2.1 Selection of Commodities

The sample includes annual data from 1960 to 2021 for 20 agricultural, energy, and mineral commodities. In choosing the commodities in our sample, we first follow Alvarez et al. (2023) and consider those commodities that are among the top 10 most traded commodities (by USD value of exports 2019, BACI data) in agricultural goods and minerals, respectively. Alvarez et al. (2023) also add those commodities that are on the US or UK critical minerals lists. They include palm oil due to its importance for food production and as a biofuel.

We exclude those commodities where data availability is an issue, notably silicon, sun-flower seeds, tobacco, and titanium. Natural gas is excluded because of significant market segmentation between Europe, North America, and Asia during the sample period. We add bananas, bovine, tea, and cereals because of their importance as food commodities. Cereals is the calorie-weighted average of wheat, maize, soybeans, and rice based on global production numbers. For metals, we use refined production and consumption data when the data quality is high enough, and revered to mined production data if necessary.

Commodities in our sample:

• Food and beverages: Bananas, Bovine, Cocoa, Coffee, Maize, Palm Oil, Rice, Soybeans, Sugar, Tea, Wheat, and Cereals.

• Raw agricultural materials: Cotton and Rubber (natural).

• Energy: Crude oil and Coal.

• Minerals: Aluminum, Copper, Lead, Tin, and Zinc.

2.2 Data Sources

For the production and consumption of agricultural commodities, by-country data are from the Food and Agricultural Organization (FAO, 2023). The International Energy Agency (IEA, 2024) provides the by-country data for the consumption and production of crude oil and coal.

By-country data on refined consumption of aluminum, copper, lead, tin, and zinc is gathered from Stuermer (2017) until 1994. The data-series are then extended based on spliced data from the World Bureau of Metals Statistics (WBMS, 2024) for the period from 1995 to 2021. Data on the production of aluminum, lead (refined), and copper (mined) are from the British Geological Survey (2023) for the period 1960 to 2021, while data for the production of tin and zinc are based on Bems et al. (2023) for the period 1960 to 1994. The data are then spliced onto series from WBMS (2024) for the years 1995 to 2021.

Price data are from the World Bank (2024) as well as Schwerhof and Stuermer (2019). Series are adjusted for inflation using the US consumer price index from US Bureau of Labor Statistics (2024).

Working with historical data for a large set of countries faces the challenge of inconsistent series with breaks, zero observations, and other issues. To deal with that, we use an algorithm to sort out unreliable consumption and production data series. We keep those country series that fulfill the following criteria:

1. All observations are larger than zero in levels.

2. Log changes of all observations are within the 10th and the 90th percentile of the distribution.

3. Less than 20 zero entries in log changes.

4. The country is above the 25th percentile in terms of its volume of consumption (or production).

These criteria are applied to agricultural and energy commodities. For the five mineral commodities, we check for consistency of the series by hand. Crude oil series are exempted from criterion 4.

3.1 Constructing the Granular Instrumental Variables

Let the following two equations represent supply and demand (in log-differences) for country i in deviation from its steady state in year t:

It is assumed that the idiosyncratic shocks $u_{it}^d\sim N(0,{\sigma }_{d,u}^2)$ and $u_{it}^s\sim N(0,{\sigma }_{s,u}^2)$ are country-specific and mutually independent. This means that they are uncorrelated with the common shocks, between supply and demand, and across countries. As for the factor loadings for the common shocks, note that the simplest case is when the factor structure is that of a single year fixed effect, i.e., ${\lambda }_i^d{\eta }_t^d={\eta }_t^d$ and ${\lambda }_i^s{\eta }_t^s={\eta }_t^s$.

To estimate the supply and demand elasticity pair {ϕ^d,ϕ^s}, we implement the following algorithm. Let us refer to the set of countries on the consumption and production side that fulfill the four criteria described in section 2 as I_d and I_s respectively.

1. A panel regression is performed for both consumption and production. Using consumption as an example, we estimate:

which gives us ${\widehat{ϵ}}_{it}$. The time fixed effects δ_t capture the price and any other common factors. There are, however, common factors in the residuals if these have heterogeneous impacts across countries. The next step accounts for this possible residual common factor.

2. Following Bai (2009), country-specific components are extracted from ${\widehat{ϵ}}_{it}$:

where F_t is a matrix of factors, and Λ is a matrix of heterogeneous (i.e., country-specific) loadings.¹ We save the residuals ${\hat{u}}_{it}$ and the estimated factors ${\hat{F}}_t$, as the latter can be used to increase the efficiency of the IV regressions. The same steps 1 and 2 are executed for production with i ∈ I_s. To differentiate between demand and supply, we refer to the saved residuals as ${\hat{u}}_{it}^d$ and ${\hat{u}}_{it}^s$ respectively.

