## _wp08289 - 1. Granger Causality Tests

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---

### I. Introduction: scope and terminology
- Paper examines policy responses by a sample of central banks to oil and food price shocks and draws lessons for South Africa.
- Shocks treated as changes in relative prices; persistence of shocks is a key uncertainty.
- Terminology:
  - "Relative price shocks" = price rises in food and fuel.
  - "Underlying inflation" = rise in prices of all other consumer goods.
- Figure 1 data source: WEO, April and June 2008.

### II. First- and second-round effects: concepts and South Africa exposures
- Conceptual distinction:
  - First round effects: direct impact on general price index and indirect cost-push effects on low-margin goods that use food and fuel as inputs.
  - Second round effects: impact on inflation expectations, wage settlements, and price setting economy-wide.
- South Africa-specific exposures and estimates:
  - Food represents 26 percent of the CPIX basket.
  - Gasoline accounts for 5.1 percent of the CPIX basket.
  - Using the 2002 input-output matrix, estimated total (direct plus indirect) first round effect of a 1 percent rise in prices of a broad set of food items is a 0.35 percent rise in the cost of consumption.
  - CPIX is CPI excluding the interest on mortgage loans.
  - Input-output goods include agricultural products, meats, fish, fruit and vegetables, and several other products, accounting for 26 percent of household consumption in the 2002 input-output table (Statistics South Africa (2006)).

### III. Evidence of second-round effects in South Africa
- Correlation analysis (January 2000–March 2008, seasonally adjusted):
  - A rise in food prices tends to be followed by upward movements in nonfood inflation, peaking at lags of about six months.
  - When food inflation exceeds its sample median, correlations are higher earlier and peak at six months, suggesting semiannual price revisions.
- Granger causality tests (Sample: 1998M01-2008M03):
  - Null: FOOD&FUEL does not Granger Cause REST
    - Lags: 1 — F-Statistic 5.238; Probability 0.024
    - Lags: 2 — F-Statistic 2.309; Probability 0.104
  - Null: REST does not Granger Cause FOOD&FUEL
    - Lags: 1 — F-Statistic 0.266; Probability 0.607
    - Lags: 2 — F-Statistic 0.034; Probability 0.967
  - Interpretation: monthly food and fuel inflation helps forecast inflation in the rest of the price index in South Africa (marginally for two lags), but not vice versa.
- Inflation expectations (November 2000–March 2008):
  - Expectations measured as spread between CPI-indexed and regular government bonds of comparable maturity (CPI-indexed R179 maturing January 8, 2013, and R186 maturing March 31, 2013).
  - Rise in food and fuel prices tends to lead to an increase in inflation expectations, starting two months earlier than measured CPI change and peaking one month later.
  - For November 2004–March 2008 (period with food and fuel above sample median) correlations are generally stronger and peak at a lag of two months.

### IV. Policy reaction rule and estimation strategy
- Policy rule estimated (Equation (1)):
  - it = α + βund πtund + βrel rt + γ zt + λ yt + ρ rt + εt  (notation in text: ttttrel Und tundt yzriεγλβπβα+++++= )
  - it: nominal policy interest rate.
  - πtund: underlying inflation in the last 12 months (excluding food and fuel).
  - zt: nominal depreciation over same period.
  - yt: output gap.
  - rt: indicator of relative price movements for key products (food and fuel); defined as residual from regression of headline inflation on underlying inflation and a constant.
- Expected coefficient interpretations:
  - βrel = 0 and βund > 0 when inflation expectations are well anchored and underlying inflation resilient.
  - βrel > 0 if central bank views relative price shocks as a risk to underlying inflation.
- Estimation methods and issues:
  - Potential endogeneity (e.g., exchange rate responds to interest rates).
  - OLS with one-period lags of RHS variables used; Instrumental Variables (IV) used with six months of lags as instruments.
  - Corrected standard errors via Murphy and Topel (1985) because rt is a generated regressor.

