistic -7.849273; Prob. 0.0000 (reject unit root; residuals are stationary/white noise).

### Policy implications and recommendations
- Main policy dilemma: act against inflation (risk undermining recovery) vs. accommodate growth (risk unanchoring inflation expectations).
- Key empirical inferences for policy
  - Considerable inertia in inflation expectations in India; past inflation and food prices explain a large share of expected inflation.
  - Food price shocks revert slowly; supply-side inflation alone cannot be relied on to contain expectations.
  - Real interest rate has a significant negative effect on inflation expectations, outweighing effects of fiscal policy and exchange rate changes; calibrated increases in policy rates can help anchor expectations.
  - Timing matters: output gap significance with one-period lag highlights speed at which demand translates into expected inflation.
- Operational recommendations
  - Step up exit from extraordinary liquidity provision facilities instituted during the global crisis; follow up with more active liquidity drainage, including aggressive use of reserve requirements.
  - Distinguish liquidity policy operations (regular) from monetary policy operations (quarterly review cycle); use rate channel to signal and achieve real policy tightening.
  - Monetary policy should act in measured steps to indicate firm intent and stay ahead of the inflation curve rather than waiting for a cold-turkey intervention.
- Recent policy context and outlook
  - RBI projections and actions cited:
    - April 2009 APS projected WPI inflation around 4.0 per cent by end-March 2010; First Quarter Review raised projection to 5.0 per cent.
    - RBI October 2009 baseline projection raised to 6.5 per cent "with an upside bias".
    - RBI January 2010 quarterly review raised baseline projection for WPI inflation for end-March 2010 to 8.5 per cent.
    - RBI actions: in review for October–December 2009 announced on January 29, 2010, RBI raised the cash reserve ratio by 75 basis points but kept key policy rates unchanged; on March 19, 2010 the RBI increased key policy repo and reverse repo rates by 25 basis points each.
  - Current liquidity context: abundant liquidity with absorptions through RBI’s absorption window averaging Rs 1.1 trillion daily; effectiveness of policy rate increases may be weakened without liquidity drainage.

### Conclusion (policy framing)
- Inflation expectations centrally influence monetary policy effectiveness; anchoring expectations is crucial to prevent medium-term inflation entrenchment.
- Given empirical evidence of persistence and the prominent role of food and fuel, monetary policy in India should:
  - Use calibrated real rate increases to signal anti-inflation intent and anchor expectations.
  - Complement rate action with decisive liquidity management (exit from extraordinary facilities, aggressive reserve requirement use).
  - Improve measurement and public availability of inflation-expectation indicators (RBI household survey release and development of systematic series) to reduce imperfect information and better align policy with public perceptions.

*Source: _wp1084 - 6.2 percent this year. China, a few ASEAN economies and most emerging European economies (IMF PDF content provided).*

