## Commodity Prices and Monetary Policy: High Frequency Analysis (Online Annex 1.1, Chapter 1)

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---

### Data and indices
- Regressions use disaggregated daily data on nominal commodity prices, denominated in USD, for 39 different commodities.
- Sample period for high-frequency analysis: 1990-2019 (daily frequency for the whole sample period).
- Nine sub-indexes constructed: base metals, crude oil, precious metals, food, beverages, cereals, cotton and rubber, meat, and oilseed; trade weights from the IMF Primary Commodity Price System (PCPS) database.

### High-frequency local projections (LP) method
- LP specification (Jordà, 2005):
  - Dependent variable: ln y_{i,t+h} − ln y_{i,t−1}.
  - Key regressor: MPS^{US}_t, the “pure” monetary policy shock (measured in basis points) to three-months-ahead federal funds futures estimated by Jarociński and Karadi (2020), which eliminates surprises that correlate positively with the stock market.
  - Controls: 12 lags of the impact log-change of commodity prices and 12 lags of the monetary policy shock.
- Sample period: January 1990 to May 2019.
- Confidence bands: 90% confidence error bands calculated as ±1.645⋅SE_h, where SE_h is the robust standard error at horizon h.

### Responses to a 10-Basis-Point US monetary policy shock
- Aggregate dynamics:
  - After a 10 basis points monetary policy shock the fed funds rate shows a strong and persistent increase.
  - The dollar index shows a temporary appreciation.
- Statistically significant commodity price responses identified for: Coal, Nickel, Gasoline, Zinc, Lead, Coffee, Sugar, Palladium, Copper, Oil, Aluminum, Silver, Platinum, Tin, Wheat, Milk, and Gold.
- Natural gas (Henry Hub):
  - No effect in the full sample.
  - For 2015-2019, when US natural gas exports surged, there is strong evidence of a negative response of US natural gas prices to US monetary tightening shocks.
- Peak responses:
  - The analysis reports horizon (day) of the maximum decline for each commodity (90 percent error bars displayed in figures).

### Structural change in commodity–dollar relationship
- Unconditional correlation between commodity prices and the US dollar historically generally negative but:
  - Evidence suggests this correlation became positive since 2015 (rolling window correlations on daily data).
- Conditional on a monetary policy shock:
  - The US dollar and commodity prices continue to present a negative correlation.
  - Responses of US dollar and commodity prices to a monetary policy shock are robust to splitting the sample into before and after 2014.

### Commodity price responses to ECB monetary policy shocks
- Identification uses Jarociński and Karadi (2020) shocks for the ECB; controls include 24 business days lags of the one-year US bond yield to account for US monetary policy stance.
- Main findings:
  - Effects on oil prices are analogous to those documented for the US but less precisely estimated.
  - No effect on base metals, raw materials, and cereals.
  - In general ECB shocks have negative effects on commodity prices, but responses are not precisely estimated in part due to a shorter sample (1999-2019).

### Proxy-SVAR: identification, method, and impulse responses
- Structural SVAR: y_t = Σ_{l=1}^L Φ_l y_{t−l} + B ε_t; reduced form: y_t = Σ_{l=1}^L Φ_l y_{t−l} + u_t.
- Instrumental identification: external instrument z (Jarociński and Karadi (2020) pure monetary policy shock) used to identify US monetary policy shock; instrument satisfies:
  - E[ε^{MonPol}_t, z′_t] ≠ 0 and E[ε^{others}_t, z′_t] = 0.
- Two-stage procedure:
  - First stage: regress instrument on reduced-form VAR innovation for the one-year treasury bill to identify impact on the interest rate.
  - Second stage: regress predicted value from first stage on remaining VAR innovations to recover impact coefficients (matrix B) up to a scaling factor.
- Impulse responses computed iteratively:
  - IR_0 = B for t = 0.
  - IR_t = φ IR_{t−1} for t = 1, 2, ..., H.

