What commodities and countries impact inequality in the global food system?

We reconstructed the global food trade network based international food production and trade records. Within a network analysis framework, each node is a country with food production and consumption and each link is food trade between countries. We examine this network in terms of dietary energy (calories) rather than tonnage. We evaluated how each node and link contribute to overall inequality in food availability based on changes in the Gini coefficient when links were iteratively added and removed from the global trade network. The Gini coefficient is a widely used metric of inequality that ranges from 0 to 1, where higher values indicate more inequality (Gini 1936). We use this analytical framework to ask three questions:

• (1)  
  What countries contribute most to increasing and decreasing inequality in the global food system?
• (2)  
  What commodities contribute most to increasing and decreasing inequality in the global food system?
• (3)  
  For the commodities contributing most to increasing and decreasing inequality in the global food system, which countries contribute most to inequality through these commodities?

We reconstructed the global food trade network for the years 1986–2011 based on production and bilateral trade records from the Food and Agricultural Organization (FAO) of the United Nation's FAOSTAT database (http://faostat.fao.org/). For each commodity m and year y a trade matrix N_m(y) was generated where the i, j element of the matrix is the total export tonnage of the commodity m from country i to country j. We created these matrices for 390 commodities in the FAOSTAT database that are used for human consumption. Tonnages for the commodities were converted to kilocalorie equivalents using conversions from the FAO Nutritive Factors Database (D'Odorico et al 2014, SI table 1). Hence, the results of our analysis represent inequality in dietary energy availability. While animal products were included in this study, live animals were not considered because we could not convert the carcass weight to calories available for human consumption without detailed information on the age demographics of the animals which are not available in FAOSTAT. Fish and fish products were also not considered as detailed bilateral trade data is unavailable in a format consistent with FAOSTAT (e.g. Gephart and Pace 2015).

For our network analysis, we used production data for 159 primary commodities, but trade links were created for all 390 commodities (see supplemental information for lists of commodities). This approach limits the potential for double counting dietary energy production (D'Odorico et al 2014, Carr et al 2015). For example, beef is a secondary commodity produced in part by feeding maize to cows. Counting the energy content of both cows (secondary products) and maize (primary products) would overestimate the dietary energy availability for humans. By basing production on primary commodities only, we minimize the potential for double counting while still accounting for the fact that international trade of secondary products is an important aspect of redistributing dietary energy availability at the global scale. However, we do not account for reexportation as such methods come with assumptions which can be difficult to ascertain for all secondary products (Kastner et al 2011).

We included countries with populations greater than 1 million during the period 1986–2011 in our analysis based on population records in the FAOSTAT database. National boundaries changed during the record including the reunification of Germany and the dissolution of the Union of Soviet Socialist Republics. To develop a consistent trade network, we retained the more aggregated configuration of these countries throughout the analysis (Carr et al 2013, D'Odorico et al 2014).

Given two vectors V_1,y and V_2,y for year y and where the subscripts 1, 2, denote a given quantity of interest for all n network nodes, a metric describing the inequality in the distributions such as the Gini coefficient (G), can be calculated. A common example is when V_1,y is income and V_2,y household size, then the inequality metric describes the inequality in income among households (Deininger and Squire 1996). In this study V_1,y is dietary energy availability of different countries (in kilocalories) and V_2,y is the population of those countries and the inequality metric describes the inequality in mean dietary energy availability among countries.

In this study we use the Gini coefficient to quantify inequality. Given ${x}_{i}=\displaystyle \frac{{V}_{1,i,y}}{{V}_{2,i,y}}$ and ${\mu }_{x}=1/n\displaystyle {\sum }_{i=1}^{n}{x}_{i},$ the adjusted Gini coefficient is calculated as (Kendall and Stuart 1958):

$$\begin{eqnarray}&&{G}_{y}=\displaystyle \frac{1}{n{\mu }_{x}}\displaystyle \sum _{i=1}^{n}\,\displaystyle \sum _{j=1}^{n}\displaystyle \frac{| {x}_{i,y}-{x}_{j,y}| }{2n},\end{eqnarray} \tag{ 1 }$$

The contribution of an individual node (country) i $({g}_{i,y})$ can be calculated as

$$\begin{eqnarray}&&{g}_{i,y}=\displaystyle \frac{1}{n{\mu }_{x}}\displaystyle \sum _{j=1}^{n}\displaystyle \frac{| {x}_{i,y}-{x}_{j,y}| }{2n}.\end{eqnarray} \tag{ 2 }$$