### V. Econometric results: selected coefficients and distributions
- Selected point estimates (OLS with lagged RHS; t-statistics in parentheses where reported):
  - United Kingdom:
    - Underlying inflation(t-1): 0.423 (t = 6.34)
    - "Relative price" shocks(t-1): 1.673 (t = 13.90)
    - R-squared: 0.835
  - South Africa:
    - Underlying inflation(t-1): 1.532 (t = 9.75)
    - "Relative price" shocks(t-1): 0.217 (t = 1.12)
    - R-squared: 0.663 (observations 61)
- Distributional patterns across countries and model variants:
  - Underlying inflation (πtund) generally positive and significant in most model variants for: Australia, Brazil, Chile, Colombia, Iceland, Korea, New Zealand, Norway, South Africa, Turkey, United Kingdom (Variant 1).
  - Relative price shocks (rt) are often statistically insignificant, but positive and significant in some specifications and countries, notably Colombia and United Kingdom (Variant 1), and Chile, Iceland, United Kingdom in Variant 2.
  - Countries exhibiting significant βrel in some specifications include Colombia, Chile, Iceland, South Africa, and United Kingdom.
  - Replacing rt with oil price produces significance in several cases (Variant 3), but results vary by country.
- Regime changes / inflation targeting effects:
  - Re-estimations for post-inflation targeting periods show strengthened evidence that UK and Australia react to relative price shocks.
  - For South Africa, policy rates react to relative price shocks and became more systematic after adoption of inflation targeting in 2001.
  - Rolling 30-month window estimates for South Africa: coefficient on relative price shocks diminished and stabilized at a positive level similar to coefficient on underlying inflation after adoption of inflation targeting; prior to targeting coefficients were unstable and large in absolute value with opposite signs.

### VI. Recent central bank decisions (mid-2007 to mid-2008): selected tightenings and easings
- Selected tightenings (mid-2007–mid-2008):
  - Australia, March 2008: Hike 25 bp; commodity prices discussed as TOT shock to demand; high headline and underlying inflation; demand growth outpacing capacity; tight labor market.
  - New Zealand, July 2007: Hike 25 bp; rising food and fuel prices mentioned; high, rising domestic (nontraded) inflation; high capacity utilization; tight labor market; strong currency.
  - Colombia, Feb. 2008: Hike 25 bp; food caused inflation to breach band; nonfood inflation and expectations rising; demand slowed but still strong.
  - Chile, June 2008: Hike 50 bp (larger than previous increases); supply shocks raised headline and core inflation and expectations; inflation well above target’s “tolerance range”; demand growth strong.
  - Turkey, May 2008: Hike 50 bp (start of tightening cycle); aim to contain second round effects; inflation projected to stay high; slowing demand; pass-through from currency depreciation supports inflation.
- Selected easings (mid-2007–mid-2008):
  - Brazil, July and Sep. 2007: Cuts 50 bp + 25 bp—risk from global inflation mentioned; inflation projected within target; import growth a relief valve.
  - Canada, Jan. and March 2008: Cuts 25 bp + 50 bp; headline 2.2 percent and core 1.4 percent in 2007; concern over US slowdown; strong Canadian dollar.
  - United Kingdom, Dec. 2007 and Feb. 2008: Cuts 25 bp + 25 bp; food and oil expected to raise inflation “quite sharply” but pressures to fade; essentially on target (2.1 percent); measures of expectations “currently elevated”; concerns over deceleration abroad.
  - Turkey, Dec. 2007 and Jan. 2008: Cuts 50 bp + 25 bp; supply shocks raised inflation temporarily but also weakened demand; projected to fall despite food and fuel risks; monetary tightening from 2007 still working through system.
- Policy horizon extension and target revisions:
  - Some central banks implicitly/explicitly lengthened the policy horizon for returning inflation to target consistent with gradual tightening (typical hikes 25 or 50 basis points).
  - Chile (June 2008) referenced commitment to “reduce the current elevated inflation toward 3 percent in the policy horizon.”
  - Turkey (June 2008) increased inflation targets for 2009, 2010 and 2011 to 7.5, 6.5, and 5.5 percent, respectively, from 4 percent; authorities stated revision “does not necessarily mean that monetary policy will be looser in the forthcoming period.”