### Proxy-SVAR results and decomposition
- A 10-basis points shock to the Fed Funds Rate induces:
  - a 2 percent decline in oil prices.
  - a 1 percent decline in food prices.
- Responses of macro variables (headline CPI, core CPI, excess bond premium (EBP), industrial production (IP)) align with results in Jarociński and Karadi (2020).
- Decomposition exercise:
  - To assess the role of oil prices in pass-through, the exercise sets the response of oil prices equal to zero at all horizons (by setting coefficients of the oil price equation to zero).
- Exchange rate spillovers (one-year horizon average responses):
  - After a US monetary policy shock that increases the interest rate by 10 basis points, local currencies of most countries tend to depreciate against the US dollar after a year (except Nigeria; response not statistically significant).
  - Average one-year nominal exchange rate increase:
    - Benchmark model: 0.60%.
    - When neither oil nor food prices react: 0.28%.
  - Decomposition implies that reactions in oil and food prices amplify local currency depreciation following a US monetary tightening.

### Robustness: mediation analysis
- A mediation analysis (Dippel et al., 2017) is used as robustness to study the commodity-price channel of monetary policy.

*International Monetary Fund | October 2023 — Online Annex 1.1, Chapter 1*

### Methodological objective and two-step mediation strategy (Section 2)

### Objective and overall strategy
- Aim: unpack the causal chain when a treatment (interest rates) and its outcome (commodity prices) jointly cause a second outcome (consumer price inflation).
- Strategy: two-step estimation combining linear local projections and 2SLS to isolate the dynamic causal effect of US monetary policy shocks on commodity prices and the passthrough of commodity prices to headline inflation.

### Step 1 — Effect of US monetary policy on commodity prices
- Specification: linear local projection estimated via 2SLS using monthly data between 1990m2 to 2019m6 (equation (6)).
- Variables:
  - r_t: US 12-months treasury bills rate.
  - c_t: commodity price index.
  - X_t: constant and lags of monthly industrial production, the nominal effective exchange rate and of the outcome variable itself.
  - φ_h(L): polynomial in the lag operator.
- Instrument:
  - z_t: US monetary policy shocks identified by Jarociński and Karadi (2020).
- Interpretation:
  - Under instrument relevance and exogeneity, β1_h identifies the h-months ahead effect of a US monetary policy tightening on commodity prices.
- Inference remark:
  - Draws are taken from wild cluster bootstrap samples using the Rademacher distribution with 500 replications.

### Step 2 — Passthrough of commodity prices to headline inflation
- Specification: panel 2SLS estimating cumulative CPI change between t-1 and t+h (equation (7)):
  - Left-hand side: P_{i,t+h} − P_{i,t−1} where P_{i,t} is country i’s CPI.
  - Right-hand side includes r_t (US 12-months T-bill rate), c_t (commodity price index), φ_h(L)X_{i,t−l}, and country fixed effects μ_i.
  - X_{i,t} includes lags of a country’s industrial production, bilateral exchange rate with the dollar, and of headline inflation.
- Sample: unbalanced panel of 58 countries including both advanced economies and emerging and developing economies.
- Identification challenge and extra assumption:
  - Both interest rate and commodity prices are allowed endogenous; only one instrument (z_t) is available.
  - Extra identifying assumption: unobserved drivers of interest rates are unconditionally orthogonal with unobserved drivers of inflation and can affect inflation only through commodity prices (ε_r ⟂ ε_π and ε_r ⟂̸ ε_π | c_t). In the linear model this reduces to uncorrelatedness.
  - Tests on estimated residuals for ε_r and ε_π show that orthogonality cannot be rejected.
- Mediated effect:
  - Commodities-mediated effect of monetary policy on inflation is β1_h β3_h.
- Total effect:
  - Estimated via 2SLS analogously (equation (8)): P_{i,t+h} − P_{i,t−1} = β4_h r_t + γ_h(L) X_{i,t−l} + η_{t+h}^π, where β4_h identifies the total effect of monetary policy on headline inflation.
- Computation:
  - Compute the share of the mediated effect on the total effect as (β1_h β3_h) relative to β4_h.

