## _wp10129 - INTRODUCTION

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---

### Overview
- Food commodity prices experienced large swings since the mid-1990s, including a sharp run-up peaking in mid-2008 followed by a precipitous decline and earlier rapid declines during 1995-2000.
- Macroeconomic effects of large food price swings include impacts on balance of payments, budgets, inflation, and poverty.
- Volatility—both levels and persistence—has powerful effects; volatility can be decomposed into high-frequency (seasonal/weather/pest related) and low-frequency (changes persisting for more than one harvest year) components.
- Low-frequency volatility is of particular policy interest because its persistence is harder to manage and creates greater uncertainty for investment and consumption decisions.

### Stylized facts on long-run real food price volatility
- Over rolling 10-year periods since 1885 annualized volatility of real food prices has ranged from:
  - a low of just under 8 percent (in the mid-1960s) to
  - over 20 percent (during the 1920s).
- Periods of high and low volatility have persisted for sustained periods (e.g., low volatility 1955–1970; high volatility through mid-1980s).
- Four large increases in long-run volatility occurred in the sample:
  - First World War and inter-war years,
  - Second World War,
  - Breakdown of the Bretton Woods regime in the early 1970s,
  - 10-year volatility reached its highest level in almost 30 years in 2009.
- Figure 1: Real Food Price Volatility, 1875-2009 (annualized standard deviation percent) — index is equally-weighted of 6 commodities (corn, palm oil, rice, soybeans, sugar, wheat), U.S. dollar denominated, deflated by U.S. CPI.

### Methodology
- Primary model: spline-GARCH from Engle and Rangel (2008), which extends GARCH(1,1) by incorporating a time-varying latent trend τ (an exponential-quadratic spline) to capture low-frequency volatility.
- Benchmark GARCH(1,1) variance equation (1b): h_t = ω + α ε_{t-1}^2 + β h_{t-1}; unconditional variance constant per equation (2).
- Spline-GARCH mean and variance specified in (3a), (3b), with spline trend τ defined in (3c) across P equally-spaced partitions of T; parameters estimated include { μ, ρ, α, β, k, w_0, w_1, ..., w_P }.
- The latent trend τ serves as time-varying unconditional forecast of variance: E_t(h_t) = τ_t (equation (4)).
- Estimation by maximum likelihood; boundary issues handled by extrapolating spot price forward using GARCH(1,1) simulations to avoid spline boundary overshooting.
- Cross-sectional analysis: annualized average unconditional standard deviation s_t computed from monthly τ estimates per (5); fixed-effects regressions (equation (6)) and multivariate system regressions (equations (7)–(8)) estimated using GMM with Newey-West standard errors.
- Two regressors (oil price volatility and open interest) exhibited potential endogeneity and were instrumented with one-period lags.

### Data
- Commodity spot prices sample: January 1875 – December 2009 (full sample) and January 1957 – December 2009 (IMF IFS-based series).
- Six commodities: corn (maize), palm oil, rice, soybeans, sugar, wheat.
- Prices quoted in U.S. dollars, deflated by U.S. CPI.
- Summary statistics (monthly log change in deflated U.S. dollars multiplied by 100, approximate percent) for Full sample 1/:
  - Corn: Mean -0.1, Std. deviation 7.9, Skew -0.36, Maximum 52.0, Minimum -61.1
  - Palm Oil: Mean -0.2, Std. deviation 7.5, Skew 0.08, Maximum 32.2, Minimum -30.6
  - Rice: Mean -0.1, Std. deviation 7.3, Skew 0.14, Maximum 66.6, Minimum -74.3
  - Soybeans: Mean -0.1, Std. deviation 7.1, Skew -0.25, Maximum 39.4, Minimum -44.9
  - Sugar: Mean -0.2, Std. deviation 8.0, Skew 0.51, Maximum 52.7, Minimum -34.5
  - Wheat: Mean -0.1, Std. deviation 7.3, Skew -0.08, Maximum 52.6, Minimum -55.4
- IMF index sample 2/ (January 1957–December 2009) summary statistics also reported in Table 1.
- Start dates by commodity for full sample: Corn, Sugar, Wheat begin January 1975; Palm Oil January 1957; Rice October 1914; Soybeans November 1913.