This calculation of an individual node's contribution to inequality is complicated if there is international trade because a portion of inequality contributed by node j (increased or decreased inequality) should be attributed to node i. We can account for this using the trade matrix N_1,y, described in section 2.2, to acquire a new distribution of resources V'_1,y and calculate a new Gini coefficient G'. Following equation (1), let ${x}_{i}^{\prime }=\displaystyle \frac{{V}_{1,i,y}^{\prime }}{{V}_{2,i,y}},$ then ${G}_{y}^{\prime }\,=\displaystyle \frac{1}{n{\mu }_{x}^{\prime }}\displaystyle {\sum }_{i=1}^{n}\displaystyle {\sum }_{j=1}^{n}\displaystyle \frac{| {x}_{i,y}^{\prime }-{x}_{j,y}^{\prime }| }{2n}.$ The individual contribution of link ij to inequality can then be estimated by,

$$\begin{eqnarray}&&{\rm{\Delta }}{\hat{G}}_{ij,y}=\displaystyle \frac{{G}_{y}^{\prime }-{G}_{-ij,y}^{\prime }+{G}_{+ij,y}-{G}_{y}}{2},\end{eqnarray} \tag{ 3 }$$

where ${G}_{-ij,y}^{\prime }$ is the Gini coefficient after removing link N_ij,y from the network and recalculating G'. Similarly, ${G}_{+ij,y}$ is the Gini adding only link N_ij,y to the network and recalculating G_y. In other words, ${G}_{+ij,y}$ considers a world where there is only one trade link, link ij, and ${G}_{-ij,y}^{\prime }$ considers a world with all trade links present except link ij. In this manner a positive or negative effect, ${\rm{\Delta }}{\hat{G}}_{ij,y}$ on inequality can be estimated for all links ij in N_1,y. It is important to note that ${\rm{\Delta }}{\hat{G}}_{ij,y}$ is only an estimate, with ${G}_{y}^{\prime }-{G}_{y}\cong \displaystyle {\sum }_{i=1}^{n}\displaystyle {\sum }_{j=1}^{n}{\rm{\Delta }}{\hat{G}}_{ij,y}$.

This impact of link ij on the Gini coefficient of all nodes k can be calculated as:

$$\begin{eqnarray}&&{\rm{\Delta }}{\hat{g}}_{k,ij,y}=\displaystyle \frac{g{^{\prime} }_{k,y}-g{^{\prime} }_{k,-ij,y}+{g}_{k,+ij,y}-{g}_{k,y}}{2}.\end{eqnarray} \tag{ 4 }$$

It is important to note that the directed link N_ij,y is thus transformed into a vector of impacts (positive and negative) on all nodes. We can then group these individual impacts by node, ${\rm{\Delta }}{\hat{g}}_{i}=\displaystyle {\displaystyle \sum }_{k,j}\,{\rm{\Delta }}{\hat{g}}_{k,ij},$ the impact to one's self by exporting

$$\begin{eqnarray}&&{\rm{\Delta }}{\hat{g}}_{{\rm{s}}{\rm{e}}{\rm{l}}{\rm{f}}}=\displaystyle \sum _{k,j=i}{\rm{\Delta }}{\hat{g}}_{k,ij},\end{eqnarray} \tag{ 5 }$$

and the impact to the other nodes in the network or

$$\begin{eqnarray}&&{\rm{\Delta }}{\hat{g}}_{{\rm{o}}{\rm{t}}{\rm{h}}{\rm{e}}{\rm{r}}}=\displaystyle \sum _{k,j\ne i}{\rm{\Delta }}{\hat{g}}_{k,ij},\end{eqnarray} \tag{ 6 }$$

and the ratio of ${\rm{\Delta }}{\hat{g}}_{{\rm{s}}{\rm{e}}{\rm{l}}{\rm{f}}}$ to ${\rm{\Delta }}{\hat{g}}_{{\rm{o}}{\rm{t}}{\rm{h}}{\rm{e}}{\rm{r}}}$ in order to examine the behavior of nodes. Lastly, this analysis can be further dissected by commodity trade, thus instead of link ij, the analysis is done on link ijm, where m is the commodity in question. Similarly, these individual commodities can be recombined into FAO groups, to examine the impact of various commodity groupings (e.g., cereals). We stress that the calculation of the Gini coefficient expressed by the above equations takes population into account in the initial ratios x_i and ${x}_{i}^{\prime }$. As such, a smallF transfer between two populous countries can have little impact on the Gini coefficient, whereas the same transfer to, or from, a less populous country can have greater impact on the Gini coefficient.