### US monetary policy spillovers to other central banks
- Evidence:
  - Monetary policy rates of G-20 central banks comove strongly with the US monetary policy rate, especially during periods when common global shocks are dominant (e.g., Global financial crisis and COVID-19).
  - The average 60 months rolling-window correlation among US monetary policy rate and G-20 rates fluctuates between -0.4 and 0.6, averaging 0.25 for the whole period with the exception being the 2017-18 period.
  - High policy rate co-movement could be only given by global factors.
- Granger-causality tests:
  - Using monetary policy surprises for US, Canada, Japan, ECB, and UK show that US monetary policy shocks Granger cause monetary policy surprises in Canada and the European union.
- Implication:
  - During periods of monetary policy coordination, the commodity-price channel could be amplified by coordinated tightening or loosening of other central banks.

### State-dependent passthrough of food and oil price shocks
- Objective: estimate state-dependent impulse response functions (IRFs) of domestic inflation to global commodity price shocks using panel local projections (Jordà, 2005) and compare IRFs across states (Ramey and Zubairy, 2018).
- States assessed:
  - (i) commodity price boom phase versus bust phase,
  - (ii) rising versus declining commodity prices,
  - (iii) large versus small commodity price shocks.
- Two exercises:
  1. Food passthrough: regress domestic food inflation at horizons on food commodity price shocks.
     - Panel: 130 advanced economies (AEs) and emerging markets (EMs), years 1991-2019.
  2. Energy passthrough: regress domestic energy inflation on oil price shocks.
     - Panel: 30 AEs, years 1991-2019.
- Estimation details:
  - Use lag-augmented local projections (Montiel Olea and Plagborg-Møller (2021)) to construct IRFs of cumulative commodity price pass-through.
  - Monthly frequency for all variables.
  - For each horizon h=0,1,2,...12 estimate equation (9) for the food price exercise:
    - Left-hand side: p^f_{i,t+h} − p^f_{i,t−1}, where p^f_{i,t} is log of food CPI.
    - State dummy I^+ = 1 during state A (e.g., rising commodity prices); I^− is complement.
    - Shock variable: p^f_{i,t,int} = log of IMF’s (international) food and beverages commodity price index.
    - Controls x_{i,t}: country exchange rate (in logs) against the USD (LCU/USD).
    - Country fixed effect α_{i,h}.
    - Number of lags L is matched to horizon and set to 12.
    - Dynamic causal effects during the two states represented by IRFs (h, β^+_h) and (h, β^−_h).
  - Energy exercise analogous:
    - Left-hand side: log-difference of energy CPI.
    - Shock variable: ∆p^{oil,int}_{i,t} = monthly log-difference of IMF’s average petroleum spot price index.
- Instrumental-IV variants:
  - Food commodity prices instrumented with harvest shocks from De Winne and Peersman (2021).
  - Oil prices instrumented with oil supply news shocks from Känzig (2021).

### Data sources and samples
- Food CPI data, food commodity prices, and average petroleum spot prices: IMF’s international finance statistics and IMF’s primary commodity price system.
- Energy CPI data: global inflation dataset assembled by Ha et al. (2023).
- Sample periods explicitly used:
  - Step 1 commodity-price local projection: monthly data between 1990m2 to 2019m6.
  - Food and energy panel exercises: years 1991-2019.
- Panels:
  - Passthrough panel: unbalanced panel of 58 countries.
  - Food passthrough panel: 130 AEs and EMs.
  - Energy passthrough panel: 30 AEs.