### ANNEX I: DETERMINANTS OF INFLATION EXPECTATIONS

### ANNEX I: DETERMINANTS OF INFLATION EXPECTATIONS

### Model-based Forecasts (Table 7: Determinants of Inflationary Expectation)
- Model constant: Coefficient 0.009680  Std. Error 0.002842  t-Statistic 3.406411  Prob. 0.0011
- Lagged Inflation(-1): Coefficient 0.467190  Std. Error 0.043458  t-Statistic 10.75035  Prob. 0.0000
- Lagged Inflation (-11): Coefficient -0.347933  Std. Error 0.064165  t-Statistic -5.422460  Prob. 0.0000
- Lagged Inflation (-12): Coefficient 0.341650  Std. Error 0.068878  t-Statistic 4.960187  Prob. 0.0000
- GDPGAP(-1): Coefficient 0.138062  Std. Error 0.029408  t-Statistic 4.694740  Prob. 0.0000
- G(EXPN)(-1): Coefficient -0.000253  Std. Error 0.000199  t-Statistic -1.272781  Prob. 0.2071
- G(EXPN) (-4): Coefficient -0.000502  Std. Error 0.000200  t-Statistic -2.507965  Prob. 0.0143
- G(EXPN) (-5): Coefficient -0.000679  Std. Error 0.000205  t-Statistic -3.306937  Prob. 0.0015
- G(EXPN) (-8): Coefficient -0.000580  Std. Error 0.000196  t-Statistic -2.958714  Prob. 0.0041
- G(REER)(-10): Coefficient -0.089328  Std. Error 0.024469  t-Statistic -3.650673  Prob. 0.0005
- G(REER)(-11): Coefficient 0.060025  Std. Error 0.023426  t-Statistic 2.562294  Prob. 0.0124
- Real Interest Rate(-1): Coefficient -0.011054  Std. Error 0.007776  t-Statistic -1.421526  Prob. 0.1594
- Real Interest Rate (-2): Coefficient -0.012793  Std. Error 0.008050  t-Statistic -1.589191  Prob. 0.1163
- Real Interest Rate (-4): Coefficient -0.012719  Std. Error 0.008247  t-Statistic -1.542301  Prob. 0.1273
- Real Interest Rate (-9): Coefficient -0.007842  Std. Error 0.008158  t-Statistic -0.961338  Prob. 0.3395
- Real Interest Rate (-12): Coefficient -0.016666  Std. Error 0.008233  t-Statistic -2.024344  Prob. 0.0465
- πPR: Coefficient 0.174784  Std. Error 0.026323  t-Statistic 6.639931  Prob. 0.0000
- πPR (-12): Coefficient 0.115489  Std. Error 0.024187  t-Statistic 4.774825  Prob. 0.0000
- πFL: Coefficient 0.068762  Std. Error 0.022961  t-Statistic 2.994748  Prob. 0.0037
- πFL (-1): Coefficient 0.088694  Std. Error 0.026505  t-Statistic 3.346371  Prob. 0.0013
- πFL (-12): Coefficient -0.051769  Std. Error 0.010271  t-Statistic -5.040437  Prob. 0.0000

Key model statistics:
- R-squared 0.977566
- Adjusted R-squared 0.971503
- Mean dependent var 0.054068
- S.D. dependent var 0.022268
- S.E. of regression 0.003759
- Sum squared resid 0.001046
- Log likelihood 407.5067
- Akaike info criterion -8.136982
- Schwarz criterion -7.572441
- Hannan-Quinn criter. -7.908865
- F-statistic 161.2296
- Prob(F-statistic) 0.000000
- Durbin-Watson stat 1.859746

Diagnostic tests (reported values and p-values in brackets where provided):
- ARCH 1-6 test: 1.3248 [0.2597]
- AR 1-6 test: 1.0565 [0.33]
- Normality test: 9.0155 [0.0110]
- Hetero test: 0.50548 [0.9799]
- RESET test: 0.41338 [0.5223]

