solely on predefined geospatial features from a range of sources.

These comparisons are important because simpler approaches that rely on publicly available data could be both easier and cheaper to implement at scale, particularly for public organizations interested in their widespread application, and so understanding performance tradeoffs across model architectures and inputs is critical to under- standing how to scale promising new measurement approaches.

Second, a key advantage in our setting is the use of accurate, high-resolution data from national censuses or extracts for model training and evaluation. In contrast to earlier work that relied primarily on publicly available household survey data characterized by spatially imprecise location data and limited household samples, our data cover a much larger set of households in a given location and in some cases are precisely georeferenced. Comparisons against such “gold standard" data allow us to understand whether model prediction errors are a result of inaccurate predictions or noise in the measure of ground truth – an understanding that was often elusive in earlier work in developing countries [6, 29]. In addition, it allows us to consider a wide range of sample sizes to assess the minimum training data requirements for advanced machine learning methods to produce accurate estimates. To quantify the importance of training sample size for performance, we extensively test the extent to which additional training data affects model performance across multiple settings.

Third, our high-resolution census data enables a novel understanding of how satellite imagery and other geospatial data can be used to predict variation in livelihoods within urban areas in Africa – a capability that was again hard to evaluate in previous settings given limited samples and spatial noise in training data. This could be particularly consequential in urban environments that exhibit substantial spatial variability in livelihoods even within small spatial domains. Using comprehensive and precisely georeferenced census data from two cities in Malawi, we are able to train and test models using different resolutions of satellite data, and we find that the models are surprisingly accurate in predicting street- and neighborhood-level variation in wealth within these cities.

Fourth, the censuses and extracts allow us to evaluate whether imagery-based models can make accurate predictions of changes in wealth over time. Previous efforts were again substantially constrained by ground data that did not repeatedly sample the same locations in different surveys [29]. As a result, it remains unclear whether an imagery-based model trained largely to predict spatial variation in wealth or consumption would be able to predict temporal variation, as the latter is typically both smaller and potentially driven by changes that are harder to detect in imagery. Repeated census data from the same locations 10 years apart in Malawi and Mozambique allows us to evaluate whether models can indeed extract information from imagery capable of predicting temporal variation in asset wealth.

# **Results**

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

For country-level wealth prediction, we train each model on each country individually and conduct country-wise five-fold cross validation for each model. The CNN model uses only Landsat satellite imagery as input. XGBoost utilizes geospatial features (geo-features) either alone or combined with satellite image statistical features. All models were trained to predict the asset wealth index (AWI) [29]. Estimates of AWI were generated and linked to imagery at fine administrative levels in Madagascar, Malawi, and Mozambique. In Burkina Faso, AWI estimates are only available for 334 communes (Table 1). This reduced the effective sample size of the training data in Burkina Faso, as seen in the clumped pattern of survey-measured asset wealth shown in the right panel of Figure 1d. This difference is reflected in the results. As shown in Figure 1a, a naive transformer model that does not condition on geo-features consistently outperforms other models across the Malawi, Mozambique, and Madagascar datasets. In those countries, predictions using the transformer model achieve values of 0.83, 0.70, and 0.62, respectively, when trained on the full census extract. In Burkina Faso, because of the smaller effective sample size, XGBoost using satellite RR<sup>2</sup> imagery and geospatial features achieves the best average performance among the models (62.9% of variation explained). A naive transformer, when using only satellite imagery, remains competitive (57.4% of variation explained). We also limit the number of training samples to 1%, 5%, 10%, 25%, and 50% of the original training dataset to analyze how model performance varies with training sample size. Based on the results from these four countries, we empirically identify 10% as a critical inflection point for model performance, below which the accuracy of the estimates deteriorates rapidly.

Another key factor in reducing training sample collection costs for wealth prediction is the number of households aggregated per sample. To analyze this factor, we randomly sample 10 households per administrative area to construct the training sample, yielding a “10-household” training dataset for each country. We then train a naive transformer model on this “10-household” training set while still evaluating its performance on the original full household test set. The results (Figure 1b) indicate that our transformer models trained with the 10-household data exhibit comparable performance to those trained with data on all households. Using Malawi as an example, the 10-household data only include approximately 23% of all surveyed households. The performance gap between models trained on all households and the 10household sample is only 3 percentage points (82% versus 79%). In contrast, when reducing the number of training samples, the performance gap between models trained on full training samples and those trained on 25% of the samples is as large as 12 percentage points (82% versus 70%).

These results offer significant insights into data-efficient wealth measurement. When at least 10 households are available per image, surveying more enumeration areas takes precedence over surveying additional households within the enumeration area for predicting wealth with our transformer model. Geospatial features, recognized as valuable auxiliary data for improving economic measurement [21], are widely used in wealth prediction. Here we design a conditioning module (see “Methods”) for our transformer model, enabling the efficient fusion of geospatial features and deep visual features. The results, as shown in Figure 1c, suggest that geospatial features significantly improve the ~~-~~ Page 2 of 11