metadata: authors: 0: author: Blankespoor,Brian
1: author: Ru,Yating
2: author: Wood-Sichra,Ulrike
3: author: Thomas,Timothy S.
4: author: You,Liangzhi
5: author: Kalvelagen,Erwin
count: World
docna: 0: docna: Estimating Local Agricultural GDP across the World
docty: Policy Research Working Paper
abstracts: cdata!: Economic statistics are frequently
            produced at an administrative level such as the sub-national
            division. However, these measures may not adequately capture
            the local variation in the economic activities that is
            useful for analyzing local economic development patterns and
            the exposure to natural disasters. Agriculture GDP is a
            critical indicator for measurement of the primary sector, on
            which 60 percent of the world’s population depends for their
            livelihoods. Through a data fusion method based on
            cross-entropy optimization, this paper disaggregates
            national and subnational administrative statistics of
            Agricultural GDP into a global gridded dataset at
            approximately 10 x 10 kilometers using satellite-derived
            indicators of the components that make up agricultural GDP,
            namely crop, livestock, fishery, hunting and timber
            production. The paper examines the exposure of areas with at
            least one extreme drought during 2000 to 2009 to
            agricultural GDP, where nearly 1.2 billion people live. The
            findings show an estimated US$432 billion of agricultural
            GDP circa 2010.
display_title: Estimating Local Agricultural GDP
            across the World
listing_relative_url: /research/2022/06/33853609/estimating-local-agricultural-gdp-across-world
topicv3: Agriculture and Food Security m1326205 435
publishtoextweb_dt: 2022-06-27T00:00:00Z
dois: 10.1596/1813-9450-10109
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: 957135
1: author_key: NA
2: author_key: NA
3: author_key: 166335
4: author_key: 1072043
5: author_key: 1075297
model_extractions: Policy Research Working Paper 10109

# Estimating Local Agricultural GDP across the World

_Brian Blankespoor Yating Ru Ulrike Wood-Sichra Timothy S. Thomas Liangzhi You Erwin Kalvelagen_ Development Economics Development Data Group June 2022
Policy Research Working Paper 10109

# **Abstract**

Economic statistics are frequently produced at an administrative level such as the sub-national division. However, these measures may not adequately capture the local variation in the economic activities that is useful for analyzing local economic development patterns and the exposure to natural disasters. Agriculture GDP is a critical indicator for measurement of the primary sector, on which 60 percent of the world’s population depends for their livelihoods. Through a data fusion method based on cross-entropy optimization, this paper disaggregates national and subnational administrative statistics of Agricultural GDP into a global gridded dataset at approximately 10 x 10 kilometers using satellite-derived indicators of the components that make up agricultural GDP, namely crop, livestock, fishery, hunting and timber production. The paper examines the exposure of areas with at least one extreme drought during 2000 to 2009 to agricultural GDP, where nearly 1.2 billion people live. The findings show an estimated US$432 billion of agricultural GDP circa 2010.

This paper is a product of the Development Data Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at bblankespoor@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Estimating Local Agricultural GDP across the World**<sup>_†_</sup>

_Keywords_ : agriculture, regional economic activity, GDP, cross-entropy _JEL Classification Codes_ : Q10, R12

> _†_ The authors would like to thank the following people for discussions and prior reviews: Claudia Berg (World Bank), Gero Carletto (World Bank), Uwe Deichmann (World Bank), Rashmin Gunasekera (World Bank), Barbro Hexeberg (World Bank), Glenn-Marie Lange (World Bank), Michael Lokshin (World Bank), Eric Roland Metreau (World Bank), Jose Pablo Valdes Martinez (World Bank), Tim Robinson (FAO), Steven Rubinyi (World Bank), Juha Siikam ̈aki (IUCN), Ben Stewart (World Bank), Jeffrey R. Vincent (Duke University). We appreciate the use of non-timber value data from Juha Siikam ̈aki and ports data from Gilles Hosch. The authors would like to thank the participants of conferences including: American Association of Geographers Annual Meeting 2019 in Washington, DC, 3-7 April 2019; United Nations Economic Commission for Europe Workshop on Data Integration: Realising the Potential of Statistical and Geospatial Data in Belgrade, Serbia, 21-23 May 2019; International Institute for Applied Systems Analysis seminar in Laxenburg, Austria, 27 September 2019; IFPRI RISE Workshop in Washington, DC, 19 November 2019; and the Committee for the Coordination of Statistical Activities and United Nations Geospatial Network Joint virtual Workshop on the Integration between Geospatial and Statistical Information, 28 April 2021. We appreciate the support of the World Bank Strategic Research Program on Big Data. The maps displayed in this paper are for reference only. The boundaries, colors, denominations and any other information shown on these maps do not imply, on the part of the World Bank Group any judgment on the legal status of any territory, or any endorsement or acceptance of such boundaries.