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### Consensus Expectations (Table 8: Determinants of Inflationary Expectation)
- C (constant): Coefficient 0.017022  Std. Error 0.001845  t-Statistic 9.225329  Prob. 0.0000
- Lagged Inflation(-1): Coefficient 0.347068  Std. Error 0.058696  t-Statistic 5.912935  Prob. 0.0000
- Lagged Inflation (-7): Coefficient -0.090265  Std. Error 0.051328  t-Statistic -1.758569  Prob. 0.0845
- Lagged Inflation (-12): Coefficient 0.203359  Std. Error 0.041968  t-Statistic 4.845585  Prob. 0.0000
- GDPGAP: Coefficient -0.017869  Std. Error 0.007247  t-Statistic -2.465546  Prob. 0.0170
- GDPGAP(-6): Coefficient -0.126999  Std. Error 0.019108  t-Statistic -6.646312  Prob. 0.0000
- GDPGAP(-7): Coefficient 0.125718  Std. Error 0.023346  t-Statistic 5.384914  Prob. 0.0000
- GDPGAP(-9): Coefficient -0.142886  Std. Error 0.025860  t-Statistic -5.525282  Prob. 0.0000
- GDPGAP(-10): Coefficient 0.115813  Std. Error 0.023874  t-Statistic 4.850896  Prob. 0.0000
- GDPGAP(-12): Coefficient -0.072185  Std. Error 0.013173  t-Statistic -5.479910  Prob. 0.0000
- g(EXPN): Coefficient -0.000107  Std. Error 5.42E-05  t-Statistic -1.977921  Prob. 0.0532
- g(EXPN) (-1): Coefficient -0.000106  Std. Error 4.93E-05  t-Statistic -2.157440  Prob. 0.0356
- g(EXPN) (-6): Coefficient 0.000206  Std. Error 4.32E-05  t-Statistic 4.783180  Prob. 0.0000
- g(EXPN) (-7): Coefficient 0.000176  Std. Error 4.66E-05  t-Statistic 3.764838  Prob. 0.0004
- g(EXPN) (-9): Coefficient 0.000186  Std. Error 4.54E-05  t-Statistic 4.101182  Prob. 0.0001
- g(EXPN) (-10): Coefficient 0.000177  Std. Error 4.85E-05  t-Statistic 3.647505  Prob. 0.0006
- g(EXPN) (-11): Coefficient 0.000157  Std. Error 4.35E-05  t-Statistic 3.620301  Prob. 0.0007
- g(REER): Coefficient -0.029892  Std. Error 0.005689  t-Statistic -5.254570  Prob. 0.0000
- g(REER) (-1): Coefficient 0.019997  Std. Error 0.005664  t-Statistic 3.530355  Prob. 0.0009
- g(REER) (-4): Coefficient -0.006000  Std. Error 0.003012  t-Statistic -1.992264  Prob. 0.0516
- g(REER) (-10): Coefficient 0.013184  Std. Error 0.004391  t-Statistic 3.002714  Prob. 0.0041
- g(REER) (-12): Coefficient 0.021522  Std. Error 0.004882  t-Statistic 4.408700  Prob. 0.0001
- Real Interest Rate(-3): Coefficient 0.003338  Std. Error 0.001818  t-Statistic 1.835895  Prob. 0.0721
- Real Interest Rate (-6): Coefficient -0.003868  Std. Error 0.001773  t-Statistic -2.181444  Prob. 0.0337
- Real Interest Rate (-7): Coefficient 0.004173  Std. Error 0.001935  t-Statistic 2.155953  Prob. 0.0357
- Real Interest Rate (-8): Coefficient -0.008026  Std. Error 0.001827  t-Statistic -4.393624  Prob. 0.0001
- Real Interest Rate (-11): Coefficient -0.005933  Std. Error 0.001884  t-Statistic -3.149495  Prob. 0.0027
- Real Interest Rate (-12): Coefficient -0.011026  Std. Error 0.002303  t-Statistic -4.787435  Prob. 0.0000
- πPR (-2): Coefficient 0.040585  Std. Error 0.006836  t-Statistic 5.937223  Prob. 0.0000
- πPR (-4): Coefficient 0.034070  Std. Error 0.009212  t-Statistic 3.698537  Prob. 0.0005
- πPR (-7): Coefficient 0.044695  Std. Error 0.008520  t-Statistic 5.245788  Prob. 0.0000
- πPR (-11): Coefficient 0.065006  Std. Error 0.009020  t-Statistic 7.207241  Prob. 0.0000
- πFL (-2): Coefficient 0.031461  Std. Error 0.005959  t-Statistic 5.279978  Prob. 0.0000
- πFL (-3): Coefficient -0.010559  Std. Error 0.005583  t-Statistic -1.891478  Prob. 0.0641
- πFL (-9): Coefficient -0.014964  Std. Error 0.003844  t-Statistic -3.892462  Prob. 0.0003
- πFL (-12): Coefficient 0.006605  Std. Error 0.003207  t-Statistic 2.059457  Prob. 0.0445

Key model statistics:
- R-squared 0.992581
- Adjusted R-squared 0.987160
- Mean dependent var 0.050639
- S.D. dependent var 0.006763
- S.E. of regression 0.000766
- Sum squared resid 3.05E-05
- Log likelihood 549.1639
- Akaike info criterion -11.21239
- Schwarz criterion -10.13631
- Hannan-Quinn criter. -10.77826
- F-statistic 183.0916
- Prob(F-statistic) 0.000000
- Durbin-Watson stat 2.602310

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### Cointegration and Long-Run Relationships (ANNEX II)
- Variables included in the cointegrating vector: Inflation, GDP Gap, Real Expenditure Growth (Centre), Change in Real Effective Change Rate, Real Interest Rate, and Changes in Primary Articles Prices and Changes in Fuel Prices.

