# Introduction

Doll, Muller, and Elvidge (2000) were the first to use satellite data to spatially distribute GDP on a geographic grid. Their methodology relied on night‐time lights, which generally gave an indication of where cities were, while the intensity of the light gave an indication of both population density and intensity of production, with the more intense lights being associated with higher GDP per unit area. The methodology they used was especially helpful in countries for which finely distributed subnational data on economic activities were not available. It allowed researchers and policy makers to have a better idea as to which cities and locales were of high importance to the national economy, and which were under‐ developed.

However, this methodology performed poorly for countries with relatively large agricultural GDPs, since the night‐time lights were more of an indication of manufacturing and urban population rather than farming and rural population. In 2006, Nordhaus (2006) proposed using population to distribute GDP. If GDP per capita were relatively evenly distributed within administrative areas in which the values were aggregated, this could provide a reasonably accurate estimate of the geographic distribution of GDP. Several authors since then have used this idea and similar methodology to distribute agriculture GDP using rural population<sup>5</sup> or land cover (e.g. Ghosh, Powell, and Elvidge, et al., 2010; Gunasekera et al. 2015; Rafa, Moyer, and Wang et al., 2017).

In this paper, we propose two new methods for distributing agricultural GDP across a geographic grid. The first is a spatial allocation methodology which relies on several gridded data sets showing location of agricultural production. It starts with several components of agricultural GDP such as crop, livestock, fishery and timber production to provide a prior estimate of gridded agricultural GDP. The estimate is then reconciled with national and sub‐national agricultural GDP values using an entropy‐based data fusion method. The second is a “spatial disaggregation” method that relies on imposing a data‐ generating process at the gridcell level with the variable of interest (in our present case, agricultural GDP, though the technique can be applied to many types of questions) – which is not measured at the gridcell level ‐‐ being defined by a combination of known gridded explanatory variables and a set of parameters to be estimated. The equations are aggregated up to the level at which the variable of interest is known, and a multiple regression is used to solve for the parameters, which in turn can be used to make predictions at the gridcell level.

In this paper, we use Brazilian agricultural GDP data to test these two new techniques against the traditional technique of using rural population to distribute the agricultural GDP. We have data available at the municipio level, with 5,564 units. However, we instead use the data at a more aggregated microregion level, with 558 units. Then we make predictions at the gridcell level and aggregate up to the municipio, at which level we compute two measures of predictive accuracy.

## Review of Previous Work

Previous analyses use two primary geographically‐referenced data types to locate GDP. The one that has been used the longest is nighttime light emissions captured by satellite imagery (Doll, Muller, and

> 5 It should be pointed out that gridded population data sets are technically not satellite data sets but GIS raster (gridded) data sets, but they may include satellite data sets as inputs to their construction.

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