> _‡_ World Bank. Corresponding author can be reached at: bblankespoor@worldbank.org

> _⋆_ These authors contributed equally to this work.

> _§_ Cornell University. Email: YR97@cornell.edu

> _¶_ International Food Policy Research Institute

> _∥_ International Food Policy Research Institute. Email: T.Thomas@cgiar.org

> _∗∗_ International Food Policy Research Institute. Email: L.YOU@cgiar.org
# **1 Introduction**

According to the Food and Agriculture Organization of the United Nations, over 60 percent of the world’s population depends on the agricultural sector for their livelihoods and it provides a key source of income and employment for the poor and vulnerable people (FAO, 2013; FAO, 2019). Yet, economic statistics of the agricultural sector are frequently produced at a national or lower administrative level and may not adequately capture the local variation. Furthermore, a spatial mismatch may exist between the geographic unit of interest like the natural area of a river and the administrative area.

Detailed agricultural data are critical to examining a wide range of agricultural issues including technology and land use (e.g. Bella and Irwin, 2002; Luijten, 2003; Samberg et al., 2016; Staal et al., 2002), exposure to natural hazards (e.g. Murthy, Laxman, and Sai, 2015) and patterns of and productivity of economic development (e.g. Elhorst and Strijker, 2003; Gollin, Lagakos, and Waugh, 2014; G. C. Nelson, 2002; Reddy and Dutta, 2018). Carr ̃ao, Naumann, and Barbosa (2016) examine the exposure of people and economic activity to drought using measures of physical elements (e.g. cropland and livestock). Rentschler and Salhab (2020) find that low and middle-income countries have 89% of global flood exposed population and poor people account for almost 600 million, who are directly exposed to the risk of intense flooding. Vesco et al. (2021) examine linkages between climate variability and agricultural production as well as conflict. They find that climate variability contributes to an increase in the spatial concentration of agricultural production within countries. Furthermore, in countries with a high share of agricultural employment in the national workforce, they find this combined effect increases the likelihood of conflict onset. To better target rural development strategies for economic growth and poverty reduction, as well as conserve the natural resource base for long-term sustainable development, we need to accurately delineate the spatial distribution of agricultural resources and production activities (Wood et al., 1999).

One method to partially address spatial mismatch between administrative and other geographic units such as natural hazards uses the gridded (raster) data format by providing an intermediate and consistent unit for disaggregation and aggregation (e.g. UNISDR, 2011). Data-disaggregation methods can use detailed data to inform estimates of aggregated data from large areas at the local level (e.g. see review in Pratesi et al., 2015). Several spatial data products from global models are available to estimate population at a local level (see review in Leyk et al., 2019).

Previous evidence-based risk analyses take advantage of global data of hazards to estimate exposure of population and economic activity (e.g. Gunasekera et al., 2018; Rashmin 3
Gunasekera et al., 2015; Rentschler and Salhab, 2020; Ward et al., 2020). Gross Domestic Product (GDP) is a critical economic indicator in the measurement and monitoring of an economy in a country that is typically only available at national and occasionally subnational levels. Regional indicators play a key role in the necessary variation to forecast regional GDP (Lehmann and Wohlrabe, 2015) and food security (Andree et al., 2020). Previous efforts to estimate local GDP use high resolution spatial auxiliary information such as luminosity or population data to provide local variation. Methods by Kummu, Taka, and Guillaume (2018), Murakami and Yamagata (2019), Nordhaus (2006), and World Bank and UNEP (2011) took advantage of gridded population data, which is the result of a model disaggregating the most detailed level population data into grids (e.g. see review in Leyk et al., 2019). However, wealth is not evenly distributed among people nor infrastructure (Berg, Blankespoor, and Selod, 2018). In fact, the divide between the rich and poor is even widening in our time (Dabla-Norris et al., 2015). The method used in World Bank and UNEP (2011) stratify the population by rural and urban, yet definition of these geographic areas can vary based on the selection of the population model (Leyk et al., 2019). These measurements matter in application to stylized facts such as the strong negative correlation of the level of urbanization with the size of its agricultural sector (Roberts et al., 2017). Also, the uniform distribution of labor in agriculture is another key concern (Gollin, Lagakos, and Waugh, 2014). Other methods used land cover such as vegetation and built-up indices, however did not incorporate types of agriculture like cropland and livestock (Goldblatt, Heilmann, and Vaizman, 2019; Rashmin Gunasekera et al., 2015).