*International Monetary Fund | October 2023 — ch1onlineannex*

### Section 1

### Commodity Prices and Monetary Policy: High Frequency Analysis (Online Annex 1.1, Chapter 1)

### Data
- Regressions use disaggregated daily data on nominal commodity prices, denominated in USD, for 39 different commodities.
- Sample period for high-frequency analysis: 1990-2019 (daily frequency for the whole sample period).
- Nine sub-indexes constructed: base metals, crude oil, precious metals, food, beverages, cereals, cotton and rubber, meat, and oilseed; trade weights from the IMF Primary Commodity Price System (PCPS) database.

### High-Frequency Local Projections (LP) Method
- LP specification (Jordà, 2005):
  - Dependent variable: ln y_{i,t+h} − ln y_{i,t−1}.
  - Key regressor: MPS^{US}_t, the “pure” monetary policy shock (measured in basis points) to three-months-ahead federal funds futures estimated by Jarociński and Karadi (2020), which eliminates surprises that correlate positively with the stock market.
  - Controls: 12 lags of the impact log-change of commodity prices and 12 lags of the monetary policy shock.
- Sample period: January 1990 to May 2019.
- Confidence bands: 90% confidence error bands calculated as ±1.645⋅SE_h, where SE_h is the robust standard error at horizon h.

### Responses to a 10-Basis-Point US Monetary Policy Shock
- Aggregate dynamics:
  - After a 10 basis points monetary policy shock the fed funds rate shows a strong and persistent increase.
  - The dollar index shows a temporary appreciation.
- Statistically significant commodity price responses (Figure 2) found for:
  - Coal, Nickel, Gasoline, Zinc, Lead, Coffee, Sugar, Palladium, Copper, Oil, Aluminum, Silver, Platinum, Tin, Wheat, Milk, and Gold.
- No effect on natural gas prices (Henry Hub) in the full sample; however:
  - For the more recent period 2015-2019, when US natural gas exports surged, there is strong evidence of a negative response of US natural gas prices to US monetary tightening shocks.
- Peak responses (horizon reporting):
  - The analysis reports horizon (day) of the maximum decline for each commodity (90 percent error bars displayed in figures).

### Structural Change in Commodity–Dollar Relationship
- Unconditional correlation between commodity prices and the US dollar historically generally negative but:
  - Evidence suggests this correlation became positive since 2015 (rolling window correlations on daily data).
- Conditional on a monetary policy shock:
  - The US dollar and commodity prices continue to present a negative correlation.
  - Responses of US dollar and commodity prices to a monetary policy shock are robust to splitting the sample into before and after 2014.

### Commodity Price Responses to ECB Monetary Policy Shocks
- Identification: Jarociński and Karadi (2020) shocks for the ECB; controls include 24 business days lags of the one-year US bond yield to account for US monetary policy stance.
- Main findings:
  - Effects on oil prices are analogous to those documented for the US but less precisely estimated.
  - No effect on base metals, raw materials, and cereals.
  - In general ECB shocks have negative effects on commodity prices, but responses are not precisely estimated in part due to a shorter sample (1999-2019).

### Proxy-SVAR Analysis: Identification and Method
- Structural SVAR: y_t = Σ_{l=1}^L Φ_l y_{t−l} + B ε_t.
  - Reduced form: y_t = Σ_{l=1}^L Φ_l y_{t−l} + u_t.
- Instrumental identification: external instrument z (Jarociński and Karadi (2020) pure monetary policy shock) used to identify US monetary policy shock; satisfies:
  - E[ε^{MonPol}_t, z′_t] ≠ 0 and E[ε^{others}_t, z′_t] = 0.
- Two-stage procedure:
  - First stage: regress instrument on reduced-form VAR innovation for the one-year treasury bill to identify impact on the interest rate.
  - Second stage: regress predicted value from first stage on remaining VAR innovations to recover impact coefficients (matrix B) up to a scaling factor.
- Impulse responses computed iteratively:
  - IR_0 = B for t = 0.
  - IR_t = φ IR_{t−1} for t = 1, 2, ..., H.