### Long-run volatility estimation results
- Spline-GARCH provides better fit than GARCH(1,1) per AIC and BIC for all commodities and sample periods (Tables 2 and 3).
- ARCH (α) coefficients around 0.10 in most cases; spline-GARCH models show significantly less volatility persistence (β) than GARCH(1,1).
- Optimal number of spline knots varies by commodity but is almost identical across sample periods; two partitioning schemes considered: 5-year and 10-year partitions.
- Low-frequency volatility τ exhibits smooth, lower-amplitude dynamics compared with total conditional volatility h_t and shows positive average cross-commodity correlations:
  - Average correlation between low-frequency volatilities: 0.1 for full sample, 0.3 for shorter sample (1957–2009).
  - Excluding sugar and rice, correlations rise to 0.5 (full sample) and 0.6 (short sample).
- Common low-frequency volatility episodes: inter-war years 1918–39 (increase), 1950–70 (low), 1970s (rise after Bretton Woods), and last 5–10 years (upward trajectory).

### Determinants of low-frequency food price volatility (1968–2009)
- Out of 16 candidate variables, seven emerged as statistically significant and relatively consistent determinants (Table 5; system regression with restrictions across commodities except inflation measures).
- Key determinants with sign and qualitative magnitude:
  - Real U.S. interest rate (level): negative relationship with low-frequency volatility.
    - Quantified example: one standard deviation decline in real U.S. interest rates (equivalent to about 1¼ percentage point) raises low-frequency price volatility by about ½ percentage point; effects particularly strong for soybeans and wheat.
  - Inflation volatility: positive and significant effect on low-frequency volatility.
    - Example magnitude: a one standard deviation increase in annualized inflation volatility (about 4 0 basis points since 1968) would increase long-run real food price volatility by between 1 and 4 percentage points, depending on commodity.
  - U.S. dollar exchange rate volatility: positive and significant effect.
    - Example magnitude: a one standard deviation increase in volatility of U.S. dollar nominal effective exchange rate (about 2 percentage points since 1968) raises low-frequency food price variation by between 1 and 2 percentage points.
  - Futures market volumes (annual average of daily observations across benchmark contracts): higher volumes increase low-frequency volatility; statistically significant but economically small.
    - Example: the average 68 percent increase in volumes over 2008 would lead to an increase in long-run volatility of less than 1½ percentage points.
  - Real global activity index (Kilian index / Baltic Dry Freight extension): lower real activity levels and higher activity volatility increase low-frequency food price volatility; effects statistically significant but small.
    - Quantified: a two standard deviation fall (or rise in volatility) in real activity would increase low-frequency volatility by less than 1 percentage point.
  - ENSO measures (Southern Oscillation Index and Niño 3.4 SST anomalies): statistically significant but small effects.
    - Example: a 2 degrees Celsius decline in Niño 3.4 SST anomalies (La Niña) would increase low-frequency food price variation by about 0.2 percentage points; a 2 standard deviation increase in SOI has a similar magnitude.
  - Stock market volatility: unexpectedly negative and statistically significant coefficient in multivariate specifications (robust inverse relationship after controlling for other financial variables); interpretation unclear.
- Regression estimation details:
  - System regressions estimated by GMM with Newey-West standard errors.
  - Restrictions imposed for parsimony: coefficients on explanatory variables set equal across commodities except inflation measures; coefficients on volatility of oil prices, equity prices, and open interest set to zero (accepted by likelihood ratio tests).
  - Two regressors (oil price volatility and open interest) set to zero in the restricted system.

### Factors found not to affect low-frequency volatility (joint regressions)
- Inventory-use (stock-use) ratios: no significant effect in jointly estimated regressions; some individual commodity evidence (wheat) but insufficient for broad claims.
- Oil price volatility: no significant impact in joint regressions; modest bivariate correlations for some commodities (corn and wheat ~0.2) but biofuel linkages may be too recent to detect robust long-run relationships.
- Policy variables (OECD producer support measures) over 1986–2007:
  - Nominal Producer Coefficient (NPC): insignificant for panel, significant only for wheat (Table 6).
  - Single Commodity Transfer (SCT): statistically significant and negative for panel driven largely by wheat; excluding wheat, no robust effect.

### What explains the recent rise in food price volatility?
- The model decomposes low-frequency volatility year-by-year by multiplying estimated coefficients by explanatory variables (example shown for corn in Figure 4).
- One common and large contributor: rising U.S. inflation volatility between 1995 and 2009.
- Between 1995 and 2009, inflation volatility increased from about 0.5 percent to about 2.3 percent. Combined with the largeestimated coefficients for corn, palm oil, and soybeans, certain factors "have contributed almost 10 percentage points to the increase in low frequency price volatility during this period for these commodities."
- Rising U.S. dollar volatility has trended higher from "about 3-5 percent in the mid-1990s to reach almost 10 percent in 2009." Based on the estimated model, this "has contributed to an additional 2-3 percentage points to food commodity price volatility."