### VII. South Africa: SARB actions, assessments, and CPI basket change
- SARB posture:
  - Emphasis on containing second round effects while highly concerned about original shocks.
  - Described oil prices as a “threat” when Brent crude reached $70 dollars a barrel in April 2006.
  - Tightening resumed in April 2008; MPC noted “a series of supply side shocks” and large increase in inflation expectations which had breached the target band.
  - SARB increased the repo rate by usual 50 basis points in April 2008; acknowledged that inflation would take longer to return to the 3–6 percent target band.
  - SARB forecasts (Figure 7) show implicit lengthening of the policy horizon in response to expectations, underlying inflation, and credibility risks.
- CPI basket change and effects:
  - On July 1, 2008, Statistics South Africa announced CPI basket changes effective January 2009: lower weight to food products (18.8 percent of CPI as opposed to 26.6 percent), higher weight to durable goods.
  - Some analysts estimate mid-2008 inflation in South Africa would have been about 2 percent lower had the new basket been implemented starting January 2008.

### VIII. Conclusions, policy implications, and research recommendations
- Summary of central-bank tradeoffs:
  - Central banks generally accept some first round level effects from relative price shocks while acting to contain second round effects that threaten inflation control.
  - Distinguishing first and second round effects is practically difficult; indirect first round effects can blur the line.
- Empirical conclusions:
  - Several effective central banks, including Bank of England and Reserve Bank of Australia, under inflation targeting have leaned toward reacting to relative price shocks.
  - SARB reacts both to underlying inflation and relative price shocks; policy reaction function became more stable and response to relative price shocks became more aggressive after adoption of inflation targeting.
- Policy implications:
  - Even if targeting a core index, central banks should remain vigilant and act when relative price shocks threaten to contaminate the general inflation process.
  - A policy of containment of second round effects may imply a more aggressive stance when goods with spiking prices represent a large share of consumption basket and where there is history of high and variable inflation.
  - Specific policy actions depend heavily on broader economic context—high inflation, rising expectations, strong demand, and other pressures tend to warrant more aggressive responses.
  - Trade-offs exist between faster disinflation (higher short-term output costs) and gradual approach (risks to credibility and higher long-run output costs).
  - Effective communication of the nature of ongoing shocks and the strategy of monetary policy is essential.
- Recommendation for further research:
  - Identify main structural features of an economy (including degree of vulnerability of price indexes to shocks) that counsel a more or less aggressive approach to relative price shocks.

### IX. Appendix — decomposition, derivation of rt, and data sources
- Headline inflation decomposition:
  - Headline index: h = w u + (1-w) n, where u is underlying inflation index, w its weight, n index for non-underlying goods.
  - Non-underlying inflation πn written as πn = a0 + a1 πu + vt, where vt is orthogonal to underlying inflation.
  - Residual rt from regression of headline inflation on underlying inflation captures orthogonal component combined with weight of non-underlying goods.
  - Importance of residual depends on weight 1-w and variance of vt; if w close to 1, residual is small.
- Data sources and indicators (selected):
  - Oil prices: World Economic Outlook.
  - Exchange rates: International Financial Statistics.
  - Country-specific headline and underlying inflation measures and policy rates listed (examples: United Kingdom RPIX and RPIX excl. food, petrol and oil; South Africa CPIX and CPIX excl. food and petrol).
  - Output gaps estimated by Hodrick-Prescott filter applied to output indicators.
  - Policy rates and statistical institute sources listed for each country in appendix table.

