Equivalence scales in a developing country with extensive inequality

This study estimates food budget share equations to calculate household equivalence scales that incorporate base‐independence and address 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, allowing for heterogeneity in household preferences. The application is founded on the most recent income and expenditure data that are available for South Africa. We find that there is extensive heterogeneity and that endogeneity matters. Failing to account for endogeneity leads to overstated equivalence scales in nearly every circumstance. When we fit our calculated scales to a typical (A+κK)ψ equivalence structure via non‐linear least squares, we find values of κ near unity and values of ψ 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.