### Proxy-SVAR Results and Decomposition
- A 10-basis points shock to the Fed Funds Rate induces:
  - a 2 percent decline in oil prices.
  - a 1 percent decline in food prices.
- Responses of macro variables (headline CPI, core CPI, excess bond premium (EBP), industrial production (IP)) align with results in Jarociński and Karadi (2020).
- Decomposition exercise:
  - To assess the role of oil prices in pass-through, the exercise sets the response of oil prices equal to zero at all horizons (by setting coefficients of the oil price equation to zero).
- Exchange rate spillovers (one-year horizon average responses):
  - After a US monetary policy shock that increases the interest rate by 10 basis points, local currencies of most countries tend to depreciate against the US dollar after a year (except Nigeria; response not statistically significant).
  - Average one-year nominal exchange rate increase (i.e., depreciation of local currency expressed as increase in the nominal exchange rate):
    - Benchmark model: 0.60%.
    - When neither oil nor food prices react: 0.28%.
  - Decomposition implies that reactions in oil and food prices amplify local currency depreciation following a US monetary tightening.

### Robustness: Mediation Analysis
- A mediation analysis (Dippel et al., 2017) is used as robustness to study the commodity-price channel of monetary policy.

*International Monetary Fund | October 2023 — Online Annex 1.1, Chapter 1*

### Section 2

### ch1onlineannex - Section 2

### Methodological objective
- Aim: unpack the causal chain when a treatment (interest rates) and its outcome (commodity prices) jointly cause a second outcome (consumer price inflation).
- Strategy: two-step estimation combining linear local projections and 2SLS to isolate the dynamic causal effect of US monetary policy shocks on commodity prices and the passthrough of commodity prices to headline inflation.

### Step 1 — Effect of US monetary policy on commodity prices
- Specification: linear local projection estimated via 2SLS using monthly data between 1990m2 to 2019m6 (equation (6)).
- Variables:
  - r_t: US 12-months treasury bills rate.
  - c_t: commodity price index.
  - X_t: constant and lags of monthly industrial production, the nominal effective exchange rate and of the outcome variable itself.
  - φ_h(L): polynomial in the lag operator.
- Instrument:
  - z_t: US monetary policy shocks identified by Jarociński and Karadi (2020).
- Interpretation:
  - Under instrument relevance and exogeneity, β1_h identifies the h-months ahead effect of a US monetary policy tightening on commodity prices.
- Inference remark:
  - Draws are taken from wild cluster bootstrap samples using the Rademacher distribution with 500 replications.

### Step 2 — Passthrough of commodity prices to headline inflation
- Specification: panel 2SLS estimating cumulative CPI change between t-1 and t+h (equation (7)):
  - Left-hand side: P_{i,t+h} − P_{i,t−1} where P_{i,t} is country i’s CPI.
  - Right-hand side includes r_t (US 12-months T-bill rate), c_t (commodity price index), φ_h(L)X_{i,t−l}, and country fixed effects μ_i.
  - X_{i,t} includes lags of a country’s industrial production, bilateral exchange rate with the dollar, and of headline inflation.
- Sample: unbalanced panel of 58 countries including both advanced economies and emerging and developing economies.
- Identification challenge and extra assumption:
  - Both interest rate and commodity prices are allowed endogenous; only one instrument (z_t) is available.
  - Extra identifying assumption: unobserved drivers of interest rates are unconditionally orthogonal with unobserved drivers of inflation and can affect inflation only through commodity prices (ε_r ⟂ ε_π and ε_r ⟂̸ ε_π | c_t). In the linear model this reduces to uncorrelatedness.
  - Tests on estimated residuals for ε_r and ε_π show that orthogonality cannot be rejected.
- Mediated effect:
  - Commodities-mediated effect of monetary policy on inflation is β1_h β3_h.
- Total effect:
  - Estimated via 2SLS analogously (equation (8)): P_{i,t+h} − P_{i,t−1} = β4_h r_t + γ_h(L) X_{i,t−l} + η_{t+h}^π, where β4_h identifies the total effect of monetary policy on headline inflation.
- Computation:
  - Compute the share of the mediated effect on the total effect as (β1_h β3_h) relative to β4_h.