*Source — IMF staff estimates and calculations based on central bank and statistical institute data contained in the referenced chapter (References, _wp08289).*

### 1. Granger Causality Tests .............................................................................................

### _wp08289 - 1. Granger Causality Tests .............................................................................................

### Sections
- 1. Granger Causality Tests .........................................................................................................6
- 2. Estimation of Equation 1 for Selected Countries.................................................................10
- 3. Distribution of the Coefficient on the Variable Representing Underlying Inflation ...........11
- 4. Distribution of the Coefficient on the Variable Representing Relative Price Shocks .........11
- 5. Re-Estimation of Equation 1 for the Period Under Inflation Targeting ..............................14
- 6. Selected Recent Tightening Decisions.................................................................................15
- 7. Selected Recent Easing Decisions. ......................................................................................16

### Figures
- Figure 1. Food and Price Shocks in Perspective ...................................................................................3
- Figure 2. Evidence of Second Round Effects of Shocks to Food Prices...............................................5
- Figure 3. Effects of Relative Price Shocks on Inflation Expectations ..................................................7
- Figure 4. Second Round Effects May Already Be in Train in South Africa.........................................7
- Figure 5. Indicators of Inflation in Sample Countries.........................................................................12
- Figure 6. Rolling Estimates of Equation 1 for South Africa ...............................................................13
- Figure 7. Implicit Lengthening of the Policy Horizon in South Africa ..............................................18

### Appendix
- Appendix..................................................................................................................................22

*Source: _wp08289 - 1. Granger Causality Tests (PDF).*

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

### References

### I. Introduction
- Paper examines policy responses by a sample of central banks to oil and food price shocks and draws lessons for South Africa.
- Shocks are treated as changes in relative prices; persistence of shocks is a key uncertainty.
- Cites Mishkin (2007): an energy price shock may not merit tightening “as long as the permanent change in relative energy price does not lead to a change in the underlying trend rate in inflation—a crucial assumption.”
- Terminology: price rises in food and fuel are referred to as “relative price shocks”; rise in prices of all other consumer goods is referred to as “underlying inflation.”
- Figure 1 data source: WEO, April and June 2008.

### II. First and Second Round Effects of Relative Price Shocks
- Conceptual distinction:
  - First round effects: direct impact on general price index and indirect cost-push effects on low-margin goods that use food and fuel as inputs.
  - Second round effects: impact on inflation expectations, wage settlements, and price setting economy-wide.
- South Africa-specific exposures:
  - Food represents 26 percent of the CPIX basket.
  - Gasoline accounts for 5.1 percent of the CPIX basket.
  - Using the 2002 input-output matrix, estimated total (direct plus indirect) first round effect of a 1 percent rise in prices of a broad set of food items is a 0.35 percent rise in the cost of consumption.
  - CPIX is CPI excluding the interest on mortgage loans.
  - Input-output goods include agricultural products, meats, fish, fruit and vegetables, and several other products, accounting for 26 percent of household consumption in the 2002 input-output table (Statistics South Africa (2006)).

### Evidence of Second Round Effects in South Africa
- Correlation analysis (January 2000–March 2008, seasonally adjusted):
  - A rise in food prices tends to be followed by upward movements in nonfood inflation, peaking at lags of about six months.
  - When food inflation exceeds its sample median, correlations are higher earlier and peak at six months, suggesting semiannual price revisions.
- Granger causality tests (Sample: 1998M01-2008M03):
  - Null: FOOD&FUEL does not Granger Cause REST
    - Lags: 1 — F-Statistic 5.238; Probability 0.024
    - Lags: 2 — F-Statistic 2.309; Probability 0.104
  - Null: REST does not Granger Cause FOOD&FUEL
    - Lags: 1 — F-Statistic 0.266; Probability 0.607
    - Lags: 2 — F-Statistic 0.034; Probability 0.967
  - Interpretation: monthly food and fuel inflation helps forecast inflation in the rest of the price index in South Africa (marginally for two lags), but not vice versa.
- Inflation expectations analysis (November 2000–March 2008):
  - Inflation expectations measured as the spread between CPI-indexed and regular government bonds of comparable maturity (CPI-indexed R179 maturing January 8, 2013, and R186 maturing March 31, 2013).
  - Rise in food and fuel prices tends to lead to an increase in inflation expectations, starting two months earlier than measured CPI change and peaking one month later.
  - For November 2004–March 2008 (period with food and fuel above sample median) correlations are generally stronger and peak at a lag of two months.
  - Critical values referenced: Kymn (1968) for derivation.

