Recovering Individual Labor Earnings from Household Consumption: A Collective Model Approach with an Application to the Sahel G5

In the Sahel G5 countries-Burkina Faso, Chad, Mali, Mauritania, and Niger-household surveys collect detailed consumption expenditure data but individual labor earnings are either absent, plagued by massive item nonresponse, or contain implausible values. This paper addresses two linked challenges: (i) recovering total household labor income from consumption data via the household budget constraint, and (ii) allocating that householdlevel aggregate to individual workers. We ground the allocation problem in the collective household model (Chiappori, 1988, 1992), which provides a theoretically consistent sharing rule for distributing household labor income among employed members. The sharing rule depends not only on predicted earnings-as in simple proportional allocation-but also on distribution factors that affect intrahousehold bargaining power, including spousal education and age gaps, polygamy, and local sex ratios. We combine this framework with grouped-data estimation of Mincer equations (Deaton, 1985) and machine learning methods (Random Forests and Gradient Boosting Machines) to estimate latent wage structures from household-level intensive-form data. We validate the approach using the 2019 Bolivian Household Survey, where both consumption and individual earnings are observed, employing formal distributional tests (Kolmogorov-Smirnov statistics, Gini coefficient comparisons, and quantile analysis). The collective sharing rule significantly outperforms simple proportional allocation in recovering the observed earnings distribution. Applying the method to the Sahel G5, we find average returns to schooling ranging from 5% (Mauritania) to 10% (Burkina Faso), with women exhibiting significantly higher returns to education but lower returns to experience than men. Sectoral and regional segmentation patterns account for a substantial share of earnings variance. These estimates provide baseline labor earnings data for microsimulations of fiscal policy, climate adaptation, and structural transformation in one of the world's poorest regions.