### Major findings on food price volatility
- Low frequency (slow-moving) spot price volatility is positively correlated across different food commodities, indicating common factors explain part of price variability.
- During the last 10 years, this measure of volatility has risen for a range of different commodities.
- Combined with large estimated coefficients for corn, palm oil, and soybeans, certain factors "have contributed almost 10 percentage points to the increase in low frequency price volatility during this period for these commodities."
- The variables with the largest effects and which also explain a relatively large part of the rise in volatility since the mid-1990s were "U.S. inflation volatility and the variability of the U.S. dollar exchange rate." The paper emphasizes commodities' sensitivity to these nominal variables because commodities act as real assets that hedge against both inflation and U.S. dollar depreciations.

### Role of futures market volumes
- Futures market volumes appear to have had a marginal effect, largely because of "the small size of the estimated coefficient from the model (a result which is subject to the caveat related to the possible endogeneity of volumes)."
- The largest change in volume in recent years was for corn, which experienced "an increase of about 150 percent in 2008 (marketing year)." Based on the estimated coefficient, this "contributed about 5 percentage points to volatility in 2008," but "sustained increases would be required to have a lasting influence on volatility."
- For other commodities, the contribution of rising volumes was smaller and mainly confined to the 2007-08 period. The paper concludes that "volumes appeared to play no major role in the broad rise in low frequency volatility which has occurred over the last 10 years."
- The paper finds a statistically significant positive relationship between trading volumes in commodity futures and low frequency food price volatility, but controlling for endogeneity remains difficult because futures trading volumes likely depend to some extent on expectations of future volatility. Other studies have failed to establish a robust relationship between futures volumes and price volatility.

### Conclusion and research needs
- It is useful to consider volatility as made up of high and low frequency components; greater understanding of low frequency volatility is particularly important because it "may be subject to a greater level of uncertainty with respect to its persistence and its causes."
- The paper points to aspects of food price volatility in need of further research, especially the endogeneity issues surrounding futures trading volumes and their relationship to future volatility expectations.

*Source: _wp10129 - INTRODUCTION (IMF PDF).*

### INTRODUCTION

### _wp10129 - INTRODUCTION

### Overview
- Food commodity prices experienced large swings since the mid-1990s, including a sharp run-up peaking in mid-2008 followed by a precipitous decline and earlier rapid declines during 1995-2000.
- Macroeconomic effects of large food price swings include impacts on balance of payments, budgets, inflation, and poverty.
- Volatility—both levels and persistence—has powerful effects; volatility can be decomposed into high-frequency (seasonal/weather/pest related) and low-frequency (changes persisting for more than one harvest year) components.
- Low-frequency volatility is of particular policy interest because its persistence is harder to manage and creates greater uncertainty for investment and consumption decisions.

### Stylized facts on long-run real food price volatility
- Over rolling 10-year periods since 1885 annualized volatility of real food prices has ranged from:
  - a low of just under 8 percent (in the mid-1960s) to
  - over 20 percent (during the 1920s).
- Periods of high and low volatility have persisted for sustained periods (e.g., low volatility 1955–1970; high volatility through mid-1980s).
- Four large increases in long-run volatility occurred in the sample:
  - First World War and inter-war years,
  - Second World War,
  - Breakdown of the Bretton Woods regime in the early 1970s,
  - 10-year volatility reached its highest level in almost 30 years in 2009.
- Figure 1: Real Food Price Volatility, 1875-2009 (annualized standard deviation percent) — index is equally-weighted of 6 commodities (corn, palm oil, rice, soybeans, sugar, wheat), U.S. dollar denominated, deflated by U.S. CPI.

### Methodology
- Primary model: spline-GARCH from Engle and Rangel (2008), which extends GARCH(1,1) by incorporating a time-varying latent trend τ (an exponential-quadratic spline) to capture low-frequency volatility.
- Benchmark GARCH(1,1) variance equation (1b): h_t = ω + α ε_{t-1}^2 + β h_{t-1}; unconditional variance constant per equation (2).
- Spline-GARCH mean and variance specified in (3a), (3b), with spline trend τ defined in (3c) across P equally-spaced partitions of T; parameters estimated include { μ, ρ, α, β, k, w_0, w_1, ..., w_P }.
- The latent trend τ serves as time-varying unconditional forecast of variance: E_t(h_t) = τ_t (equation (4)).
- Estimation by maximum likelihood; boundary issues handled by extrapolating spot price forward using GARCH(1,1) simulations to avoid spline boundary overshooting.
- Cross-sectional analysis: annualized average unconditional standard deviation s_t computed from monthly τ estimates per (5); fixed-effects regressions (equation (6)) and multivariate system regressions (equations (7)–(8)) estimated using GMM with Newey-West standard errors.
- Two regressors (oil price volatility and open interest) exhibited potential endogeneity and were instrumented with one-period lags.