### III. Historical Perspective on Monetary Policy Responses to Relative Price Shocks
- Premises:
  - Central banks try only to contain second round effects.
  - Policy levers engaged only when underlying inflation trends are at risk.
- Policy rule used (Equation (1)):
  - it = α + βund πtund + βrel r t + γ zt + λ yt + ρ rt + εt  (expression in text: ttttrel Und tundt yzriεγλβπβα+++++= )
  - it is the nominal policy interest rate.
  - πtund is underlying inflation in the last 12 months (excluding food and fuel).
  - zt is nominal depreciation over same period.
  - yt is the output gap.
  - rt is indicator of relative price movements for key products (food and fuel); defined as residual from regression of headline inflation on underlying inflation and a constant.
- Expectations on coefficients:
  - βrel = 0 and βund > 0 when inflation expectations are well anchored and underlying inflation resilient.
  - βrel > 0 if central bank views relative price shocks as a risk to underlying inflation.
- Estimation challenges and methods:
  - Potential endogeneity (e.g., exchange rate responds to interest rates).
  - OLS with one-period lags of RHS variables used; Instrumental Variables (IV) used with six months of lags as instruments.
  - Corrected standard errors via Murphy and Topel (1985) due to generated regressor rt.
- Data note: In some richer countries where food weight is small, underlying inflation better predicts headline inflation, reducing influence of rt.

