critical mass of training data to estimate predictive models. In general, when the number of images we used to train the model fell below 10% of the population, predictive performance deteriorated rapidly. However, the results were far more robust to restricting the size of the sample used to generate the training data labels. Furthermore, prediction accuracy remained high in Burkina Faso, despite a reduced effective sample size of the training data due to linking satellite images to survey data at a much higher geographic level. Future work could investigate methods to further improve performance when training transformer models using the types of small samples typically collected for household surveys.

Finally, the results demonstrate the potential of using transformer models to predict changes in wealth and household wellbeing more generally. Future work can examine the extent to which the parameters in change models are stable across time and/or space. This could point the way toward the use of geospatial data to generate approximate micro estimates of welfare change in settings where survey data are unavailable.

# **Methods**

We describe the details of our large-scale, multi-resolution, and multi-temporal wealth dataset, wealth and its change prediction approaches, and evaluation methods.

## **Multi-resolution and multi-temporal wealth dataset.** We

utilize data from four low-income countries (Malawi, Mozambique, Burkina Faso, and Madagascar) and two cities in Malawi as study areas in Africa. These countries were selected due to the availability of location identifiers in available census extracts. This allows us to pinpoint models on the most comprehensive scale to date, to tune a general model to specific countries and even cities, and to robustly simulate the impact of data scarcity on model performance across three spatiotemporal scenarios: country-level wealth level prediction, decadal country-level wealth change prediction, and city-level wealth level prediction.

**Asset wealth index (AWI).** We construct the asset wealth index using data from the national census questionnaire. We utilize full census data in Mozambique and Madagascar, and census extracts in Malawi and Burkina Faso, resulting in a total dataset comprising over 12 million households across four countries, with more than 700,000 households represented in each country’s dataset. In contrast, previous studies [29, 23] leveraging DHS data included approximately 500,000 households across 23 African countries, while LSMS data measured about 9,000 households across five countries. Table 1 provides a full description of the size of the datasets.

From the census questionnaire, we rank seven housing characteristics (housing type, wall material, roof material, floor material, water source, toilet type, and energy source) on a scale of 1 to 5. Additionally, we assess the presence of six assets (radio, television, landline, car, motorbike, and bicycle) using a binary classification (ownership/non-ownership). This data is then standardized and used to construct a principal components analysis (PCA) model, from which the first principal component was extracted as the asset wealth index [13, 25, 29]. Asset wealth index labels are then aggregated from the household to the

**Table 1**

National census data details.

|Country|#Images # Admin areas # Households Surveyed|
|---|---|
|Malawi (2008)|3,432<br>12,412<br>572,764|
|Malawi (2018)|3,432<br>18,700<br>796,925|
|Mozambique (2007)|37,325<br>45,244<br>4,797,372|
|Mozambique (2017)|37,325<br>67,218<br>6,119,847|
|Burkina Faso (2019)|13,142<br>334<br>875,872|
|Madagascar (2018)|31,182<br>14,328<br>4,518,322|

administrative area level, and then each pixel of the images is labeled based on the administrative area to which they belong. Finally, we average the pixel-wise asset wealth index map to obtain a scalar value as the ground truth for each image. Since a different PCA is constructed for each country, a value of 0 in one country does not correspond to the same level of wealth as a 0 in another country.

**Satellite imagery.** For country-level wealth and its change prediction, we collected daylight Landsat (30m/pixel) satellite imagery for Malawi, Mozambique, Madagascar, and Burkina Faso, where Malawi and Mozambique have bitemporal image pairs. Our Landsat imagery dataset was constructed using a 3-year median of cloud-free pixels, centered around the census year for each country. For countries with two census periods, imagery from Landsat 5 and Landsat 7 was used for the earlier census, while Landsat 8 was utilized for the more recent census. Each Landsat image has a fixed size of 150 × 150 pixels, resulting in each image covering 20.25km<sup>2</sup> (4.5 × 4.5km<sup>2</sup> ). These images have six bands that are red, green, blue, near-infrared, short-wave infrared 1, and short-wave infrared 2. For city-level wealth prediction, we collect PlanetScope (3m/pixel) and SkySat (0.5m/pixel) multispectral satellite imagery to cover each administrative area in Lilongwe and Blantyre. Based on the average size of administrative areas, we empirically define the size of each grid as 0.3 × 0.3km<sup>2</sup> , which results in each PlanetScope image with 100 × 100 pixels and each SkySat image with 600 × 600 pixels. Despite using 2018 household-level census data, we utilized available PlanetScope and SkySat imagery acquired in April 2023. These images contain red, green, blue, and near-infrared bands.

**Geospatial features.** In addition, we supplement satellite imagery with publicly available processed geospatial features, which we refer to as _geo-features_ . These geo-features capture population, developmental, and environmental statistics. These features are population structure [18], population density [28], annual rainfall [1], minimum and maximum temperature [1], nighttime lights [3, 11], terra net primary product [10], aqua net primary production [24], cellphone tower count [22], impervious surface change year [15], land cover type [5], GHSL [26], building counts [27], building areas [27], soil pH [16], and soil organic carbon [16]. A visual representation of one datapoint is provided in Figure 5; note that final asset wealth labels are combined into a single scalar value.

## **Training wealth measurement models**

The comparisons include a tree-based model, namely extreme gradient boosting (XGBoost) [7] and two advanced deep learning models (convolutional neural networks and transformers based on an encoder-linear architecture [29]. Based on empirical and Page 8 of 11