### Data
- Commodity spot prices sample: January 1875 – December 2009 (full sample) and January 1957 – December 2009 (IMF IFS-based series).
- Six commodities: corn (maize), palm oil, rice, soybeans, sugar, wheat.
- Prices quoted in U.S. dollars, deflated by U.S. CPI.
- Summary statistics (monthly log change in deflated U.S. dollars multiplied by 100, approximate percent) for Full sample 1/:
  - Corn: Mean -0.1, Std. deviation 7.9, Skew -0.36, Maximum 52.0, Minimum -61.1
  - Palm Oil: Mean -0.2, Std. deviation 7.5, Skew 0.08, Maximum 32.2, Minimum -30.6
  - Rice: Mean -0.1, Std. deviation 7.3, Skew 0.14, Maximum 66.6, Minimum -74.3
  - Soybeans: Mean -0.1, Std. deviation 7.1, Skew -0.25, Maximum 39.4, Minimum -44.9
  - Sugar: Mean -0.2, Std. deviation 8.0, Skew 0.51, Maximum 52.7, Minimum -34.5
  - Wheat: Mean -0.1, Std. deviation 7.3, Skew -0.08, Maximum 52.6, Minimum -55.4
- IMF index sample 2/ (January 1957–December 2009) summary statistics also reported in Table 1.
- Start dates by commodity for full sample: Corn, Sugar, Wheat begin January 1975; Palm Oil January 1957; Rice October 1914; Soybeans November 1913.

### Long-run volatility estimation results
- Spline-GARCH provides better fit than GARCH(1,1) per AIC and BIC for all commodities and sample periods (Tables 2 and 3).
- ARCH (α) coefficients around 0.10 in most cases; spline-GARCH models show significantly less volatility persistence (β) than GARCH(1,1).
- Optimal number of spline knots varies by commodity but is almost identical across sample periods; two partitioning schemes considered: 5-year and 10-year partitions.
- Low-frequency volatility τ exhibits smooth, lower-amplitude dynamics compared with total conditional volatility h_t and shows positive average cross-commodity correlations:
  - Average correlation between low-frequency volatilities: 0.1 for full sample, 0.3 for shorter sample (1957–2009).
  - Excluding sugar and rice, correlations rise to 0.5 (full sample) and 0.6 (short sample).
- Common low-frequency volatility episodes: inter-war years 1918–39 (increase), 1950–70 (low), 1970s (rise after Bretton Woods), and last 5–10 years (upward trajectory).

### Determinants of low-frequency food price volatility (1968–2009)
- Out of 16 candidate variables, seven emerged as statistically significant and relatively consistent determinants (Table 5; system regression with restrictions across commodities except inflation measures).
- Key determinants with sign and qualitative magnitude:
  - Real U.S. interest rate (level): negative relationship with low-frequency volatility.
    - Quantified example: one standard deviation decline in real U.S. interest rates (equivalent to about 1¼ percentage point) raises low-frequency price volatility by about ½ percentage point; effects particularly strong for soybeans and wheat.
  - Inflation volatility: positive and significant effect on low-frequency volatility.
    - Example magnitude: a one standard deviation increase in annualized inflation volatility (about 4 0 basis points since 1968) would increase long-run real food price volatility by between 1 and 4 percentage points, depending on commodity.
  - U.S. dollar exchange rate volatility: positive and significant effect.
    - Example magnitude: a one standard deviation increase in volatility of U.S. dollar nominal effective exchange rate (about 2 percentage points since 1968) raises low-frequency food price variation by between 1 and 2 percentage points.
  - Futures market volumes (annual average of daily observations across benchmark contracts): higher volumes increase low-frequency volatility; statistically significant but economically small.
    - Example: the average 68 percent increase in volumes over 2008 would lead to an increase in long-run volatility of less than 1½ percentage points.
  - Real global activity index (Kilian index / Baltic Dry Freight extension): lower real activity levels and higher activity volatility increase low-frequency food price volatility; effects statistically significant but small.
    - Quantified: a two standard deviation fall (or rise in volatility) in real activity would increase low-frequency volatility by less than 1 percentage point.
  - ENSO measures (Southern Oscillation Index and Niño 3.4 SST anomalies): statistically significant but small effects.
    - Example: a 2 degrees Celsius decline in Niño 3.4 SST anomalies (La Niña) would increase low-frequency food price variation by about 0.2 percentage points; a 2 standard deviation increase in SOI has a similar magnitude.
  - Stock market volatility: unexpectedly negative and statistically significant coefficient in multivariate specifications (robust inverse relationship after controlling for other financial variables); interpretation unclear.
- Regression estimation details:
  - System regressions estimated by GMM with Newey-West standard errors.
  - Restrictions imposed for parsimony: coefficients on explanatory variables set equal across commodities except inflation measures; coefficients on volatility of oil prices, equity prices, and open interest set to zero (accepted by likelihood ratio tests).
  - Two regressors (oil price volatility and open interest) set to zero in the restricted system.

