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# Equivalence Scales with Endogeneity and Base Independence

## Author

Listed:
• Steven F. Koch

(Department of Economics, University of Pretoria, Private Bag X20, Hatfield, South Africa)

## Abstract

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 $(A+\kappaK)^\psi$ equivalence structure via non-linear least squares, we find values of $\kappa$ near unity and values of $\psi$ 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.

## Suggested Citation

• Steven F. Koch, 2021. "Equivalence Scales with Endogeneity and Base Independence," Working Papers 202185, University of Pretoria, Department of Economics.
• Handle: RePEc:pre:wpaper:202185
as

File URL: http://www.up.ac.za/media/shared/61/WP/wp_2021_85.zp213348.pdf
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## References listed on IDEAS

as
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4. Ye, Yuxiang & Koch, Steven F., 2021. "Measuring energy poverty in South Africa based on household required energy consumption," Energy Economics, Elsevier, vol. 103(C).
5. Kseniya Abanokova & Hai-Anh H. Dang & Michael M. Lokshin, 2020. "The Important Role of Equivalence Scales: Household Size, Composition, and Poverty Dynamics in the Russian Federation," Working Papers 539, ECINEQ, Society for the Study of Economic Inequality.
6. Margaret Grosh & Paul Glewwe, 2000. "Designing Household Survey Questionnaires for Developing Countries," World Bank Publications - Books, The World Bank Group, number 25338, December.
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