### IV. Econometric Results (Selected countries and summary)
- Table 2 (policy reaction estimates using OLS on lagged RHS and IV):
  - Countries analyzed include: United Kingdom, Australia, New Zealand, Norway, Iceland, Korea, Colombia, Chile, Turkey, Brazil, South Africa.
  - Frequency and sample dates vary by country; e.g., United Kingdom Jan'88 - Jan'08 (Bimonthly), Australia Q1'90 - Q4'07 (Quarterly), South Africa Jan'98 - Feb'08 (Bimonthly).
  - Selected coefficient examples (OLS with lagged RHS variables; coefficients followed by t-statistics in the table):
    - Underlying inflation(t-1) for United Kingdom: 0.423 (t = 6.34)
    - "Relative price" shocks(t-1) for United Kingdom: 1.673 (t = 13.90)
    - Underlying inflation(t-1) for South Africa: 1.532 (t = 9.75)
    - "Relative price" shocks(t-1) for South Africa: 0.217 (t = 1.12)
  - R-squared examples: United Kingdom 0.835; South Africa 0.663 (observations 61).
- Table 3: Distribution of OLS coefficient on underlying inflation across model variants:
  - Model variant 1 (Equation 1): Coefficient positive and significant at 10% in Aus, Bra, Chl, Col, Ice, Kor, NZ, Nor, SA, Tky, UK.
  - Variant 2 (πtund replaced with one-year lead): positive/significant in Aus, Bra, Chl, Ice, Kor, Nor, SA, UK; statistically insignificant in Col, NZ, Tky.
  - Variant 3 (Oil price replaces rt): positive/significant in Aus, Bra, Chl, Col, Ice, Kor, NZ, Nor, SA, UK; statistically insignificant in Tky.
  - Variant 4 (combines 2 and 3): positive/significant in Aus, Bra, Chl, Col, Ice, Kor, NZ, SA, UK; statistically insignificant in Nor, Tky.
- Table 4: Distribution of OLS coefficient on relative price shocks:
  - Model variant 1: Coefficient positive and significant at 10% in Col, UK; statistically insignificant in Aus, Bra, Chl, Ice, Kor, NZ, Nor, SA, Tky.
  - Variant 2 (πtund replaced with one-year lead): positive/significant in Chl, Ice, UK; statistically insignificant in Aus, Bra, Col, Kor, NZ, Nor, SA, Tky.
  - Variant 3 (Oil price replaces rt): positive/significant in Col, UK; statistically insignificant in Aus, Bra, Chl, Ice, Kor, NZ, Nor, SA, Tky.
  - Variant 4 (combines 2 and 3): positive/significant in Ice; statistically insignificant in Aus, Bra, Chl, Col, Kor, NZ, Nor, SA, Tky, UK.
- Main patterns:
  - Majority of countries and models show significant responses to underlying inflation, but not to relative price shocks.
  - Countries with significant responses to relative price shocks in some specifications include Colombia, Chile, Iceland, South Africa and the UK.
  - Possible explanatory factors: higher exposure to food shocks, higher inflation regimes, or history of variable inflation; however, exceptions exist (e.g., UK shows βrel > 0 despite moderate inflation; Brazil does not show βrel > 0 despite relatively higher inflation).
- Regime change and inflation targeting:
  - Re-estimations for periods after adoption of inflation targeting (Table 5) show strengthened evidence that UK and Australia react to relative price shocks.
  - For South Africa, policy rates react to relative price shocks and policy became more systematic after inflation targeting adoption in 2001.
  - Rolling 30-month window estimates for South Africa show coefficient on relative price shocks diminished and stabilized at a positive level similar to coefficient on underlying inflation after adoption of inflation targeting; prior to targeting coefficients were unstable and large in absolute value with opposite signs.

### V. Recent Monetary Policy Decisions Around the World (mid-2007 to mid-2008)
- Central bank responses are context-dependent: responses vary by recent inflation, future inflation trajectory, expectations, demand strength, and other factors.
- Selected tightenings (Table 6):
  - Australia, March 2008: Hike 25 bp; commodity prices discussed as TOT shock to demand; high headline and underlying inflation; demand growth outpacing capacity; tight labor market.
  - New Zealand, July 2007: Hike 25 bp; rising food and fuel prices mentioned; high, rising domestic (nontraded) inflation; high capacity utilization; tight labor market; strong currency.
  - Colombia, Feb. 2008: Hike 25 bp; food caused inflation to breach band; nonfood inflation and expectations rising; demand slowed but still strong.
  - Chile, June 2008: Hike 50 bp (larger than previous increases); supply shocks raised headline and core inflation and expectations; inflation well above target’s “tolerance range”; demand growth strong.
  - Turkey, May 2008: Hike 50 bp (start of tightening cycle); aim to contain second round effects; inflation projected to stay high; slowing demand; pass-through from currency depreciation supports inflation.
- Selected easings (Table 7):
  - Brazil, July and Sep. 2007: Cuts 50 bp + 25 bp—risk from global inflation mentioned; inflation projected within target; import growth a relief valve.
  - Canada, Jan. and March 2008: Cuts 25 bp + 50 bp; headline 2.2 percent and core 1.4 percent in 2007; concern over US slowdown; strong Canadian dollar.
  - United Kingdom, Dec. 2007 and Feb. 2008: Cuts 25 bp + 25 bp; food and oil expected to raise inflation “quite sharply” but pressures to fade; essentially on target (2.1 percent); measures of expectations “currently elevated”; concerns over deceleration abroad.
  - Turkey, Dec. 2007 and Jan. 2008: Cuts 50 bp + 25 bp; supply shocks raised inflation temporarily but also weakened demand; projected to fall despite food and fuel risks; monetary tightening from 2007 still working through system.
- Time horizon extension:
  - Some central banks implicitly/explicitly extended the policy horizon for returning inflation to target, consistent with gradual tightening practices (typical hikes 25 or 50 basis points).
  - Chile June 2008 decision referenced commitment to “reduce the current elevated inflation toward 3 percent in the policy horizon.”
- Turkey’s explicit change:
  - In June 2008, Turkey increased inflation targets for 2009, 2010 and 2011 to 7.5, 6.5, and 5.5 percent, respectively, from 4 percent.
  - Rationale: failed to meet targets in 2006 and 2007; headline inflation in double digits; food and energy shocks expected to persist; expectations increasingly backward-looking; target losing effectiveness.
  - Authorities stated revision “does not necessarily mean that monetary policy will be looser in the forthcoming period.”
  - Risk: inflation expectations could become unhinged; decision could freeze impact of shocks on expectations and forgo potential benefits from a future reversal in commodity prices.

