Second, we assume that these crops receive the same share of input subsidies as the share of their values. So, if maize accounts for 10 percent of a country’s overall production value among these crops, it would receive 10 percent of total input subsidies. So, if a grid cell produces 20 percent of the country’s total maize production, we would estimate it to receive 10 percent x 20 percent—that is, 2 percent—of the country’s total input subsidy. In sum, these assumptions assign input subsides based on the value produced by selected crops in each region. Based on these assumptions, figure 3 shows the distribution of input subsidies across the world.

Finally, we use data on income per capita for each grid cell from Kummu, Taka and Guillaume (2018) to rank grid cells within each country from poorest to richest. We then use this ranking to examine whether relatively poorer grid cells within a country receive a share of subsidies that is proportionate to their agricultural production.

# **4 Methodology**

Lorenz curves (Lorenz 1905) are commonly used in equity analyses to graphically portray a population’s cumulative distribution function of income. Although the technique is most commonly used to show income distribution, it is possible to use it to represent any variable distributed across a population, including subsidies. Since Kakwani (1977) expanded and generalized the concept to cover the analysis of correlations between the distributions of different economic variables, studies have used Lorenz curves to investigate poverty and income inequality (Lucky and Sam 2018), the horizontal and vertical equity of electric vehicle rebate allocation (Guo and Kontou 2021), the equity of transit service accessibility (Lope and Dolgun 2020), and the distributional impact of climate change across income deciles and regions (Mideksa 2010; Tol 2021). In agricultural economics, the Lorenz curve has been used to study the equity effects of the US agricultural subsidy program (Kirwan 2007), inequalities in the distribution of estimated income among urban farmers in northern Thailand (Jaitiang, Huang and Yang 2021), inequality between CAP beneficiaries in the EU (Garcia-Bernardo, Jansky and Misak 2021), income inequality due to the adoption of agricultural technology in Northern Western Ethiopia (Shita, Kumar and Singh 2021), and inequality between rural households under the Conversion of Croplands to Forest and Ecological Welfare Forest Programs in rural Anhui, China (Zhang et al. 2019). Samman (2005) also uses Lorenz curves to study farm subsidies in Europe, the United States, and Brazil, to compare the distribution of subsidies across countries.

We calculate Lorenz curves to plot the cumulative subsidy received for a given percentile of per capita GDP. These are illustrated in figure 4. In this example, the cumulative amount of total subsidy (plotted in blue) measures the share of subsidy at each point received by grid cells in the GDP per capita percentile on the x axis, or lower. For example, by tracing upwards from the 20<sup>th</sup> percentile on the x axis, we see that the bottom 20 percent of grid cells in terms of income receive about 90 percent of the total subsidy. The total value of all agricultural production (red line) is plotted in the same way. The red line shows that these 20 percent of grid cells produce about 10 percent of agricultural production.

Borrowing from the risk aversion literature, the subsidy is said to first-order stochastically dominate production value if the blue line sits above the red line for the full distribution. This implies that the share 7