3. The consumption (production) instrument can then be constructed as the share-weighted average of the estimated idiosyncratic shocks:

where ${\omega }_i^k$ represents the time-invariant share of country i in total production (consumption) over the entire sample. If there is one common factor with homogeneous loadings, i.e., a year fixed effect, to estimate the idiosyncratic shocks, equation (4) reduces to the following expression which can be used to obtain the instrument directly from the data:

In addition to using $z_t^d$ and $z_t^s$ as instruments, the difference $z_t^d-z_t^s$ can also be used as an instrument (as suggested in Appendix H14 of Gabaix and Koijen (2020)). Thus, we have a consumption-based GIV, a production-based GIV, and the difference of the two, which is the preferred approach according to Gabaix and Koijen (2020). Furthermore, we create three variations of each instrument: one with a single time fixed effect (for which thus step 2 of the algorithm is skipped), one with one common factor with heterogeneous loadings, and one with two common factors with heterogeneous loadings. This implies there are nine GIVs in total for each commodity.

3.2 Regression Analysis

The unweighted average of consumption (or production) is defined as $y_{Et}^k=\frac{1}{I^k}{\displaystyle \sum }_{i=1}^{I^k}{y}_{it}^k$. To estimate the elasticities of supply and demand at different horizons, we then estimate the following series of local projections with instrumental variables for each horizon h = 0, 1, 2, . . . , 5:

Where $y_{E,t+h}^k$ is the average h + 1 period log-difference, that is, $y_{E,t+h}^k\equiv In\left(y_{i,t+h}^k\right)-In\left(y_{i,t-1}^k\right)$. At horizon h = 0 we are back at the simple annual log-difference, while δ_h(L) and β_h(L) are polynomials in the lag operator L = 5. The efficiency of the local projections estimates is further improved by adding the estimated factors from step 2 of the GIV algorithm.

To identify a causal effect of prices on average production (consumption) we instrument p_t with both the contemporaneous and lagged GIVs, that is, we use the pair $\left\{z_t^{k}mL\mathrm{.}{z}_t^k\right\}$. We thus have nine such pairs of instruments for each commodity, on both demand and supply side.

We select the instrument pair that exhibits the strongest first stage, as measured by the F-score, conditional on the elasticity (so the 2nd stage) also having the right sign for our baseline results (see Miranda-Pinto and Young, 2022, for a silimar approach). If that second condition is not met (so the elasticity has the wrong sign), we go to the second-best IV pair, and so forth until we find a specification with the right sign.

5.1 Commodities are Mostly Inelastic

On the supply side, results for the one year elasticities show that metals, especially copper and zinc, tend to have the lowest elasticities, while agricultural commodities generally have the highest (see Figure 3 and Table 2). For example, copper and zinc show supply elasticities close to zero. In contrast, the results for cereals show that the supply elasticity is around 0.6, implying that a 10 percent increase in prices raises output by 6 percent within a year. This is in line with the fact that crop switching or applying more fertilizer are relatively easy within a year, whereas the expansion and opening of mines is subject to longer lead times.

In the same vein, there is also an important distinction within agriculture between multi-year perennial crops such as coffee, cocoa, palm oil, and rubber on the one hand, and annual crops for cereals like maize and soybeans on the other hand. Perennial crops are characterized by smaller supply elasticities compared to annual crops due to the extended growing period needed for palm oil trees, coffee trees, and cocoa trees, which typically take at least two, three, and five years respectively, to bear fruit. The supply elasticities of energy commodities tend to be in-between those for the mineral and agricultural commodities.

The demand side is less determined by the type of commodity. Instead, commodity specific characteristics seem to play a larger role. This is in line with the fact that there are several mechanisms on the demand side that allow for adjustment: substitution by other commodities, more efficient use, and the substitution of downstream products by other products. For agricultural goods, rice is atypical, showing a price elasticity of demand close to zero, probably reflecting that only about 10 percent of rice production is traded internationally. Being a staple food in Asia, rice prices are also typically subsidized. Elasticities for tea, cotton, and wheat are above 0.4. For crude oil and coal, the results show demand elasticities below 0.2 in line with the difficulties to switch from one fuel to the other due to technical constraints over the short term. Finally, copper and zinc show demand elasticities close to zero, whereas those for lead and tin are between 0.2 and 0.3. The former metals are essential for electrical appliances and steel production, respectively, while lead and tin are much easier to substitute.

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Impulse response functions of commodity demand and supply

Citation: IMF Working Papers 2024, 077; 10.5089/9798400271953.001.A001

Sources: Food and Agriculture Organization; World Bureau of Metal Statistics; and IMF staff estimates.Note: Impulse response functions (IRFs) show the change in the quantity supplied (blue line) or demanded (red line) due to a1 percent increase in prices as a function of time measured in years. IRFs are based on a combination of local projections and the granular instrumental ariable approach (Gabaix and Koijen, forthcoming). 90 percent confidence bands are shown.