Other methods to estimate GDP at a local level take advantage of the lights at night dataset. Doll, Muller, and Morley (2006) and Elvidge et al. (2009) found nighttime lights to provide a uniform, consistent, and independent estimate for economic activity, and several other studies (e.g. Bundervoet, Maiyo, and Sanghi, 2015; Chen and Nordhaus, 2011; Eberenz et al., 2020; Ghosh et al., 2010; Henderson, Storeygard, and Weil, 2012; Wang, Sutton, and Qi, 2019) utilized this striking correlation between luminosity and economic activities to estimate economic output on the ground. While night light is a good reflection of economic activities in manufacturing and urban areas, night light data may not capture the agricultural activity as it requires areas to emit light. Bundervoet, Maiyo, and Sanghi (2015) suggest that agricultural indicators rather than rural population could improve the estimation of GDP given the importance of agriculture in many of the economies in their sample of Africa. Gibson et al. (2021) find that night time lights data are a poor predictor of economic activity in low density rural areas.

In this paper, we present a high resolution gridded Agricultural GDP (henceforth AgGDP) dataset that is produced through a spatial allocation model by distributing national 4
and sub-national statistics to 5 arcminute pixels based on satellite-derived information of constituents of AgGDP, including forestry, hunting, and fishing, as well as cultivation of crops and livestock production.<sup>1</sup> We make two main contributions. First, we construct a global dataset of gridded AgGDP. This entails a massive effort of data collection and integration. We extend and apply the cross-entropy framework developed in the Spatial Production Allocation Model (SPAM) for crops that pioneered the use of cross-entropy optimization in spatial allocation (You and Wood, 2003; You, Wood, et al., 2014; You, Wood-Sichra, et al., 2018; Yu et al., 2020). We construct and integrate global datasets of the components of agricultural GDP as priors and then reconcile the values with the regional account statistics using cross-entropy optimization. Second, we contribute to efforts assessing the exposure of economic activity to natural hazards with a focus on agricultural GDP. Significant progress has been made to measure physical assets such as built-up area and estimate hazards to quantify its exposure to natural disasters. However, the spatial distribution of agricultural GDP is less known. So, we apply these data to inform efforts quantifying the population and agricultural GDP at risk to drought and water scarcity.

The rest of this paper is structured as follows. The next section provides a detailed description of the methodology and data. Then, we present the model results and data. Then, we discuss the results along with validation followed by usage notes from a fitness-foruse perspective. Finally, we provide concluding remarks.

# **2 Methodology and data**

Following the composite structure of agricultural GDP, we disaggregate the national and sub-national statistics into a global grid through a cross-entropy allocation model. Given the availability of data and the global scope, our efforts varied on adjusting official statistics and creating priors for different components. Below we discuss the construction of each component, AgGDP statistics and the allocation model followed by the global natural hazards data. Given the spatial resolution and year of reference of the input data for the crop value of production, we estimate AgGDP for the year 2010 into 5 arc-minute grids (10x10 km) across the world.

> 1Agriculture, forestry, and fishing corresponds to ISIC divisions 1-3 and includes forestry, hunting, and fishing, as well as cultivation of crops and livestock production

5
# **2.1 Construction of components**

For each pixel, we construct an estimated value of production based on high spatial resolution information of the five components that serve as priors in the modeling process: crop, livestock, forestry, fishing, and hunting. Given the lack of information on the hunting component, we disaggregate the forestry component into two parts: timber and non-timber products of forestry. The non-timber products of forestry includes an even distribution of hunting. The construction of the five components is described below in four subsections: crop, livestock, forestry (timber and non-timber) and fishing.

## **2.1.1 Crop value of production**

The crop component in the gridded AgGDP is generated by multiplying the quantity of production from the global SPAM 2010 version 1 dataset<sup>2</sup> (You, Wood-Sichra, et al., 2018) with the producer prices at the country level from FAOSTAT (FAO, 2016) for each crop and then summed together.<sup>3</sup> As mentioned earlier, SPAM is a cross-entropy model, which calculates a plausible allocation of crop areas and production to approximately 10 km pixels, based on agricultural statistics at national and sub-national levels, combined with gridded layers of cropland, irrigated areas, population density and potential crop areas and yields (Yu et al., 2020). SPAM’s output distinguishes between 42 crops (33 individual crops, 9 aggregated crops) that together add up to practically all cultivated crops in a country with four parameters including production, yield, physical area and harvest area.

For aggregated SPAM crops (such as other cereals, other pulses, vegetables, fruits, etc.), we computed their prices by taking the weighted average of their components, as follows: where _Jagg_ is the aggregated crop group, _j_ is any crop that belongs to _Jagg_ , _PriceJagg_ is the price of the aggregated crop group, _pricej_ is the price of crop _j_ , and _prodj_ is the production of _j_ .

