Equivalence Scales

Many economic policies are directed towards the family. However, this presents a problem for policy makers, as no two families are identical, in terms of composition and income, among other variables. There are a wide variety of factors effecting family welfare, and income is just one of them. Many of these factors may not be exogenous. How do we adjust family income to take account of size and composition in a way that is consistent with economic theory?

Before discussing adjustment for family size and composition, we must first address what is best measure of resources: income or consumption/expenditure? From a practical level, certain levels of income are difficult to measure. Cross-section studies typically provide income measures which are snapshots in time and thus take no account of the difference between transitory and permanent income

Since expenditure decision are usually made with reference to permanent income, expenditure measures may be preferable. However, this is also problematic, as expenditure on “sin” items such as alcohol, tobacco and gambling are typically under-reported. In addition, expenditure over a two-week period may not be a reliable measure of consumption, particularly for mature households who may have a large stock of durables from which they derive services.

The minimum needs approach is one such measurement, popularized by Beveridge. It takes a two-person family or couple as a starting point, and then calculates what minimum level of income they need. It then scales this, as family size increases or decreases. For example, under Beveridge’s approach a single person requires 59% of what 2 people do, while a family of 2 adults and 4 children would require 188%.

This minimum needs approach, while useful, is not without its flaws. Needs are assessed by “experts”, which can become controversial. The focus is on cost of meeting minimum needs – hence not appropriate at higher levels of spending. In addition, since they ignore optimisation they do not measure the true “economic” cost – they ignore fact that as income rises substitution between goods is possible and relativities may change.

Another method is to use Engel curves. It measures what percentage of income is spent on food, and uses this as a proxy for welfare. Identifies welfare with budget share of food based on the empirical regularity observed by Engel that better-off families spend a smaller % of their budget on food. This is known as the “isoprop” method and can in principle be applied to any good.

There is however, a strong likelihood of overestimating the cost of children on welfare since they tend to be relatively intensive consumers of food –a child is largely the addition of a food-consuming unit to the household – the marginal effect of a child may differ from the average effect. Moreover, economies of scale are less likely to apply to food, so the Engel approach may give overestimate of equivalence scale.  Engel approach assumes that the effect of an additional child on the consumption of goods is the same for all goods.

An alternative approach is the Rothbarth method. This measures percentage of total income spent on adult goods as a proxy for welfare. If changes in the demographic structure of family affects consumption of adult goods via income effects only, then the additional income required to maintain adult goods consumption constant after a demographic change can be used to construct an equivalence scale

But is it true that consumption of these goods will be affected by changes in income only? This approach implies a separability between the utility derived from adult goods and those goods affected by demographic changes. For example, according to this method, the amount spent on cigarettes or alcohol is unaffected by the number of children in a household. Empirically goods such as alcohol and tobacco (especially) unresponsive to changes in income.

One fundamental assumption underlying equivalence scales is that there are economies of scale because consumption goods can be divided into collective goods, those which are consumed collectively by all the members of the household and individual consumption goods which are consumed only by one individual. As a collective good, we have mainly housing, as an individual good, we can quote adult clothing or tobacco. The model of Prais and Houthakker (1955) explains the household consumption of various items as a function of income and of the size of the household. Are thus explained the structure of consumption and the influence of the structure of the household from which an equivalence scale can be derived. Consumption is divided into K different items such as lodging, food, clothing, leisure. The size of the household is called N which means the total number of persons which are members of the household. The size effect is introduced both as a deflator of income and as an explanation of a particular consumption item. After various computations which are not reproduced here, the model is written as

log(Ck) = Ak + αk log(N) + βk log(R/Nα ),

where Ck is the consumption of good k, R household income, and N the size of the household. This model can also be expressed in term of budget shares

ωk = Ck/R: log(ωk) = Ak + (αk − α) log(N) + (βk − 1) log(R/Nα ).

We have as many equations as there are consumption items, but only K − 1 equations are independent. This model analyses how the structure of consumption is modified as a function of N, when we compare two households which have the same income R.

We have two effects:

·         A size effect. The budget share of individual goods for which αk > α increases. The budget share of collective goods for which αk < α decreases.

·         An income effect. When N is increased, R/Nα decreases. The structure of consumption is modified. The budget share of luxury goods which have a βk greater than 1 is decreased while the budget share of primary goods which have a βk lower than 1 increases.