While income inequalities have been extensively studied, they give a rather limited idea on the inequalities of living conditions. Inequalities of consumption give a better picture of inequalities of living conditions. Unfortunately, most surveys provide information on household consumption but not on individual consumption. So, individual-level consumption has to be recovered from household based observations, taking into account the size of the household. But families share household public goods (meaning that both the spouses benefit from that good, without preventing the other from consuming the good), like housing, heating, etc. So, instead of a head count, economists use an equivalence scale. It says, for example that 2700€ (and not 3000€) for a couple give a similar individual level of consumption as 1500€ for a single adult. However, the equivalence scale method suffers from a main drawback. It assumes that consumption is equally shared between the members of the household. The economic literature on the family has now reached an agreement: resources are not equally shared within the household. In a recent paper, Jeremy Lise (University College London and Institute for Fiscal Studies) and Shannon Seitz (Boston College and Queen’s University) propose a method to recover individual consumption level from household observations. They show that the traditional measures of scale equivalence ignore within-household inequalities and then produce misleading estimates of inequalities at the individual level.
The VerySmall Island tale
Consider that on VerySmall Island, there are only three households, two couples and one single. Mr. and Mrs. Unequal have 9 units of resources, 1 is dedicated to the public good, 6 for Mr. Unequal’s private consumption and 2 for Mrs. Unequal’s private consumption. So Mr. Unequal consumes 7 (1+6) and Mrs. Unequal consumes 3 (1+2) units. Mr. and Mrs. Equal also have 9 units of resources, 1 is dedicated to the public good, 4 for Mr. Equal’s private consumption (so he consumes 5) and 4 for Mrs. Equal’s private consumption (so she consumes 5). Last, Mr. Single consumes 7 units.
A casual observer is interested in inequalities between the individual levels of consumption. She wants to measure the dispersion of the consumption levels, using the most common measure of dispersion, the variance. Unfortunately, the casual observer only knows the total level of consumption: both the Unequals and the Equals have 9 units of resources and M. Single consumes 7 units. In order the take the size of the household into account, she uses equivalence scale (considering that the first adult accounts for 1 and the second adult accounts for 0.8). She would conclude that the variance of individual consumption is equal to 0.64. But using the real level of individual consumption, the variance is equal to 2.24: so the society is much more unequal than what the observer concludes!
Now let’s go one step further. Assume that Mrs. Unequal decides to start working. She increases her private consumption by 3 units. Both Mr. And Mrs. Equal and Mr. Single keep exactly the same level of consumption. The casual observer only sees that the total resources of Mr. And Mrs. Unequal increased from 9 to 12. Using the equivalence scale method, she concludes that the variance of individual consumption slightly increased from 0.64 to 0.78. But using real levels, we can see that the variance of individual consumption dramatically decreases from 2.24 to 0.8! Therefore, she would conclude that the level of inequalities increased in VerySmall Island, although it actually decrased.
It is possible (for us, but not for the casual observer) to decompose the variance into what comes from the inequalities within the household, and what comes from inequalities between households. It shows that the within household variance decreased from 1.6 to… 0.1! In the meantime, between-household inequalities slightly increased from 0.64 to 0.7. The equivalence scale approach considers that household equally split their resources between members. So it only measures between household inequalities.
What about inequalities in the UK ?
As the casual observer of VerySmall Island, most surveys do not allow one to observe private consumption within household, but only total expenditure of the household. As a consequence, most studies focus on between-household inequalities. Lise and Seitz’s paper proposes a way to disentangle private consumptions within the household. They apply this method to UK data and study the evolution of within and between household inequalities.
The UK experienced two large changes over the 1968-2001 period. First, there has been a large rise in earnings inequalities between households, with a corresponding rise in consumption inequalities (measured at the individual level, taking into account the size the household using traditional method of scale equivalence). Second, increasing female labor supply led to an increase in the correlation between earnings of husbands and wives.
But according to Lise and Seitz results’, those well-known changes hide even more striking changes. The authors compute the overall inequalities between individuals and they decompose those inequalities into a within household component and a between household component. They show that the trend of the evolution of total inequalities in individual consumption is stable over time. This stability is explained by the increasing between-household inequalities, which are offset by the decreasing within-household inequalities. In 1970, 50% of the overall inequalities between individual levels of consumption is explained by within household inequalities. As the traditional equivalence scale method only measures the between household inequalities, it underestimates the initial level of individual consumption inequalities by 50%, because the inequalities within households were mostly generated by large differences in earnings between husband and wife. In 2000, within household inequalities explain 25% of the overall inequalities in individual consumption. So, the traditional measures still underestimate the overall level of inequalities in 2000, but only by 25%. But they lead to misleading conclusions on the evolution of inequalities.
Lise and Seitz paper gives a rather unusual picture of inequalities in the UK.
It demonstrates how important it is to have a more precise look at what happens within the household. The implications in terms of public policies could be completely changed depending on whether most of inequalities come from within-household inequalities or between-household inequalities: who benefits from public transfers does matter in case of within household inequalities while only the total level of expenditure matters in case of between household inequalities.
 There is a large literature on the computation of equivalence scale. Here, I use the common equivalence scale used in France by the INSEE that says that a couple consumes 1.8 times what a single adult consumes.
 Lise, J., et S. Seitz (2011): “Consumption Inequality and Intra-household Allocations,” The Review of Economic Studies, 78, 328–355.
 Classic formula of the decomposition of the variance : V(X)=E(V(X|Y))+ V(E(X|Y)). The first term is considered as the within group variance and the second term as the between groups variance.