For each grid, the value of crop production is thus: where _Cropvali_ is the value of total crop production in pixel _i_ , _prodi,j_ is the production of

> 2Available at www.mapSPAM.info

> 3As for the producer price, ideally, we need sub-national level figures, but such a dataset is not available globally. Therefore, we use the FAOSTAT’s national producer prices.

6
<!-- Start of picture text --> 80°N-<br>60°N - we ok a a 3a 3 biti do - .<br>a: Snag ey re te<br>ON: Ci CO ee ge ST<br>20°N - : Saha os re ye ie ie ta o f<br>ae an : we re : eos pr fy i A 4<br>20°S- pe cae. 9 %<br>40°S 7 ‘+ a " Ww >»<br>120°W 60°W 0° 60°E 120°E<br>Crop Production value (USD ca. 2010)<br>IP)| 5.000 Low10,000- production- 9,209 49,999 /NA|||__500,000-60,000-100,000 99,999- 499,999 999,999 [lll[JJJ)[I 5,000,0001,000,000 >= 10,000,000 -- 4,999,999 9,999,099<br><!-- End of picture text -->
**Table 1:** This table shows the livestock type with the conversion factor. Sources: Eurostat (2018)

|**livestock type**|**conversion factor**|
|---|---|
|Cattle|1|
|Pigs|0.3|
|Goats|0.1|
|Sheep|0.1|
|Chicken|0.01|

of the animal equivalent values are multiplied by pixel areas to get the count of animals per grid, which is multiplied by the FAOSTAT’s value of production to obtain the livestock production prior for each pixel.

where _lsvali_ is the total value of livestock production in pixel i; _lsvalx_ is the value of livestock production (meat, milk, eggs, honey and wool) that is reported at the national level; _lsnumi_ is the total number of equivalent animals in pixel _i_ ; and _X_ is a set including all pixels that fall within the boundary of a nation.

A map of global gridded livestock production value as a prior is shown in Figure 2.

# **2.1.3 Forestry production and hunting**

Forest resources have been utilized by people since the advent of civilization (Hossain, Alam, Miah, et al., 2008). Up until now, over a billion people still rely on forest resources for food security and income generation to some extent (FAO, 2018). In the world’s least developed regions, 34 countries depend on fuelwood to provide more than 70% of energy, among which 13 nations require 90% of energy (FAO, 2018).

The contribution of forest production to AgGDP can be classified into two broad types: wood (logging) products and non-wood forest products. Wood (logging) products are the most exploited commodities in the forestry sector. The trees are cut down to be the raw materials for producing timber and pulp, which are further processed and converted into a number of derivatives, such as construction materials and paper products. Non-wood forest products are defined by the Food and Agriculture Organization of the United Nations (FAO).<sup>4</sup> It is estimated that millions of households around the world depend on non-wood

> 4These products are “goods of biological origin other than wood derived from forests, other wooded land and trees outside forests”, including foods (nuts, fruits, mushrooms, etc.), food additives (herbs, spices, sweeteners, etc.), fibers (for construction, furniture, clothing, etc.), and plant and animal products with chemical, medical, cosmetic or cultural value.

8
<!-- Start of picture text --> Se ee | So ,<br>a\ soee t a hae api. oteee alle NSiF 7 ‘<br>09mn nnn a= SS ee mice ned Ga<br>20°S= ee «ae |<br>A0"s [an 7 é<br>120°W1 60°W1 0°1 60°E1 120°E1<br>Livestock Production value (USD ca. 2010)<br>Low production/ NA i 5,000 - 9,999 a 100,000- 499,999<br>1)_ 5001,000- 999- 4,999 50,00010,000-- 49,99999,999 || | 500,000>= 1,000,000- 999,999<br><!-- End of picture text -->
<!-- Start of picture text --> 80°N-<br>-<br>a wae Wes ) gel, ae a Beto<br>won _a. Se weae<br>GeAX4 | £ ‘ Meaeee a<br>0°- ss yo Sides<br>a 4 ie Pt §<br>40°S - 4 id<br>120°W 60°W o° 60°E 120°E<br>Wood Forest Production value (USD ca. 2010)<br>Low production/ NA 50,000 - 99,999 a 500,000- 999,999<br>10,000 - 49,999 100,000 - 499,999 || >= 1,000,000<br><!-- End of picture text -->
# **2.1.4 Fishery production**

Fish makes up approximately 17% of animal-sourced protein in the human diet worldwide (Mathiesen, A.<sup>`</sup> M., 2018). The fishery industry supports the livelihood of 12% of world population by creating 200 million jobs along its value chain. In the global trade system, 80 billion USD worth of fish is exported from developing countries and it plays a crucial role in promoting local economic development (Kelleher, Willmann, and Arnason, 2009).

