This study estimates food budget share equations to calculate household equivalence scales that address both base-independence and potential endogeneity, even though an instrument that satisfies the usual exclusion restriction may not be available. The application incorporates semi-parametric methods, control functions and heteroscedasticity instrumentation. The application is founded on the most recent income and expenditure data that is available for South Africa. We find that endogeneity matters, and that failing to account for it leads to overstated equivalence scales in nearly every circumstance. When we fit our calculated scales to a typical equivalence structure via non-linear least squares, we find values of Kappa near unity and values of Phi mostly below 0.5. Thus, our analysis suggests that a square-root scale is more appropriate than other scales that have been used to examine poverty and inequality in South Africa.