### VI. South Africa: Reserve Bank Actions and Assessment
- SARB emphasis on containing second round effects while highly concerned about original shocks.
- Example: SARB described oil prices as a “threat” when Brent crude reached $70 dollars a barrel in April 2006.
- SARB tightened policy resumed in April 2008; MPC noted “a series of supply side shocks” and large increase in inflation expectations which had breached the target band.
- SARB increased the repo rate by usual 50 basis points in April 2008; acknowledged that inflation would take longer to return to the 3–6 percent target band.
- SARB’s forecasts (Figure 7) show implicit lengthening of the policy horizon in response to expectations, underlying inflation, and credibility risks.
- CPI basket change noted:
  - On July 1, 2008, Statistics South Africa announced CPI basket changes effective January 2009: lower weight to food products (18.8 percent of CPI as opposed to 26.6 percent), higher weight to durable goods.
  - Some analysts estimate mid-2008 inflation in South Africa would have been about 2 percent lower had the new basket been implemented starting January 2008.

### VII. Concluding Remarks
- Central banks balance acceptance of some first round level effects with need to contain second round effects that threaten inflation control.
- Distinguishing first and second round effects is practically difficult; indirect first round effects can blur the line.
- Empirical findings:
  - Several effective central banks, including Bank of England and Reserve Bank of Australia, under inflation targeting have leaned toward reacting to relative price shocks.
  - SARB reacts both to underlying inflation and relative price shocks; policy reaction function became more stable and response to relative price shocks became more aggressive after adoption of inflation targeting.
- Policy implications:
  - Even if targeting a core index, central banks should remain vigilant and act when relative price shocks threaten to contaminate general inflation process.
  - A policy of containment of second round effects may imply a more aggressive stance when goods with spiking prices represent a large share of consumption basket and where there is history of high and variable inflation.
  - Specific policy actions depend heavily on broader economic context—high inflation, rising expectations, strong demand, and other pressures tend to warrant more aggressive responses.
  - Trade-offs exist between faster disinflation (higher short-term output costs) and gradual approach (risks to credibility and higher long-run output costs).
  - Effective communication of the nature of ongoing shocks and the strategy of monetary policy is essential.
- Recommendation for further research:
  - Identify main structural features of an economy (including degree of vulnerability of price indexes to shocks) that counsel a more or less aggressive approach to relative price shocks.