We estimate both freshwater inland fisheries and marine production values using the FISHSTAT (FAO, 2009) data with a classification based on the fish production categories. The inland fishery production value is the result of disaggregating corresponding country level statistics in proportion to areas of inland water bodies in pixels. The distribution of inland water bodies is obtained from the ESA-CCI (Lamarche et al., 2017). Thus, the value of inland fishing production in each grid is calculated as follows: where _fishvali_ is the value of fishery production in pixel _i_ ; _freshvalx_ is the value of fresh fish production at the national level which is aggregated from FISHSTAT; _waterbodyi_ is the area of water bodies in pixel _i_ ; and _X_ is a set including all pixels _i_ that fall within the boundary of a nation _x_ .

The value of marine fisheries production is based on its proximity to fish landing ports weighted by a composite indicator of equal weight from the number of visits and sum of the vessel hold of fishing vessels. We use the port database from the World Port Index (National Geospatial-Intelligence Agency, 2019) and the number of port visits with a vessel hold of fishing vessels from Hosch et al. (2019) to create a composite variable as the prior based on the sum (for each port) of the number of visits (each event in the database) and total vessel hold at the port. The geographic coverage of the ports is calculated for each port using the minimum port distance provided in (Hosch et al., 2019). Any distance greater than 150km is calculated at 150km. The value of marine fishing production in each grid is calculated as follows: where _marinevali_ is the value of fishery production in pixel _i_ ; _portindexi_ is an equal weighted composite index of the number of visits in pixel and the total vessel hold in pixel _i_ ; and _X_ is a set including all pixels _i_ that fall within the boundary of a nation _x_ .

A map of global gridded fishery production value as a prior is shown in Figure 4.

11
<!-- Start of picture text --> 80°N -<br>=<br>6O°N- ee “a i ae Se > :<br>ee Re :s om. The “te<br>20°N- ias BAS a . eae ie all<br>20°S - ee a i ae -<br>40°S- pee we P<br>120°W 60°w 0° 60°E 120°E<br>Fishery Production value (USD ca. 2010)<br>Low production/ NA 1,000- 4,999 fill} >= 10,000<br>151 - 999 i 5,000- 9,999<br><!-- End of picture text -->
To overcome discrepancies in temporal coverage and currency terms (constant and current), and to keep the data consistent and comparable for countries across the world, shares from sub-national statistics are calculated and then applied to a national total to derive a calibrated number at the sub-national level. The national totals are obtained from the World Development Indicators (World Bank, 2019) and averaged over three years around 2010. For a few countries, which do not report their national agricultural GDP in the WDI database, sums of all agricultural GDP components are used as proxies.

The calibrated statistics are then linked to grids through a shapefile of the Global Administrative Unit Layers (GAUL) that maintains global geographic layers with a consistent and comprehensively unified coding system (FAO, 2015). Then, we overlay the GAUL administrative boundaries on the grid network to assign the corresponding codes of the administrative units to each grid. For areas where sub-national AgGDPs have different administrative areas than GAUL, the GAUL areas are merged or split to match the sub-national AgGDP area.

# **2.3 Spatial Allocation Model**

After constructing all the components, we define a spatial allocation model in a crossentropy framework following (You, Wood, et al., 2014) to allocate administrative statistics to 5 arc-minute pixels.<sup>8</sup> National and sub-national AgGDP values are used as a constraint, while the distribution of crop, livestock, fishery, and forestry production (hunting is included in non-timber products of forestry) is used to create priors for estimating pixel-level AgGDP. Measurement units are unified using deflators and exchange rates.<sup>9</sup> The first step is to transform all real-value parameters into corresponding probabilities. Let _Si_ be the share of the total agricultural GDP allocated to pixel _i_ within a country x. _AgGDPi,x_ is the agricultural GDP allocated to pixel _i_ in country _x_ and X is a set including all pixels that fall within the boundary of a nation. Therefore: Let _PreAgGDPi_ be the pre-prior allocation of AgGDP share from our best estimate. The first approximation can be done by summing all five calculated pixel level components of

> 8A comprehensive presentation of the cross-entropy method is in Rubinstein and Kroese (2004)

> 9The currency varies by source. Crops are in local currency. Livestock are in International USD 20042006. Fish are USD 2009. Non-timber forest products are in USD 2012 and Timber (forest) are in USD 2011.

13
AgGDP: where we assume hunting occurs in areas with equal probability.

Theoretically, the sum of these components should be close to the official values obtained from the World Development Indicators. We make sure that the official AgGDP values are guaranteed to be no less than the sum of all five components of agricultural GDP. Therefore, we first sum up all prior estimations of AgGDP.