Table 9: Cointegration LR Test Based on Maximal Eigenvalue of the Stochastic Matrix
- r = 0 vs r = 1: Statistic 142.6694  95% Critical Value 42.3  90% Critical Value 39.39
- r <= 1 vs r = 2: Statistic 107.0166  95% Critical Value 36.27  90% Critical Value 33.48
- r <= 2 vs r = 3: Statistic 34.7275  95% Critical Value 29.95  90% Critical Value 27.57
- r <= 3 vs r = 4: Statistic 23.0125  95% Critical Value 23.92  90% Critical Value 21.58
- r <= 4 vs r = 5: Statistic 14.8864  95% Critical Value 17.68  90% Critical Value 15.57
- r <= 5 vs r = 6: Statistic 7.1997  95% Critical Value 11.03  90% Critical Value 9.28
- r <= 6 vs r = 7: Statistic 0.09874  95% Critical Value 14.16  90% Critical Value 3.04

Table 10: Cointegration LR Test Based on Trace of the Stochastic Matrix
- r = 0 vs r >= 1: Statistic 329.6105  95% Critical Value 110.1  90% Critical Value 105.44
- r <= 1 vs r >= 2: Statistic 186.9415  95% Critical Value 83.18  90% Critical Value 78.47
- r <= 2 vs r >= 3: Statistic 79.9249  95% Critical Value 59.33  90% Critical Value 55.42
- r <= 3 vs r >= 4: Statistic 45.1973  95% Critical Value 39.81  90% Critical Value 36.69
- r <= 4 vs r >= 5: Statistic 22.1849  95% Critical Value 24.05  90% Critical Value 21.46
- r <= 5 vs r >= 6: Statistic 7.2985  95% Critical Value 12.36  90% Critical Value 10.25
- r <= 6 vs r = 7: Statistic 0.09874  95% Critical Value 14.16  90% Critical Value 3.04

Note: Apart from two dummies for end of the year fiscal bunching and abnormal call money rate spike coinciding with limit placed by the RBI on Reverse Repo in March 2007, the cointegrating equation includes 11 centered dummies.

Table 11: Estimated Cointegrated Vectors in Johansen Estimation (Normalized in Brackets)
- Vector 1
  - Inflation 14.1422  (-1.0000)
  - GDPGAP -0.2597  (.018364)
  - g(LEXPN) -0.0050098  (.3542E-3)
  - g(REER) (0.25451  (-.017996))
  - Interest Rate 6.0158  (-.42537)
  - πPR -6.9023  (.48807)
  - πFL -3.9656  (.28040)
- Vector 2
  - Inflation 7.3138  (-1.0000)
  - GDPGAP -2.6466  (0.36187)
  - g(LEXPN) 0.059423  (-.0081248)
  - g(REER) -0.15829  (0.021643)
  - Interest Rate -1.6344  (0.22347)
  - πPR -4.9309  (0.67419)
  - πFL -4.1982  (0.57402)
- Vector 3
  - Inflation -13.7251  (-1.0000)
  - GDPGAP 1.302  (0.82346)
  - g(LEXPN) 0.073902  (0.0053845)
  - g(REER) 1.4233  (0.1037)
  - Interest Rate -1.3396  (-.097602)
  - πPR 4.8468  (0.35313)
  - πFL 2.0382  (0.1485)

*Source: _wp1084 - ANNEX I: DETERMINANTS OF INFLATION EXPECTATIONS*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1084.pdf_