### Factors found not to affect low-frequency volatility (joint regressions)
- Inventory-use (stock-use) ratios: no significant effect in jointly estimated regressions; some individual commodity evidence (wheat) but insufficient for broad claims.
- Oil price volatility: no significant impact in joint regressions; modest bivariate correlations for some commodities (corn and wheat ~0.2) but biofuel linkages may be too recent to detect robust long-run relationships.
- Policy variables (OECD producer support measures) over 1986–2007:
  - Nominal Producer Coefficient (NPC): insignificant for panel, significant only for wheat (Table 6).
  - Single Commodity Transfer (SCT): statistically significant and negative for panel driven largely by wheat; excluding wheat, no robust effect.

### What explains the recent rise in food price volatility?
- The model decomposes low-frequency volatility year-by-year by multiplying estimated coefficients by explanatory variables (example shown for corn in Figure 4).
- One common and large contributor: rising U.S. inflation volatility between 1995 and 2009.
- Source text truncates mid-sentence: "Between 1995 and 2009, inflation volatility increased from about"

*Source: _wp10129 - INTRODUCTION (IMF PDF)._

### 0.5 percent to about 2.3 percent. Combined with the largeestimated coefficients for corn,

### _wp10129 - 0.5 percent to about 2.3 percent. Combined with the largeestimated coefficients for corn,

### Major findings on food price volatility
- Low frequency (slow-moving) spot price volatility is positively correlated across different food commodities, indicating common factors explain part of price variability.
- During the last 10 years, this measure of volatility has risen for a range of different commodities.
- Combined with large estimated coefficients for corn, palm oil, and soybeans, certain factors "have contributed almost 10 percentage points to the increase in low frequency price volatility during this period for these commodities."
- Rising U.S. dollar volatility has trended higher from "about 3-5 percent in the mid-1990s to reach almost 10 percent in 2009." Based on the estimated model, this "has contributed to an additional 2-3 percentage points to food commodity price volatility."

### Determinants of low frequency volatility (identified in the paper)
- Real U.S. interest rates
- Real global economic activity levels and volatility
- U.S. inflation
- The U.S. dollar exchange rate
- Global stock market volatility
- Futures market volumes
- The La Niña weather cycle

- The variables with the largest effects and which also explain a relatively large part of the rise in volatility since the mid-1990s were "U.S. inflation volatility and the variability of the U.S. dollar exchange rate." The paper emphasizes commodities' sensitivity to these nominal variables because commodities act as real assets that hedge against both inflation and U.S. dollar depreciations.

### Role of futures market volumes
- Futures market volumes appear to have had a marginal effect, largely because of "the small size of the estimated coefficient from the model (a result which is subject to the caveat related to the possible endogeneity of volumes)."
- The largest change in volume in recent years was for corn, which experienced "an increase of about 150 percent in 2008 (marketing year)." Based on the estimated coefficient, this "contributed about 5 percentage points to volatility in 2008," but "sustained increases would be required to have a lasting influence on volatility."
- For other commodities, the contribution of rising volumes was smaller and mainly confined to the 2007-08 period. The paper concludes that "volumes appeared to play no major role in the broad rise in low frequency volatility which has occurred over the last 10 years."
- The paper finds a statistically significant positive relationship between trading volumes in commodity futures and low frequency food price volatility, but controlling for endogeneity remains difficult because futures trading volumes likely depend to some extent on expectations of future volatility. Other studies have failed to establish a robust relationship between futures volumes and price volatility.

### Conclusion and research needs
- It is useful to consider volatility as made up of high and low frequency components; greater understanding of low frequency volatility is particularly important because it "may be subject to a greater level of uncertainty with respect to its persistence and its causes."
- The paper points to aspects of food price volatility in need of further research, especially the endogeneity issues surrounding futures trading volumes and their relationship to future volatility expectations.

*Source: IMF working paper content provided in the supplied PDF excerpt.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10129.pdf_