Then, we rescale the prior _AgGDP_ to be consistent with the official AgGDP value: Then we calculate the prior for Si as a probability by normalizing PriorAgGDP: Finally, we formulate a cross entropy model in the following mathematical optimization framework: Subject to the following three conditions: where _i_ : i=1,2,3,. . . are pixel identifiers within the allocation unit (e.g. Brazil); and _k_ : k=1,2,3, . . . are identifiers for sub-national geopolitical units (e.g. a state) where AgGDP values ( _SubAgGDPk_ ) are available. The objective function is defined as the cross entropy of AgGDP shares and their prior. The first constraint (Equation 13) is the pycnophylactic or volume-preserving constraint (e.g. Tobler, 1979) that ensures the sum of all allocated AgGDP values is equal to the total AgGDP of the country. The next equation (14) sets the sum of all allocated AgGDP within those subnational units with available data to be 14
equal to the corresponding sub-national AgGDP values. The last equation (15) is a natural constraint for the percentage of AgGDP, which is also the probability in the cross-entropy model. The modeling framework is flexible in that more constraints can be added if more data are available and/or more reasonable assumptions on how AgGDP should be spatially disaggregated are discovered.<sup>10</sup> Last but not least, we multiply the total regional agricultural GDP by the probability in the cross-entropy model to derive the final pixel level agricultural GDP:

# **2.4 Natural hazards**

We use measures of two natural hazards to gain insight into the spatial distribution of agricultural activity with regards to drought and water scarcity. We calculate the Standardized Precipitation-Evapotranspiration Index (SPEI) (Sergio M Vicente-Serrano, Beguerıa, and L ́opez-Moreno, 2010), which measures the difference between observed precipitation and estimated potential evapotranspiration with a 3 month interval using the base climatology of 1980 to 2019, which is implemented in R (Beguer ́ıa and Sergio M. Vicente-Serrano, 2017) using climate data from Harris et al. (2020). Extra dry years are defined as the number of years that are less than or equal to -2.0 during the period from 2000 to 2009. Figure 5 shows the results of the SPEI.

The Water Crowding Index (WCI) is a measure of water scarcity considering the local population as the annual water availability per capita (Falkenmark, 1986; Falkenmark, 2013). Veldkamp et al. (2015) model global water crowding index with return periods. We take the mean of any pixels of the ensemble WCI with a 10 year return period within an agricultural GDP pixel. Following the literature (e.g. Alcamo, Fl ̈orke, and M ̈arker, 2007; Arnell, 2003; Kummu, Ward, et al., 2010; Veldkamp et al., 2015), we categorize the WCI into four categories: Absolute is less than 500 m<sup>3</sup> /capita per year; severe is less than or equal to 1000 m<sup>3</sup> /capita per year; moderate is less than or equal to 1,700 m<sup>3</sup> /capita per year; and low is the remainder (Figure 6). Then, we evaluate water shortage events using a threshold of 1,700 m<sup>3</sup> /capita per year with a return period of 10 years.

> 10For instance, market access may play a role in determining the spatial distribution or spatial structure of AgGDP and can be included as a constraint in the model. However, we provide a parsimonious model without market access.

15
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<!-- Start of picture text --> 80°N-<br>6O°N -<br>Aa. . ES<br> ae oe eee OS<br>40°N - —..' aa ri oe es ste<br>20°N - = wo Ae “a Nas ‘<br>Ca A Vaso BS sod Seine<br>i fee? Re 2 >" Ta )<br>40°S - se - 7<br>120°W 60°W o° 60°E 120°E<br>Agricultural GDP (USD ca. 2010)<br>Low Agricultural GDP / NA 600,000 - 799,999 2,000,000 - 3,999,999<br>|| 200,000 - 399,999 800,000 - 999,999 4,000,000 - 5,999,999<br>|| 400,000 - 599,999 || 1,000,000 - 1,999,999 >= 6,000,000<br><!-- End of picture text -->
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population AgGDP model as measured by the Mean Absolute Deviation (MAD) and Root Mean Square Error (RMSE).<sup>14</sup> While the spatial regression performs the best, global data requirements that allow high enough degrees of freedom is a challenge.

Given these data requirements and challenges, we compare the cross-entropy model to another spatial allocation model based on rural population at the country level. Then we extend a comparison of both models at the global level by mapping the correlation.

