# f. Predictions across time are much less accurate than predictions across space

In contrast to the many studies that have used satellite imagery to predict welfare levels across space, only two published studies to our knowledge have evaluated intertemporal predictions using geospatial data. Yeh et al. (2020) attempt to use daytime imagery to predict changes in wealth measured in the Demographic and Health Surveys. The CNN was only able to explain 15 to 17 percent of the estimated changes across African villages, however. When using self-reported changes in assets from the most recent survey, the figure rose to 35 percent. When aggregating up to districts, and using self-reported changes from the endline survey, imagery can explain about half of the variation in self-reported changes. However, self-reported changes are subject to recall error and may only capture major changes in assets.

Meanwhile, Khachiyan et al. (2022) look at variation across census blocks in the US, and find that a CNN trained on daytime imagery predicted half of the change in population density between 2000 and 2020, and 42 percent of the variation in income change between 2000 and 2017. Both Khachiyan et al (2022) and Yeh et al (2022) use convolutional neural networks for prediction. Further studies would be very useful to test the ability of different methods and data sources to predict changes over time.

# g. Summary of key lessons on using geospatial data for small area prediction

Overall, the main conclusion from this nascent literature is that geospatial data are strongly predictive of geographic variation in wealth and poverty. Exactly how predictive accuracy varies depending on a myriad number of factors. In general, wealth is easier to predict than consumption. Nonetheless, when national geospatial estimates of poverty or wealth are compared against census-based estimates for sampled areas, the R<sup>2</sup> appear to consistently range from about 0.74 to 0.95, as shown in Table 1.

Because geospatial data are particularly predictive of population density (Leasure et al, 2020, Engstrom et al, 2020) and population density is systematically related to economic welfare (Castaneda et al, 2018), geospatial data can help “fill in” two-stage household surveys with model-based predictions, boosting efficiency and accuracy. Most of the studies that have compared geospatial estimates with direct survey estimates find that the model-based estimates are more accurate, although the comparisons are not shown here. There is also evidence that prediction accuracy is highly dependent on the strength of the training data, suggesting that partial registries that collect proxy indicators may be a valuable supplement to household survey data when publicly available geospatial data can be linked. Finally, outof-sample estimates are generally less accurate than in-sample estimates, and occasionally very inaccurate. This suggests that there are benefits from including as many target areas as possible in the sample, and from additional research and tools to improve out-of-sample prediction accuracy.

At the same time, the early literature has utilized a dizzying number of approaches to integrating survey and geospatial data. Many of these papers train a CNN model directly to imagery, others use machine learning methods applied to specific features, while others use linear mixed models. Those that either use deep learning or tree-based machine learning either ignore or may not properly estimate or evaluate uncertainty, and many of the papers ignore the well-established statistical literature on small area estimation. The following section explores these issues in greater detail.

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