Overall inequality in dietary energy production (measured by G_y) has increased from 1986 to 2011 (0.44 increasing to 0.48). Redistribution of dietary energy availability through international trade reduces inequality by about 25%–33% relative to the distribution of production, depending on the year (i.e. ${G}_{y}^{\prime }\lt {G}_{y}$ ). Basic results from our analysis are visualized in figure 1, in which the ordinate is the contribution of individual trade links to the Gini and the abscissa is the number of links ordered from lowest (negative, trade link decreases inequality) to highest (positive, trade link increases inequality) contribution to inequality. The number of trade links increased over time (see also table 1), illustrated by the wider spread of data on the abscissa, consistent with previous analyses of the global food trade network (e.g. D'Odorico et al 2014). The vast majority of international trade links have little or no impact on the total inequality in global food availability, and only a small percentage of links provide almost all of the increases and decreases in inequality. This is illustrated by the broad bottom of the curves where most links reside with little or no contribution to the Gini coefficient (figure 1).

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Table 1.  The Gini coefficient prior to and after trade, the change in the Gini from the two perspectives and the estimated change resulting from averaging the two perspectives along with the error in the estimate. Number of links for each year in the multigraph network, what fraction of those links act to decrease inequality, the total reduction that fraction provides, and the increase due to the remaining links.

	1986	1996	2006	2011
Production ${G}_{y}$	0.4415	0.4381	0.4423	0.4768
After trade ${G}_{y}^{\prime }$	0.3319	0.3302	0.2987	0.3211
Change ${\rm{\Delta }}{G}_{y}$	−0.1096	−0.1079	−0.1436	−0.1557
${\rm{\Delta }}{G}_{+ij,y}$	−0.1662	−0.1868	−0.2721	−0.2428
${\rm{\Delta }}{{G}^{\prime }}_{-ij,y}$	−0.0569	−0.0476	−0.0300	−0.0780
Estimate ${\rm{\Delta }}{\hat{G}}_{ij,y}$	−0.1115	−0.1172	−0.1512	−0.1604
% error	1.2	8.6	5.2	2.9
Max reduction	−0.152	−0.159	−0.205	−0.214
Max increase	0.040	0.042	0.054	0.054
# links	636 32	125 520	192 302	216 537
% of links reducing	63.6%	58.3%	58.6%	58.6%

Plotting the Gini as a function of cumulative calories transferred reveals that most of the trade links which have little to no impact on inequality are associated with very small transfers as indicated by the distinct minima in the curves (figure 2). From this calorie based perspective, links which cause small changes in inequality from large transfers appear as horizontal jumps in the curves and correspondingly links which cause larger changes in inequality from small transfers appear as vertical jumps. It is interesting to note that some of the links which have largest impacts on inequality, both positive and negative, are associated with smaller transfers.

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Across all years, about 58% of the total trade links act to reduce inequality and these trade links are associated with roughly three quarters of the calorie transfers. These decreases in inequality and transfers remain concentrated, with ∼4% of the links providing 95% of the reduction in inequality and ∼70% calorie transfers for all years. The percentage of links providing 95% of the increases in inequality rose from 2.6% in 1986 to 4.1% in 2011, but was still consistently ∼24% calorie transfers across all years, indicating a similar level of concentration.

In 1986, 63 632 individual commodity trade links generated 8399 424 distinct increases and decreases in inequality. In 2011, 216 537 individual commodity trade links generated 32 913 624 distinct increases and decreases in inequality. One way to think of these impacts on inequality is as a matrix, M, that has a number of rows, r equal to the number of individual trade links, and number of columns, c, equal to the total nodes in the network. Each entry in M_rc is the the impact of link r = ijm (i.e., the trade link of commodity m between nodes i and j) on country c. Summing across the rows of M provides the total impact of each individual commodity link (table 2, shown in figure 3). Summing down the columns of M (or impacts on each individual country from each trade link) estimates the contribution to the change in inequality that a country exerts by merely participating in global trade (figure 3). This is a measure of both direct participation (impacts generated via a country's own import and export choices) and indirect participation (impacts generated by other country's trade).

Table 2.  Top ten nodes that increase (red) or reduce (blue) inequality in 2011 via their export links, their impact to their own contribution to inequality, the impact to the other nodes contribution, ratio of a nodes impact to itself to its global impact, and the percent of the total change that node via exports is responsible for.

