countries, the wealth distribution changes are not uniform, suggesting that certain areas are benefiting more from economic growth while others are falling behind. This wealth disparity could provide insights into economic policies, development programs, or external factors such as climate impacts that have influenced these changes.

## **Performance on prediction of city-level wealth**

The Landsat-based wealth prediction models above produced wealth maps with a spatial resolution of 4.8 km. For some applications, such as targeting aid within urban areas, finerresolution wealth maps are of interest. To that end, we utilized household- level census data from two cities to test wealth prediction using high-resolution satellite imagery (PlanetScope and SkySat). Following the same settings with the above two subsections, we evaluate the CNN, transformer, and XGBoost models, as shown in Figure 4a. The CNN and Transformer models consistently perform better than XGBoost (with or without geospatial features) across both cities. This highlights the importance of deep visual representation from high-resolution satellite imagery for city-level wealth prediction, which constitutes the main gap between deep learning–based models and XGBoost. Our transformer model outperforms the CNN by a noticeable margin in Blantyre, especially when utilizing the full dataset, demonstrating greater scalability with increased data while also achieving comparable performance to the CNN in Lilongwe. Across both cities, all models exhibit significant improvements as the training data fraction increases; however, performance gains begin to plateau after approximately 25%-50% of the data, resulting in diminishing gains beyond that threshold.

We compare two kinds of commonly used proprietary highresolution, multi-spectral satellite imagery, i.e., PlanetScope (3m) and SkySat (0.5m), as shown in Figure 4b. The results indicate that SkySat consistently outperforms PlanetScope across various training data fractions in both cities. Both sensors capture 4-band (red, green, blue, and near-infrared) satellite imagery, but they differ in spatial resolution and swath width. This highlights the importance of urban spatial detail in accurately measuring wealth using our transformer model. While PlanetScope demonstrates lower average performance than SkySat, its broader swath width and high revisit frequency yield more comprehensive satellite imagery, facilitating large-scale wealth mapping with commendable accuracy (Figures 4g and 4i). Consequently, SkySat is well-suited for wealth measurement in local areas with high accuracy requirements, and PlanetScope is more suitable for large-scale wealth mapping to obtain macro insights.

While city-level wealth prediction is promising, training a city-level transformer still requires sufficient samples that are expensive to collect. We also evaluate whether integrating geospatial features can reduce the required training samples for city-level wealth prediction. As presented in Figure 4c, we find that unlike for country-level predictions, geospatial features generally reduce model performance. This is because geospatial features are al- ways derived from low-resolution satellite imagery, e.g., Landsat (30m), to achieve global coverage. These low-resolution geospatial features introduce spatial errors into high-resolution satellite image–based wealth prediction. For <u>example, a coarse land cover map can ignore small but important</u> spatial details in urban areas. In this case, our transformer model can learn more accurate wealth representations solely from satellite images, even when trained on varying sample sizes.

Overall, we demonstrate accurate large-scale, city-level wealth mapping in two cities in Malawi, i.e., Lilongwe and Blantyre. Compared to country-level wealth maps at a 4.8km resolution (Figures 4f and 4 h), our 0.3km resolution city-level wealth maps (Figures 4g and 4i) provide an unprecedentedly granular spatial distribution of wealth across these two cities and with strong performance explaining up to 76% of the variation for Lilongwe and up to 67% for Blantyre (Figure 4d).

# **Discussion**

This paper proposes and evaluates the use of a vision transformer architecture to solve multiple open problems pertaining to combining survey and satellite data to produce wealth estimates at fine spatial scales. For cross-sectional wealth predictions, careful evaluations using georeferenced census extracts from four countries show that estimates from the transformer model perform well. When paired with Landsat imagery, R<sup>2</sup> values for transformer models that incorporate geo-features outperform commonly used CNN and XGboost models for asset index prediction in all four countries, for all sample sizes considered. Across all countries, accuracy degrades rapidly when using less than 10% of the census extract for training. In Mozambique and Madagascar, estimates produced using transformer models explained approximately 20 to 30 percentage points more of the variation in wealth than estimates produced using XGboost and geo-features. Trans- former models also outperform CNNs in all four countries, by amounts up to approximately 5 percentage points in Madagascar and Mozambique. Incorporating geofeatures into the transformer architecture improves performance by 5 to 10 percentage points at small sample sizes in Mozambique, Madagascar, and Burkina Faso. Transformer models also perform well when predicting variation within cities at 0.3km scales, achieving up to 0.76 in Lilongwe and 0.67 in Blantyre. However, incorporating geofeatures at this scale reduced performance, because they are RR<sup>2</sup> constructed from lower-resolution Landsat imagery. Finally, the transformer model also generates more accurate estimates than CNNs and XGboost when predicting decadal changes in the asset wealth index in Mozambique and Malawi. Model predictions achieve values of 0.57 in Malawi and 0.42 in Mozambique at fine spatial levels, despite the lack of available geo-features. This is a large improvement over the 0.15 to 0.17 RR<sup>2</sup> reported by [29] in comparable settings, and demonstrates the feasibility of combining transformer models with imagery to estimate wealth RR<sup>2</sup> changes at granular levels, given sufficient training data.

The results point to the benefits of applying transformer models that incorporate geospatial features to generate highresolution predictions of asset wealth. This in turn underscores the importance of developing tools, documentation, and training materials to make estimation feasible for national statistics offices, international organizations, and other data providers. In addition, developing and evaluating methods for estimating the uncertainty associated with predictions is crucial to facilitate implementation.

The results also highlight the importance of having access to a Page 7 of 11