One advantage of the cross-entropy is the volume preserving pycnophylactic property, which ensures the sum of the gridded data is the original value and allows the possibility to include all information that is available from mixed levels of data (e.g. You, Wood, et al., 2014). However, this presents a challenge in terms of an assessment of a global model. Previous work on gridded data products includes evaluations of accuracy. Typically, studies evaluate the internal accuracy of the model exploiting multiple geographic levels of data (as mentioned above in Thomas et al., 2019). Similarly, Van Boeckel et al. (2011), who examine duck data in Thailand, conclude that input levels do matter, especially the importance of the presence of administrative level 1 data. Robinson et al. (2014) evaluate the livestock model in Brazil and find a positive association between the model accuracy and the administrative level of the training data used in the model. They also illustrate this inverse relationship of prediction accuracy and level of intensification in the case of chickens in Europe (Robinson et al., 2014). At the local cell level, previous models of land or population have compared results to independent local data (Siebert, D ̈oll, and Hoogeveen, 2002) or identified errors of omission in a gridded population model using the locations from household surveys (e.g. Tiecke et al., 2017).

Since we can not perform an evaluation of prediction accuracy for all countries, we compare the global cross-entropy model with another allocation model, which is similar to the global assessment of maize and rice production in You, Wood, et al. (2014). For the comparison, we construct a proportional allocation model using rural population density following the method in Thomas et al. (2019) for the case of Brazil.<sup>15</sup> Then, we can test the similarity of the two maps. Following Levine et al. (2009), we assume a normal distribution over the 2 million land pixels and perform a pairwise student t test to test the null hypothesis that both maps were identical. This test allows us to examine whether the mean difference in 14Specifically, the MAD and RMSE for each model are respectively: the rural population density model (28,744 and 25,397), Cross-entropy spatial allocation (8,249 and 18,347) and Spatial disaggregation from a regression on agricultural production (7,214 and 16,673).

> 15We use the 2010 Gridded Population of the World version 4 from Center for International Earth Science Information Network - CIESIN - Columbia University (2017) adjusted to the United Nation’s World Population Prospects followed by including the rural area defined by the Global Human Settlement grid for 2015: namely, “Rural cluster”, “Low Density Rural grid cell”, or “Very low density rural grid cell” (Pesaresi and Freire, 2019).

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the corresponding pixel value from one map to another was greater than would be expected by chance alone. The t test statistic tell us that we can not reject the null hypothesis which provides some evidence of similarity between the two models using all the global pixels. Figure 10 displays three global maps: the two models and their Spearman correlation.<sup>16</sup> We exclude areas from the analysis with values that are less than 200,000. The correlation shows both areas of high and low correlation as the input of the models draws from the relationship of agriculture from productions values or a (rural) population perspective.

The cross-entropy model can also propagate errors from the ancillary data that are inputs to the components. For the SPAM model, the CGIAR network held expert consultation and validation workshops according to each crop and subsequently incorporated their feedback with modifications of the priors used in the model (You, Wood, et al., 2014). The authors of Gridded Livestock Of the World (GLW) note regional differences in accuracy (i.e. RMSE values) are the result of the variation of production intensity and thus dependence on the initial conditions of the land upon which the prediction variables are mainly drawn (spatial agro-ecological variables)(Robinson et al., 2014). Lastly, the models integrate higher spatial resolution data to inform the spatial disaggregation procedures, which is subject to the MAUP (Openshaw, 1981).

# **3.2 Usage Notes**

We provide descriptive statistics of the data and modeling from a fitness-for-use perspective (e.g. Leyk et al., 2019). The data are most appropriate for applications at global, continental and regional scales (You and Wood, 2006). Decisions regarding the use of this version over smaller spatial extents should be carefully considered in relation to the underlying assumptions and characteristics of a particular area. However, as the spatial refinement of ancillary data advances along with greater currency, coverage and representativeness, we expect validation possibilities to increase and inform a better understanding of the uncertainty and the associated fitness-for-use. Also, we intend to improve spatial and temporal coverage when it is feasible.

The data disaggregation model from source to target level does impose spatial relationships and is subject to error (T. Li et al., 2007). The measurement of GDP is also challenging (Angrist, Goldberg, and Jolliffe, 2021), especially agricultural production (Carletto, Jolliffe, and Banerjee, 2015). The level of uncertainty associated with these results includes the thematic, spatial and temporal accuracies. Below, we discuss these data and modeling issues in relation to two aspects: regional accounts and the regional components of AgGDP (mainly

> 16The raster correlation in R performs a simple moving window correlation between two grids with a 3x3 pixel window.

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crop, fishery, forest, and livestock production values) that are priors in the cross-entropy model, and the outcome of the cross-entropy model.