### US monetary policy spillovers to other central banks
- Evidence:
  - Monetary policy rates of G-20 central banks comove strongly with the US monetary policy rate, especially during periods when common global shocks are dominant (e.g., Global financial crisis and COVID-19).
  - The average 60 months rolling-window correlation among US monetary policy rate and G-20 rates fluctuates between -0.4 and 0.6, averaging 0.25 for the whole period with the exception being the 2017-18 period.
  - High policy rate co-movement could be only given by global factors.
- Granger-causality tests:
  - Using monetary policy surprises for US, Canada, Japan, ECB, and UK show that US monetary policy shocks Granger cause monetary policy surprises in Canada and the European union.
- Implication:
  - During periods of monetary policy coordination, the commodity-price channel could be amplified by coordinated tightening or loosening of other central banks.

### State-dependent passthrough of food and oil price shocks
- Objective: estimate state-dependent impulse response functions (IRFs) of domestic inflation to global commodity price shocks using panel local projections (Jordà, 2005) and compare IRFs across states (Ramey and Zubairy, 2018).
- Types of state-dependence assessed:
  - (i) commodity price boom phase versus bust phase,
  - (ii) rising versus declining commodity prices,
  - (iii) large versus small commodity price shocks.
- Two exercises:
  1. Regress domestic food inflation at horizons on food commodity price shocks.
     - Panel: 130 advanced economies (AEs) and emerging markets (EMs), years 1991-2019.
  2. Regress domestic energy inflation on oil price shocks.
     - Panel: 30 AEs, years 1991-2019.
- Estimation details:
  - Use lag-augmented local projections (Montiel Olea and Plagborg-Møller (2021)) to construct IRFs of cumulative commodity price pass-through.
  - Monthly frequency for all variables.
  - For each horizon h=0,1,2,...12 estimate equation (9) for the food price exercise:
    - Left-hand side: p^f_{i,t+h} − p^f_{i,t−1}, where p^f_{i,t} is log of food CPI.
    - State dummy I^+ = 1 during state A (e.g., rising commodity prices); I^− is complement.
    - Shock variable: p^f_{i,t,int} = log of IMF’s (international) food and beverages commodity price index.
    - Controls x_{i,t}: country exchange rate (in logs) against the USD (LCU/USD).
    - Country fixed effect α_{i,h}.
    - Number of lags L is matched to horizon and set to 12.
    - Dynamic causal effects during the two states represented by IRFs (h, β^+_h) and (h, β^−_h).
  - Energy exercise analogous:
    - Left-hand side: log-difference of energy CPI.
    - Shock variable: ∆p^{oil,int}_{i,t} = monthly log-difference of IMF’s average petroleum spot price index.
- Instrumental-IV variants:
  - For some exercises use LP-IV:
    - Food commodity prices instrumented with harvest shocks from De Winne and Peersman (2021).
    - Oil prices instrumented with oil supply news shocks from Känzig (2021).

### Data sources
- Food CPI data, food commodity prices, and average petroleum spot prices: IMF’s international finance statistics and IMF’s primary commodity price system.
- Energy CPI data: global inflation dataset assembled by Ha et al. (2023).
- Sample periods explicitly used:
  - Step 1 commodity-price local projection: monthly data between 1990m2 to 2019m6.
  - Food and energy panel exercises: years 1991-2019.
- Panels:
  - Passthrough panel: unbalanced panel of 58 countries.
  - Food passthrough panel: 130 AEs and EMs.
  - Energy passthrough panel: 30 AEs.

*International Monetary Fund | October 2023 — ch1onlineannex - Section 2*

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_Source: https://www.imf.org/-/media/files/publications/weo/2023/october/english/ch1onlineannex.pdf_