# 2.2  The Use of Allocation Rules

In the previous subsection the welfare metric was based on an assumption of equal sharing within the household to produce the measure of income per adult equivalent person. Further distinctions were then made depending on the choice of income unit. Yet another approach is to use an explicit sharing rule to allocate disposable income to individual members of each household. The particular sharing rule used may be based on special surveys which provide information about income sharing, or it may be rather more ad hoc.[15] Suppose that the allocation rule is based on an additive household size, s, defined as:

Hence the first adult is given a weight of 1, while all other adults are given a weight of 0.5 and all children are given a weight of 0.3. These values are chosen arbitrarily, merely for illustrative purposes.[16] For example, household 2 has a total disposable income of 45+35=80. The size of this household for sharing purposes is 1.5, so the amount allocated to the first adult is 80/1.5=53, and the amount allocated to the second adult is (0.5)(80)/1.5=27. Using this approach, the distribution of individual disposable incomes is shown in the left-hand panel of Table 3.

Disposable income Final income   A1 A2 C1 C2 A1 80 - - - 78 - - - 53 27 - - 58 34 - - 55 28 17 - 60 35 25 - 43 21 13 13 49 30 22 22

This type of explicit income-sharing rule is naturally associated with the use of the individual as the income unit. The distribution of individual disposable income, after application of the sharing rule, is thus:

[80, 53, 27, 55, 28, 17, 43, 21, 13, 13].

In examining the redistributive effect of taxes and transfers, care is then needed in selecting the comparison distribution of gross or pre-tax incomes. For example, comparing the above individual distribution with market income per adult equivalent person, on an individual basis, would retain the same number of observations but would be spurious.[17] This is because each household's adult equivalent income is assumed to be obtained equally by each individual in the household: as shown above, that distribution is:

[100, 57.5, 57.5, 48.1, 48.1, 48.1, 41.5, 41.5, 41.5, 41.5].

The closest comparison is obtained by constructing an individual distribution of market income, on the similar (though again artificial) assumption that market income is shared, though of course the tax and transfer system is not applied to the shared market incomes. This distribution is found to be:

[100, 67, 33, 55, 28, 17, 48, 24, 14, 14].

As mentioned earlier, it is sometimes possible to allow for indirect taxes and thus to construct an additional distribution of (individual) disposable income after the deduction of existing indirect taxes. This is somewhat more complex than when adult equivalent scales are used, because certain goods (such as alcohol and tobacco) need to be attributed to adults, while other goods (such as children's clothing) are necessarily consumed by children. This distribution is again not treated separately here, only because it raises no special issues from the point of view of comparisons.

Fiscal incidence studies go further and attempt to allocate some components of government expenditure to individuals. In particular, health expenditure can be allocated based on age, gender and summary information about individuals' use of publicly financed health services. Similarly primary, secondary and tertiary education expenditure can be allocated to individuals based on age.[18]

The right-hand block of Table 3 shows a hypothetical distribution of ‘final' income resulting from the allocation of some government expenditure and the deduction of indirect taxes. These numbers again are not based on specific assumed policies but reflect for example the tendency for children to benefit most from education and health policies (and, by assumption, the adults are of working age). The distribution of final income, with the individual as unit of analysis, is thus:

[78, 58, 34, 60, 35, 25, 49, 30, 22, 22].

### Notes

• [15]Early studies of income sharing include Lazear and Michael (1988), Jenkins (1991) and Borooah and McKee (1994). See also Bonke and Browning (2003).
• [16]These values coincidentally correspond to the ‘after housing costs' adult equivalence scales used by the OECD.
• [17]This is true even if the sharing or allocation structure in (3) were also used as the adult equivalence scales.
• [18]There would of course be little point in obtaining a measure of final income per adult equivalent (by aggregating the individual final incomes in the household and then dividing by the number of adult equivalents) since, for example, education benefits cannot be thought of as being shared equally within the household. However, in a wider context the absence of tax-financed government expenditure of this kind would require an intra-household transfer.
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