### VIII. Appendix: Derivation of the Regressor rt and Data Sources
- Headline inflation decomposition:
  - Headline index: h = w u + (1-w) n, where u is underlying inflation index, w its weight, n index for non-underlying goods.
  - Non-underlying inflation πn written as πn = a0 + a1 πu + vt, where vt is orthogonal to underlying inflation.
  - Residual rt from regression of headline inflation on underlying inflation captures orthogonal component combined with weight of non-underlying goods.
  - Importance of residual depends on weight 1-w and variance of vt; if w close to 1, residual is small.
- Data sources and indicators (summary from appendix table):
  - Oil prices: World Economic Outlook.
  - Exchange rates: International Financial Statistics.
  - Country-specific headline and underlying inflation measures and policy rates as listed (United Kingdom RPIX and RPIX excl. food, petrol and oil; Australia CPI and CPI excl. volatile items; New Zealand CPI and CPI excl. government charges, food and fuel; Norway CPI adjusted for tax changes and excl. energy; Iceland CPI excl. agricultural products, vegetables, fruits and petrol; Korea CPI excl. agricultural products and oils; Colombia CPI excl. staple food, public utilities and fuel; Chile CPI excl. fresh fruit, vegetable and fuel; Turkey CPI excl. unprocessed food and energy; Brazil CPI excl. food and energy; South Africa CPIX and CPIX excl. food and petrol).
  - Output gaps estimated by Hodrick-Prescott filter applied to output indicators.
  - Specific policy rates and statistical institute sources listed for each country in appendix table.

*Italic: Source — IMF staff estimates and calculations based on central bank and statistical institute data contained in the referenced chapter (References, _wp08289).*

### References

### References

### Cited works
- Aoki, Kosuke (2001), “Optimal Monetary Policy Responses to Relative Price Changes,” Journal of Monetary Economics, v.48 (2001), 55-80
- Clarida, Richard, Jordi Gali and Mark Gertler (1998), “Monetary Policy Rules in practice: Some International Evidence,” European Economic Review, v. 42, 1033-1067
- Gramlich, Edward (2004), “Oil Shocks and Monetary Policy,” remarks at the Annual Economic Luncheon, Federal Reserve Bank of Kansas City, September 16, 2004, http://www.federalreserve.gov/boarddocs/speeches/2004/20040916/default.htm
- Harjes, T., and Ricci, L. A. (2008), “A Bayesian-Estimated Model of Inflation Targeting in South Africa,” International Monetary Fund Working Paper WP/08/48, 24 p.
- Kamps, Cristophe, and Pierdzioch, Christian (2002), “Monetary Policy Rules and Oil Price Shocks,” Kiel Institute of World Economics Working Paper 1090, 38 p.
- Kymn, Kern O. (1968), “The Distribution of the Sample Correlation Under the Null Hypothesis,” Econometrica, Vol. 36, No 1, 187-189
- Mishkin, Frederic (2007), “Headline versus Core Inflation in the Conduct of Monetary Policy,” Speech at the Conference on Business Cycles, International transmission, and Macroeconomic Policies, HEC, Montreal, October 2007
- Murphy, Kevin M., and Topel, Robert (1985), “Estimation and Inference in Two-Step Econometric Models,” Journal of Business & Economics, October 1985, Vol. 3, No. 4, 88-97
- Oritz, Alberto, and Sturzenegger, Federico (2008), “Estimating SARB’s Policy Reaction Rule,” Center for International Development at Harvard University, Working Paper No.165, 26p.
- Statistics South Africa (2006), Final Supply and Use Tables, 2002: An Input-Output Framework, Statistics South Africa, Pretoria, 69 pages. (The data can be downloaded from http://www.statssa.gov.za)
- Taylor, John B. (1993), “Discretion versus policy rules in practice,” Carnegie-Rochester Conference Series on Public Policy 39 (1993) 195-214

### Central bank press releases, monetary policy statements, and minutes (websites used)
- Australia: www.rba.gov.au
- Brazil: www.bcb.gov.br
- Canada: www. bank-banque-canada.ca
- Chile: www.bcentral.cl
- Colombia: www.banrep.gov.co
- Iceland: www.sedlabanki.is
- Korea: www.bok.or.kr
- New Zealand: www.rbnz.govt.nz
- Norway: www.norges-bank.no
- South Africa: www.reservebank.co.za
- Turkey: www.tcmb.gov.tr
- UK: www.bancofengland.co.uk

*Source: _wp08289 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08289.pdf_