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Alternative Distributions for Inequality and Poverty Comparisons

2  A Hypothetical Population

To make the various ideas and comparisons concrete, it is useful to construct a small hypothetical dataset. Suppose there are just four households, which is a sufficient number for present purposes. In order to reduce the number of possible comparisons here, households and families are considered to be synonymous; the term ‘household' is used throughout to refer to an income unit, consisting of one or more individuals, within which resources may be shared.

The left-hand block of Table 1 shows the hypothetical market incomes of members of the households in the relevant period. The term ‘market income' here refers to an individual's income from all sources, such as labour income, self-employment income and the ownership of assets (including rental and interest income, and so on). In some contexts, emphasis may of course be on a particular source, such as wage and salary income from employment. Market income is necessarily assigned to individuals.

In Table 1, a dash indicates that there is no one in the particular cell, while zero indicates that the person has no market income. Thus household 1 consists of one adult (A1) with a market income of 100, while household 2 consists of two adults (A1 and A2) with market incomes of 60 and 40 respectively. Household 3 has one child (C1) and household 4 has two children (C1 and C2). The incomes of the adult individuals have been deliberately chosen so that total household market income is 100 for each household. Non-income differences, other than the demographic structure of households, are not considered relevant here. However, in practice judgements may well depend on other features of individuals and income sources.

The right-hand block of Table 1 shows the hypothetical disposable incomes of each individual, after the application of the income tax and transfer (or benefit) system. This system, which need not be specified in detail for present purposes, is progressive in form. The worker (adult A1) in household 4 is assumed to have a higher disposable income than the single individual in household 1, despite having the same market income. This can be considered to result from some kind of in-work payment related to children. Adult A2 in household 3 has a higher disposable income than market income, also reflecting the nature of the benefit system.

Table 1 - Individual Gross and Disposable Incomes
  Market income Disposable Income
HH A1 A2 C1 C2 A1 A2 C1 C2
1 100 - - - 80 - - -
2 60 40 - - 45 35 - -
3 75 25 0 - 70 30 0 -
4 100 0 0 0 90 0 0 0

A range of income distributions may be considered based on the market and disposable incomes of Table 1. If the focus of attention is on individual market incomes, the distribution has six non-zero observations and is:

[100, 60, 40, 75, 25, 100],

where elements are arranged by taking each household, and adults within households from Table 1, in turn. Here the zero incomes of relevant adults and children are necessarily excluded from the population of market incomes. This distribution may be compared with that of the six individual disposables incomes, given by:

[80, 45, 35, 70, 30, 90].

If concern is primarily with how the market distributes the flow of income, and the way this is altered by the tax and transfer system, these distributions containing six observations are the focus of analysis. However, there is clearly a complex relationship between the distribution of market incomes and inequality in the distribution of resources, as more widely perceived, over all individuals in the population. This relationship clearly depends on the incomes of partners and the treatment of those without market incomes.

If concern is with comparisons of total market income among households, rather than individuals, the distribution has just four observations of:

[100, 100, 100, 100],

where elements are arranged by taking each household in turn. Inequality is in this case clearly zero. There is a corresponding distribution of household disposable income, with the household as unit of analysis, of:

[80, 80, 90, 100].

In this case, because the benefits available in the tax and transfer system depend on the existence of children, the use of the household as unit of analysis suggests that the structure introduces inequality. In practice the distributions are likely to show a reduction in inequality, but this example shows why the comparison between these two distributions, having the household as the unit of analysis, may not be very instructive.

Nevertheless, it should be recognised that - given the ubiquitous role of value judgements - some people may actually take the view that household structure is irrelevant in making comparisons. They would object to the special treatment of household composition by the tax and benefit structure and would judge that taxes and transfers (in this example) have indeed increased inequality. Those who take this view may, for example, object to treating children in terms merely of a cost or burden faced by parents, rather than as a desired benefit or advantage. They may consider household structure, fertility decisions, household production and market income as jointly determined to a considerable extent.

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