# **3.2.1 Regional accounts**

We collect regional accounts by sector from various sources into a global database. The data are not balanced over time nor at the geographic level. The variation in the reference year of the regional accounts data influences the temporal balance of the database. This mismatch can influence the regional distribution of the agricultural GDP that may be different than the target reference year of 2010. Given climate<sup>17</sup> and specifically rainfall is important input to crop and livestock production and may contribute to variation across years (Stanimirova et al., 2019; Y. Zhang et al., 2020), we attempt to reduce this source of error by averaging over multiple years when data are available similar to You, Wood, et al. (2014). However, this does not eliminate this mismatch. The availability of data varies when grouped by World Bank income (low or lower middle, upper middle and high income). The average absolute temporal difference (ATD) defined as the mean difference in years between the reference regional accounts and the target year (2010) is higher in the low and lower middle income group. Likewise, the mean deviation of the share of AgGDP by country over the year(s) is larger in low or lower middle compared to high income.

The global regional account database includes national and subnational units at various administrative levels.<sup>18</sup> Following Robinson et al. (2014) in their assessment of Gridded Livestock Of the World (GLW) 2.0, we summarize the average spatial resolution (ASR) of the input regional data, which is the square root of the land area divided by the number of administrative units. We find that on average the ASR decreases from high to low income groups.

# **3.2.2 Components**

Another source of uncertainty is indirect temporal inaccuracy propagated from the input datasets of the components, which are modeled. We discuss all five components of agricultural GDP: crop, livestock, forest, fish and hunting. The SPAM model (You, Wood, et al., 2014) is a result of several gridded modeled datasets including rural population density from Global Rural-Urban Mapping Project (GRUMP) Alpha version (Balk et al., 2006). Likewise, the Gridded Livestock of the World v2.0 includes rural population density in 2006 (GRUMP) along with other predictors such as precipitation (Hijmans et al., 2005) and a

> 17For a discussion on climate yield factors see Block et al. (2008).

> 18This also includes cases where administrative units at the same level are merged to match the geography of the regional accounts data.

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modeled travel time to places with 50,000 inhabitants circa 2000 (A. Nelson, 2008). (Anderson et al., 2015) find variation in their examination of global data products of cropping systems models. For livestock, we transform the 5 major livestock into international values from livestock products (namely, meat, milk, eggs, honey and wool). The forest (non-wood products, wood-products) components relies on a remote sensing model to estimate forest loss. With regards to the non-timber values, limitation from the sources present two challenges. The estimates use simple averages from the literature that accordingly assume a property of uniformity in the value of a hectare of forest as similar across the world and the sample of forests with literature drawn for the study is representative of the world (Siikam ̈aki, Santiago-Avila,<sup> ́</sup> and Vail, 2015). The fishing model relies on proximity and association with ports or water bodies.<sup>19</sup> Finally, since we do not incorporate any information on hunting, the result is an even distribution across units and time.

Another source of uncertainty is the geographic distribution of the components. Ideally, we would use subnational prices, however it was not feasible, and the results do not reflect this occurrence, including administrative units with higher variation of prices due to the heterogeneity of distinct urban and rural areas.

# **4 Conclusion**

Natural disasters impact both lives and livelihoods and a higher frequency and severity of disasters will likely increase in a changing climate. Socio-economic estimates at the local level inform disaster preparations of the exposure of physical assets and production to natural disasters and have implications for food security. Significant advancement in the spatial allocation of indicators has occurred in the past 10 years such as population (e.g Leyk et al., 2019). The advantages of gridded data as a common spatial unit of integration and the cross-entropy models are clear. These common units allow us to examine within-country characteristics, especially in the case of spatial data that do not conform with each other such as administrative boundaries and natural hazards to inform analyses with local estimates. We present a novel data set that disaggregates the national and regional accounts of the agriculture sector across areas as a result of a model where we use ancillary data including satellite data. This allows us to estimate especially in countries that have a relatively higher share of agricultural activity in the entire economy. Then, we examine the exposure of areas with at least one extreme drought during 2000 to 2009 to agricultural GDP, where nearly 1.2 billion people live, and find an estimated US$432 billion of agricultural GDP in 2010.

> 19The freshwater case does not account for any variation, whereas the marine port locations incorporate variation on vessel holds.

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These data are the result of data collection and collaboration across multiple entities to ensure the most current, widest coverage and creativity of the users to apply it. However, persistent challenges to data collection remain, including limited geographic levels and temporal lag at low frequencies. Also, the reference year and spatial resolution of the local AgGDP estimates are limited to the contemporaneous availability of the economic statistics and components such as the crop production model. We often have to consider the fitnessfor-use while considering the accuracy; the model has lower average spatial resolution in areas where we have little data, however these same areas may benefit from the availability of these estimates to inform policy. Predictions are dependent on the availability and quality of the training data on which the model is based and the modeling process is flexible to update individual countries as the data are available. In the near future, we hope to increase the currency and number of countries with subnational data as updates of the regional account data and models of the components upon which the model relies become available.

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