A Probabilistic Model for Household Labor Income and Consumption: Theory and Application with Saudi HICES Microdata

Abstract

This study proposes a hierarchical probabilistic model for household labor income and consumption, designed for microsimulation and policy analysis. Labor income is modeled as a compound count--lognormal sum, arising from zero-truncated household size, Bernoulli labor participation, and i.i.d. lognormal wages, yielding a point mass at zero and a heavy right tail. Consumption follows a log-linear Engel curve in total resources, capturing sub-unitary elasticity and heteroskedasticity. The model provides closed-form cumulants and moments, supports lognormal-sum approximations, and integrates survey-weighted estimation aligned with Saudi HICES reference periods and design. Simulations confirm accurate parameter estimation, while a Universal Basic Income (UBI) counterfactual shows nonlinear inequality reductions, stronger for consumption due to Engel curve concavity, with decomposition highlighting the distinct roles of participation and wage dispersion. The framework is extensible and policy-ready.