## From the household to the individuals: measuring child poverty

Poverty is in general measured at the household level. The headcount measures the numbers of persons living below a threshold that depends on the size of the household. It is constructed as follows: usually, the observer only knows the composition of the family and the total resources of the household. She uses the traditional method of equivalence scale to recover the individual level of consumption. For example, she considers that a family composed of 2 parents with 2 children consumes 2 times what a single individual would consume[1]. If the total amount of resources of the household divided by the scale equivalence (2 in the example) is below the poverty threshold, then the household is considered as poor (+ 4 poor individuals to the headcount of poverty). The World Bank indicates that a person is poor if she lives with less than 2\$ a day[2].

The measure is based on the implicit assumption that resources are equally shared within the household[3]. The assumption of equality within the household lead to the following statement: in a household, either all members are poor or all members are not poor. But if resources are not equally shared within the household, it could be possible that some members of the household are poor while others are not. In a recent paper[4], Geoffrey Dunbar (Simon Fraser University), Arthur Lewbel (Boston College) and Krishna Pendakur (Simon Fraser University) assess the measure of child poverty when the assumption that resources are equally shared within the household is not made. They propose to give some new measures of child poverty in Malawi and they show that the poverty rate of children is higher than what classic methods measure.

Dunbar, Lewbel and Pendakur’s paper aims at measuring the share of resources devoted to children, in order to derive a measure of child poverty which is not necessarily connected to the poverty of the other members of the household. They estimate child poverty in two steps. First they propose a way to measure the children’s share of household expenditure, which is composed of private consumption and how much they benefit from goods that are shared by members of the household, such as housing, heating, cars, etc. (they are called public goods). Second, using this measure of the share devoted to children consumption, they reconstruct the value of what is consumed by children and compare it to the 2\$/day threshold. The estimation of children’s share of household expenditure requires technical assumptions on the household’s behavior. Readers interested in the method can refer to the appendix of this post (last two paragraphs).

What about child poverty in Malawi?

The results proposed by the authors are striking. Although Malawi is considered among the poorest countries in the world, traditional measures tend to underestimate child poverty in Malawi.

First, the authors show that children roughly command a share of 20% of the household expenditures for the first child, and 5-10 percentage points per additional child. This share is quite large, although it highlights the fact that resources are indeed not equally shared.  Second, going deeper in the details reveals gender discrimination within the household: girls are dedicated a lower share of the household expenditure, and fathers command a larger share of resources than mothers.

Finally, the authors use their estimates of resources shares to construct estimates of the poverty incidence in Malawi. Constructing the traditional poverty measures, they found a poverty rate of 91%. Allowing for unequal resources share, they show that all members are not equally at risk of poverty: while the incidence of poverty is roughly 60% for men, it is 85% for women and 95% for children!

To conclude, the authors give an interesting picture of the measure of poverty in Malawi. They show that taking into account within household inequalities exhibit dramatic differences between the members of the household and a much higher incidence of poverty for children than for adults. However, this method does not take into account all the dimensions of the children life. Consider for example time spent on children: some children may get many toys but parents don’t devote any time to them. Other children have almost no toys but get lots of attention and play creatively without needing toys. According to the methodology used in the paper, the child in the second family would be considered poor. But taking into account time devoted to children reminds us that poverty is most of the time measured in material terms while many other aspects of the life should be considered, especially to gauge the well being of children.

Appendix : How can we measure individual poverty?

Estimating the resource share devoted to children is not straightforward. The main difficulty comes from a) the presence of public goods that do not necessarily benefit equally to all members of the household, b) it is not always possible to know who consumes a private good (for example, we might know food consumption, but it does not indicate how much of food each member actually consumed). However, the authors show that although the consumption decisions of the household is a collective choice of how to allocate resources between public and private goods, it can be assimilated to an individual choice of allocating the individual share of resources to private consumption and the provision of the public goods. Moreover, it is possible to observe who consumes some private goods, for example it is possible to distinguish female clothing from male clothing. Such a good is said to be assignable.

Moreover, economists have observed some regularities in the link between the level of consumption of a good (whatever the good) and the available resources[5]. So if the resources and consumption of specific goods are jointly observed, the shape of the link can be estimated, and if the shape of the link is known and the consumption of a specific good is observed, then the resources can be derived. These regularities were first estimated at the household level, but they exist at the individual level: if we know the individual’s consumption and the shape of the regularity between resources and consumption for that good, the individual resources can be estimated… and this is what the authors do. They impose a certain shape to the relationship between individual resources and the consumption of the private assignable good, so that they can recover the individual share of resources from the observation of one private assignable good.

[1] This equivalence of scale is the traditional measure proposed by the OECD that counts that a household of size n consumes sqrt(n) times what a single individual consumes.

[2] There are different ways to define the poverty line. Here, I consider the absolute value of 2\$/day per capita, which the level under which a person is considered as moderately poor by the World Bank. The level of extreme poverty is 1\$/day par capita. The choice of this threshold as a poverty line is arbitrary. Discussions on this exciting issue go far beyond the scope of this post.

[3] In a previous post, I presented the question the consequence of the implicit assumption of equal sharing within the household on the measure of inequalities of consumption at the individual level. It tends to underestimate inequalities and then, it gives a biased picture of the evolution of inequalities.

[4] Geoffrey Dunbar, Arthur Lewbel and Krishna Pendakur (2012) « Children’s Resources in Collective Households: Identification, Estimation and an application to child poverty in Malawi » forthcoming in the American Economic Review

[5] These regularities are know as Engel curves, named after Ernst Engel (1821-1896)