Abstract
The objective of this chapter is to introduce the use of the concentration curves and the Gini methodology in the areas of taxation and progressivity of public expenditures. Most of the literature in these areas considers the case of a representative individual, which means that issues of income distributions are ignored and the only issue that is considered is efficiency. For the Gini methodology and concentration curves to be useful we extend the model to include issues of income distributions as discussed by Diamond (1975) and Atkinson and Stiglitz (1980). We start with a crude characterization of optimal (mostly indirect) taxation which includes the issue of redistribution in addition to efficiency considerations. In a typical model the investigator assumes a social welfare function (SWF) and optimizes it subject to the behaviors of the individuals and to the instruments that are used by the government. Using those ingredients she gets the first-order conditions for optimization so that the relationships among the instruments in an optimal setting are determined (see, as a background, Atkinson &Stiglitz, 1980, pp. 386–393). Note that by assuming the existence of an SWF, the issues of horizontal equity and of comparisons of utilities of households with different structures are skipped because the mere existence of an SWF implies that one knows how to rank individuals according to economic well-being.
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- 1.
Mayshar and Yitzhaki (1996) extend the approach so that “economic well-being” can be affected by two parameters—ability and needs. Then, the investigator should be able to agree that given ability, the higher the needs the lower the well-being of the household, and given needs, the higher the ability the higher is its well-being. This kind of extension is useful for handling family size (needs increase with the number of children but one does not want to commit himself to a specific magnitude) or rural–urban distinctions (e.g., rural populations need less income to achieve a certain level of well-being than urban populations (Ravallion, 1993, p. 31)). There are some technical requirements for this extension to hold. This and other types of extensions are beyond the scope of this book.
- 2.
One can derive this relationship under two alternative sets of assumptions: (a) the household is a utility maximizer and by Roy’s identity \( \partial {{\rm{v}}^{\rm{h}}}\left( {} \right){/}\partial {{\rm{t}}_{\rm{i}}} = - {{\uplambda }^{\rm{h}}}{\rm{x}}_{\rm{i}}^{\rm{h}} \), where v is the indirect utility function and \( \lambda \) is the marginal utility of income. The marginal benefit is the income equivalent of the change caused by the reform, or (b) no optimization is carried out by the household and we are only interested in a Slutsky’s compensation to the household.
- 3.
This distinguishes Pareto improving reform from DI reform. Under Pareto improving reform all MBh, h = 1,..,H must be nonnegative.
- 4.
An instrument is a parameter that the government can change.
- 5.
- 6.
To see this note that E = PQ, where P is price and Q is quantity. Let Y be income then \( \Delta E \approx P\Delta Q + Q\Delta P \). Hence \( {\frac{{\Delta E}}{{\Delta Y}}} {\frac{E}{Y}} \approx \frac{{\Delta Q}}{{\Delta Y}} {\frac{Y}{Q}} + \frac{{\Delta P}}{{\Delta Y}} {\frac{Y}{P}}. \)
- 7.
To see the amount of efficiency gain, add up the MECFs multiplied by the revenue changes: 1.0 × 1.083 − 1.035 × 1.083 + 0.035 × 2.70 = 0.008.
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Yitzhaki, S., Schechtman, E. (2013). Policy Analysis. In: The Gini Methodology. Springer Series in Statistics, vol 272. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4720-7_14
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