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Examining the impact a country's exports or imports have on inequality provides a means for exploring the direct, or controllable contributions of a country to inequality (figure 4). This is different than the combined direct and indirect effects reported in figure 3 (SI table 2), as this only considers the impacts generated by the trade links in which a country is participating. Major changes due to export impacts remain concentrated to the few countries with large exports such as the United States of America, with some countries not exporting at all (whited out countries). In contrast almost all countries participate in importation, and thus, the impacts from importation are less concentrated to a few countries. In 2011, across all commodities, Slovenia, Singapore, Oman, Germany and the United Kingdom are the major contributors to increasing inequality via their exports, while the United States, Malaysia, Argentina and Canada are the major contributors to reducing inequality relative to patterns of production (table 2, figure 4). The export of Cake of Soybeans, Soybeans, Maize, Refined Sugar, and Fresh Whole Cow Milk, from Slovenia, alone account for 8.8% of the global increase in inequality via trade for 2011. In contrast exports from the United States of America account for 12% of the decrease in inequality in 2011 (tables 1 and 2).

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The top ten commodity transfers that increase and decrease inequality are comprised of only a handful of commodities: Palm oil, Soybeans, Cake of soybeans, Wheat, Maize and Barley (table 3). However, summing the impact of all transfers for each commodity reveals that the top commodities whose trade leads to increased inequality are Cocoa beans, Bananas, Molasses, Coconut (copra) oil and Groundnuts (Shelled). The top commodities whose transfers overall reduce inequality are Sugar (Refined), Rice (Milled), Palm oil, Maize and Wheat (tables 4, SI table 3). While individual links and commodities can be examined, the combined impact of a primary product and its secondary products should be also considered. For example, transfers of Cocoa beans increases the Gini coefficient in the system by 0.00066, trade of Chocolate (Prsns) reduces the Gini coefficient by 0.00054 (SI table 3). In this regard, it is also important to examine how groups of commodities impact inequality.

Table 3.  Top 10 commodity transfers that increase (red) and decrease (blue) inequality, the impact on the inequality of that individual trade link and the portions of that impact that directly belong to the exporter and importer (e.g. the direct impact of link ij on country i and country j). Impacts were evaluated as the difference in Gini coefficient with and without the commodity specific trade links in order to determine the major contributors to inequality.

Table 4.  The total positive (red) or negative (blue) impact on inequality due to the trade of specific commodities. The portion of that total impact which reduces inequality, the portion which increases inequality and the absolute ratio between the positive and negative portions of the total impact.

In 1986, trade of cereal commodities accounted for 72.6% of the decrease in inequality. Roots, fruits and stimulants combined contribute most to increasing inequality, but only account for 1.5% of the total change in inequality. This contrast indicates that reductions in inequality are dominated by a single commodity group, but that increases in inequality are not commodity group specific (table 5). This pattern held throughout the study record. In 2011, trade of cereal commodities was responsible for 62.5% of the decrease in the Gini coefficient. In contrast, fruits and stimulant categories combined in 2011 only provided a 0.57% increase in inequality (table 6).

We can focus the analysis, for example the trade of the cereal commodity group for the year 2011, to help decipher the impacts of specific trade links (table 7). The top five countries that reduce inequality via exports (table 7), are responsible for 23.5% of the −0.214 maximum drop in the Gini coefficient (table 1, figure 1). On the other hand, the top five nations that increase inequality via trade of cereal commodities represent only the 5.5% of the 0.054 maximum increase in inequality due to trade. These results can then be further filtered to identify the specific links within the cereal commodity grouping that best contribute to decreasing the Gini coefficient such as the export of wheat from France to Algeria or Maize from the United States to Japan. In contrast, the cereal trade links associated with the largest increases in inequality are the export of Maize from Slovenia to Italy and the export of Barley from Argentina to Uruguay (table 8).

Table 7.  Top 10 nodes that increase (red) or reduce (blue) inequality within the cereal commodity grouping, their impact to their own contribution to inequality, the impact to the other nodes contribution, ratio of a nodes impact to itself to its global impact, and the percent of the total change that node via exports is responsible for.

Table 8.  Top ten transfers that increase (red) and decrease (blue) inequality within the cereal commodity network, the kilocalories traded, the impact of that link, the impact of that link to the exporting country and the impact of that link to the importing country.