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Table 1 compares our elasticity estimates against a range of estimates from previous papers, as summarized by Fally and Sayre (2018). The table shows first that our results are not only the first that provide consistent estimates across a broad set of commodities, but that half of our estimates are for new commodities in the literature. When comparing our estimates with those found in the literature, our results point to a higher supply elasticity for coal; the demand elasticity for rice is not statistically different from zero and is at the upper bound of the Fally and Sayre (2018)’s range of estimates. The point-estimate for the soybean short-term demand elasticity is higher than in the literature, while for wheat the elasticity is towards the low-end range. The long-run copper supply elasticity is within the range of estimates in the literature, while demand seems more elastic than previously estimated.

Table 2 in the annex shows the detailed local projection estimation results of the supply and demand elasticities at different horizons for all 20 commodities. The table also indicates whether the specification that was chosen for the baseline based on the strongest instrument uses a consumption-based IV, a production-based IV, or an IV based on the difference of these two IVs.

5.2 Supply and Demand Become More Responsive over Time

The results also demonstrate that commodities tend to become more responsive over time as markets adjust. However, based on long-run multipliers at different horizons the results show notable differences across the three different types of commodities. The results for agricultural commodities indicate that, for the most part, supply responses are relatively fat over a five-year horizon. At the same time, some commodities show a statistically significant strong peak about two to three years after the shock. This includes perennial multi-year crops such as rubber, coffee, and cocoa. For most of the metals and energy the supply elasticities are upward sloping, but only in a significant way for copper.

On the demand side, results are generally not very precisely estimated. Metals show the largest increases in the multipliers over the horizon. At the same time, for most agricultural commodities the demand multipliers have not become larger.

Overall, demand and supply for agricultural goods appear to be generally more responsive to shocks than minerals and energy commodities, which is consistent with the smaller price volatility observed for agricultural goods, compared to metals and energy commodities (Figure 4). Agricultural commodities also see the least increase in their responsiveness after a couple of years, whereas the responsiveness increases quite strongly for mineral commodities.

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Commodity Price Volatility

Citation: IMF Working Papers 2024, 077; 10.5089/9798400271953.001.A001

Sources: IMF Primary Commodity Price System; and IMF staff calculations.Note: Volatility is the standard deviation of log-differences in monthly prices over the repective periods. Base metal, food, cereal, coal, and natural gas are price indexes. The crude oil price refers to the IMF average petroleum spot price.

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5.3 Comparison to Other Identification Methods

Table 3 in the Annex provides a comparison between the supply shocks identified by narrative identification in Caldara et al. (2019) and those identified by the GIV approach at the example of the oil market. The table shows all episodes of large country-specific oil production drops considered by Caldara et al. (2019), and marks those that are identified as exogenous by the authors. Note that there are major differences in the frequency and scope of these episodes. While Caldara et al. (2019) identify monthly oil supply shocks at the global level and then attribute them to outages in individual countries, we identify shocks at the annual frequency and at the country-level in our setup.

The comparison is reassuring. In those cases where the monthly supply shocks identified by Caldara et al. (2019) lead to a supply shock at the annual frequency, the shocks based on the narrative approach are broadly similar to those identified using the GIV. For example, take the case of the USA in September 2005, when hurricane Rita hit oil production in the Gulf of Mexico. In Caldara et al. (2019), the actual decline in US monthly output of -18.9 percent leads to a negative supply shock of -1.3 percent in global oil output. This monthly decline spills over to an actual annual decline of -5.2 percent in our data, and to an idiosyncratic shock in the GIV of -5.3 percent.

For other examples like Iran’s supply shock in 1987 due to war with Iraq, there is not much overlap between the two instruments. However, this can be explained by the different frequencies. Iran’s output declined by 22 percent in September but considering the annual average it increased by 12 percent in 1987. The GIV picks up the latter as an idiosyncratic shock. In other cases, e.g., Ecuador in 1987, our algorithm does not consider the country because data is not consistent over the entire sample length.

Differences with Caldara et al. (2019) are related to the temporary nature of the shock (at most two months) and subsequent rebound (Iran Jan 1985, Nigeria Jun 1985, Qatar Apr 1986, UAE Aug 1990) or to a drop after a spike in production (Saudi Arabia Sept 1986, Iran Sept 1987, UAE Jan 1988). Caldara et al. (2019) also compare their shock series with those identified in Kilian (2008). There are quite some notable differences that indicate that the literature is not settled on this question.

Overall, the results of this comparison show that the GIV method identifies similar shocks when the data is comparable at the monthly and annual frequency.