Google are also critical inputs into small area estimation, as they are both strong predictors of welfare and also essential for aggregating predictions to higher administrative levels.

Information on building footprints is also valuable when they can be obtained. Worldpop has made statistical information on building footprints available for much of Africa (Dooley et al, 2020); these are derived by Ecopia using Maxar imagery. The Microsoft planetary computer also now contains building footprint data for a variety of countries, including most of Europe and the Americas, and parts of Africa and Southeast Asia. Google recently released a new version of its Open buildings layer covering Africa and Southeast Asia, and the German Aerospace Center recently released the World Settlement Footprint global database of 3-D building footprints (Esch et al, 2023). Liu et al. (2023) recently showed that building footprints can be modeled accurately using Sentinel 1 and Sentinel 2 imagery, but the resulting indicator data have not yet been publicly released. Dynamic information on building footprints should become increasingly available in the near future. In addition, a variety of data pertaining to agriculture and food security are posted online through FAO’s hand-in-hand geospatial platform, which contains information on food security, crops and vegetation. Recent subnational estimates of crop type and yield estimates are only available for a few countries at this time, but coverage will likely expand significantly in the coming years. Overall, an impressive amount of geospatial imagery and indicators is already publicly available, and more should be coming online in the next few years.

b. Geospatial data predicts poverty and wealth accurately across space Several studies have examined how predictions of wealth or poverty derived from linking survey and geospatial data compare with either survey or census-based measures of poverty and welfare. Accuracy is often assessed using R<sup>2</sup> , defined as: Where i is the target area, yi is the reference measure of poverty or welfare for target area i , ŷi is the predicted value for target area i, and y̅i is the mean across target areas. Some studies instead report the Pearson correlation between the predicted and reference measure, which can be squared to obtain R<sup>2</sup> . Table 1 lists the actual or implied R<sup>2</sup> values reported by several studies.

An important early paper on how geospatial data predict poverty and wealth was Jean et al (2016). This paper used “deep learning” in the form of a convolutional neural network (CNN) to predict welfare, using daytime imagery taken from Google Earth and the luminosity of night-time lights in several countries in Sub-Saharan Africa. Each layer of the CNN successively filters the original image into more and more condensed abstract features, until the final layer represents the predicted luminosity value. Jean et al. (2016) transfer the features from the penultimate layer of the CNN to a ridge regression that estimates the value of an asset index or per capita consumption in withheld villages.

In Jean et al (2016), the target areas are survey clusters, the reference measure yi is the predicted average values of a wealth index or per capita consumption for cluster i taken from the household survey and withheld from the training sample, and ŷi are predictions generated from convolutional neural network models. Out-of-sample R<sup>2</sup> is assessed through survey cross-validation and varied from 0.37 to 0.55 for per capita consumption, and from 0.55 to 0.75 for asset wealth. However, because the 3